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Supported by GreenNet-EU27 EIE/04/049/S07.38561 GreenNet-EU27 GUIDING A LEAST COST GRID INTEGRATION OF RES-ELECTRICITY IN AN EXTENDED EUROPE Intelligent Energy – Europe (EIE) Type of action: Type 1: General Action (GA) Key action: VKA5.3 – Grid System Issues Deliverable D5b Disaggregated system operation cost and grid extension cost caused by intermittent RES-E grid integration Derk Jan Swider (Ed.), Alfred Voß (Ed.), Rüdiger Barth, Heike Brand: Institute of Energy Economics and the Rational Use of Energy (IER), University of Stuttgart, DE Christoph Weber, Philip Vogel: Chair for Energy Management, University of Duisburg-Essen, DE Peter Meibom: System Analysis Department, Risoe National Laboratory, DK Goran Strbac, Mary Black, Vera Figueiredo: Control and Power Group, Imperial College London, UK Hans Auer, Carlo Obersteiner, Lukas Weissensteiner, Wolfgang Prüggler, Thomas Faber, Gustav Resch: Energy Economics Group (EEG), Vienna University of Technology, AT

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Page 1: Supported by GreenNet-EU27 - European Commission...Tel. 0049-711-780-6115 Fax. 0049-711-780-3953 Email. ds@ier.uni-stuttgart.de Prof. Dr. Alfred Voß University of Stuttgart Institute

Supported by

GreenNet-EU27

EIE/04/049/S07.38561

GreenNet-EU27

GUIDING A LEAST COST GRID INTEGRATION OF RES-ELECTRICITY IN AN EXTENDED EUROPE

Intelligent Energy – Europe (EIE)

Type of action: Type 1: General Action (GA)

Key action: VKA5.3 – Grid System Issues

Deliverable D5b

Disaggregated system operation cost and grid extension cost caused by intermittent RES-E grid integration

Derk Jan Swider (Ed.), Alfred Voß (Ed.), Rüdiger Barth, Heike Brand: Institute of Energy Economics and the Rational Use of Energy (IER), University of Stuttgart, DE

Christoph Weber, Philip Vogel: Chair for Energy Management, University of Duisburg-Essen, DE

Peter Meibom: System Analysis Department, Risoe National Laboratory, DK

Goran Strbac, Mary Black, Vera Figueiredo: Control and Power Group, Imperial College London, UK

Hans Auer, Carlo Obersteiner, Lukas Weissensteiner, Wolfgang Prüggler, Thomas Faber, Gustav Resch: Energy Economics Group (EEG), Vienna University of Technology, AT

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Date of preparation: 28 February 2006

The sole responsibility for the content of this report lies with the authors. It does not represent the opinion of the Community. The European Commission is not responsible for any use that may be made of the information contained therein.

Co-ordination of work package 2 and editors of this report:

Derk Jan Swider University of Stuttgart Institute of Energy Economics and the Rational Use of Energy (IER) Hessbruehlstr. 49a D – 70565 Stuttgart Germany Tel. 0049-711-780-6115 Fax. 0049-711-780-3953 Email. [email protected]

Prof. Dr. Alfred Voß University of Stuttgart Institute of Energy Economics and the Rational Use of Energy (IER) Hessbruehlstr. 49a D – 70565 Stuttgart Germany Tel. 0049-711-780-6111 Fax. 0049-711-780-3953 Email. [email protected]

Co-ordination of the overall project GreenNet-EU27:

Dr. Hans Auer Scientific co-ordinator of GreenNet-EU27 Vienna University of Technology Energy Economics Group (EEG) Gusshausstrasse 25-29/373-2 A – 1040 Vienna Austria Tel. 0043-1-58801-37357 Fax. 0043-1-58801-37397 Email. [email protected]

Prof. Dr. Reinhard Haas Project co-ordinator of GreenNet-EU27 Vienna University of Technology Energy Economics Group (EEG) Gusshausstrasse 25-29/373-2 A – 1040 Vienna Austria Tel. 0043-1-58801-37352 Fax. 0043-1-58801-37397 Email. [email protected]

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CONTENTS

Deliverable D5b of the project GreenNet-EU27:

DISAGGREGATED SYSTEM OPERATION COST AND GRID EXTENSION COST

CAUSED BY INTERMITTENT RES-E GRID INTEGRATION

Editorial ..............................................................................................................1

Derk J. Swider and Alfred Voß

Least cost intermittent RES-E integration under different cost allocation policies ..............................................................................................5

Hans Auer, Carlo Obersteiner, Lukas Weissensteiner, Wolfgang Prüggler, Thomas Faber and Gustav Resch

Integrating electricity production from fluctuating sources – valuation of variability and unpredictability ................................................29

Christoph Weber

Role of storage in integrating wind energy ....................................................51 Goran Strbac, Mary Black and Vera Figueiredo

Integration costs of wind due to changed system operation and investment decisions in Germany ..................................................................79

Derk J. Swider and Christoph Weber

A stochastic model for the European electricity market and the integration costs for wind power...................................................................107

Christoph Weber, Philip Vogel and Derk J. Swider

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Operational costs induced by fluctuating wind power production in Germany and Scandinavia ...........................................................................133

Peter Meibom, Christoph Weber, Rüdiger Barth and Heike Brand

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1

EDITORIAL

DERK J. SWIDER* ALFRED VOß Institute of Energy Economics and the Rational Use of Energy University of Stuttgart, Germany

Within the European energy markets large amounts of fluctuating renewable energy sources for electricity production (RES-E) notably wind energy are ex-pected to be integrated in the electricity system in the coming years. By their intermittent nature these RES-E will impact both the technical operation of the electricity system and the electricity market. In order to cope with the fluctua-tions in the wind power production other units in the power system have to be operated more flexible to maintain the stability of the power system. Techni-cally this means that larger amounts of intermittent RES-E will require more capacities of spinning and non-spinning power reserves and an increased use of these reserves. This implies more frequent start-ups and a higher fraction of less efficient part-load operation of the conventional power plants. Hence, intermit-tent RES-E will influence the performance of the whole system and cannot be valued as conventional power sources. This leads to a great interest in simula-tion and optimization models for estimating the costs of integrating RES-E and especially wind energy in the European electricity system.

Following this discussion it is essential to have models able to take the sto-chastic behaviour of wind generation into account in order to adequately ana-lyse market impacts and RES-E integration costs. Such models have been de-veloped in two recently finished EC projects on renewable energy integration measures, effects and costs: • The stochastic European Electricity Market Model for the UCTE and UM-

IST’s Storage Model for the UK have been developed within the project Pushing a least cost integration of green electricity into the European grid (GreenNet, Contract No. NNE5-2001-660, http://www.greennet.at).

______ * To whom correspondence should be addressed. Email: [email protected]

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Swider and Voß 2

• The Joint Market Model for the Nordel-region has been developed within the project Wind power integration in liberalised electricity markets (Wil-mar, Contract No. ENK5-CT-2002-00663, http://www.wilmar.risoe.dk). The two consortia joint in the project Guiding a least cost grid integration

of RES-electricity in an extended Europe (GreenNet-EU27, Contract No. EIE-04-049-S07.38561, http://www.greennet-europe.org) focussing on deriving de-tailed cost figures for renewable energy integration on extended European level. This report forms part of this project and aims at analysing the changing system operation costs due to large-scale intermittent RES-E integration for different European system configurations on disaggregated level: • Nordic power system with an enormous hydro power penetration. • UK power system with limited interconnections. • UCTE power system with a high fraction of thermal power generation.

The analysis of changing system operation costs due to large-scale intermit-tent RES-E integration is mainly based on model evaluations applying the three models mentioned before.

Auer et al. provide an analysis of least cost integration of RES-E in Europe. Within this overview the authors present results of a simulation model and demonstrate that the degree of unbundling and the implemented allocation prin-ciples of disaggregated cost elements significantly influence intermittent RES-E deployment. The major conclusion is that serious unbundling and correct allo-cation of RES-E related grid integration costs is necessary to achieve the ambi-tious EC goals of RES-E integration with minimal costs for society.

Weber discusses the valuation of variability and unpredictability of integrat-ing electricity production from fluctuating sources. The author presents a sys-tematic approach on the categorization of various types of integration costs and on their quantification. Thereby the focus is on the use of modern numerical methods of stochastic modelling and optimization, which allow quantifying dis-aggregated integration costs if adequately employed.

Strbac et al. applies the UMIST’s Storage Model to derive system operation costs for different RES-E penetrations in the UK power system. Thereby the authors present a new methodology to quantify the value of storage in the inte-gration of intermittent sources. The major conclusion is that a higher share of storage facilities in providing power systems reserve can increase the efficiency of system operation and the amount of wind power that can be absorbed.

Swider and Weber apply the stochastic European Electricity Market Model to estimate the integration costs of wind due to changed system operation and investment decisions in Germany. With this model the authors cover the inter-mittency of wind by a stochastic recombining tree and the system is considered

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Editorial 3

to adapt on increasing wind integration over time by endogenous modelling of reserve requirements and investments in thermal power plants. The results high-light the need for stochastic optimization models and the strong dependency on the actual system and its development over time to get adequate estimates of the integration costs of wind’s intermittency.

Weber et al. apply the stochastic European Electricity Market Model to es-timate the integration costs of wind in the UCTE system. The model empha-sises the connection between green and conventional electricity markets and the consequences of the uncertainties associated with intermittent wind generation while taking inter-regional transmissions into account. Again, integration costs for different RES-E penetration scenarios are derived. The authors conclude that the considered power plant system plays a major role in estimating these costs and well inter-regionally connected systems with a high share of hydro power plants have lower integration costs than an isolated by thermal power plants dominated system.

Meibom et al. apply the Joint Market Model to calculate the change in op-erational costs due to wind power production. The model is based on a stochas-tic optimization of the electricity systems of Germany and the Nordic countries. Integration costs related to partial predictability and variability of wind power are estimated. Thereby the authors discuss three different wind power penetra-tion levels and conclude that integration costs are lower in hydro dominated systems compared to thermally dominated and are higher in power systems having a relatively large ratio between wind power production and the sum of average power demand and transmission capacities to neighbouring regions.

With these papers this report contributes to the growing literature on effects and costs of large-scale wind integration, cf. e.g. [1]-[7]. Thereby results on disaggregated system operation costs are presented based on the application of innovative bottom-up models of the most important electricity system configu-rations in Europe. It is thereby important to note that two of the three models applied are based on considering the partial predictability and variability of in-termittent sources by stochastic modelling. Hence, the results discussed can be seen to be more robust than results based on static simulation models or deter-ministic optimization models often applied in the literature.

References

[1] MacDonald, M., Intermittency Literature Survey. Annex 4 to the Carbon Trust and DTI Renewables Network Impact Study. [online] <http://www.thecarbontrust.co.uk>, London, 2003.

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Swider and Voß 4

[2] Norgard, P., Giebel, G., Holttinen, H., Söder, L., Petterteig, A., Fluctuations and Predict-ability of Wind and Hydropower. Report of the EU Project: Wind Power Integration in Lib-eralised Electricity Markets. [online] <http://www.wilmar.risoe.dk/>, Roskilde, 2004.

[3] Auer, H., Stadler, M., Resch, G., Huber, C., Schuster, T., Taus, H., Nielsen, L.H., Twidell, J., Swider, D.J., Cost and Technical Constraints of RES-E Grid Integration. Report of the EU Project: Pushing a Least Cost Integration of Green Electricity into the European Grid. [online] <http://www.greennet.at>, Vienna, 2004.

[4] Ackermann, T. (Ed), Wind Power in Power Systems, Wiley, Chichester, 2005. [5] Justus, D., Wind Power Integration into Electricity Systems, Case Study 5 to the OECD/IEA

report on International Energy Technology Collaboration and Climate Change Mitigation. [online] <http://www.oecd.org> Paris, 2005.

[6] Gül, T., Stenzel, T., Variability of Wind Power and other Renewables: Management Options and Strategies. Report by the International Energy Agency. [online] <http://www.iea.org>, Paris, 2005.

[7] van Werven, M., Beurskens, L., Pierik, J., Integrating Wind Power in EU Electricity Sys-tems. Report of the EU Project: Pushing a Least Cost Integration of Green Electricity into the European Grid. [online] <http://www.greennet.at>, Vienna, 2005.

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5

LEAST COST INTERMITTENT RES-E INTEGRATION UNDER

DIFFERENT COST ALLOCATION POLICIES BASED ON THE

SIMULATION MODELL GREENNET

HANS AUER* CARLO OBERSTEINER LUKAS WEISSENSTEINER WOLFGANG PRÜGGLER THOMAS FABER GUSTAV RESCH Energy Economics Group (EEG) Vienna University of Technology, Austria

Abstract. Market integration of Renewable Energy Technologies for electricity generation (RES-E) is one of the core topics in the energy policy agenda of the European Commission (EC). However, legislation in this context still faces a variety of lacks (e.g. ignoring unbundling principles) in almost all countries of the European Union (EU). The recently finished EC-Project GreenNet addresses these existing inadequacies and models dynamic time paths up to the year 2020 for a variety of least-cost RES-E grid integration cases in the EU for different degrees of unbundling and different cost allocation schemes. The major results derived from GreenNet clearly demonstrate that the degree of unbundling and the implemented allocation principles of different disaggregated cost elements significantly influence RES-E deployment both on national as well as on EU level up to the year 2020. The major conclusion is that serious unbundling and correct allocation of RES-E related grid integration costs only guarantee fulfilment of the ambitious EC goals with minimal costs for society.

Keywords: Intermittent RES-E Generation, Least-Cost Modeling, Unbundling, System Operation, Grid Infrastructure, Cost Allocation, Socialization of Cost

______ * To whom correspondence should be addressed. Email: [email protected]

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Auer et al.

6

1. Introduction

The EC-Directive on liberalisation of electricity markets (EC (2004)) requires the electricity supply industry to be competitive, yet realises that many aspects of electricity supply are natural monopolies. Consequently, it is considered best for different segments of the electricity system to be separated into clearly defined and separately accounted entities, as there are electricity generation, high-voltage transmission, low-voltage distribution and customer supply. This is called unbundling, which is one of the cornerstones of the liberalised electricity market. Separation of the competitive segments electricity generation and customer supply from the grid infrastructure is seen as a precondition for non-discriminatory grid access for third parties (e.g. RES-E generators) as well as for transparent grid regulation procedures and grid tariff determination.

For RES-E generators, particular difficulties arise when connecting dispersed generation to the existing grids. Who should pay for the connection and extra transmission and distribution lines that may be necessary? In practice, for relatively large-scale RES-E grid integration (e.g. wind), the corresponding measures and costs are frequently charged directly to the RES-E power plant. Thus the new RES-E generator has to pay for the extra capital costs of grid infrastructure elements; yet the grid is supposed to be unbundled. This is a relatively new phenomenon, since in the past, e.g. for centralised power plants, the costs of the grid infrastructure were not allocated to the long-run marginal generation costs (see e.g. Soeder (2004)). The intermittent nature of some RES-E generation technologies like wind, furthermore, expects additional measures for overall system operation. Moreover, the consideration of different time scales is important for managing generation and load in general, and with large amounts of intermittent RES-E generation in the system in particular. These time scales vary from seconds to minutes to days and longer: • In the short-term (times scales below seconds to several hours) a variety of

balancing (ancillary) services are necessary for maintaining stable system operation. The driver for short-term system balancing requirements is the magnitude of random power fluctuations, caused by unpredictable changes in both load and generation. Currently, in different European countries a variety of different schemes exist for the allocation of corresponding balancing costs.

• In the long-term, in competitive electricity markets the market itself shall be responsible for providing enough generation capacities being able to meet peak demand in the system. This is also true for systems with large amounts of intermittent RES-E generation. Nevertheless, the corresponding requirements due to large-scale intermittent RES-E generation have to be

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Least Cost Intermittent RES-E Integration 7

estimated in order to maintain adequate security of supply standards in the system. In particular, the capacity contribution of generation technologies like wind has to be estimated based on robust approaches (capacity credit). Moreover, the corresponding additional costs for the overall system have to be determined and allocated correctly. The discussion above indicates that a variety of different unbundling aspects

are still unsolved in the context of large-scale intermittent RES-E grid integration. Therefore, the analysis of unbundled RES-E grid integration costs in subsequent sections requires the consideration of the following separated segments of the electricity supply chain: • Grid infrastructure (grid connection, grid reinforcement/extension) • Electricity generation based on (intermittent) RES-E technologies • System operation services (incl. storage options and demand response)

Literature on critical reviews of unbundling in the context of RES-E grid integration is scarce. Strategic approaches on grid infrastructure planning (and operation) meeting the future requirements of large-scale RES-E grid integration are presented e.g. in Soeder (2004) or Dowling/Hurley (2005). On country specific level corresponding publications exist e.g. for The Netherlands (Hooft (2003)), Denmark (Bach (2004)) or the UK (ILEX (2002)). Remaining literature mainly addresses selected aspects of RES-E grid integration (e.g. in the recently published German DEWI (2005) study separation of grid connection of offshore wind isn’t addressed explicitly).

The major objective of this paper is to model different least-cost RES-E grid integration scenarios in the EU15 countries and selected new Member States for different unbundled cases based on the simulation software GreenNet. The data base of this software tool contains comprehensive and consistent empirical data on several disaggregated cost elements of RES-E technology grid integration on EU country level.

The paper is organised as follows: Section 2 provides background information and a brief discussion on the major unbundled segments in the electricity supply chain. Section 3 presents and discusses the major results derived from the simulation software GreenNet. And finally, section 4 derives conclusions on correct cost allocation of different disaggregated cost elements in the context of large-scale intermittent RES-E grid integration.

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Auer et al. 8

2. Unbundled segments in the electricity supply chain

2.1. Grid infrastructure (grid connection, grid reinforcement/extension)

Grid connection often is a significant economic barrier for RES-E generation technologies in dispersed locations. If the new RES-E developer has to pay all the costs of grid connection up-front, then a compromise between the best generation sites and acceptable grid conditions has to be made, as is often the case for wind and small-hydro power (see e.g. Resch et al (2003)).1 To pay for the connection, the RES-E developer includes the costs into the long-run marginal generation costs. However, if the grid connection costs are covered by the grid operator (i.e. the costs are ‘socialised’ via grid tariffs of ‘per unit’ charges), then the initial burden does not fall on the first RES-E developer. Obviously, RES-E developers should not have a ‘right’ to be connected anywhere irrespective of connection costs, so the regulatory authority has to give guidance and adjudicate about disagreements.

The need for reinforcements and extensions of the existing grid infrastructure has a variety of reasons. Changes in generation and load at one point in the network, in principle cause changes throughout the system, which may cause power congestion (bottlenecks). Usually, it is not possible to identify one (new) point of generation as the single cause of such difficulties. Therefore, the allocation of changes of load flows in a system to a single new generator connected to the system (e.g. a new wind farm) is ambiguous, since established conventional generators or changes in demand may cause an equal burden on the grid infrastructure. Therefore, one of the major unbundling issues is to discuss different cost allocation strategies for intermittent RES-E grid integration. According to the textbooks in economic theory it is expected to allocate both grid connection costs and grid reinforcement extension costs to the grid infrastructure and to spread (socialize) these costs through the transmission and distribution tariffs.2 In practice, however, grid connection costs are still allocated to the RES-E power plant in almost all European countries (except e.g. Denmark). According to ongoing discussions on that issue in a few countries (e.g. UK, The Netherlands, Germany) this pattern may change in the future. Nevertheless, in the existing version of the GreenNet model the grid connection costs are not unbundled in the default settings.

______ 1 On contrary, grid connection for biomass – in general – is no crucial barrier as the particular

location of the plant is even more independent from resource conditions. 2 In principle, there exist both options: (i) socialisation within a supply area of a grid operator

or (ii) socialisation across the whole country (i.e. covering also several other grid operators).

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Least Cost Intermittent RES-E Integration 9

2.2. Electricity generation based on (intermittent) RES-E technologies

Currently, large electricity systems mainly operate without advanced energy storage technologies (except those systems with large amounts of pumped hydro-storage plants). Therefore, at any instant, output from all electricity generators has to be controlled to equal total consumer demand. In addition, the electricity system must be reliable and robust, able to continue operation in the event of concurrent failures. For these reasons, system operators have to forecast load and generation on timescales from seconds to years, and have methods to control the balance continuously.

In this context, when having large amounts of RES-E technologies in a system, two characteristics of intermittent electricity generation (in particular wind) have to be addressed briefly: variability and predictability. Variability of wind generation is often spoken of as a major problem. However, the variability has distinctive characteristics, e.g. • for individual wind turbines the variations of the power output on second

scale can be quite large, depending on the type of wind turbine control and conversion system. Furthermore, there can be substantial short-term variations during transients (e.g. start-up at high wind speed, shut down);

• for an individual wind farm, the variation in the total output power is small for timescales of tens of seconds, due to the averaging of the output of individual turbines across the wind farm;

• for a number of wind farms spread across a large area, such as a national electricity system, the variation in the total output power of all wind farms is small for timescales of minutes or less, perhaps tens of minutes. This is termed “geographic diversity”. Grid operators only need to deal with the net output of groups of wind

farms, and so the important question is what variability needs to be planned for, on timescales of minutes or tens of minutes and upwards?

Methods and models for power output forecasting from wind farms have been substantially improved in recent years. Forecasting wind power aims to increase the predictability of the wind resource and so ease the balance of generation and load. In general, wind forecasting has greater value where financial balancing markets are part of a competitive trading system for electricity than if forecasting is purely a tool for system operators with their technical balancing. This is because the balancing market provides a financial incentive to both retailers and generators to fulfil their output projections accurately. The more precise they are, the less the financial penalties and the greater the system technical efficiency (see e.g. van Werven et al (2005)).

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Auer et al. 10

2.3. System operation requirements due to large-scale RES-E integration

Due to large-scale intermittent RES-E generation the system operator has to take care of additional arrangements for both short-term balancing of generation and load as well as long-term generation capacity adequacy maintaining system security. Previous paragraphs already indicate that there are still many open questions, e.g. • where to allocate the corresponding costs, • whether or not the corresponding markets (balancing/wholesale markets)

send out the right price signals or • which mechanisms and procedures prevent competition in system operation.

In the short-term system frequency is the parameter used to indicate the balance between generation and load. System frequency must be maintained continuously within narrow statutory limits around 50 Hz. With no change in generation, system frequency decreases when load is greater than generation and increases when generation is greater than load. In order to manage frequency effectively, system operators utilize a range of balancing (ancillary) services that operate according to different time horizons and predominantly involve changes in generation rather than load.

Long-term analyses estimate the capacity contribution of intermittent RES-E generation (in particular wind) on system level. Although wind power throughout a national network makes some contribution to assured capacity, this contribution is significantly less than for equivalent conventional generation or non-intermittent RES-E generation. The relevant parameter in estimating the system capacity requirement caused by intermittent RES-E generation is the capacity credit (see e.g. Giebel (2001)). This capacity credit is equal to the average capacity factor at low wind penetrations, but decreases with increasing wind penetration in a system.3 Therefore, in the GreenNet modelling approach the amount of conventional capacity has to be determined that can be displaced by intermittent RES-E generation, whilst maintaining the same degree of system security.

3. Results derived from the least-cost simulation software GreenNet

The evaluation of strategies for an enhanced least-cost grid integration of RES-E generation technologies (with and without consideration of additional costs for grid reinforcement/extension and/or system operation) for different ______

3 For a comprehensive discussion on the capacity credit see Appendix A.2.

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Least Cost Intermittent RES-E Integration 11

unbundled cases is conducted based on the simulation model GreenNet. Section 3.1 below briefly describes this software tool.

3.1. The GreenNet computer model

The GreenNet model enables a comparative and quantitative analysis of least-cost RES-E grid integration strategies in the liberalised European electricity market (i.e. several ‘old’ EU15 countries and the new Member States Czech Republic, Hungary, Poland and Slovakia). The analysis can be conducted on aggregated (EU Member States’) level or for individual Member States on an annual basis for the period 2005 to 2020 (2004 is the initial year). The major purpose of this software tool is to investigate the costs of RES-E deployment under different constraints and different strategies on allocating the corresponding grid related and system related costs, see Figure 1.

Econom icassessm entsupply-side

per technologypotential, costs,

offer prices

Econom icassessm entdem and-side

per sub-sectordemand elasticity,

switch prices

Trade-offslink of different technologies and

m arkets (supply and dem and)RES-E, CHP, DSM, power market, TEA

Results Costs and Benefitson a yearly basis (2004-2020 )

Scenario selection on a yearly basis (2004-2020)

Policy strategiesSocial behaviour

Investor/consumerExternalities

General framework conditions

(primary energy prices, ..)

Feedback year n+1 Feedback year n+1

Determ ination of cost-

resources curve year n supply-side

per technology

RES-ECHP

conv. power

Determ ination of cost-

resources curves year n dem and-side

per sub-sector

IndustryHousehold

Tertiary

Fig. 1. Overview of the least-cost modelling approach in GreenNet

The general modelling approach in GreenNet is to describe both electricity

generation technologies (supply curve) and energy efficiency options (demand curve) by deriving corresponding dynamic cost-resource curves. The costs as well as the potentials of these dynamic cost-resource curves can change year by year. These changes are given endogenously in the model depending on the

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Auer et al. 12

outcome of the previous year (n-1) and the policy framework conditions set for the simulation year (n).

Based on the derivation of the dynamic cost-resource curves an economic assessment takes place considering scenario specific settings like RES-E policy selection, socio-economic parameters (consumer and investor behaviour) as well as wholesale electricity price and demand forecasts. Wholesale electricity price projections on the conventional power market are implemented exogenously in GreenNet. Different wholesale price scenarios (e.g. for different fuel prices, CO2 certificate prices, etc.) are calculated based on the optimisation Software E2M2s. A comprehensive model description of E2M2s can be found in Swider et al (2005).4

Then, in the economic assessment additional costs for system operation (with versus without storage options) and grid reinforcement/extension are modelled and – in case of selection – allocated to the marginal generation costs of the corresponding RES-E technology. The overall economic assessment includes a transition from generation and saving costs to bids, offers and switch prices.

Promotion instruments for RES-E technologies include the most important price-driven strategies (feed-in tariffs, tax incentives, investment subsidies, subsidies on fuel input) and demand-driven strategies (quota obligations based on tradable green certificates (including international trade), tendering schemes). In addition, electricity taxes and other direct promotion instruments supporting energy efficiency measures on the demand side can also be chosen and investigated. As GreenNet is a dynamic simulation tool, the user can change RES-E policies and parameter settings within a simulation run on a yearly basis. Furthermore, several instruments can be set for each country individually.

The results are derived on a yearly basis by determining the equilibrium level of supply and demand within each market segment considered. For a further detailed description of the GreenNet modelling approach it is referred to

______ 4 The format of result presentation in E2M2s is compatible with the GreenNet model. An

iterative approach is used in modelling the interactions between the conventional power market (E2M2s) and RES-E generation (GreenNet). In a first step, RES-E deployment up to 2020 is modelled based on GreenNet assuming a wholesale electricity price forecast derived from a E2M2s model run (using estimates on RES-E deployment from literature). In a second step, RES-E projections and the residual request for conventional power generation determined in GreenNet are used as input parameter for a new E2M2s model run. In a third step, an updated wholesale electricity price forecast again is used as an input for a new GreenNet model run. This procedure is repeated iteratively until predefined deviations are acceptable (details see e.g. in Huber et al (2004c)).

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Least Cost Intermittent RES-E Integration 13

Huber (2004c). Moreover, a detailed description of the derivation of dynamic cost-resource curves as well as the comprehensive GreenNet data base is conducted in Resch et al (2003).

3.2. Scenarios selection in GreenNet

Several simulation runs in GreenNet are based on the assumption that currently implemented RES-E policy instruments remain without any adaptation up to 2020 (Business as Usual (BAU) RES-E policy). Sensitivity analyses consider the spread of options to allocate grid-related and system-related costs. This means that either the RES-E developer or society as a whole pay the additional costs of RES-E grid integration. Wind power is considered especially because of its dominant position for new RES-E technologies, now and in the future. Wind power also relates to (i) grid connection with both transmission and distribution; the latter including weak grid conditions (i.e. causing additional grid reinforcement/extension costs) and, (ii) the possibility of requiring additional system capacity for periods of weak wind.

The scenario whereby ‘society as a whole’ pays costs requires further explanation for the liberalised electricity market, since the concepts derive from previously vertically integrated power systems. Previous to liberalisation, society can be said to have owned the grid infrastructure, since it was initially funded by governments through taxation. In the liberalised electricity market now it is unclear, however, where to allocate the costs of new equipment for grid connection and/or grid reinforcement/extension. Either these costs have to be paid for by the owner of the new RES-E power plant, which may be a company with investors, or by the grid company, which is always a licensed monopoly. In the former case, expenditures initially come from investors and then have to be recovered from future generation income. In the latter case, expenditures come from internal reserves of the established grid company and are later recovered from the ‘use of system’ per unit tariff levied on the eventual electricity suppliers, who pass on the expenses to their consumers, i.e. to ‘society’. In detail, the following cost allocation scenarios can be selected now in the GreenNet model: • Full unbundling between electricity generation and the grid/system: Society

pays for both grid reinforcement/extension and system operation costs caused by RES-E technologies. The RES-E developer can neglect several additional grid-related and system-related costs in its investment decision. This scenario is used as reference case, since this approach is implemented

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Auer et al. 14

in many EU Member States (grid connection costs, however, are not unbundled in the reference case; see section 2.1).

• Grid reinforcement/extension costs only are allocated to the RES-E plant developer: In this case it is assumed that system operation costs are still fully covered by society, but grid reinforcement/extension costs are imposed on the RES-E developer. Different sensitivity analyses on the effects of grid reinforcement/extension costs (low, medium, high per unit costs) can be conducted both for new and existing RES-E plants as well as and for new RES-E plants only.

• System operation costs only are allocated to the RES-E developer: Starting from the fully unbundled case, now the opposite sensitivity analyses are conducted. In detail, the consideration of additional system operation costs – being imposed on intermittent RES-E generators – on overall RES-E deployment can be studied. Important parameter variations refer to the settings of (i) the capacity credit of wind and (ii) the range of the corresponding system operation costs (assuming low, medium, and high cost scenarios).

• Both grid reinforcement/extension and system operation costs are allocated to the RES-E developer: Again, sensitivity analyses are carried out to investigate the cumulative effects of grid reinforcement/extension and system operation on RES-E deployment over time.

Figure 2 gives an overview of different cost allocation scenarios being implemented in the GreenNet model. Further assumptions are described in the Appendix.

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Least Cost Intermittent RES-E Integration 15

GE and SO costs are directly imposed on society

SO costs are directly imposed on society

GE costs are imposed on generators

GE costs are directly imposed on society

SO costs are imposed on generators

GE and SO costs are imposed on generators

Soci

ety,

cons

umer

Inve

stor

s,ge

nera

tors

No

unbu

ndin

gU

nbun

ding

Grid

exte

nsio

n(G

E) a

nd s

yste

mop

erat

ion

(SO

) co

sts

are

impo

sed

on

n

RES-E deploy-ment

Fig. 2. Overview of different cost allocation scenarios implemented in the GreenNet simulation software

3.3. Full unbundling (reference case): extra grid and system costs are allocated to ‘society’

Figure 3a indicates RES-E deployment in the reference scenario up to the year 2020. Already existing RES-E generation in Europe is dominated by large-scale hydro power, followed by wind onshore and biomass. However, the amount of large-scale hydro power will not increase significantly in the future due to adverse environmental impact (addressed e.g. in the Water Framework Directive (EC (2000))5 as well as limited additional potential. The most significant increase can be expected for wind energy: for onshore plants in the entire period 2005-2020 and for offshore plants especially beyond 2013. Moreover, it can be expected that around 45% of RES-E generation from new RES-E plants comes from wind onshore and 28% from wind offshore. This leads to a share of 29% wind onshore and 14% wind offshore on total RES-E generation in the year 2020.

______ 5 Taking into account the negative effects of the Water Framework Directive (EC (2000)) on

electricity generation, the total electricity generation from large-scale hydro power can even be lower in the year 2020 compared to the status quo.

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Auer et al. 16

0

100

200

300

400

500

600

700

800

90020

04

2005

2006

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2008

2009

2010

2011

2012

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2018

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2020

RES

-E g

ener

atio

n [T

Wh/

yr]

Wind Offshore

Wind Onshore

Tide & Wave

Solar ThermalElectricity

Photovoltaics

Hydro Small-Scale

Hydro Large-Scale

Geothermal Electricity

Biowaste

Solid Biomass

Biogas

Fig. 3a. RES-E deployment of new RES-E technologies in the period 2005 – 2020 within the EU15+4 (PL, CZ, SK, HU) in the BAU RES-E scenario

In Table 1 below, furthermore, the share of total RES-E generation

compared to total electricity generation on EU15 (EU15+4) country level for 2010 and 2020 is shown. From the RES-E policies’ point-of-view the year 2010 is important since each EU Member State has to fulfil indicative targets with respect to RES-E generation according to the EC-Directive 2001/77/EC (see e.g. EC (2001)). The results in Table 1 on aggregated EU15 (EU15+4) country level show that the indicative targets are not entirely met.6

______ 6 Please note, that comprehensive RES-E policy assessments as well as several dynamic

interactions between RES-E generation, conventional electricity and CHP generation, energy efficiency measures on the demand side, and GHG-reductions in the electricity sector in several EU27 Member States can be modelled with the simulation software Green-X. Green-X has also been developed in recent years at Energy Economics Group (EEG) at Vienna University of Technology, Austria (see Huber et al (2004b) and www.green-x.at). The common interface between GreenNet (“RES-E infrastructure tool”) and Green-X (“RES-E policy tool”) is the data base on potentials and costs of RES-E technologies in various countries and the RES-E BAU policy settings. Finally, Green-X is also the software tool used in the recently finished EC-Project “FORRES 2020 - Analyses of the EU renewable energy sources’ evolution up to 2020”. For further details on FORRES 2020 please see Ragwitz et al (2005).

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Least Cost Intermittent RES-E Integration 17

Tab. 1. Comparison: RES-E deployment based on GreenNet and EC-Directive

RES-E deployment based on GreenNet

Indicative targets due to EC-Directive

Comparison

EU15 (%) EU15+4 (%) EU15 (%) EU15+4 (%)

2010 18,5 17,5 22,1 20,7 2020 24,7 23,0

Derived from Figure 3a the corresponding annual RES-E capital

expenditures over time – assuming BAU RES-E policies up to the year 2020 – are indicated in Figure 3b. Significant investments are necessary to realise these new RES-E capacities in the reference scenario. Around €9,000m per year are estimated up to 2010, around €14,000m per year in the decade thereafter. On RES-E technology level the capital expenditures significantly vary over time. While annual investments in wind onshore and biogas are constant in the investigated period, investments in solid biomass and (bio)waste plants are mainly expected from 2005 to 2015. Beyond 2015 only limited biomass and (bio)waste potentials are implemented since their competitiveness compared to remaining RES-E technologies is worse. Finally, high investments in wind offshore are expected beyond 2010.

0

2000

4000

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18000

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RES

-E C

apita

l Exp

endi

ture

/ In

vest

men

t Nee

ds [

€m/y

r]

Wind Offshore

Wind Onshore

Tide & Wave

Solar Thermal Electricity

Photovoltaics

Hydro Small-Scale

Hydro Large-Scale

Geothermal Electricity

Biowaste

Solid Biomass

Biogas

Fig. 3b. Annual RES-E capital expenditures in the period 2005 – 2020 within the EU15+4 (PL, CZ, SK, HU) in the BAU RES-E scenario

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Auer et al. 18

According to wind deployment (both onshore and offshore) presented in

Figure 3a the corresponding annual grid reinforcement/extension costs are depicted in Figure 4 up to the year 2020. Assuming average specific grid reinforcement/extension costs of the existing grids based on a literature survey (details of model implementation are shown in the Appendix A.1), it can be expected that in 2020 annual grid infrastructure costs of around €450m per year are required to integrate new wind onshore and offshore capacities.7 Considering already implemented wind specific grid reinforcement/extension measures, annual costs rise from about €50m to €500m, see Figure 4.

0

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due

to w

ind

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oym

ent [

€m/y

r]

High cost scenario - incl. historical cost

High cost scenario

Average cost scenario - incl. historical cost

Average cost scenario

Low cost scenario - incl. historical cost

Low cost scenario

Fig. 4. Development of annual additional grid reinforcement/extension costs due to RES-E deployment up to the year 2020 in the BAU RES-E scenario

The additional system operation costs caused by system balancing and provision of system capacity margins due to intermittent wind generation are

______ 7 Note, that in this context just the grid reinforcement/extension costs on the existing grid

infrastructure are addressed. Grid connection costs of wind farms to the existing grids are included in the long-term marginal generation costs. Therefore, a clear distinction in the “wording” is necessary in this section 3.

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Least Cost Intermittent RES-E Integration 19

depicted in Figure 5. Again, two cases are considered: (i) wind energy can contribute to system capacity (i.e. a capacity credit is taken into account) and (ii) cannot. It is important to note, however, that wind in fact has a capacity credit (see e.g. Giebel (2001)) and the example is merely to illustrate the overall bandwidth in the cost calculations. The sensitivity analyses below estimate the system operation costs in the different scenarios.

0

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d de

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t [€m

/yr]

High cost scenario - without capacity credit

High cost scenario - with capacity credit

Average cost scenario - without capacity credit

Average cost scenario - with capacity credit

Low cost scenario - without capacity credit

Low cost scenario - with capacity credit

Fig. 5. Development of annual additional system operation costs due to RES-E deployment up to the year 2020 in the BAU RES-E scenario

3.4. No unbundling: extra grid and system costs are allocated to RES-E developer

The results on allocating both grid reinforcement/extension costs and system operation costs to the RES-E developer are summarized in Figure 6a. The changes in the total RES-E portfolio in the ‘EU15+4’ Member States caused by these extra costs compared to the reference case are depicted in Figure 6b. It can be seen that the share of both wind onshore and offshore will be reduced. Again, the deviation depends on the assumed framework conditions. If no capacity credit is awarded to wind power, significantly less wind deployment occurs. The reduction is partly compensated by larger deployment of remaining

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Auer et al. 20

RES-E technologies as their competitiveness increases in relation to wind power. Moreover, an increased growth can be expected for biogas, biomass, hydro power as well as tide and wave energy.

60%

65%

70%

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80%

85%

90%

95%

100%

2005

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Cum

ulat

ed in

stal

led

capa

city

of w

ind

pow

er p

lant

s: D

iffer

ent

scen

ario

s co

mpa

red

to th

e re

fere

nce

case

[%]

Reference case (full unbundling- no impact on producer)

Low cost scenario - GE for newplants, SO (with CC) for newand existing plants

Average cost scenario - GE forexisting and new plants, SO(with CC) for new and existingplants

Average cost scenario - GE forall plants (incl. Historical cost),SO (with CC) for new andexisting plants

Average cost scenario - GE fornew plants, SO (with CC) fornew and existing plants

High cost scenario - GE for newplants, SO (with CC) for newand existing plants

Average cost scenario - GE fornew plants, SO (without CC) fornew and existing plants

Fig. 6a. No unbundling: Impact of grid reinforcement/extension costs and system operation costs on cumulated installed wind capacity compared to the reference case (full unbundling) on EU15+4 Member States’ level. Legend: GE = Grid reinforcement/extension, SO = System Operation, CC = Capacity Credit

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Least Cost Intermittent RES-E Integration 21

-11%

-10%

-9%

-8%

-7%

-6%

-5%

-4%

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-1%

0%

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Bio

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s

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te

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mal

Elec

tric

ity

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ro L

arge

-Sca

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l-Sca

le

Phot

ovol

taic

s

Sola

r the

rmal

Elec

tric

ity

Tide

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ave

Win

d O

nsho

re

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d O

ffsho

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RES

-E g

ener

atio

n fr

om n

ew in

stal

led

capa

citie

s in

202

0:

Dev

iatio

n to

the

refe

renc

e sc

enar

io [%

]

Minimal Changes Maximal Changes

Fig. 6b. No unbundling: Deviation of RES-E generation from new installed RES-E capacities compared to the reference case (full unbundling) on EU15+4 Member States’ level

The impact of additional grid reinforcement/extension costs and system

operation costs significantly varies between the EU Member States. The effects mainly depend on the particular RES-E policy scheme. Figure 7 below compares the two extreme cases of Germany (feed-in tariff scheme) and UK (obligated quota system): • The influence on total new RES-E generation is significant for price-driven

instruments (i.e. feed-in tariff, investment incentive and tax relief), since no compensation mechanism is available to reduce the negative impact of the additional costs allocated to the RES-E developer. Moreover, if grid-related and system-related costs are not unbundled and, simultaneously, wind deployment shall remain, then an adaptation of the price-driven instruments is necessary (i.e. increase of the feed-in tariff).

• On contrary, for capacity-driven instruments (i.e. quota systems with and without tradable green certificates, tender procedure) the additional costs are partly compensated by an increase of the green certificate price and the (marginal) bid price. The reason is that a certain quantity of new RES-E capacity has to be reached. The consideration of grid-related and system-related costs reduces the competitiveness of wind energy compared to

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Auer et al. 22

remaining non-intermittent RES-E technologies. Therefore, the deployment portfolio of different RES-E technologies changes only, but not the total new RES-E capacity.

-40%

-35%

-30%

-25%

-20%

-15%

-10%

-5%

0%

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Biog

as

Solid

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ctric

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Pho

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ctric

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ave

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shor

e

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-E g

ener

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om n

ew in

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citie

s - d

evia

tion

to re

fere

nce

case

[%] _

-4,0%

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Biog

as

Solid

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s

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aste

Geo

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mal

ele

ctric

ity

Hyd

ro la

rge-

scal

e

Hyd

ro s

mal

l-sca

le

Phot

ovol

taic

s

Sol

ar th

erm

al e

lect

ricity

Tide

& w

ave

Win

d on

shor

e

Win

d of

fsho

re

RES

-E g

ener

atio

n fr

om n

ew in

stal

led

capa

citie

s - d

evia

tion

to re

fere

nce

case

[%] _

Germany United Kingdom

Fig. 7. No unbundling: Deviation of RES-E generation from new installed RES-E capacities from the BAU RES-E reference case (full unbundling) in Germany (feed-in tariff scheme (left)) and the UK (obligated quota system (right))

The major conclusion based on the results shown in Figure 7 is that the

degree of unbundling and the allocation principles of different disaggregated cost elements significantly influences RES-E deployment in Europe up to the year 2020 in general (and wind in particular).

The effects of imposing either grid reinforcement/extension costs or system operation costs on the RES-E developer are not presented separately. Imposing grid reinforcement/extension costs to the RES-E developer results in RES-E deployments similar to the fully unbundled case (see section 3.3) and vice versa for system operation costs according to RES-E deployment in section 3.4.

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Least Cost Intermittent RES-E Integration 23

4. Conclusions

In general, grid infrastructure issues address the entire natural monopoly in the electricity supply chain. For large-scale intermittent RES-E integration, therefore, it is necessary to investigate both 1. grid connection to the existing grids (regardless of the distance and/or

voltage level of connection), and 2. grid reinforcement/extension measures elsewhere in the existing network

due to changed load flows Moreover, considering the currently ongoing benchmarking and grid tariff

regulation procedures in many European countries,8 the implementation of correct cost allocation principles is vital. Not least due to these ongoing grid regulation procedures, it is essential to start a fundamental discussion on the allocation of both RES-E related grid connection costs and grid reinforcement/extension costs. In the past, for small scale RES-E integration, the share of grid-related costs has been small compared to the long-run marginal costs of RES-E generation. Therefore, grid-related costs have not been clarified, but often treated as part of the long-run marginal costs of the RES-E power plant and, subsequently, were socialised via the corresponding RES-E promotion instrument.

But this practice clearly violates the unbundling principles of the EC-Directive (as well as economic theory of network industries in general): • Moreover, in countries like Germany it is still foreseen to allocate grid

connection costs of (offshore) wind farms to the wind project and, subsequently, to socialise corresponding costs via feed-in tariffs. This practice (mixing up costs of kWh’s generated and grid infrastructure assets) is at least questionable.9

• On contrary, in countries like Denmark grid connection costs of (offshore) wind farms are already allocated to the grid infrastructure and socialised correctly. Moreover, the results of the modelling examples based on the GreenNet

software show that – using currently implemented RES-E promotion instruments in the different EU Member States and assuming in the BAU RES-

______ 8 I.e., the determination of eligible costs for construction and operation of grids and,

subsequently, socialisation of corresponding costs via grid tariffs. 9 In general, grid infrastructure assets (natural monopolies) are depreciated differently

compared to assets being subject to competition or feeding into competitive markets (like RES-E electricity generation).

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Auer et al. 24

E scenario that these instruments remain up to the year 2020 – the pattern of RES-E deployment significantly varies depending on the degree of unbundling and the allocation strategy of the different disaggregated cost elements of RES-E grid integration.

When assessing cost for balancing intermittent RES-E generation it is important to note, that current balancing markets often don’t work efficiently (e.g. due to abuse of market power, etc.) and therefore the corresponding costs are higher than they might be from the system’s point of view (therefore within the GreenNet model balancing cost are implemented using a cost based rather than a price based approach). For an efficient market integration of intermittent RES-E there is the need for electricity markets that provide adequate prices and give market players the opportunity to adjust their programmes intra-day (e.g. in form of an organised intra-day market).

As a consequence of the inadequacies mentioned throughout this paper, it is recommended to establish a strategic EU-wide policy for long-term large-scale RES-E grid integration. In this context, a fundamental unbundling discussion is indispensable. This means in particular, that a re-definition of the interface between the RES-E power plant (incl. the “internal grid” and the corresponding electrical equipment) and the “external” grid infrastructure (i.e. new grid connection lines and reinforcement/extension of the existing grid) has to be discussed. This does not necessarily mean that the additional grid tariff component due to RES-E grid integration has to be paid by the local/regional end-users only. The costs can be socialised also within a “grid infrastructure component” on national or even EU-level. Of course, corresponding accounting rules have to be established for the grid operators.

Finally, for acceptance of large-scale intermittent RES-E generation in a system, several existing barriers in the wholesale and balancing markets (incl. settlement procedures) have to be overcome. A critical review in this context is necessary in several EU Member States. In the short-term, improved wind forecasting tools are needed to reduce the impact of intermittency and, subsequently, balancing costs. In the long-term, however, it is also important to address demand response options to minimise additional system balancing requirements and costs.

References

Auer Hans, Michael Stadler, Gustav Resch, Claus Huber, Thomas Schuster, Hans Taus, Lars Henrik Nielsen, John Twidell, Derk Jan Swider: “Cost and Technical Constraints of RES-E Grid Integration”, Project Report, WP2, August 2004, available on www.greennet.at

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Least Cost Intermittent RES-E Integration 25

Auer H., C. Huber, G. Resch, T. Faber, C. Obersteiner: “Action plan for an enhanced least-cost integration of RES-E into the European grid”, Project Report, WP10, February 2005, available on www.greennet.at

Bach P.F.: „Costs of Wind Power Integration into the Electricity Grids in Denmark“, Proceedings, IEA Workshop on Integration of Wind Power into Electricity Grids, Paris, 25 May 2004.

DEWI: „Energiewirtschaftliche Planung für die Netzintegration von Windenergie in Deutschland an Land und Offshore bis zum Jahr 2020“, Studie im Auftrag der Deutschen Energie-Agentur GmbH (dena), Konsortium: DEWI, E.ON Netz, EWI, RWE Net, VE Transmission, February 2005.

Dowling P., B. Hurley: „A strategy for locating the least-cost wind energy sites within the EU electrical load and grid infrastructure perspective”, Proceedings, 5th International Workshop on Large-Scale Integration of Wind Power and Transmission Networks for Offshore Wind Farms, Glasgow, 7-8 April 2005.

European Commission (2000): Directive 2000/60/EC of the European Parliament and of the Council of 23 October 2000 establishing a framework for Community action in the field of water policy.

European Commission (2001): Directive 2001/77 of September 27th 2001 on the Promotion of Electricity produced from Renewable Energy Sources in the internal electricity market.

European Commission (2004): Directive 2003/54/EC of June 26th 2003 concerning common rules for the internal market in electricity and repealing Directive 96/92/EC.

Giebel G.: “On the Benefits of Distributed Generation of Wind Energy in Europe”, Phd thesis from the Carl von Ossietzky Universität Oldenburg, VDI Reihe 6, Nr. 444, Düsseldorf, VDI Verlag, ISBN 3-18-344406-2, 2001.

Groenhuijse L.: “Minimising the costs of integrating wind power into the grid: the Dutch situation”, Proceedings, IEA Workshop on Integration of Wind Power into Electricity Grids, Paris, 25 May 2004.

Hooft, Jaap ‘t: “Survey of integration of 6000 MW offshore wind power in the Netherlands electricity grid in 2020”, Proceedings, European Wind Energy Conference (EWEC), Madrid, 16-19 June 2003.

Huber C., T. Faber, G. Resch, R. Haas: „Deriving Optimal Promotion Strategies for Increasing the Share of RES-E in a Dynamic European Electricity Market“, Action Plan of the Project Green-X, October 2004(a), available on www.green-x.at

Huber C., T. Faber, R. Haas, G. resch, J. Green, S. Ölz, S. White, H. Cleijne, W. Ruijgrok, P.E. Morthhorst, K. Skytte, M. Gual, P. Del Rio, F. Hernandez, A. Tacsir, M. Ragwitz, J. Schleich, W. Orasch, M. Bokemann, C. Lins: “Final report of the project Green-X” Green-X report, November 2004(b), available on www.green-x.at

Huber C., T. Faber, G. Resch, H. Auer: “The Integrated Dynamic Formal Framework of GreenNet”, Project Report, WP8, December 2004(c), available on www.greennet.at

ILEX Energy Consulting: “Quantifying the system costs of additional renewables in 2020“, A report of ILEX Energy Consulting in association with Manchester Centre for Electrical Energy (UMIST) for the Department of Trade and Industry (DTI), October 2002.

Milborrow D.J.: “The Real Cost of Integrating Wind”, Windpower Monthly, February 2004, p.35-38, 2004.

Pantaleo A., A. Pellerano, M. Trovato: “Technical issues on wind energy integration in power systems: projections in Italy”, Proceedings, European Wind Energy Conference 2003, Madrid, 16-19 June 2003.

Ragwitz M., C. Huber, G. Resch, T. Faber, M. Voogt, W. Ruijgrok, P. Bodo: “FORRES 2020 – Analyses of the renewable energy’s evolution up to 2020”, Final report of the project

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Auer et al. 26

FORRES 2020 – on behalf of DGTREN, Fraunhofer IRB Verlag: ISBN 3-8167-6893-8, Karlsruhe, November 2005.

Resch G., H. Auer, M. Stadler, C. Huber, L.H. Nielsen, J. Twidell, D.J. Swider: „Dynamics and basic interactions of RES-E with the grid, switchable loads and storage“, Project Report, WP1, October 2003, available on www.greennet.at

Smith P.: “A simulation of integration of wind generation into the Irish grid: impacts and remedies, Proceedings, IEA Workshop on Integration of Wind Power into Electricity Grids, Paris, 25 May 2004.

Soeder L.: “The Value of Wind Power”, Proceedings, IEA Workshop on Integration of Wind Power into Electricity Grids, Paris, 25 May 2004.

Swider D.J., C.: “Scenarios on the conventional European electricity market”, Project Report, WP6, February 2005, available on www.greennet.at

Tembleque L.J.S.: “Costs of wind power integration into electricity grids in Spain”, Proceedings, IEA Workshop on Integration of Wind Power into Electricity Grids, Paris, 25 May 2004.

Van Werven, M.J.N., L.W.M. Beurskens, J.T.P. Pierik: “Integrating Wind Power in EU Electricity Systems: Economics and Technical Issues”, Project Report, WP4, February 2005, available on www.greennet.at

Appendix: Assumptions in the GreenNet model

A.1 Assumptions on extra grid reinforcement/Extension costs

Derived from the results of country-specific studies on large-scale wind integration (based on detailed load flow analyses), the long-run marginal costs for grid reinforcement/extension allocated to wind penetration are identified. This set of data (determining grid reinforcement/extension costs as a premium per MWh wind generation and depending on wind penetration) is described in the GreenNet model by a continuous mathematical function, see Figure A.1. Uncertainties are taken into account by implementing two alternative scenarios for high and low costs.

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Least Cost Intermittent RES-E Integration 27

0

1

2

3

4

5

6

7

0% 5% 10% 15% 20% 25% 30%

Wind penetration - in terms of electricity generation [% of total demand]

Grid

ext

ensi

on c

osts

[€/M

Wh]

high cost-scenario

average cost-scenario

low cost-scenario

costs as identified in country-specific case-studies

cost-functions as applied in the model GreenNet

Figure A.1. Model implementation of additional grid reinforcement/extension costs caused by wind integration (expressed as a premium in €/MWh wind generation)

A.2 Assumptions on extra system operation costs

In the GreenNet model, the costs for short-term system balancing allocated to wind generation are derived from different country-specific case studies and literature. Depending on wind penetration they are in a range of 0-3€/MWh (for details see e.g. Auer et al (2004)).

Long-term system capacity requirements and corresponding costs relate to the limited contribution that intermittent wind generation can make to system security. For small levels of wind penetration in the system (i.e. more precisely, installed wind capacity compared to system peak load), the capacity credit for wind generation is equivalent to the load factor. As the capacity of wind penetration increases, wind becomes increasingly less reliable in a system for displacing the capacity of conventional plants – even in case of geographical spread of wind sites – since system reliability is increasingly dominated by wind. Therefore, the capacity credit begins to tail off (see e.g. also DEWI (2005), Auer et al (2004), Pantaleo et al (2003), ILEX (2002), Giebel (2001)).

Figure A.2 quantifies the average capacity credit of wind onshore and offshore depending on installed wind capacity in a system. The results in Figure A.2 (indicating an average of several case studies analysed and being also implemented in the GreenNet model) are derived from a comprehensive literature survey (publications cited above as well as others).

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Auer et al. 28

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

50%

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%Wind penetration - in terms of power (Pwind/Ppeak-load) [%]

Cap

acity

cre

dit

[% o

f ins

talle

d w

ind

capa

city

]

wind onshore wind offshore

Figure A.2. Model implementation for the calculation of the capacity credit of wind (onshore and offshore)

The calculation of the additional system capacity costs in the GreenNet

model finally is based on the “thermal equivalent” approach according to ILEX (2002): “The annual wind generation is calculated from the installed capacity in MW and the annual full load hours. Then the equivalent amount of conventional capacity is determined required to produce the same annual electricity, assuming a CCGT (Combined Cycle Gas Turbine) at an average load factor. However, conventional capacity can be viewed as delivering two services, energy and capacity. If it is considered that wind provides no contribution to capacity margin, then to be equivalent to conventional generation, wind would require back-up from equivalent conventional capacity. This capacity could come from a number of sources, including old conventional and pumped-hydro generation, new CCGTs or new Open Cycle Gas Turbines (OCGTs). For the cost calculation the capacity requirements are allocated to new, but not leading-edge OCGT, suitable for peaking operation, considering that at the margin only OCGTs will be used, as any economically feasible existing generation would already be utilised on the system. The annualized capital costs are finally determined depending on annual wind generation. If it is considered that wind does contribute to system security, albeit at a smaller rate than conventional capacity, then the above capacity requirement is reduced by the level of that contribution. Then also the annualized capacity costs are derived depending on annual wind generation.”

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29

INTEGRATING ELECTRICITY PRODUCTION FROM

FLUCTUATING SOURCES – VALUATION OF VARIABILITY AND

UNPREDICTABILITY

CHRISTOPH WEBER* Chair of Energy Management, University of Duisburg-Essen, Germany

Abstract. This paper provides a systematic approach to the issue of quantifying the costs of integrating fluctuating sources like wind or solar into an existing electricity system. The paper notably stresses that integration costs are always measured against some reference technology and it highlights the link between integration costs and changes in system costs. Moreover the costs related to wind and solar integration are decomposed into several components, including notably the costs of variability and the cost of unpredictability. Furthermore it is discussed, how these cost components may be determined using stochastic op-timization approaches.

Keywords: wind energy, stochastic optimization, integration costs

1. Introduction

The rise of wind and solar energy as ecological, emission free energy sources has always been accompanied by the question, whether the inherent fluctuations in their production don’t make them very poor substitutes of conventional, con-trollable electricity production from coal, gas and other power plants. Put in other terms, the question is whether their installation, being costly by itself, does not induce further costs necessary for the fluctuating renewables to be able to contribute to the overall power supply system. These costs are often summa-rized under the general term of “integration costs”. ______

* To whom correspondence should be addressed. Email: [email protected]

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Weber 30

Grubb (1991) provides a detailed discussion and quantitative estimates of the additional costs induced by the installation of fluctuating renewables. In the context of optimal policy design, Elsässer (2002) and Fuchs (2003) give results on the costs of increased part-load operation, start-ups and backup costs for wind energy, without much detail however on the calculation methodology. ILEX (2002) discusses the additional costs related to the integration of large amounts of renewables in the British electricity system, following closely the approach developed by Grubb (1991). In the various presentations given at IEA (2004), different approaches to the quantification of integration costs and also corresponding numerical values are given. Auer et al. (2004) provide an over-view of relevant cost components and discuss cost estimates taken from studies in various European countries. Swider and Weber (2004) derive the value of wind energy from an electricity system model, which includes explicitly the stochasticity of wind as well of hydro sources. They tend to define as integra-tion cost the entire difference between the marginal value of wind energy pro-duction and the average system price. Brand et al. (2005) use a stochastic sys-tem operation model to compute two different values for the integration costs – including the impacts of more frequent part-load operation, increased number of start-ups and higher reserves.

These various contributions are characterized as much by a broad variety of numerical results given as by a challenging diversity of methods used. Söder (2005) gives there an overview of key differences between approaches and their implications. In this context, the present contribution aims at providing a sys-tematic approach both to the categorization of various types of integration costs and to their quantification. Thereby the focus is on the use of modern numerical methods of stochastic modelling and stochastic optimization, which allow quan-tifying integration costs with much detail - if they are adequately employed.

The structure of the present paper is as follows: in the next section, a unify-ing framework for analysing integration costs is developed. The focus is hereby on clarifying the different causalities inducing integration costs for renewables. These various causalities are mirrored differently in the perspectives on renew-ables integration taken by various authors. And also the diverse methodologies proposed for numerical assessment are suited more or less to capture these dif-ferent causal links. This is discussed in detail in section 3 with a focus on those costs related to modified operation of the conventional system. In this context basic analytical relationships are derived, which link integration costs as deter-mined through various approaches. In section 4 then integration costs are quan-tified for an exemplary system, highlighting the impact of the various ap-proaches on the height of integration costs.

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Integrating Electricity Production from Fluctuating Sources 31

2. A systematic framework for assessing integration costs

The general term of integration costs is coined to designate additional costs of integrating something new into a pre-existent system. In the context relevant here, the pre-existent system is a power system, which consists basically of generators, transmission lines and consumers, distributed over a certain geo-graphical area (cf. Fig. 1). The new things are novel generation technologies, based on other than conventional energy transformation processes. Formulated this way, three obvious questions arise: 1. What makes the new technologies new and different? 2. Can there be also integration costs for conventional technologies, if they are

newly installed? 3. Does the system remain the same, or does it adapt – and to what extent – to

the new technologies? Ad 1: The new technologies under study are usually based on renewable en-

ergy1. Yet this is not the key difference in the present context. Key is the fluctu-ating output of solar and wind based electricity generators. In order to cope with integration costs adequately, we will hence have to look more precisely at what is meant by fluctuations.

Ad 2: Apparently also the grid connection costs for a new coal-fired plant are expenses, which go beyond the cost of simply putting up the new plant. And also a new conventional plant may require a grid extension for reliable opera-tion – as is apparently the case for the new to be built Finnish nuclear power plant. This point is often omitted when integration cost for wind and solar en-ergy are discussed. Yet it should not be overestimated. In many cases new con-ventional power plants are built on brown-field sites, making use of the infra-structure already in place for old plants. And especially grid connection tends to be cheaper per unit of MW or MWh connected, since the power is delivered at one location with a very high power density. Nevertheless, a precise definition and categorization of integration costs is needed before proceeding.

______ 1 Albeit the term renewable is a misnomer from a fundamental thermodynamic point of view:

from the second law of thermodynamics one may deduce that all energy transformations and energy flows, which occur in finite time, are at least partly irreversible. Correspondingly most of the renewables are limited through the finite lifetime of the sun as energy source for our world. Yet obviously this is at an entirely different timescale than the expiration of fossil resources like oil and gas.

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Weber 32

Ad 3: Obviously the system has to adapt to the new power stemming from wind and others – and be it only to maintain the balance between supply and demand. But the types of adaptation reactions considered differ from one au-thor to another and have to be classified.

In order to cope with the issues identified in the previous paragraphs and to lay the basis for a subsequent coherent analytical and numerical treatment of integration costs, let us first define the system considered when talking about integration costs.

2.1. General system definition

Definition: An electric system S is defined as a triple {E; Q; R}. E is thereby a set of elements e. Each element e belongs to one (and only one) of the follow-ing subsets of E: G, the set of generators in S, D, the set of consumers in S and O, the set of other elements in S (e.g. transformers, switches …)2.

Each element e of E is characterised by a vector de of coordinates, which de-scribe the location of the element in an adequate reference system (e.g. geo-graphical latitude and longitude). Furthermore each element of E may have fur-ther time-independent attributes, summarized in the vector ae, e.g. the rated power. Moreover time-dependent attributes may be associated with each ele-ment e, e.g. the instantaneous power flow Pe(t). These time-dependent attributes are summarized in the vector be(t).

In order to simplify further notation, the vectors ae are summarized in a set A, also the vectors be(t) are condensed in the set B(t). The vectors ae are not necessarily of equal length for all elements e, therefore the set A does not di-rectly correspond to a matrix. The same holds for the set B(t).

Q is a set of triples (l, n1, n2), which describe the connections between lines and consumers resp. generators. If we take l as an element of L, i.e. a line, and n1 and n2 as elements of N, Q describes the topology of the electrical grid.

R is a set of relations and properties defined on the elements of S. One ele-ment of R is clearly the energy balance BEl for the whole system, which should sum up for each moment in time to 0. Another element of R is the cost balance BCost for the whole system, which provides the total costs of the system as a function of the elements installed and their operation. ______

2 Note that the partitioning (division without overlapping) between consumers and generators is useful for theoretical considerations, but in reality is not always applicable– one might think of households or industrial companies, who both consume electricity and produce some themselves, e.g. in CHP installations. These can however be put into the theoretical framework by including two nodes connected by a line of (almost) infinite capacity.

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Integrating Electricity Production from Fluctuating Sources 33

The definition given is far from providing a complete characterisation of the electric system considered. Yet this a key issue when comparing different stud-ies on integration costs: they differ in the system definition, which they rely on (implicitly or explicitly). E. g. which time resolution is chosen for the energy balance clearly has an effect on how the impact of fluctuations can be assessed. Based on hourly balances much more effects can be taken into account than if only yearly balances are considered.

A further key issue for assessing integration costs obviously is the definition chosen for the cost balance. In a rather general way, the cost balance may be described in discrete time as3:

( ) ( )( ) ( )( )∑∑∑∑ +=e t

eeeVare t

eeeFixTot ttCttCSC ,, ,, b,ab,a (1)

i.e. the total costs CTot of the system are defined as the sum of the fixed costs of all elements e and the variable costs summed over elements e and time t.

The following remarks are thereby important: • The time span covered by the time periods t is important and appropriate

discounting has to be done, if longer time spans are to be considered. This discounting is part of the cost functions CFix,e and CVar,e as defined here.

• In almost every case considered, there will be energy (and material) flows across the system boundary. These have to be assessed and taken into ac-count appropriately.

• As formulated above, the cost function is only valid for deterministic sys-tems or ex-post for systems with stochastic elements. For an ex-ante as-sessment of system costs for stochastic systems, some expectation operator has to be applied to the cost elements and (implicit or explicit) risk prefer-ences have to be taken into account.

• The cost function as framed incorporates a further restriction compared to the general case: separability of costs in time and between elements. Espe-cially the first one is less innocent as it might first appear, since it makes difficult the inclusion of start-up costs.

______ 3 In principle, a treatment in continuous time would also be possible. Yet for the numerical so-

lutions later on anyhow a discretisation is necessary. Therefore here from the outset a notation in discrete time is chosen, simplifying partly the notational burden. Given that the size of the time invervalls is for the time being left open, the discrete time intervals may be thought of being part of a series of partitions converging to infinitesimal time steps approximating continuous time at any degree of precision required.

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Weber 34

2.2. Key issues for the definition of integration costs

In order to determine the integration costs, differences between systems with and without renewables will usually be looked at. Yet for this purpose the defi-nition of system costs given in equation (1) is too vague. Indeed the system costs as defined there depend on all parameters ae and be(t). In order to assess the impact of a requirement like a certain amount of renewable generation, it is preferable to look at the minimum additional costs, which they impose on the system considered. Hence first the minimum costs CTot

*(S; AF, BF(t)) for a given system have to be defined. These can be generally described through:

( )( ) ( )

RQtrw

SCtSC TotFFTot

...

min,;,

*

B'A'BA =

(2)

Hence for the cost optimisation usually the links contained in set Q and the relations summarized in set R are taken as given. Moreover usually also part of the parameters are fixed, e. g. the demand profile in the demand nodes (set D) or the installed capacities of some or all elements. Therefore the vectors con-tained in the sets A and B(t) are subdivided into fixed parameters aF,e and bF,e(t) on the one side and variable parameters (or variables for short) a’e and b’e(t). These vectors are then again regrouped as previously into the sets AF, BF(t), A’ and B’(t) used in equation (2).

Three important cases may be distinguished here: 1. Only the demand parameters (load curves) and the investment and opera-

tion costs for the various elements are taken as fixed4. The capacities of generators and transmission lines are part of the optimisation variables A’. Simultaneously their operation is optimised, the corresponding variables are including in the set B’(t).

2. The installed capacities are also considered as fixed. The optimisation only covers the operation of the generators and transmission lines, which leads to corresponding variables in set B’(t), while set A’ remains almost void in this case.

______ 4 The more general case, where also investment costs are variable and depend on system deci-

sions, is not treated here. This case of endogenous technological learning is mostly relevant when long time-spans and global systems are considered (cf. e.g. Seegbregts et al. 1999).

When parameters are taken as fixed or given, this however does not necessarily imply that they are deterministic. Especially for fluctuating renewables, the stochastic production process can be considered as given, without the precise values for each hour being known ex-ante.

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Integrating Electricity Production from Fluctuating Sources 35

3. Demand is not taken as entirely fix. Rather demand flexibility is introduced by including money-metric utility losses for reduced demand in the cost function (cf. Ravn 2001). This feature can be combined both with fixed and with variable generation and transmission capacities and leads mostly to ad-ditional variables in B’(t). These basic cases are relevant for the determination of minimum system

costs. In order to get from system costs to integration costs, the costs for differ-ent system configurations have to be compared, namely the minimum costs CTot

*(S; AF,Ren, BF,Ren(t)) for the system with given renewables capacity (abbre-viated CTot,Ren

*) and the minimum costs CTot*(S; AF,0, BF,0(t)) for a reference case

(CTot,0* for short). Yet thereby several pitfalls have to be avoided.

• The difference

*0,

*Re,Re, TotnTotnAdd CCC −= (3)

is easily computed and describes the additional system costs caused by the introduction of a certain amount of renewables - or more generally the costs caused by the requirements AF,Ren and BF,Ren (t) as compared to the refer-ence case characterised by AF,0 and BF,0(t). Yet this difference is strongly determined by the investment costs for the renewables capacities. But usu-ally what is meant by integration costs is precisely additional costs for re-newables which go beyond the cost of installing them.

• If these renewables investments are taken out, the aforementioned cost dif-ference usually gets negative: if renewable energy is provided at zero in-vestment cost, it leads in all except the most extreme cases to cost savings in the conventional system, notably savings in fuel costs. So a simple correc-tion of the difference CTot,Ren

* - CTot,0* by the renewable investments CFix,Ren

does not solve the problem either. • The cost savings in the conventional system are however in general lower

than “what would be expected”. This difference between the expected cost savings and the actual ones with renewables generation is what can be rea-sonably labelled “integration costs” and this is also the way, the term is usu-ally understood. Yet this not operational as long as the cost savings “which would be expected” are not precisely defined. In order to formalize the last point, we define integration costs as follows:

( )AltFixTotAltTotnFixTotnTotInt CCCCCCC ,*

0,*

,Re,*

0,*

Re, Δ−−−−−= (4)

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Weber 36

Hence the integration costs are defined as the difference in the cost savings by the renewables (except investment costs) compared to the cost savings through some alternative (new) generation CTot,Alt

* - CTot,0*- ΔCFix,Alt, whereby

the investment costs for the alternative ΔCFix,Alt are also excluded. In order to determine integration costs, it is hence not only necessary to pre-

cisely define what the variable elements are, when (minimum) system costs are determined. But moreover also the alternative considered has to be made ex-plicit, when it comes to splitting the cost savings by renewables in an expected part and a reduction due to “integration cost”. The following alternatives could be thought of: 1. Naively, one might consider as alternative the reference case. Yet in this

case, we get CTot,Alt* = CTot,0

* and ΔCFix,Alt = 0. Hence the integration costs would correspond directly to the savings in operation and – as far as rele-vant – investment costs in the conventional system, when renewables are in-troduced. Thus we would again end up with negative integration costs.

2. Another possibility is to determine the integration costs by comparing the renewable generation using technology TRen to a hypothetical conventional, controllable generation technology T1 with same cost characteristics. I.e. al-ternatively to the use of renewables it is assumed that the same generation capacity is built of this hypothetical technology T1, which has the same uni-tary investment and operation costs than the renewable technology, but has similar controllability and availability characteristics than conventional technologies. This obviously leads to rather high integration costs, since the alternative technology will produce more5 and save much more conven-tional fuel and thus costs than the renewable technology, given that it does not depend on a fluctuating input. Yet this hypothetical generation alterna-tive is too good to be true and thus is not “what is expected”. Therefore such a measure of integration costs is not adequate.

3. A less unrealistic alternative could be a conventional, controllable technol-ogy T2 with same cost characteristics but also with the same average avail-ability than the renewables under study.

4. The controllable alternative T2 is able to produce the same annual energy amount than the renewable TRen and this production will be fully absorbed by the system, since it will be made available at almost zero variable cost,

______ 5 Remember that e.g. wind energy has at on-shore locations typically full load hours between

1600 h and 2500 h, i.e. an average availability between 0.18 and 0.29. Conventional power plants by contrast have technical availabilities between 0.85 and 0.92.

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Integrating Electricity Production from Fluctuating Sources 37

like wind or solar power. The availability of technology T2 can be taken as constant over time6. Then obviously the power production with TRen using renewables will lead to higher costs than the use of T2 due to the fluctuating nature of the renewables considered. Moreover the power production using TRen might induce further costs compared to technology T2, if TRen is more geographically dispersed and needs more grid investments for connection or is more geographically concentrated, so that more long-distance transporta-tion needs arise. Obviously also the inverse may occur.

5. All these additional costs can in principle be determined using equation (4) and can be termed rather properly as integration costs. Their height obvi-ously is dependent on the exact specification of the technology T2, which is clearly also not a real but a constructed alternative. For the results to be convincing, it is essential that the characteristics of this technology are plau-sible.

6. Instead of assuming that the alternative technology provides power at a constant rate, a less demanding assumption is that the alternative technology delivers power at each moment in time like the renewable source, but that this power output is perfectly predictable. When comparing this technology T3 to the renewables technology TRen, the integration costs consist mostly of the additional system costs induced through the unpredictability of fluctuat-ing renewables plus eventual additional or reduced costs through modified geographical distribution.

2.3. Operational definition of integration costs

The above discussion has shown that the computation of integration costs al-ways remains dependent on the definition of a hypothetical technology alterna-tive. This may also be illustrated through rewriting the integration cost defini-tion from equation (4) using equation (3):

( )

*,

*Re,

,Re,*

,*

Re,

AltAddnAdd

AltFixnFixAltAddnAddInt

CC

CCCCC

−=

Δ−−−= (5)

with the second part of the identity holding given that we have assumed similar investment costs for TRen and the alternatives T1, T2 and T3. Thus the in-tegration costs are equal to the difference between the additional system costs ______

6 Exceptions for conventional plants are planned revisions and unforeseen outages, yet these can be neglected in a first approximation.

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Weber 38

when imposing renewables and the additional system costs when using the al-ternative technology. This can also be put another way:

*

,*

Re, AltAddIntnAdd CCC += (6)

Hence, the additional system costs resulting from a renewables requirement can be decomposed in the so-called integration costs and the additional costs when requiring an alternative technology. Obviously the additional system costs are independent of the specification of the technology alternative, yet the de-composition into integration costs and alternative additional costs is not.

Despite these caveats it is obviously of interest of having a closer look at the height of the integration costs and the factors determining them. Thereby we base the further investigation on the definition:

*

2,*

Re, cTAddnAddInt CCC −= (7)

Hence the integration costs are determined as the difference between the ad-ditional costs for renewables minus the additional costs for the hypothetical technology T2 with identical output, investment and variable costs and geo-graphically distributed as conventional power plants (therefore subscript c). This definition seems most in line with what is usually denominated integration costs.

It lends also to the following decomposition, which allows looking closer at the causes for integration cost:

VariabUnpredextGridconGridInt CCCCC +++= ,, (8)

Thereby we define as components of the integration costs: • Grid connection costs:

( )*,,

*,, rRenAddRenAddconGrid CCC −= (9)

They correspond to the increase (or decrease) in cost due to the fact that the renewables are distributed, dispersed generation technologies. They are de-termined by comparing the additional costs to those of a hypothetical sys-tem, where the renewable technologies would have the same distribution over regions (therefore the index r), but are concentrated within the regions at the location of conventional power plants.

• Grid extension costs:

( )*,,

*,,, cRenAddrRenAddextGrid CCC −= (10)

Those reflect the uneven distribution of some renewable sources (like wind in the German case) over the regions. This uneven distribution causes costs

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Integrating Electricity Production from Fluctuating Sources 39

for additional grid investments, as emphasized recently in Germany by the so-called dena-study (cf. dena et al., 2005). Here they are computed by comparing the costs of the aforementioned system with regionally concen-trated renewables (index r) to those of a system with renewables distributed like the existing conventional plants (index c), both within and between re-gions.

• Costs of unpredictability:

*

,3,*

,, cTAddcRenAddUnpred CCC −= (11)

These are the additional costs occurring when comparing the system with renewables to one with the hypothetical technology T3 having same, time-varying output but perfect predictability. This cost, taken with the opposite sign, corresponds to the value of perfect information, commonly referred to in the stochastic programming literature (e.g. Birge, Louveaux 1997).

• Costs of variability

*

,2,*

,3, cTAddcTAddVariab CCC −= (12)

This finally describes the cost gap between using the aforementioned tech-nology T3 and using the technology T2, which provides the same energy output as constant flow. This cost difference could be negative, if the varia-tions in renewable output would correspond by-and-large to the variations in electricity demand. For wind, these costs will be positive in almost every real-world case– when applying photovoltaics in some desert climate with demand peaking strongly linked to solar irradiation (due to cooling require-ments), this might be different. Obviously the height of the various components of integration costs is de-

pendent on the order, in which the decomposition is performed (cf. similar re-sults in many approaches to decompose the impact of demand changes, e.g. Zhang, Ang 2001). However we will not look in detail at this question here, especially since the chosen ordering has a rather strong internal coherence.

The remainder of the paper will also not look in more detail at the grid con-nection and grid extension costs. The definitions derived here correspond to those used by Auer et al. (2004) and these authors have also compiled ample empirical evidence on these cost components. Instead emphasis will be laid on assessing the costs of variability and unpredictability, as defined above.

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Weber 40

3. Assessing costs of variability and unpredictability

Given that we have defined integration costs with reference to some optimal system costs, it is natural to turn towards some optimising energy system model when it comes to assessing the costs of variability and unpredictability. Thereby obviously a stochastic framework is necessary in order to assess the costs of unpredictability, since in a deterministic framework prediction errors will not appear. This weakens the validity of studies such as the one by Krämer (2003), who looks at wind integration into a power system using a deterministic optimi-sation approach. With such an approach it is possible to assess the costs of vari-ability of wind power, but nothing can be said on the costs of unpredictability. And even for the costs of variability the results might be biased, since not only uncertainties related to wind are neglected but also other uncertainties such as demand uncertainties.

3.1. Basic equations and types of intertemporal restrictions

Yet the use of a stochastic optimisation approach comes at a heavy computa-tional burden, since the problem size increases exponentially with the number of decision stages included and goes linearly with the number of stochastic re-alizations (environmental states) considered at each decision stage. The deci-sion problems in energy systems usually have a wait-and-see structure (cf. Birge and Louveaux 1997), i.e. only part of the decisions has to be taken now, whereas for other decisions it is possible to wait until new information has been revealed (cf. Fig. 1.).

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Integrating Electricity Production from Fluctuating Sources 41

Decision vector for immediate decision(Period 1)

Scenario 1

Scenario 2

1sy

Period 1 Period 2

x

t

2sy

x

21, ss yy Decision vectors for delayed decision

(Period 2) wait and see Fig. 1. Decision structure in wait-and-see models

This obviously also holds for optimal system operation in the presence of

fluctuating renewables. At time t0 only those decisions on unit commitment, load dispatch etc. have to be taken, which can not be postponed until the next time step t1, i.e. which directly concern system operation in the time interval [t0 t1). If the optimal choices for these decisions are independent of the realization of the stochastic events at time t1 and later, no stochastic programming is re-quired. Then the decisions will be dependent on the actual realizations, but no anticipation is required of future possible developments. In a very basic model-ling of electricity systems this is the case. In this basic modelling, the set of re-lations R contains • capacity constraints for each generator G at each point in time:

MAXeste PP ≤,, SsTtGe ∈∀∈∀∈∀ ,, (13)

• flow restrictions for generators G’’, which depend on a fluctuating, non-storable energy inflow:

Insteeste PP ,,,, η≤ SsTtGe ∈∀∈∀∈∀ ,, (14)

• capacity constraints for each transmission line L:

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Weber 42

MAXTRl

TRANSstl PP ,

,, ≤ SsTtLl ∈∀∈∀∈∀ ,, (15)

energy balances for each zone z (element of a set Z), defined as a set of nodes, between which no relevant capacity constraints on transmission lines exist:

( ) ( )∑∑∑∑

∈∧∈∉∧∈∧∈∉∧∈∧∈∈∧∈

=−+Ceze

stezezeQeell

TRANSstl

zezeQeell

TRANSstl

Gezeste PPPP ,,

,,,,

,,,,,,

21211221

SsTtZz ∈∀∈∀∈∀ ,, (16)

Decision variables in this setting are the output quantities of the controllable generators and the flows on the transmission lines. Yet there are no equations, in which variables or time-varying parameters of different time steps appear. Consequently the optimal choices of the decision variables at time t do not de-pend on later stochastic outcomes.

Unfortunately, this description is too simple for most real world electricity systems. Rather start-up costs, minimum operation times, minimum down times and similar restrictions imply that the optimal decision now depends on the ex-pectations for the future.

Yet the nature of this dependency may be different in various systems. The key difference is the one between integral constraints and differential con-straints. Water reservoir restrictions are the prime example of integral con-straints:

MAXeste VV ≤,, SsTtGe HYDRO ∈∀∈∀∈∀ ,, (17)

( ) tPWPVV instestestesteste Δ++−+=− − ,,,,,,,1,,, SsTtGe HYDRO ∈∀∈∀∈∀ ,, (18)

MAXeste WW ≤,, SsTtGe HYDRO ∈∀∈∀∈∀ ,, (19)

Thereby Ve,t,s describes the reservoir level and We,t,s the possible feeding of the reservoir through pumping.

These constraints are integral, since our key decision variable power output Pe,t,s is related to the difference of another decision variable, namely water res-ervoir level Ve,t,s. And other restrictions are directly related to this integral vari-able, here the restriction (17) imposing the maximum reservoir capacity MAX

eV . Ramping constraints are the simplest example of differential constraints.

More relevant is however the introduction of start-up costs. This can be done by defining the variable U of capacity (or units) put online (cf. Weber 2005).

The start-up costs are then clearly related to a (positive) difference of this variable:

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Integrating Electricity Production from Fluctuating Sources 43

( ) ( )⎩⎨⎧ >−

= −−− else0

if*, ,,1,,,,1,,

_

1,,,,

ONLINEtsi

ONLINEtsi

ONLINEtsi

ONLINEtsi

UPSTARTiONLINE

tsiONLINE

tsiiPPPPc

PPs

(20)

The capacity online provides an upper bound to the power output at each moment in time:

ONLINEsteste PP ,,,, ≤ SsTtGe ∈∀∈∀∈∀ ,, (21)

and through the minimum load factors λe also a lower limit:

ONLINEsteeste PP ,,,, λ≥ SsTtGe ∈∀∈∀∈∀ ,, (22)

Thus the costs are linked to a difference in the (bounds of the) key decision variable power output. However these costs will only have an effect on the power plant operation, if the fuel consumption is not proportional to the power output but if the marginal efficiency is higher than the efficiency at minimum load. This can be approximated through a linear affine fuel consumption func-tion (cf. Weber 2005):

( )ONLINEsteesteMARG

ONLINEsteeMIN

FUELste PPPP

ee

,,,,,,,,11 λ

ηλ

η−⋅+⋅=

SsTtGe FUEL ∈∀∈∀∈∀ ,, (23)

Then the optimization performs a trade-off in low load periods between con-tinued operation at part load and thus reduced efficiency and a shut-down with start-up at later periods inducing corresponding costs.

Typical restrictions in unit commitment also include minimum operation and minimum shut down times. These can be interpreted as restrictions on the second order differential restrictions on the key decision variables, given that they restrict the curvature in the power output. Yet these restrictions will not be included here, since in a large-system perspective, as taken here, they often turn out not to be binding. At the same time they often put a high computational burden on the problem.

Thus generally, intertemporal restrictions are occurring in a thermal system as differential restrictions7. Given that the time-varying exogenous parameters ______

7 Exceptions are constraints on fuel quantities to be used within one year or so. Those may re-sult e.g. from take-or-pay contracts. Yet with liquid fuel markets, these constraints on fuel quanti-ties can be handled separately from the restrictions on power production. They are therefore not considered further here.

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Weber 44

load and wind power production exhibit cyclical or at least mean-reverting be-haviour and that at the same time the power output is bounded from above by the maximum installed capacity, the impact of stochastic events in the far future on operation decisions of today through the intertemporal restrictions will be rather limited. Consequently a planning period of a few days at maximum should be sufficient in thermal systems.

Things are different in hydro-based systems like the Scandinavian one. Here the integral constraints require that the cost of using water now is mostly deter-mined through the value the same amount of water may have in the future. Ap-propriate methods here are especially the methods of stochastic dual dynamic programming (cf. Pereira …), which allows handling the valuation problem through backward induction. It is manageable, if only a limited number of status variables with a limited number of possible statuses has to be considered (e.g. hydro reservoir levels). Yet this case shall not be considered here, given that only few electricity systems in the world are hydro dominated. Moreover in hydro dominated systems, the costs of variability and unpredictability of wind power tend to be low, given the large operational flexibility of hydro power. On the other hand, the benefits in terms of CO2-emission reduction will also be low in hydro-dominated systems, unless the wind power generation replaces some marginal thermal power plants (cf. Holttinen, Tukhanen 2004). But we do not consider this case further here.

Within thermal systems, lead times LEADet (cf. Weber et al. 2005) are an im-

portant issue, to which not much attention has been devoted in conventional unit commitment, but which becomes important in the presence of fluctuating wind. They describe the limited flexibility of conventional units to react to the arrival of new information. Especially coal-fired units usually cannot be started up from one hour to the next, but need several hours of preparation. This can be represented by imposing the following restriction on the capacity online across scenarios:

ONLINEste

ONLINEste PP ',,,, =

( ) ( ) ( )II

LEADeIIII

tsItsISss

ttttttTtGe

,',',

,,,2 =∴∈∀

+≤∧≥∴∀∈∀∈∀ (24)

Thus for each information stage tI, the identity ( ) ( )II tsItsI ,', = in the available information between scenarios s and s’ implies that also the capacity online ONLINE

steONLINE

ste PP ',,,, = is identical up to the time LEADeI ttt +≤ .

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Integrating Electricity Production from Fluctuating Sources 45

3.2. Mapping stochastic processes into scenario trees

The case of lead times has shown that it is essential for determining the integra-tion costs to model the arrival of new information and the possible reaction of the system to this new information. To model this continuous process, a discre-tization is necessary and the repeated nature of planning has to be reflected by a rolling planning process (cf. Fig. 2)8. In order to cope with varying terminal conditions, it is assumed in Fig. 2 that the planning horizon always ends at the end of a day, which allows taking into account e.g. the value of a unit being kept online.

At each point in time the uncertainty about future states (which is resolved by information arriving later) is represented through a scenario tree. Thereby a trade-off has to be considered between an as precise as possible modelling of the information arrival structure and computational limitations.

tI,2

tI,3

tI,4

DAY1 DAY2DAY0

tI,1

tI,0

Fig. 2. Rolling planning to model arrival of new information

This trade-off will always lead to a reduced complexity of the stochastic op-

timization problem solved compared to the original problem. The distribution of

______ 8 If the stochastic scenarios could be thought of as arising from repeated drawings in otherwise

similar circumstances, a comparison of stochastic optimisation with deterministic optimisation facing the same stochastic drawings would be appropriate. Yet in the case of electricity systems, so many other factors are influencing system operation that repeated drawings are less appropri-ate than a rolling planning based on historical time series information.

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Weber 46

future wind power is hardly describable through some analytical distribution, given the non-linear power curve for wind-turbines. Hence the approach chosen in the WILMAR project (cf. Meibom et al. 2004, Brand et al. 2005) as well as in many other stochastic optimisation approaches (cf. e.g. Gröwe-Kruska, Römisch 2005) is to make Monte-Carlo-simulations of the possible future wind power generation and use then scenario reduction techniques to select some rep-resentative scenarios. Several possibilities exist for scenario reduction (cf. the overview by Kaut, Wallace, 2003), yet they all share the property, that the re-duced scenario tree does not cover the full range of original scenarios. This is however critical in the case of wind power, given that the reliable operation of the electrical system is a key requirement. Therefore besides optimisation under conditions of stochastic scenarios, also the fulfilment of reserve requirements has to be imposed. This is illustrated in Figure 2. For sake of simplicity, the ex-pected value for wind energy (the point forecast usually considered) is assumed to remain constant.

W

W'

Fig. 3. Extreme scenarios to be considered for system reliability

The scenarios W and W’ represent those wind scenarios, which have still to

be managed in order to fulfill reliability requirements. In an extreme interpreta-tion of reliability, they would correspond to the most extreme of all possible scenarios. Under a stochastic interpretation of reliability, they will correspond to a predefined quantile of system reliability (Loss of load probability LOLP). The required condition is then that for any given information state (correspond-ing to starting time tI) at any moment in time t enough capacity is available to

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Integrating Electricity Production from Fluctuating Sources 47

be put online or offline between tI and t, so that the unlikely scenarios W and W’ can be coped with. Formally this requires:

( ) tttttGee

ONLINEte

MAXe I

ILEADe

IWPP ,, ≥−∑

−<∧∈

III ttTtTt >∴∈∀∈∀ , (25)

If reserves have to be kept not only for wind power forecast errors but also to cope with other stochastic events ttI

D , , such as plant outages or load forecast errors, then the former equation has to be modified to read:

( ) tttttGee

ONLINEte

MAXe I

ILEADe

IFPP ,, ≥−∑

−<∧∈

III ttTtTt >∴∈∀∈∀ , (26)

Thereby ttIF , can be computed as follows:

2

,2

,, tttttt IIIDWF += III ttTtTt >∴∈∀∈∀ , (27)

This relationship for the overall reserve requirement is entirely correct if the two sources of disturbances are independently distributed and if both follow a normal distribution. Then the overall disturbance distribution will be normal and reliability percentiles are expressed as a fraction of standard deviation. In practice especially outage distributions tend to be non-normally distributed – so for an exact calculation some convolution of distribution or Monte-Carlo simu-lation of combined disturbances should be used (cf. e.g. Dany, Haubrich 2000). Yet the above formula provides a first, easy-to-handle approximation.

An important point to be taken into account in rolling planning is that sub-jective information available at tI may be biased, i.e. that the expected value of wind power does not correspond to the later realisation In a repeated drawings environment, this would appear automatically given that all possible realisa-tions corresponding to current expectations would emerge in the drawings. Yet in the setting with rolling planning, there has to be a separate drawing of the shift between expectations and actual realisation. And through the repeated planning a sampling of this shift is realised, which superposes to the sampling of other stochastic or at least variable factors. Otherwise the effect of forecast errors on integration costs is not coped with, rather additional costs are in-curred, since the perfect foresight is blurred with considerations about other possibly relevant scenarios, which will however never materialise.

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Weber 48

3.3. Benefits of stochastic optimization and alternative approaches

What benefits can then be expected from a stochastic optimization as outlined above compared to a repeated deterministic planning, based on possibly biased forecasts? One would expect that integration costs will be lower and infeasibili-ties are reduced (or fully eliminated) compared to a repeated deterministic plan-ning. One possible short-cut is to do repeated deterministic optimal planning (cf. Söder 1994), but using instead of actual data artificial data, which include random forecast errors. The deterministic biased planning has then to be adapted to the arrival of new information in the next step of a looping planning structure. Through a sufficiently long sequence of rolling planning an upper bound to the costs of unpredictability can be derived, as will be shown later.

Even if there are intertemporal constraints, the use of stochastic optimisation does not always lead to better decisions than deterministic planning. If the op-timal value of the cost function given a certain scenario is a linear function of the actual realizations of the stochastic variables in this scenario, the principle of linear superposition implies that optimal cost and hence optimal decisions at time t0 can be determined through a deterministic optimisation using expected values of the stochastic variables. The more relevant the non-linearity of opti-mal cost with respect to realizations of the stochastic variables is, the higher will be the benefits of stochastic optimisation as compared to a deterministic one. Yet even with linear programming formulations, the existence of restric-tions implies that variables are bounded and this will in many cases lead to con-vex cost functions.

Another approach is to set up a stochastic problem with a recombining tree (a mesh) of environmental states and to associate with each node in the mesh unique (approximate) values of the state and decision variables, independent on the path leading to this node. This route is followed by Swider, Weber (2005) as well as Weber et al. (2006) and it reduces the “curse of dimensionality” associ-ated with stochastic programming to a linear increase in problem size when the number of decision stages is raised. Yet the quality of this approximation is dif-ficult to assess and it is probably strongly depending on the characteristics of the system studied.

4. Conclusions

The preceding analysis has shown that the evaluation of integration costs for wind energy is not an easy task. One has to be aware that the result will always be dependent on the reference system chosen. Moreover stochastic optimization approaches are needed to determine the additional costs imposed to the system through the variability and the unpredictability of wind energy or other fluctuat-

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Integrating Electricity Production from Fluctuating Sources 49

ing resources. Also the mapping of stochastic processes in a reduced set of sce-narios and additional restrictions on power reserves has to be dealt with care-fully. But novel approaches developed for this purpose will allow assessing in-tegration costs and at the same time gaining improved understanding of the sys-tem operation mechanisms.

References

Auer, H. et al., 2004, Cost and Technical Constraints of RES-E Grid Integration. Report for WP 2, EU-project GreenNet. Downloadable at http://www.greennet.at/downloads/WP2%20Re-port%20GreenNet.pdf.

Birge, J., Louveaux, F., 2000, Introduction to Stochastic Programming, Springer publishing house. New York, Heidelberg.

Brand, H., Barth, R., Weber, C., Meibom, P., Swider, D.J., 2005: Extension of Wind Power – Effects on Markets and Costs of Integration. 4. Internationale Energiewirtschaftstagung an der TU Wien.

Dany, G., Haubrich, H.-J., 2000, Anforderungen an die Kraftwerksreserve bei hoher Windener-gieeinspeisung, Energiewirtschaftliche Tagesfragen vol. 50, no. 12, pp. 890-894.

Elsässer, R. 2002, Kosten der Windenergienutzung in Deutschland”, Präsentation im Rahmen der Sitzung des Wirtschaftsbeirates der Union, Berlin, 23 Juli 2002.

Fuchs, M. , 2003, "Windpower in Germany – Present situation and outlook", Presentation Brus-sels, 23. January 2003.

Gröwe-Kuska, N., Römisch, W., “Stochastic unit commitment in hydro-thermal power produc-tion planning”, S.W. Wallace, W.T. Ziemba (eds.), Applications of Stochastic Programming, MPS-SIAM Series in Optimization, Philadelphia 2005.

Grubb, M. J., “Value of Variable Sources on Power Systems,” IEE Proceedings-C, vol. 138, no. 2, pp. 149–165, 1991.

Holttinen, H., Tukhanen, S., 2004, „The effect of wind power on CO2 abatement in the Nordic countries”, Energy Policy, vol. 32, no. 14, pp. 1639 – 1652.

IEA (2004): Integration of Wind Power into Electricity Grids: Economic and Reliability Impacts. Workshop Paris, 25 May 2004.

ILEX Energy Consulting: „Quantifying the system costs of additional renewables in 2020“, A report of ILEX Energy Consulting in association with Manchester Centre for Electrical En-ergy (UMIST) for the Department of Trade and Industry (DTI), October 2002.

Kaut, M., Wallace, S., 2003, Evaluation of scenario-generation methods for stochastic program-ming, SPEPS Paper 14-2003, downloadable at http://hera.rz.hu-berlin.de/speps/.

Krämer, M., 2003, Modellanalyse zur Optimierung der Stromerzeugung bei hoher Einspei-sung von Windenergie. VDI Fortschritt-Berichte Energieerzeugung vol. 492, Düsseldorf.

Meibom, P. Ravn, H., Söder, L., Weber, C., 2004, Market Integration of Wind Power, European Wind Energy Conference, London.

Seebregts, A.J. et al., 1999, “Endogenous Technological Change in Energy System Models. Syn-thesis of Experience with ERIS, MARKAL, and MESSAGE”, Report ECN-C_99-025 Pet-ten.

Söder, L., 1994, Integration study of small amounts of wind power in the power system, available at: http://www.ets.kth.se/personal/lennart/lennart_integration94.pdf.

Söder, L., 2005, Modelling Approach Impact on Estimation of Integration Cost of Wind Power, 7th European IAEE Conference Bergen.

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Weber 50

Swider and Weber (2004): Scenarios on the conventional European electricity market. Report for WP 6, EU-project GreenNet. Downloadable at http://www.greennet.at/downloads/WP6%20 Report%20GreenNet.pdf.

Weber, C., 2005, Uncertainties in the Electric Power Industry: Methods and Models for Decision Support, vol. I. New York, Berlin, Heidelberg: Springer.

Weber, C., 2006, Integrating electricity production from fluctuating sources – valuation of vari-ability and unpredictability. Working Paper for the GreenNet EU27 project, WP 2.

Weber, C., Brand, H., Meibom, P., 2005, Wind power integration and operational flexibility of conventional plants – the role of lead times, Working Paper, Essen.

Weber, C., Swider, D. J., Vogel, Ph., 2006, A Stochastic Model for the European Electricity Mar-ket and the Integration costs for Wind Power, Working Paper for the GreenNet EU27 project, WP 2.

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51

ROLE OF STORAGE IN INTEGRATING WIND ENERGY

GORAN STRBAC* Department of Electrical and Electronic Engineering Imperial College London, United Kingdom MARY BLACK CE Electric, United Kingdom

VERA FIGUEIREDO Department of Electrical and Electronic Engineering Imperial College London, United Kingdom

Abstract. This paper presents a new methodology to quantify the value of stor-age in the integration of intermittent resources, mainly wind. The main goal of the work is to provide quantified estimates of the potential value of storage, in managing the intermittency of wind generation, in the context of the future United Kingdom (UK) electricity system. In an electricity grid with large wind penetration additional system balancing costs are incurred due to the need for increased amount of reserve in the system to deal with unpredictability of wind power. We developed studies to evaluate the benefits of using storage for pro-viding standing reserve, as part of the overall reserve needs, in terms of savings in fuel cost, CO2 emissions and conventional energy. These studies were con-duced considering a number of generation systems characterized by different mixes of generation technologies, representative of the size of the UK system with different levels of wind penetration. From these studies we were able to conclude that providing a greater part of the increased reserves needed, from storage facilities can increase the efficiency of system operation and increase the amount of wind power that can be absorbed.

Keywords: storage, wind energy, spinning reserve, standing reserve, CO2 emissions, fuel costs, conventional energy.

______ * To whom correspondence should be addressed. Email: [email protected]

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Strbac et al. 52

1. Introduction

Due to environmental concern over CO2 emissions, it is expected that the pene-tration of intermittent renewable resources, into the electricity grid, will in-crease in future years. This has raised concerns over system costs, focused on whether these new generation technologies will be able to replace the capacity and flexibility of conventional generating plant. As intermittency and non-controllability are inherent characteristics of renewable energy based electricity generation systems, the ability to maintain the balance between demand and supply has been a major concern.

The problem of the variability of wind power and other renewable sources has been addressed in a broad perspective in (Gül and Stenzel, 2005). In this work an analysis on which extent can intermittency of natural resources will be a barrier to the integration of renewable energy is presented. The conclusions point out that it will depend mainly on economic aspects and market organiza-tion. The quantification of the additional cost of Renewable Energy Sources for electricity production (RES-E) is of major importance. In the same work the development of a portfolio of solutions to mitigate the problem of intermittency is considered as crucial for the success of this integration. These portfolios in-clude the increase of system flexibility by the construction of new flexible plants, the use of storage technologies, distributed generation and demand re-sponse techniques. Although, some examples on the Danish and German mar-ket are presented there study does not include modeling or quantitative studies how RES-E increase system costs.

This increase of costs will include: balancing, operational and capacity re-serve and transmission and distribution networks reinforcement.

In a study by Infield (Infield, 1984) it is demonstrated how the use of stor-age can assist in generation fuel cost savings. In this study storage is considered for large scale electricity generation and its role in the provision of reserve and balancing services is investigated, although the requirement for storage in gen-eration studies with significant penetration of intermittent resources is not ac-cessed in this work.

Bulk energy storage systems such as large-scale pumped storage appear to be an obvious solution to deal with the intermittency of renewable sources and the unpredictability of their output. During the periods when intermittent gen-eration exceeds the demand, the surplus could be stored and then used to cover periods when the load is greater than the generation. The use of storage as an enabling technology to increase wind integration on power systems is being object of recent research.

In (Strbac, 2002) an analysis of the breakdown of the total additional system costs incurred when extending renewable generation to 20% or 30% of demand

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Role of Storage in Integrating Wind Energy 53

is presented. This analysis included costs of balancing and capacity, transmis-sion, and distribution. This work demonstrated that balancing and capacity costs, principally the cost of maintaining system security, dominate all other costs. The concern about these costs arises because the intermittency of wind creates a large wind forecast error which leads to imbalances between the scheduled generation supply and the electricity demand that need to be met in real time.

In (Strbac & Black, 2004) we can find a study that provides the magnitude of order estimates of the potential value of storage, in managing the intermit-tency of wind, in the UK electricity system. The increase of the wind penetra-tion will increase the uncertainty under which the balance of supply and de-mand is done. As a consequence of this increase on the uncertainty, the amount of reserve in the system must also be increased. This leads to higher operational costs and a less efficient use of the resources due to the increase on the part load efficiency losses. This reserve is supplied by a combination of spinning reserve (SR) provided by the part loaded generation plants and standing reserve, in the form of storage and/or flexible generation like OCGTs or demand side man-agement (DSM). In this context OCGT and DSM technologies will be the prime competitors to storage. To clarify and quantify the advantages of Storage over OCGT further investigations on this question were conduced on the work presented in this paper.

In (Doherty & O’Malley, 2004) is presented a methodology to quantify the reserve needs in a system with significant wind penetration. The reserve level on the system in needed to cater for any possible unexpected generation deficits caused by generator outages, increases in load and decrease in wind power. This methodology copes with all these problems by considering the full outage probability of a unit probability of stopping providing its current output, the wind power and load forecast errors. The system reliability criterion used is the lost of load expectation (LOLE) and it quantifies the likelihood of failure on load supply due to the lack of reserve in the system, but it does not quantify the magnitude of the load shedding. The magnitude of the load shedding incidents is not considered in this methodology.

The work presented in this paper presents a simulation platform able to quantify the additional costs of balancing demand and supply, when the pene-tration of wind energy is increased, under alternative generation development scenarios. In particular it is concerned with the application of storage technol-ogy in enhancing the value of intermittent energy resources in the case of the UK power system.

This includes evaluating its contribution to the reduction of costs of balanc-ing supply and demand in operational timescales, given the increased uncer-tainty caused by the unpredictable nature of wind generation.

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Strbac et al. 54

This paper is organized in the following chapters: Chapter 2 presents the components of the model behind the developed methodology, Chapter 3 pre-sents some of the more relevant results obtained and finally some conclusions are outlined in Chapter 4.

2. Methodology

The developed methodology is based on a detailed simulation of the operation of the system. This is concerned with the evaluation of underlying costs associ-ated with the operation of a system with a considerable contribution of intermit-tent generation. It is focused only on the question of the management of inter-mittency by providing standing reserve.

In order to simplify the modeling process and to abstract out major trends, a number of assumptions are made: • it is sufficient to use a cost based approach (market arrangements are not

considered); • the balancing task is performed at the system level not at individual genera-

tion / supply company level; • arbitrage is excluded; • the reliability and capacity performance of storage is equal to that of other

plants. In fact we are modeling generic, flexible bulk energy storage technology

rather than specific storage technology types. It should also be noted that the model is for a single bus bar system and management of network constraints are not considered.

The evaluation model used applies a simulation approach using year round evaluation of system operation, for an hourly time series of wind and demand. This has the advantage over analytical models that there can be a more accurate allocation of spinning / standing reserve and that it can deal with chronology. The model essentially quantifies the benefits of energy storage for providing short-term demand-supply balancing capability in generation systems with high wind penetration. Figure 1 shows a forecast net demand profile (net = demand – wind) which is used for carrying out day ahead unit commitment and the reali-zation of the profile in real time on which an economic dispatch is carried out. Imbalances between supply and demand, resulting from either having too much or having insufficient generation committed, have to be handled by shedding wind or load, or by charging and discharging storage, or by using OCGT.

The selection of case studies modeled is based on the application of this methodology for reducing spinning reserve (SR) in order to increase the amount

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Role of Storage in Integrating Wind Energy 55

of wind power absorbed by the system and finding the optimal allocation of reserve between spinning and standing reserve.

The inputs of the model, used in the performed case studies are: conven-tional generation, wind generation, storage power rating and OCGT output power. The allocation of SR in terms of how many standard deviations of wind forecast uncertainty is also pre-established.

The main outputs of the model, used in the performed case studies are: the annual energy produced by conventional plants, annual generation costs (in-cluding SR cost), annual energy not supplied, annual wind curtailed, annual storage charge and discharge energies, annual energy produced by OCGT and annual CO2 emissions.

The next sections will give an insight on the major components of the model.

2.1. Unit commitment

Mixed Integer Programming (MIP) formulation or, alternatively, a priority ranking method, can be used for committing generating units on a day-ahead basis considering wind and demand forecasts. This is based on the forecast net demand and wind profile (Figure 1).

Fig. 1. Forecast and actual demand profiles

2.2. Economic dispatch

Linear Programming (LP) formulation is used for dispatching power among generators, wind, storage and OCGT standing plants in real time. This formula-

forecasted and realized net profile

0

5000

10000

15000

20000

25000

30000

35000

1 3 5 7 9 11 13 15 17 19 21 23

h

net (

dem

and-

win

d) M

W

forecast

realized

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Strbac et al. 56

tion can be implemented using any optimization software. For this project Dash Xpress (Dash, 2005) optimization tools are used, by means of accessing the built in class libraries interface (BCL) from a program written in Microsoft C ++.Net. The economic dispatch is carried out based on the actual net demand and wind profile (Figure 1). This allocates the hourly power output necessary to meet demand among the committed conventional generators, wind generators, storage facilities and/or OCGT. This is done in order to minimize the overall fuel cost over a year whilst observing power system constraints. Reserve comes from the committed generators, storage and/or OCGT and is responsible for supplying the imbalances between generations and demand. Whenever the im-balances correspond to a lack of generation capacity in the system storage in discharged, OCGT plant is started or load shed is applied. Table 1 contains the notation for the optimization formulation outlined in the following sections.

2.2.1 Minimizing Fuel Costs

The linear programming formulation objective function intends to minimize the fuel costs of conventional generation in each time period, subject to the genera-tion, storage and load shedding constraints.

Minimise f(x)

( ) ( ) ( ) ( )

( ) ( ) ( )tLshedVOLLtOcgtOutOcgtCosttOverslack

tSdischtWshedtPtCxfI

iii

**

)(1

+++

+++⎥⎦

⎤⎢⎣

⎡= ∑

=

γ

βα (1)

A high value of lost load (VOLL) is applied to shedding load to ensure that shedding only occurs if there is no alternative other possibility to meet the load balance constraint. In a situation of surplus wind which cannot be absorbed wind could either be shed or be used to charge storage without affecting fuel costs. Fuel costs apply only to the conventional generators and we use the mar-ginal cost which is given for each generator in £ per MWh (assuming a genera-tor is operating at full output). The artificial cost variables α, β and γ are used to prioritize the use of wind shed over storage discharge and both over overslack. These are defines as very low values with no quantitative impact on the results.

Tab. 1. Optimization notation

Notation Definition Notation Definition

T time horizon (24 hours for our case studies)

d(t) demand at time t in MW

t time period in hours Pmini min stable generation for

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Role of Storage in Integrating Wind Energy 57

Notation Definition Notation Definition

generator i in MW

I number of generators Pmaxi maximum capacity of gen-erator i in MW

i index for particular genera-tor

RampUpi ramp up rate of generator i in MW/hour

Ci fuel cost of generator i in £/MWh

RampDowni ramp down rate of generator i in MW/hour

Pi(t) contribution of generator i at time t in MW

μ storage efficiency as a per-centage

w(t) wind contribution at time t in MW

E(t) Energy storage state at time t

Schar(t) storage charge contribution at time t (negative) in MW

Emax maximum energy storage capacity in MWh

Sdisch(t) storage discharge contribu-tion at time t (positive) in MW

E0 initial energy storage carried over from previous day in MWh

OcgtOut OCGT contribution at time t (positive) in MW

Efin energy storage end state in MWh as a fraction of energy size.

Orating OCGT max capacity rating in MW

OcgtCost fuel cost of OCGT in £/MWh

Srating Storage max power rating in MW

VOLL Value of Lost Load = 1000

Wshed(t) wind shed contribution at time t (negative) in MW

α β γ Artificial cost variables to prioritize different options

currentWind(t) actual wind power output at time t in MW

Lshed(t) load shed contribution at time t (positive) in MW

Overslack(t) slack for surplus generation at time t in MW

Generators are less efficient when not operating at full output so we recom-

mend the application of a cost correction after performing the optimization, based on the linear interpolation described in (GreenNet, 2004). Thus we carry out some post-processing in which the drop in efficiency when running at 50%, of the maximum output, is taken to be on average 16% and the efficiency, at any other output level, is calculated by assuming the efficiency drops linearly between the maximum and the minimum output.

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Strbac et al. 58

2.2.2 Matching Supply and Demand

( ) ( ) ( ) ( ) ( ) ( )

( ) ( ) ( )tdtOverslacktOcgtOut

tLshedtWshedtSdischtSchartwtPI

ii

=++

++++++∑=1 (2)

The power supplied in each hour from conventional generation, wind and storage has to be equal to the demand for that hour. If that is not possible then wind shed or load shed occur to ensure that the balance is maintained.

2.2.3 Conventional Generation

( ) ii PtP max≤ TtIi ∈∀∈∀ , (3)

( ) ii PtP min≥ TtIi ∈∀∈∀ , (4)

( ) ( ) iii RampUptPtP ≤−− 1 TtIi ∈∀∈∀ , (5)

( ) ( ) iii RampDowntPtP ≤−−1 TtIi ∈∀∈∀ , (6)

The methodology assumes that the unit commitment phase of scheduling generators for each hourly period and synchronizing them to the grid, has al-ready taken place thus we are only concerned with the economic dispatch phase of determining the generation level of each generator. This generation level is constrained in each hourly period however by the need for it not to exceed the given maximum capacity of the generator and not to go below the given mini-mum stable generation level. It is also constrained across any two hourly peri-ods by not being allowed to exceed the given ramp up rate of a generator if the level is being increased from one time period to the next, and to not be less than the given ramp down rate if the level is being decreased from one time period to the next.

2.2.4 Wind

Wind is inflexible, that is, the optimization assumes that all the wind power available in each hour will be used to meet demand. The fuel cost applied to wind power is zero. In periods of high wind and low demand we can have wind that can not be used neither to supply load nor charge storage. In this case this wind is shed. If the generation system has a high value of must run generation this value gets higher so less wind is absorbed by the system.

2.2.5 Storage

( ) SratingtSdisch ≤ Tt ∈∀ (7)

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Role of Storage in Integrating Wind Energy 59

( ) 0≥tSdisch Tt ∈∀ (8)

( ) 0≤tSchar Tt ∈∀ (9)

( ) SratingtSchar −≥ Tt ∈∀ (10)

( ) ( ) ( ) ( )11 ++−=+ tSchartSdischtEtE μ Tt ∈∀ (11)

EfinTtE ≥= )( Tt ∈∀ (12)

Storage is regarded by the model as another generator, but one that is capa-ble of having a negative generation level, that is, when it is being charged the power is negative and conventional generators have to do more to make sure that demand is met. The fuel cost applied to storage itself is zero, though obvi-ously the fuel costs of the extra conventional generation power supplied to charge storage works through in the equation. Other constraints applied to stor-age are that it cannot discharge at greater than its power rating or at less than zero and that it cannot charge at greater than zero, that is, charging is negative power output. The optimization schedules the charging and discharging of stor-age in order to minimize fuel costs of conventional generation. Finally there is the energy balance constraint (Equation 11).

An energy balance constraint is applied to storage whereby at each time in-terval during the day, the amount of energy stored after charging or discharging cannot exceed the maximum capacity of the storage device, and cannot be less than zero. The end state of storage is constrained to be a given value which, in our modeling, is a chosen fraction of the total energy size of the storage facility (Equation 12). The initial state of storage is set outside of the LP formulation, for example in a simulation it may be set to continue each day from where it finished the day before. Efficiency losses during charging are taken into ac-count in the energy balance constraint, by multiplying the efficiency factor with the power used to charge the storage.

2.2.6 OCGT

( ) OratingtOcgtOut ≤ Tt ∈∀ (13)

( ) 0≥tOcgtOut Tt ∈∀ (14)

OCGT can be added to the unscheduled generation supplying demand in real time, in the same way as storage can be discharged, but the consideration in terms of economics in this case is the OCGT fuel cost. If it is exercised then it must deliver power within its ratings.

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Strbac et al. 60

2.2.7 Wind and Load Shed

The occasions when there is no alternative but to shed load occur when there is a shortage of scheduled generation to meet demand due to a discrepancy be-tween the predicted and actual demand and wind levels.

Wind shed may also occur when there is too much wind power in a period of low demand, for the scheduled conventional generators (including those pro-viding reserve) to be able to operate without violating the minimum stable gen-eration constraint. Wind will not be shed until there is a surplus of generation power over demand (as demand has to be met), and in order to utilize free wind and thus optimize fuel costs, conventional generation is reduced as much as possible before wind is shed.

We constrain load shed so that it cannot be less than zero in each hour as shedding load adds to capacity. Wind shed on the other hand cannot be greater than zero as it takes away from capacity.

2.3. Random walk of imbalances

We use the concept of random walk to model the imbalances whereby, at each time period, there is a random displacement step or imbalance from the forecast wind profile. The random walk that we use can be considered to take place in 1-dimensional space. An analogy commonly used to describe such a walk is of a drunk placed in a ditch in which there is also a lamppost (Kaye, 1989). The drunk can stagger over a period of time by either taking a step towards the lamppost or by taking a step away from the lamppost. Different types of ran-dom walk are defined by how these steps or displacements are made. For ex-ample the “Drunkard’s Walk” involves taking steps of equal size with equal probabilities of the step being towards or away from the lamppost. The walk that we choose to use is a random walk with step lengths from a Normal distri-bution (Weiss, 1994). This means that each step taken may vary in size but that the distribution of all the step sizes taken follows a normal distribution. This makes the assumption that the random imbalances between supply and demand throughout the system’s lifetime will follow a normal distribution. The step sizes are not described in terms of absolute sizes but instead are described in terms of numbers of standard deviations away from a mean.

A random number generator generates a uniform distribution of random numbers. These are transformed to a Normal distribution by regarding the ran-dom numbers as representations of areas under a standard Normal distribution.

Figure 2 shows an area under the probability density function curve and its corresponding number of standard deviations. A value, which we shall call ε, gives the number of standard deviations for each random number representing

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Role of Storage in Integrating Wind Energy 61

an area under the curve. It is clear from the cdf chart at the top of the figure that if random numbers are generated uniformly between 0 and 1, that most of these numbers will lie between -1 and 1 standard deviations from the mean.

Tab. 2. Sample from a standard Normal cdf look up table

x 0 1 2 3 4 5 6 7 8 9

0.00 0.5 0.504 0.508 0.512 0.516 0.5199 0.5239 0.5279 0.5319 0.5359 1.00 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 2.00 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 3.00 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.999 0.999 3.40 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998

Fig. 2. pdf, cdf and number of standard deviations

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Strbac et al. 62

Table 2 contains a selection of cumulative distribution function values in a

look up table. If the uniform random number generated, for example, is 0.9998, then this is treated as the cdf probability that x, a continuous random variable, takes on a value that is no more than 3.49 standard deviations from the mean. The number of standard deviations obtained from the look up table: ε is multi-plied by a factor σ, representing the standard deviation size. This quantity represents the displacement from the original value in the forecast wind profile. Note that it can be positive or negative. The chronologically corresponding value in the randomized wind profile is merely generated by adding the dis-placement to the original value in the forecast wind profile.

Realization y’(t) = Forecast y(t) + (ε(t) . σ) Thus each value is independent. A drift term (Black, 2005) would need to

be introduced to generate a new wind value from its previous value. However the approach used still ensures that the general shape of the wind is similar in both profiles.

Fig. 3. June random walk of imbalances

Figure 3 illustrates random imbalances simulated for the month of June,

based on a standard deviation size of 2414 MW, which is the wind forecast un-certainty for 26 GW wind penetration. The wind forecast error considered is 9% of the maximum wind penetration.

Figure 4 show that the generated random walk of imbalances follows a Normal distribution.

random walk of imbalances through June

-8000-6000

-4000-2000

02000

40006000

8000

1 47 93 139 185 231 277 323 369 415 461 507 553 599 645 691

hour

Imba

lanc

e (M

W)

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Role of Storage in Integrating Wind Energy 63

Fig. 4. Frequency distribution 1 year simulated imbalances

2.4. Statistical Methods

Statistical methods, based on wind time series data analysis and wind forecast error, for determining reserve levels are needed. Persistency based wind fore-cast techniques are used considering different lead times from one to four hours, considering the last as the typical time to start a new plant. Based on this it is reasonable to look at the output changes in wind power over a four hour period. This is detailed in (Strbac, 2004)

The forecast profile presented in Figure 1 represents the uncertainty in wind forecasting and is generated combining random walk displacements with the original historical profile.

3. Case Studies

In addition to SR, which is provided by part-loaded synchronized plants, the balancing task can be supported by so called standing reserve, which is supplied by higher fuel cost plant (such as OCGTs) and storage facilities. Application of standing reserve can improve the system performance through reduction of the fuel cost associated with system balancing. This reduction in the amount of synchronized reserve committed leads to: 1. an increase in the efficiency of system operation, 2. an increase in the ability of the system to absorb wind.

Frequency distribution of 1 year's simulated imbalances for 26 GW wind

0100200300400500600700800

-9000

-7500

-6000

-4500

-3000

-1500 0

1500

3000

4500

6000

7500

9000

Imbalance (MW)

Freq

uenc

y

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Strbac et al. 64

The allocation of reserve between synchronized and standing plant is a trade-off between the cost of efficiency losses of part-loaded synchronized plant (plant with relatively low marginal cost) and the cost of running standing plant relatively high marginal cost (British Electricity International, 1999). The cost of using energy storage facilities for this task is influenced by their efficiency. The balance between synchronized and standing reserve can be optimized to achieve a minimum overall reserve cost of system management. The scheduling of reserve in our model is detailed in (GreenNet, 2004).

Studies have been carried out for four SR reduction categories considering: • scenarios with standing reserve made up of a combination of storage and

OCGT installed; • how the value of storage changes with different wind penetration levels, in-

cluding an examination of the influence of key drivers such as the flexibility of the generation system. The studies performed consider three generating systems with different

flexibility: Low Flexibility (LF), Medium Flexibility (MF) and High Flexibility (HF). Table 3 presents the description of the test systems used in the case stud-ies presented in this document.

All the case studies were conduced considering a base case in which perfect prediction of wind and demand is considered, so no reserve is modeled. The results obtained are based on a comparative analysis of the advantages for the system of each class of SR reduction over the base case. In the next sub-sections the results of the different case studies are presented.

Tab. 3. Characteristics of the different generation systems considered

Generation System

Inflexible Gen-eration

Moderately flexible generation

Flexible Generation

LF

8.4 GW installed, has to run at 100% of max capacity

26 GW installed, minimum stable gen-eration 77% of max capacity

>25.6 GW installed, mini-mum stable generation 50% of max capacity

MF

8.4 GW installed, has to run at 100% of max capacity

26 GW installed, minimum stable gen-eration 62% of max capacity

>25.6 GW installed, mini-mum stable generation 50% of max capacity

HF None None >60 GW installed, minimum stable generation 45% of max capacity

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Role of Storage in Integrating Wind Energy 65

We consider four different classes for SR reduction. For each reduction we determine statically the amount of standing reserve needed so that the total re-serve is able to cover all the imbalances sized up to λ*σ where λ is the number of standard deviation(std) of the wind forecast error and σ is the standard devia-tion for each wind penetration. The value of λ is determined experimentally considering a load shed avoidance criterion.

3.1. Standing reserve – storage only option

Studies had been carried out for four SR reduction classes considering an in-stalled capacity of 25% of wind. For each SR reduction, standing reserve pro-vided by a storage only option is increased by increasing the storage power rat-ing. These studies present the contribution of storage on the reduction of bal-ancing costs and CO2 emission in the system for the different conventional en-ergy flexibility mixes.

Fig. 5. Balancing costs for 25% of wind penetration using the storage only option

storage balancing costs 25% wind

8.5

4.53.7

2.6 2.2

5.4

3.12.6

2 1.7

3.222.2 1.9 1.5 1.3

0123456789

0 2 3 4 5

storage rating (GW)

Cos

ts E

uro/

MW

h

LF

MF

HF

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Strbac et al. 66

Fig. 6. Reduction in CO2 emissions for 25% of wind penetration using the storage only option

Observing Figure 5 it can be seen that the balancing fuel cost reductions,

comparing to the base case, are highest in the LF system. Therefore the value of storage increases as the flexibility of the system decreases. In Figure 6 we pre-sent the contribution of the use of storage to the reduction of CO2 emission is the system. This is an output of our methodology and it’s possible to notice that the benefit of storage is higher in the LF system. This is because as the flexibil-ity of the system increases its ability of absorbing wind increases due to the lower values of must run generation. We can also observe that the reduction in balancing fuel costs and CO2 emissions increases as we increase the storage power rating. This is because a system with the reserve composed by a combi-nation of SR and standing reserve is able to absorb more wind then a system with all the reserve is synchronized. This becomes more effective as we further reduce SR and increase storage power rating due to the fact that more opportu-nities to use wind are created.

3.2. Combined standing reserve option – storage/ocgt

In reality we will expect standing reserve to be provided by a combination of different technologies. We performed case studies in order to find the value of a small amount of storage combined with OCGT. The storage only option, pre-sented in the previous section, was replaced for a combination of 1GW of stor-age with OCGT in order to get the same SR reduction categories. We find that the more expensive OCGT will only be used when storage is already discharg-ing at its full power rating. Many of the imbalances can be dealt with 1 GW of

Reduction in CO2 Emissions with 25% of Wind and Storage

4.3 5.3

6.36.8

2.6 3.1

3.8 4.1

1.1 1.4 1.8 2.0

0

1

2

3

4

5

6

7

8

2 3 4 5

Storage Rating (GW)

LF MF HF

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Role of Storage in Integrating Wind Energy 67

storage. The major contribution to the value of storage comes from the first GW of available power. We consider a wind penetration of 25% and we increase the amount of power produced by OCGT power plants as we reduce SR and in-crease standing reserve. Tables 4-6 present the balancing costs obtained consid-ering different technology options to provide standing reserve.

Tab. 4. Balancing Costs per MWh with 25% of wind penetration and combined Storage/OCGT

LF system MF system HF System

Storage (GW) OCGT(GW) Balancing Cost in €/MWh

Balancing Cost in €/MWh

Balancing Cost in €/MWh

0 (base case) 0 (base case) 8.5 5.5 3.2 1 1 4.7 3.1 2.1 1 2 3.8 2.6 1.8 1 3 2.9 2.1 1.6 1 4 2.5 2.0 1.6

Tab. 5. Balancing Costs per MWh with 25% of wind penetration and Storage only

LF system MF system HF System

Storage (GW) Balancing Cost in €/MWh

Balancing Cost in €/MWh

Balancing Cost in €/MWh

0 (base case) 8.5 5.40 3.22 2 4.50 3.10 2.20 3 3.70 2.60 1.90 4 2.6 2.00 1.50 5 2.2 1.70 1.30

Tab. 6. Balancing Costs per MWh with 25% of wind penetration and OCGT only

LF system MF system HF System

OCGT (GW) Balancing Cost in €/MWh

Balancing Cost in €/MWh

Balancing Cost in €/MWh

0 (base case) 8.50 5.40 3.22 2 4.80 3.20 2.14 3 3.95 2.66 1.86 4 2.9 2.03 1.50 5 2.5 1.73 1.35

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Strbac et al. 68

Fig. 7. Combined Storage/OCGT standing reserve balancing costs with 25% wind penetration

Fig. 8. Comparative analysis of different option to provide standing reserve for different genera-tion system flexibilities

Figure 8 presents a comparative analysis, considering the same classes for

SR reduction. It is possible to observe that the combined solution outperforms OCGT only

as spinning reduction is further reduced. The weight of the value of storage in

Comparative Analysis of Combined Storage/OCGT, OCGT only and Storage only Standing Reserve Balancing Costs for 25%

Wind

0

1

2

3

4

5

6

7

8

9

0 2 3 4 5

standing reserve rating (GW)

Cos

ts E

uro/

MW

h

LF - Storage

MF - Storage

LF - Storage

LF - Combi

MF - Combi

LF - Combi

LF - OCGT

MF - OCGT

HF - OCGT

Combined Storage/OCGT Standing Reserve Balancing Costs for 25% Wind

8.5

4.73.8

2.9 2.5

5.5

3.1 2.6 2.1 23.2

2.1 1.8 1.6 1.6

0

2

4

6

8

10

0 2 3 4 5

standing reserve rating (GW)

Cos

ts E

uro/

MW

h

LF

MF

HF

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Role of Storage in Integrating Wind Energy 69

the combined solution increases as the amount of OCGT in the combination increases. Observing Figure 8 we can conclude that the importance of the 1 GW of storage in the LF system in the combination has increasing importance as SR reduction is increased. This advantage is smaller in the MF system and not rele-vant in the HF.

Figure 9 presents the comparative analysis of different standing reserve op-tions concerning the reduction in CO2 emissions. The combined option outper-forms the storage only solution for the HF system. This can be explained be-cause lees carbon is being wasted in efficiency losses charging storage because less storage is used. Fig. 9. Comparative analysis of the reduction in CO2 emissions for different standing reserve options

3.3. Increasing wind penetration

Studies have been carried out for four different classes of SR reduction, consid-ering different wind penetrations: 15%, 25%, 35%, 45% and 55%. These stud-ies concern the impact of the change on the wind penetration in the reduction on balancing costs, CO2 emissions and wind energy savings. The impact of system flexibility is considered in the studies.

In order to be able to compare the amount of standing reserve for different wind penetrations, we keep the following SR reduction classes: Category 1: λ =2.3 std; Category 2: λ=2 std; Category 3: λ=1.5 std; Category 4: λ=1.2 std. The size of σ will be different for each wind penetration so the amount of reserve

standing reserve CO2 reductions

0

1

2

3

4

5

6

7

2 3 4 5

standing rating (GW)

redu

ctio

n (m

tonn

es p

a

LF storMF storHF storLF combiMF combiHF combiLF ocgtMF ocgtHF ocgt

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Strbac et al. 70

needed is also different. Table 7 illustrates the reserve requirements for the dif-ferent wind penetrations.

We studied the impact of the increase in wind power penetration on the re-duction of fuel costs, associated with balancing the system in real time. The costs are effectively associated with holding and exercising the reserve neces-sary for managing the forecast uncertainty of demand and generation.

Figure 10 shows that for an inflexible generation system, at all wind pene-tration levels the value of storage increases as spinning reserve is reduced fur-ther as we can see for the reduction in Balancing costs. The value of storage also gets higher as wind penetration levels increase, indicating the increased balancing task with higher wind and thus larger forecast uncertainty.

Figure 11 show that for a generation system of medium flexibility we have the same trend as for the LF system. The value of storage also gets higher as wind penetration levels increase. The value is comparatively lower than for the inflexible generation case though.

Tab. 7 Reserve capacities for different reserve levels

Wind (%)

Total Reserve (MW)

(3.5*σ)

Category 1

(2.3* σ)

(MW)

Standing

Category 1

(2.3* σ)

(MW)

Spinning

Category 2

(2.0* σ)

(MW)

Standing

15% 5202 1000 3418 2000 25% 8453 2000 5555 3000 35% 11704 3000 7691 4000 45% 14955 5000 9828 6000 55% 18206 6000 11964 8000 Category 2

(2.0* σ)

(MW)

Spinning

Category 3

(1.5* σ)

(MW)

Standing

Category 3

(1.5* σ)

(MW)

Spinning

Category 4

(1.2* σ)

(MW)

Standing

Category 4

(1.2* σ)

(MW)

Spinning

2973 3000 2229 4000 1784 4830 4000 3623 5000 2898 6688 6000 5016 7000 4013 8546 8000 6409 9000 5128 10404 10000 7803 12000 6242

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Role of Storage in Integrating Wind Energy 71

Fig. 10. Reduction in balancing fuel costs with increasing wind penetration for the LF generation system

Fig. 11. Reduction in balancing fuel costs with increasing wind penetration for the MF generation system

Figure 12 shows that for a generation system of high flexibility, as before at

all wind penetration levels the value of storage increases as spinning reserve is reduced further, as we can see for the reduction in balancing fuel costs. The values in the HF system are the lowest of all the generator flexibility systems. It’s also interesting to notice that for 55% of wind penetration the reduction in balancing costs is lower then for the other wind penetrations.

Balancing Costs: LF System

0.0

5.0

10.0

15.0

20.0

25.0

0 1 2 3 4

SR reduction category

Cos

ts E

uro/

MW

h

15%25%35%45%55%

Balancing Costs: MF System

0.02.04.06.08.0

10.012.014.016.018.0

0 1 2 3 4

SR reduction category

Cos

ts E

uro/

MW

h

15%25%35%45%55%

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Strbac et al. 72

Fig. 12. Reduction in balancing fuel costs with increasing wind penetration for the HF generation system

Fig. 13. Reduction in CO2 emissions with increasing wind penetration for the LF generation sys-tem

Figures 13-15 show that at all wind penetration levels the value of storage in

reducing emissions increases as spinning reserve is reduced further and as wind penetration levels increase. As the flexibility of the generation system increases the reduction in CO2 emissions is smaller. The additional value created by stor-age is a result of reduced of fuel consumption associated with balancing. The

Balancing Costs: HF System

0.0

2.0

4.0

6.0

8.0

10.0

12.0

0 1 2 3 4

SR reduction category

Cos

ts E

uro/

MW

h

15%25%35%45%55%

Reduction in CO2 Emissions: LF System

02468

101214161820

0 1 2 3

SR reduction category

mill

iont

onne

s/pa 15%

25%35%45%55%

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Role of Storage in Integrating Wind Energy 73

results show that this reduced fuel consumption leads to reduced CO2 emissions as well as reduced fuel cost. Fig. 14. Reduction in CO2 emissions with increasing wind penetration for the MF generation system

Fig. 15. Reduction in CO2 emissions with increasing wind penetration for the HF generation sys-tem

Further analysis was performed to get a better understanding of the differ-

ence between the value of storage for low and high wind penetrations and its correlation with the flexibility of the generation system. We found that the ad-

Reduction in CO2 Emissions: MF System

0

2

4

6

8

10

12

14

16

0 1 2 3

SR reduction category

mill

iont

onne

s/pa 15%

25%35%45%55%

Reduction in CO2 Emissions: HF System

0

2

4

6

8

10

12

0 1 2 3

SR reduction category

mill

iont

onne

s/pa 15%

25%35%45%55%

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Strbac et al. 74

vantage of storage over OCGT is higher when there is a greater SR reduction. The trends found indicate that storage performs better in the LF system for low wind penetration and in the HF system for high wind penetration. The key for this conclusion lies in storage ability to discharge. Fig. 16. Snapshot for one day in summer for the LF system

Figure 16 show that for the first SR reduction, in the LF system, every hour

of the day has surplus wind. This is due to the high wind levels on top of a gen-erating system with a high power of “must run” generation that the wind cannot displace. There is therefore no opportunity to discharge storage. Another sce-nario might be that storage cannot be charged by surplus wind because it is “full” due to previous days of high wind, with no opportunity to discharge.

56 GW wind: inflexible system

0

10000

20000

30000

40000

50000

60000

1 3 5 7 9 11 13 15 17 19 21 23

hour of day (18 June)

Pow

er (G

W) wasted wind

wind storedwind powerdischargegeneration

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Role of Storage in Integrating Wind Energy 75

Fig. 17. Snapshot for one day in summer for the HF system

Figure 17 shows that in the HF system, there is surplus wind which was not

there at lower wind penetrations. This surplus can be utilized by storage as it only exists early in the day when lower demand levels are coinciding with high wind. In this case storage has opportunity to discharge.

All this explains why storage benefit is restricted in the inflexible system at very high wind penetrations, when at lower wind penetrations surplus wind could be utilized and such a system was the most beneficial for storage. Con-versely, at lower penetrations there is less surplus wind in a flexible system. However at high penetrations, surpluses may occur which storage can utilize.

In the flexible system OCGT is not able to make use of the new opportuni-ties offered by wind surpluses at higher wind penetrations so the storage begins to outperform OCGT in a way that was not evident at lower penetrations. In the inflexible system surpluses can become so large and frequent at high wind penetrations, that storage has no opportunity to discharge and therefore its ad-vantage over OCGT so evident at lower penetrations begins to narrow.

It is interesting to consider that storage operation may have seasonal varia-tions for different wind penetrations, for example, wind surpluses that can be utilized occur in the summer at lower wind penetrations. At high penetrations these surpluses cannot be utilized, but winter surpluses that were not occurring at low penetrations may now be occurring at the higher penetrations.

56 GW wind: flexible system

0

10000

20000

30000

40000

50000

600001 3 5 7 9 11 13 15 17 19 21 23

hour of day (18 June)

Pow

er (G

W) wasted wind

wind storedwind powerdischargegeneration

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Strbac et al. 76

Fig. 18. Snapshot for one day in winter for the LF system

Fig. 19. Snapshot for one day in winter for the HF system

Figures 18 and 19 shows that both the LF and HF systems can utilize wind

stored during surpluses on previous days, these surpluses now occurring in win-ter at the high wind penetrations.

In conclusion, storage has an advantage over OCGT in flexible generation systems at higher wind penetrations, whilst at lower wind penetrations its ad-vantage occurs with the inflexible generation system. At lower wind penetra-

56 GW wind: inflexible system

0

10000

20000

30000

40000

50000

60000

1 3 5 7 9 11 13 15 17 19 21 23

hour of day (4 Jan)

Pow

er (G

W) wasted wind

wind storedwind powerdischargegeneration

56 GW wind: flexible system

0

10000

20000

30000

40000

50000

60000

1 3 5 7 9 11 13 15 17 19 21 23

hour of day (4 Jan)

Pow

er (G

W) wasted wind

wind storedwind powerdischargegeneration

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Role of Storage in Integrating Wind Energy 77

tions the advantage of storage over OCGT is less evident in flexible systems whereas at high wind penetrations it is less evident in inflexible systems.

4. Discussion of the results

In the previous section we presented results concerning three major areas: the use of storage on the provision of standing reserve combined with CCGT units providing SR; combined standing reserve provided by storage and OCGT units; impact of the increase of the wind penetration. All these studies include the in-vestigation of the influence the flexibility of the generation system in the value of storage.

The results of section 3.1 show that storage can play a valuable role in re-ducing balancing fuel costs and carbon emissions resulting from the additional balancing task associated with the increase on uncertainty introduced by the wind intermittency. Although storage is not the only technology able to provide standing reserve, because it competes with OCGT, it has significant advantages over the last one. These advantages are based on the unique ability of storage to utilize surplus wind, by charging when wind is high and demand is low and dis-charging when wind is low and demand high. This leads to a more efficient utilization of wind and helps to deal with the intermittency problem increasing the amount of wind used by the system. Other important conclusion is that the flexibility of the conventional generation mix is a key factor to the value of storage.

When storage provides standing reserve in combination with OCGT, we find that the first GW of storage makes most of the contribution to the benefit that this solution has over an OCGT only solution. Thus as standing reserve capacity increases, the weight of the value of the storage part of the solution becomes more significant.

From the studies with increasing wind penetration it becomes clear that the value of storage is interacting both with the flexibility of the generation system and the wind penetration level. The conclusions about the relation between the value of storage and the flexibility of the generation system for 15 and 25% cannot be generalized for 45 and 55 % of wind penetration. Different relations were found for different wind penetrations. At very high wind levels the num-ber of occasions of high wind and low demand becomes more frequent. This increases the amount and frequency of occurrence of surplus wind. A LF gener-ating system has a high value of “must run generation” so it becomes particu-larly vulnerable to these surpluses. If they occur frequently, storage does not have the opportunity to discharge and thus obtain value. The flexible system on the other hand, had no surplus wind occasions at lower wind penetrations, and therefore gave storage no advantage in terms of storing the surplus, does see

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Strbac et al. 78

surplus wind at the higher penetration levels. Thus the advantage of storage over OCGT increases for the flexible systems with higher wind levels.

Acknowledgements

The authors are grateful for the support of Areva T&D Technology Centre UK for the fundamental research in developing the methodology that is used this work.

References

Black, M., Brint, A., T., Brailsford, J., R, 2005, Comparing Probabilistic Methods for the Asset Management of Distributed Items, ASCE Journal of Infrastructure Systems, June.

British Electricity International, 1991, Modern Power Station Practice-3rd Edition, Volume L, System Operation, Pergamon Press.

Dash, 2005, Dash Xpress MP – Optimization Software. [online] http://www.dashoptimization.com/

Doherty R., O’Malley, M., 2005, A New Approach to Quantify Reserve Demand in Systems With Significant Installed Capacity, in IEEE Transactions in Power systems, Vol. 20, NO 2, May.

GreenNet, 2004, Cost and Technical Opportunities for Storage Integartion, GreenNet:WP3 Final Report [online] http://www.greennet.at

Gül, T., Stenzel T., 2005. Variability of Wind Power and other Renewables: Management Op-tions and Strategies. Report by the International energy Agency. [online] http://www.iea.org Paris

Infield, D,G, 1989. A study of Electricity Storage and Central Electricity Generation, Science & Engineering Research Council, Rutherford Appleton Laboratory.

Kaye, B.H, 1989, A Random Walk through Fractal Dimensions, VCH Strbac, G, ILEX, 2002, System Cost of Additional Renewables, study for DTI, October.[online]

www.dti.gov.uk/energy/developep/080scar_report_v2_0.pdf Strbac G., Black M., Future Value of Storage in the UK, study for DTI, Dec 2004 [online]

www.cst.gov.uk/energy/sepn/goranstrbac.pdf Weiss, G.H., 1994, Aspects and Applications of the Random Walk, North-Holland.

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79

INTEGRATION COSTS OF WIND DUE TO CHANGED SYSTEM

OPERATION AND INVESTMENT DECISIONS IN GERMANY

DERK J. SWIDER* Institute of Energy Economics and the Rational Use of Energy University of Stuttgart, Germany CHRISTOPH WEBER Chair for Energy Management University of Duisburg-Essen, Germany

Abstract. In this paper a stochastic fundamental electricity market model is applied to estimate the integration costs of wind due to changed system opera-tion and investments in Germany. The model's principle is cost minimization by determining the marginal system cost mainly as a function of available genera-tion and transmission capacities, primary energy prices, plant characteristics and electricity demand. To obtain appropriate estimates of the integration costs notably reduced efficiencies at part load and start-up costs are taken into ac-count. The intermittency of wind is covered by a stochastic recombining tree and the system is considered to adapt on increasing wind integration over time by endogenous modelling of reserve requirements and investments in thermal power plants. The results highlight the need for stochastic optimization models and the strong dependency on the actual system and its development over time to get sufficient estimates of the integration costs of wind’s intermittency.

Keywords: cost minimization; electricity market; fundamental model; stochastic pro-gramming; wind integration cost

1. Introduction

Within the European Union large amounts of intermittent wind generation are expected to be integrated in the electricity system in the coming years. Due to the fluctuating nature this will influence the performance of the whole system and will hence add costs to the overall system operation. Hence, debates on

______ * To whom correspondence should be addressed. Email: [email protected]

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Swider and Weber 80

wind integration mainly focus on (i) how to estimate the costs of wind's inter-mittency and (ii) how to apportion the costs between wind generators and sys-tem operators. These aspects are subject to ongoing research [1]-[3]. Within this paper a stochastic approach is applied to determine the changing system opera-tion costs of wind's intermittency in Germany.

In the literature there is a broad diversity of methodologies to estimate the costs of wind's intermittency. Grubb assesses the operation costs of a system by analyzing the effects of a variable source on the load-duration curve [4]. This statistical analysis considers the effects on start-up costs and additional reserves in a static system. Strbac discusses the integration costs in the British electricity system [5]. The simulation approach provides a detailed breakdown of costs related to distribution, transmission, reserve and unit-commitment. Thereby the system is assumed to be static and hence does not adapt to an increased share of wind generation in the system over time. Hirst and Hild simulate a relatively small system in a given year [6]. Thereby the integration costs related to reserve and unit-commitment are estimated. DeCarolis and Keith simulate a small ex-emplary system and assess the costs of increased wind input in a carbon con-strained world with the system assumed to be static [7]. Estimates of the costs related to transmission, reserve and unit-commitment are reported.

All of these studies are based on simulating an electricity system bottom-up. Such models can be expected to be a good choice in order to estimate changing system operation costs due to large-scale wind integration. However, they ne-glect the uncertainties in predicting intermittent sources. Hence, so far research focused on static simulation models or deterministic electricity market models. Thus the question remains: What is the optimal system operation considering all relevant states of the stochastic wind generation? A solution to this problem can be found with a stochastic electricity market model.

In this paper such a model based on a stochastic recombining tree and an optimization of the cost minimal system operation is applied. Thereby the sys-tem is allowed to adapt on increasing wind integration and energy policies, i.e. increasing CO2 prices, by taking endogenous investments in conventional ther-mal power plants into account. In a case study the integration costs of wind due to changed system operation and investments in Germany are estimated.

The paper is organized as follows: The model is described in Section 2. The case study data is presented in Section 3. The results are discussed in Section 4. Finally, conclusions and indications for further research are drawn in Section 5.

2. Model Description

The basic idea of fundamental models is to analyze power markets based on a description of generation, transmission and demand, combining the technical

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Integration Costs of Wind in Germany 81

and economical aspects. These models often aim at explaining electricity prices from the marginal generation costs. Of course, this basic approach has to be extended into several directions in order to cope with the reality in electricity markets. In this paper the innovative elements are: • intermittency of wind is represented by a stochastic recombining tree, • investments are endogenously modelled and • reserve requirements are based on a constant reliability margin.

In the following the general approach is discussed. Based on this a determi-nistic model version is described. This is followed by a discussion of the sto-chastic extension. Figure 1 gives an overview of the symbols used.

Variables

E Transmission flow OC Operating costs FC Fixcosts Q Production H Storage level S Stochastic stages L Capacity SC Start-up costs N Nodes TC Total costs Indices

0 Minimal r Region cyc Cycling res Power reserve irr Irreversible rev Reversible m Marginal s Stochastic Stage n Node stu Start-up new New t Time step old Old T Final time step onl Online u Unittype pum Pumping Parameters

a Annuity factor lt Lifetime d Duration oc Other variable costs D Energy demand sc Specific start-up costs f Frequency W Water interflow fc Specific fix costs η Efficiency fp Fuelprice ψ Occurring probability i Interestrate ρ Availability lf Loadfactor τ Transition probability

Fig. 1. Symbols used in the model

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Swider and Weber 82

For the implementation of any fundamental model, especially if the costs of wind integration are to be estimated, at least the following challenges arise: • existing capacities, • unit-commitment, • investments, • time resolution, • regional resolution and • stochastic modeling.

All fundamental electricity market models depend on the representation of the power plant portfolio of the considered system. The number and types of power plants represented may vary according to the considered regions and time horizon. With respect to the restricted computing time it may then be nec-essary not to model all plants separately. One attractive solution is to group the plants to classes according to the main fuel and vintage. Besides often focused thermal power plants, cf. e.g. [7], hydro power plants play a considerable role in electric power systems. Notably, hydro storage plants require a modelling ap-proach that encompasses several time steps and possibly stochastic inflow.

In order to cope with the intermittency of wind the operation of other units in the power system may change. Thereby the value of flexibility of plant op-eration to maintain a constant reliability margin may increase. Thus important aspects to be considered are start-up costs and part-load efficiencies. Those are often modelled using binary variables, cf. e.g. [8].

With the integration of wind in an existing system the remaining will co-evolve over time. All else equal, the costs of intermittency will be less if the generation mix is dominated by flexible plants, i.e. hydro storage plants or gas turbines. Hence, the consideration of intermittent wind may lead to a change in the macroeconomic cost-minimized investment behaviour that needs to be taken into account. Thus the estimation of changing system operation costs needs to be based on a dynamic representation of the system. This may again be based on a mixed-integer representation of investment decisions, cf. e.g. [9].

As this paper focuses on changing system operation costs the time resolu-tion should be as detailed as possible. On the one hand the modelling of sea-sonal hydro storage necessitates considering a full year. On the other hand the effects of intermittency on the unit-commitment of the overall system requires considering an almost hourly time resolution. Finally the wind deployment has to be considered over a reasonable time horizon. Hence, each year of the time horizon needs to be modelled subsequently and the restricted computing time leads to use load segments within a seasonally decomposed yearly model or to model typical days that comprise a defined set of typical time segments.

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Integration Costs of Wind in Germany 83

With regard to the integration of a possible high amount of wind power in future electricity system configurations, the consideration of transmission con-straints is another important aspect. A fundamental model may therefore be di-vided in different geographic entities. Those may represent today's transmission system in a way that possible transmission constraints can sufficiently be mod-elled. Thereby (i) the different evolvement of power systems over time and (ii) the spatial distribution of wind should be taken into account.

Considering stochastic fluctuations is particularly relevant if the model is to be used for short-term predictions or to give an estimate of the effects and addi-tional costs of wind's intermittency. As highlighted above, most models to as-sess integration costs of wind are based on a simulation rather than an optimiza-tion. Thereby the fluctuations are considered with a defined process of wind generation over time. This accounts well for actual variations in the wind gen-eration but does not account for the additional uncertainty conventional genera-tors have to face. The uncertainty is due to the wind generation being more or less unknown for the next hours and leads to a changing optimal operation of the system. To cope with this uncertainty two principal stochastic approaches are possible to be used in a fundamental electricity market model: (i) a branch-ing tree and (ii) a recombining tree. While the former is well suited for a shorter time horizon, the latter has advantages if a longer time horizon is considered.

2.1. Deterministic Model

The model determines the marginal generation costs as a function of available generation and transmission capacities, primary energy prices, plant characteris-tics and actual electricity demand. Also the impact of hydro-storage and start-up costs as well as endogenous investment decisions are taken into account. The principle of the model is cost minimization in the power network. The determi-nistic objective function to be minimized can be written as:

( )∑∑∑ ++=r u t

turturturtt FCSCOCfdTC ,,,,,, (1)

Thereby the total cost TC is minimized and calculated by the sum of oper-ating cost turOC ,, , start-up cost turSC ,, and fixed cost turFC ,, subject to region r , unit type u and time segment t . This sum is weighted by the duration td and frequency tf of a time segment.

The operating costs turOC ,, are assumed to be an affine function of the de-cision variable of the plant output turQ ,, . Thereby the decision variable of ca-pacity currently online onl

turL ,, is introduced [10]. The capacity online generally forms an upper bound and, multiplied with the minimum load factor, a lower

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Swider and Weber 84

bound to the output. This allows describing the difference between part-load and full-load efficiency in a linear approximation:

( )( ) ( )

⎟⎟⎠

⎞⎜⎜⎝

⎛+=⎟⎟

⎞⎜⎜⎝

⎛+=

−+−+=

0,,

0,,

,,,,0,,,,,,

andwith

1

u

turum

u

turum

uturonl

turuonl

turuturmtur

fpocp

fpocp

lfQLplfLlfQpOC

ηη

(2)

In this equation turfp ,, gives the fuel price, muη the efficiency at full load

and 0uη the efficiency at the minimum load factor ulf . The efficiencies are as-

sumed to be constant and as 0u

mu ηη > the operators have an incentive to reduce

the capacity online. Furthermore other variable costs uoc are included. Start-up costs may influence the unit-commitment. In order to avoid binary

variables the capacity currently online onlturL ,, is used. With this the specific start-

up costs due to abrasion abrursc , and fuel consumption con

ursc , arise, if the capacity online is increased, i.e. if the start-up capacity onl

turonl

turstu

tur LLL 1,,,,,, −−= gets posi-tive. The total start-up costs tuSC , are then described by:

( ) stuturtur

conur

abrurtur LfpscscSC ,,,,,,,, += (3)

Contrarily to other fundamental market models endogenous investments in new thermal power plants are taken into account. This reflects that the system may change due to an increased share of wind generation on total production. Hence, for calculating the fix costs turFC ,, the choice among different available investment alternatives with specific irreversible fix costs irr

ufc and the deci-sion variable of newly build capacity new

turL ,, is endogenously modelled:

( ) turrevu

newtur

irruutur LfcLfcltiaFC ,,,,,, , += (4)

Thereby the investments are discounted by the annuity factor ( )ultia , de-fined by the interest rate i and the lifetime ult . And reversible specific fix costs

revufc for the total installed power plant capacity turL ,, are taken into account.

The total investments per year can be restricted, e.g. in order to reflect fuel availabilities, and the first year of investing in each technologies can be given, e.g. in order to reflect investing lead times.

The key constraint of the model is that supply and demand have to be iden-tical in every region r and at every time step t :

( ) ∑∑∑ +≡−+ →→u

pumturtr

rtrrtrr

utur QDEEQ ,,,

',',',, (5)

Thereby the demand is exogenously given by the energy demand trD , and the decision variable of export flows trrE ,'→ , while supply is given by the power production turQ ,, and the decision variable of import flows trrE ,'→ . As

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Integration Costs of Wind in Germany 85

also pumped hydro plants are considered the decision variable of pumping en-ergy for hydro storage pum

turQ ,, need to be added. The production turQ ,, is constrained by the total installed capacity turL ,,

multiplied by an availability factor tu ,ρ .

tuturtur LQ ,,,,, ρ≤ (6)

The availability factor depends on the time of the year and accounts for planned outages, i.e. revisions, only. This production constraint may be formu-lated alike for the pumping energy pum

turQ ,, and, as a transmission constraint, for the import flows trrE ,'→ and the export flows trrE ,.'→ .

As this paper addresses the effects of large-scale integration of intermittent wind energy it is necessary to consider reserve power requirements. The re-serves are estimated endogenously in the model applying a probabilistic method based on Sontow [11]. Thereby the secured capacity sec

,, turL is calculated by es-timating the probability distribution of the reliable capacity of the given power plant portfolio. This distribution can be estimated by sequentially calculating the convolutions of the probability distributions of all power plants. Given the general discrete distributions kf and kg being defined on the set of capacity steps { }K...,,,21K = and with 1=∑k kf as well as 1=∑k kg the convolu-tion at index { }12...,,2,1 −∈ nl can be calculated following:

∑=

+−==l

iililll gfgfz

11* (7)

For conventional power plants two states are assumed: with probability p the plant is able to produce and with probability pq −= 1 not. In the determi-nistic setting this can also be assumed for the wind power plants. Hence, the only uncertainty is an unplanned outage due to technical reasons.

This convolution is repeated for all power plants. Setting the cumulative sum of the estimated probability of the power plant portfolio equal to a defined reliability margin leads to the wanted secured capacity. Then the reserve can be calculated by the difference between the available and the secured capacity.

Next to these overall reserve requirements restrictions at the plant level have to be satisfied. These restrictions are included in the capacity balance equation of plants able to provide them:

tuturres

turonl

tur LLL ,,,,,,, ρ≤+ (8)

When modelling hydro power storage plants, storage constraints need to be considered. It is thereby necessary to describe the filling and discharging. This may be obtained by constraining the decision variable of the storage level

turH ,, , expressed in energy units, not to be greater than the level at time step

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Swider and Weber 86

1−t minus the production turQ ,, and plus the exogenously given inflow turW ,, for all hydro storage plants.

turturturtur WQHH ,,,,1,,,, +−≤ − (9)

For the pumped storage plants an even further extension of the framework is required. The already introduced pumping energy pum

turQ ,, and a given cycling efficiency cyc

uη are required.

pumtur

cycnturturturtur QWQHH ,,,,,,1,,,, η++−≤ − (10)

Finally, an adequate terminal condition for the water reservoirs has to be in-cluded. One attractive formulation is to require that the final and the initial res-ervoir level are identical. This can be expressed with the following initial cycli-cal condition for the hydro plants (thereby the first time step is indicated by

1=t and the final time step by Tt = ):

1,,1,,,,1,, ururTurur WQHH +−≤ (11)

and for the pumped storage plants:

pumur

cycnururTurur QWQHH 1,,1,,1,,,,1,, η++−≤ (12)

2.2. Stochastic Model

The aforementioned equations need to be extended in order to cope with the stochastics of intermittent wind generation. Instead of considering one opera-tion mode of the system at one moment in time, one has to consider different alternative stochastic states depending on the actual wind generation.

For representing the stochastic wind generation a recombining tree is con-sidered. Thereby a typical day t is subdivided in S stochastic stages

{ }Ss ...,,2,1∈ (that can be equal to the considered duration td of a time seg-ment or may comprise several such time segments) and for each stage N sto-chastic states or nodes { }Nn ...,,2,1∈ are distinguished. Following this setting, the number of decision variables increases with the power of N . Hence, the consideration of stages is due to the need to reduce the resolution of the sto-chastic representation in order to limit the computational burden.

The recombining tree is depicted in Figure 2. Each node is characterized by the respective value of the stochastic variable and its probability ( ) ntsr ,,ψ (here ( )ts indicates that to each time segment t a unique stochastic stage s is asso-

ciated). It may be seen that each node n at stage s is coupled with each node 'n at stage 1+s . Thereby transition probabilities ',1, nnssr →+→τ need to be taken

into account. They give the probability that a specific stochastic state is ex-

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Integration Costs of Wind in Germany 87

pected to follow a specific state on the proceeding stage. To be more specific: In this paper the nodes represent different stochastic states, e.g. low, medium and high wind generation, at a given stochastic stage, i.e. the wind power gen-eration is assumed to be constant in the hours comprised by the stochastic stage. Additionally, at the end of each time segment the transition probabilities to the following segment are taken into account.

Fig. 2. Stochastic representation by a recombining tree

Following this the stochastic objective function is a straight-forward exten-

sion of the deterministic approach in Eq. (1). The key point is that all decision variables are simultaneously indexed over time t and node n and that the dif-ferent nodes enter the objective function with their probability ( ) ntsr ,,ψ :

( ) ( )∑∑∑∑ ++×=r u t n

nturnturnturntsrtt FCSCOCfdTC ,,,,,,,,,,,ψ (13)

For the other static equations it is necessary to add the index of the different nodes. The capacity, reserve and transmission constraints are examples of such static equations, cf. Eq. (6). However, for dynamic equations, which link differ-ent time steps, it is important to account for the transition probabilities. E.g. reservoir fillings at the beginning of a stochastic stage will be determined by the probability weighted average of the filling levels at all nodes of the prior stage.

In such a stochastic setting the probability distribution of wind power avail-ability as needed to endogenously calculate the reserve power requirements can no longer assumed to be based on two-states only. Here the considered nodes and the corresponding probabilities define the probability distribution of the

s1 s2 s3 s4Stages

Nodes

n1

n2

n3

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Swider and Weber 88

wind power plants. Hence, considering more nodes lead to a higher accuracy in representing the actual distribution.

2.3. Integration Costs

Within this paper the integration costs of wind due to changed system op-eration and investment decisions are to be estimated. In general the term “inte-gration costs” can be interpreted as the additional costs of integrating something new into a pre-existing system. Here a generation technology, i.e. wind energy, is integrated that differs from conventional generation due to (i) lower control-lability, (ii) lower predictability and (iii) higher variability. Consequently, the system operation becomes more complicated, with a need of a higher flexibility in the overall system to follow load. Thereby most import are more frequent start-ups of conventional power plants, higher fractions of part-load operation and an increased need for reserves. These aspects lead to changes in the system and its operation and hence to additional costs, i.e. to integration costs.

Following this discussion it is straightforward to conclude that models ap-plied to estimate such integration costs need to take the differing characteristics of wind energy into account. Hence a stochastic model is needed that can reflect not only the higher variability but also the lower predictability. While the for-mer can also be analysed with a deterministic simulation model the latter can-not. Here it is assumed that the described stochastic model version can be ap-plied to sufficiently model these characteristics. Then the total integration costs can be estimated by calculating the difference between the optimized overall system costs as determined with the stochastic and those determined with the deterministic model version. These costs are divided by the expected wind en-ergy generation to get the integration costs (in EUR/MWh wind).

This definition excludes the investment costs of wind energy and compares the actual system (stochastic model version) with a system where a hypothetical alternative technology is integrated (deterministic model version). Hence, the computation of integration costs remains highly dependent on the definition of this alternative. Following this discussion the alternative technology considered is assumed to have the expected wind energy production with conventional properties (constant production, i.e. firm and predictable). This energy input is assumed to be provided at zero variable costs and is hence fully absorbed by the system (as is wind energy in the stochastic model version). All other character-istics of the alternative, i.e. costs, availability and reliability, are assumed to be equal to those assumed for wind energy. Thus the system costs considering the firm and predictable alternative can generally expected to be lower than the sys-tem costs considering wind’s intermittency and low predictability.

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Integration Costs of Wind in Germany 89

3. Model Assumptions

The description of the developed stochastic fundamental electricity market model has shown that assumptions on the regional resolution, time horizon and discount rate, generation capacities and investments, electricity demand, energy policy and finally also on the considered stochastics are important parameters of the model. They may considerably influence the modelling results and are dis-cussed for a German case study in the following subsections.

3.1. Regional Resolution

The model is developed to account for several regions (within one country or between neighbouring countries) coupled by defined transmission capacities. In this case study, however, such interactions are not accounted for. Thus, addi-tional costs of transmission and distribution of wind integration are not consid-ered (as well as other additional shallow and deep costs of grid integration and wind turbine investment). Following this discussion the analysis is based on whole Germany as the only considered region in the model.

3.2. Time Horizon and Discount Rate

Here a time horizon until 2020 is considered. Thereby each year is sequentially modelled, i.e. a myopic approach is taken. The complete description of a year is omitted in order to limit the computational burden. This leads to divide each year in 12 typical days (every two months one typical weekday and weekend) and each day in 12 typical time segments.

For an appropriate choice of the discount rate, as needed to model invest-ments, the relevant risks have to be analyzed. These risks result in the uncer-tainty of the economic competitiveness of the power plant investment in the longer run. Here the discount rate is assumed to be 8 %, cf. e.g. [9], [10].

3.3. Generation Capacities and Investments

All fundamental models depend on the representation of the power plant portfo-lio of the considered system. To reduce the complexity the power plants within this paper are grouped according to the main fuel and vintage. This results in 5 classes for coal-fired plants and lignite-fired plants, in 3 classes for gas-fired combined cycle plants, gas-turbines and oil-fired plants, in 1 class for nuclear power plants and miscellaneously-fired steam-turbines, respectively. The char-acteristics of selected thermal power plant classes are given in Table 1.

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Swider and Weber 90

Tab. 1. Existing thermal power plants

Mis

c

50

1700

42

96

97

3.0

4.5

1.2

19.0

Nuc

lear

1100

2118

1

100

98

99

2.0

16.7

0.5

38.1

Gas

CC

250

1643

2

56

98

96

8.0

3.5

1.2

19.0

Gas

GT

50

2290

37

98

93

8.0

1.1

1.2

19.0

Lign

ite80

-

500

7998

40

96

97

5.0

6.2

1.6

52.4

Lign

ite-7

9

400

9084

32

95

96

5.0

6.2

1.6

52.4

Coa

l80-

300

1373

8

44

96

96

5.0

6.2

2.0

42.6

Coa

l-79

200

1192

4

36

95

95

5.0

6.2

2.0

42.6

Uni

t

(MW

)

(MW

)

(%)

(%)

(%)

(€/M

W)

(MW

th/M

Wel)

(€/M

Wh)

(€/k

W)

Type

Net

cap

acity

sing

le p

lant

Ove

rall

capa

city

Effic

ienc

y (f

ull l

oad)

Ava

ilabi

lity

(win

ter)

Rel

iabi

lity

Spec

ific

star

t-up

cost

s

Add

ition

al st

art-u

p fu

el u

sage

Oth

er v

aria

ble

cost

s

Fixe

d op

erat

ion

cost

s

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Integration Costs of Wind in Germany 91

It may be noted that in the case study full- and part-load efficiencies are dis-tinguished, cf. Eq. (2). Additionally may be noted that distinct availabilities for any two month time period are assumed, with higher availabilities in the winter months than in the summer months. The lifetime of the considered thermal power plants is assumed to be 35 years and independent of any modernization. The endogenously modelled investments are based on the data given in Table 2.

Tab. 2. Investment opportunities in thermal power plants

Type Coal Lignite Gas GT Gas CC

Net capacity single plant (MW) 750 850 100 800

Efficiency (full load) (%) 46 42 39 58

Availability (winter) (%) 96 96 98 99

Reliability (%) 97 98 94 97

Specific start-up costs (€/MW) 5.0 5.0 8.0 8.0

Additional start-up fuel usage (MWth/MWel) 6.2 6.2 1.1 3.5

Other variable costs (€/MWh) 2.0 1.6 1.2 1.2

Fixed operation costs (€/kW) 42.6 52.4 19.0 19.0

Investment costs (€/kW) 1100 1350 230 450 Variable generation costs are mainly determined by the fuel costs. Those

depend on the fuel prices and the efficiency of the respective power plant class. The development of fuel prices over time is assumed to be static, i.e. independ-ent of investments in new power plants, and given in Table 3.

Tab. 3. Fuel prices free plant (€/MWh)

2000 2001 2002 2003 2004 2005 Change (%) 2020

Coal 5.95 7.36 6.28 5.70 7.72 8.78 0.4 9.39

Lignite 3.55 3.59 3.62 3.66 3.68 3.69 0.4 3.95

Nuclear 6.14 6.14 6.14 6.14 6.14 6.14 0.0 6.14

Gas 13.46 16.59 14.22 14.88 14.40 17.76 1.1 20.86 With respect to the probabilistic approach for estimating the reserve re-

quirements considering power plant classes leads to take care in determining the probability distribution of their availability. Note that a power plant class can-not be represented with the two-state assumption for a single power plant. As-suming that the class represents n power plants of the same capacity and dis-

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Swider and Weber 92

tribution for the single plant the distribution for the class can be calculated by a ( )1−n -fold convolution following:

( ) ( ) 111* 1 −+−− −⎟⎟⎠

⎞⎜⎜⎝

⎛−

== llnnll pp

pln

fz (14)

Hydroelectric power plants play a considerable role in the German power system. Thereby three classes can be distinguished: run-of-river plants, hydro storage plants and hydro storage plants with pumping facilities (pumped storage plants). The characteristics of the considered classes are given in Table 4.

Tab. 4. Existing hydro electric power plants

Type Run-of-river Hydro-storage Pumped-storage

Overall capacity (MW) 2421 324 5103

Efficiency (full load) (%) 100 100 100

Availability (winter) (%) 98 70 70

Reliability (%) 100 100 100

Other variable costs (€/MWh) 2.5 2.5 2.5

Fixed operation costs (€/kW) 69.0 25.0 25.0 Wind integration is assumed to be the result of governmental aid and is ex-

ogenous to the model. To analyze the effects of an increasing fraction of wind serving demand several deployment scenarios are considered, cf. Figure 3.

Fig. 3. Installed wind capacity: Base case and scenarios (left); Base case on- and offshore (right)

2000 2004 2008 2012 2016 20200

15

30

45

60

Inst

alle

d W

ind

Cap

acity

(G

W)

BaseScenarios

2000 2004 2008 2012 2016 20200

15

30

45

60

Inst

alle

d W

ind

Cap

acity

(G

W)

Base off−shoreBase on−shore

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Integration Costs of Wind in Germany 93

3.4. Electricity Demand

Electricity demand is assumed to be price inelastic and is exogenously given. The development over time can be handled by using predefined growth rates as given in Table 5.

Tab. 5. National electrical consumption (TWh)

2000 2001 2002 2003 2004 Change (%) 2010 Change (%) 2020

Demand# 492 495 499 509 513 1.1 548 0.8 593 # The national electrical consumption is the net electrical consumption including the network losses without consumption for pumped storage.

Electricity demand can be understood as the sum of demand of all consumer

groups in Germany that result to one value for each typical time segment as given in Figure 4. It may be noted that the electricity demand is also subject to stochastic variations. However, such effects are not taken into account.

Fig. 4. Electricity demand at typical time segments: Workdays (left); Weekends (right)

3.5. Energy Policy

To assess the effects of energy policies on the additional costs of wind integra-tion trading of CO2 allowances is assumed. In the European Union emissions trading started in 2005. Thereby the member states set limits on CO2 emissions by issuing allowances as to how much companies are allowed to emit, with the reductions below the limits to be tradable. Hence, CO2 emissions have a price. Evidently, this price is not known ex-ante, thus assumptions on the future de-

JanHr1 MarHr1 MayHr1 JulHr1 SepHr1 NovHr1

40

50

60

70

80

Ele

ctric

ity D

eman

d (G

Wh)

JanHr1 MarHr1 MayHr1 JulHr1 SepHr1 NovHr1

40

50

60

70

80

Ele

ctric

ity D

eman

d (G

Wh)

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Swider and Weber 94

velopment are necessary. In the current version of the model the price of CO2 allowances is exogenously given by static expectations, i.e. the allowance prices do not depend on a changing power plant portfolio, cf. Table 6.

Tab. 6. CO2 allowance prices (€/tCO2)

2000 to 2003 2004 2005 2006 Change (%) 2020

Low 0.00 4.29 17.89 10.00 0.0 10.00

High 0.00 4.29 17.89 20.00 5.1 40.00 The allowance costs are determined by the sum of the fuel price and the al-

lowance price times a CO2 emission factor. Those are given in tCO2/MWh and assumed to be 0.34, 0.40 and 0.20 for coal, lignite and gas, respectively.

Finally also the governmental decision for a nuclear phase-out is presumed.

3.6. Stochastics

In the case study short-term fluctuations are of major importance. Therefore wind speed data have been combined with aggregated power curves. This is done using data from ten weather stations that reflect the spatial distribution of wind power in Germany. The time series are used to determine a high, medium and low wind case as well as corresponding probabilities of occurrence and transition. They give the capacity factor of wind production. Multiplied with the installed capacity this yields the actual generation, hence the capacity factor corresponds to the full-load hours of wind energy production, cf. Figure 5.

Fig. 5. Fluctuations of on-shore wind: Capacity factor (left); Node probability (right)

JanHr1 MarHr1 MayHr1 JulHr1 SepHr1 NovHr1

20

40

60

80

100

Cap

acity

Fac

tor

(%)

HighMediumLowExpected

JanHr1 MarHr1 MayHr1 JulHr1 SepHr1 NovHr1

20

40

60

80

100

Pro

babi

lity

(%)

LowMediumHigh

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Integration Costs of Wind in Germany 95

Note that the capacity factor over the time horizon depends on the develop-ment of on- and off-shore wind installations, i.e. the full-load hours of wind increase with the share of off-shore wind production. Thereby full-load hours of about 1650 hrs and 2850 hrs are respectively considered for on- and off-shore.

Finally the reliability margin is set to be 99 % and determines the endoge-nously modelled reserve power requirements.

4. Model Results

In this section results of the German case study are presented. Thereby the fo-cus is on the estimation of additional intermittent wind integration costs due to changing system operation and investment decisions. Hence, other additional costs e.g. due to possible grid extensions are not taken into account. The effects of high versus low CO2 allowance prices are discussed in order to assess the importance of the development of the system on wind's integration costs.

Figure 6 gives the yearly utilized capacity in the base case of installed wind capacities applying the deterministic and the stochastic model version for the low and the high CO2 allowance price path scenarios respectively. It may be seen that the utilized capacity increases in all cases due to the assumed increase in demand. The high CO2 allowance price case, cf. Figure 6 (left), shows higher investments in gas-fired power plants, while the low CO2 allowance price case, cf. Figure 6 (right), shows higher investments in lignite- and coal-fired power plants. Thus the investment decisions are highly dominated by energy policies even without considering a substantial increase of wind energy production over time. By comparing the deterministic and stochastic modelling results, cf. Fig-ure 6 (top) and (bottom) respectively, it can be seen that more investments are necessary in case the intermittency of wind is accounted for. This is mainly due to the low predictability of the wind energy production that hence results in a relatively low capacity credit. It can furthermore be seen that these investments are dominated by flexible gas-fired plants.

Figure 7 gives the new build capacity for the considered cases and high-lights the different investment decisions (without the exogenously given wind deployment). First, due to the assumed nuclear phase-out high investments in base-load plants are necessary in all considered cases. However, in the high CO2 allowance price path scenario, cf. Figure 7 (left), these investments are dominated by gas-fired combined cycle plants, while in the low CO2 allowance price path scenario, cf. Figure 7 (right), the investments in lignite-fired plants are dominant. By comparing the deterministic and stochastic modelling results, cf. Figure 7 (top) and (bottom) respectively, it can be seen that investments in gas-turbines are necessary to get a higher flexibility of the overall system in order to cope with the intermittency of wind.

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Swider and Weber 96

Fig. 6. Utilized capacity: High CO2 price path, deterministic model version (top, left); Low CO2 price path, deterministic model version (top, right); High CO2 price path, stochastic model ver-sion (bottom, left); Low CO2 price path, stochastic model version (bottom, right)

Figure 8 gives the development of wholesale electricity prices until 2020. In

the model these prices correspond to the marginal generation costs and may hence be different from the spot market prices historically observed. It can however be seen that the historic prices from 2000 to 2005 are well represented with the model. The remaining deviations are partly due to the model assump-tions. E.g. the availabilities due to maintenance outages or weather anomalies are assumed to be constant over the time horizon. In 2002 and especially in 2003 unusually high temperatures have been observed in the summer. Thus the availabilities, especially of the power plant technologies with low variable costs, have been lower than in an average year. Of course, also inaccuracies in the model data may account for some of the observed deviations. Thereby espe-

2000 2004 2008 2012 2016 20200

50

100

150

200

250

Util

ized

Cap

acity

(G

W)

WindHydroMiscOilGasCoalLigniteNuclear

2000 2004 2008 2012 2016 20200

50

100

150

200

250

Util

ized

Cap

acity

(G

W)

WindHydroMiscOilGasCoalLigniteNuclear

2000 2004 2008 2012 2016 20200

50

100

150

200

250

Util

ized

Cap

acity

(G

W)

WindHydroMiscOilGasCoalLigniteNuclear

2000 2004 2008 2012 2016 20200

50

100

150

200

250

Util

ized

Cap

acity

(G

W)

WindHydroMiscOilGasCoalLigniteNuclear

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Integration Costs of Wind in Germany 97

cially the fuel prices for coal and gas (being the marginal plants) are of major importance. Additionally may be noted that the model considers Germany only and inter-regional transmission is neglected. It is finally also possible that some of the differences are due to strategic behaviour (excessive use of market power) of the energy traders. This is subject of currently ongoing research and is heavily discussed in Germany due to the oligopolistic market structure.

Fig. 7. New capacity (without wind): High CO2 price path, deterministic model version (top, left); Low CO2 price path, deterministic model version (top, right); High CO2 price path, stochastic model version (bottom, left); Low CO2 price path, stochastic model version (bottom, right)

In the long-run the modelled electricity prices increase in case of high CO2

allowance prices, cf. Figure 8 (left), and level-out in case of low CO2 allowance prices, cf. Figure 8 (right). It may be seen that stochastic modelling of wind generation does not significantly alter the estimated price development in the considered cases. This is due to the relatively minor impact of additional wind

2000 2004 2008 2012 2016 20200

2

4

6

8

New

Cap

acity

(G

W)

Gas GTGas CCCoalLignite

2000 2004 2008 2012 2016 20200

2

4

6

8

New

Cap

acity

(G

W)

Gas GTGas CCCoalLignite

2000 2004 2008 2012 2016 20200

2

4

6

8

New

Cap

acity

(G

W)

Gas GTGas CCCoalLignite

2000 2004 2008 2012 2016 20200

2

4

6

8

New

Cap

acity

(G

W)

Gas GTGas CCCoalLignite

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Swider and Weber 98

generation on the marginal power plant in the system. Thereby, however, it has to be considered that the operation is influenced by the different investment de-cisions (different technologies and sometimes different years of investment) resulting in deviations over the modelled time horizon.

Fig. 8. Electricity price: High CO2 price path (left); Low CO2 price path (right)

Figure 9 gives the development of the endogenously calculated reserve ca-

pacities over the time horizon. It can be seen that the considered CO2 allowance price paths do not significantly influence the necessary reserve capacities. The few differences are due to the changed investments. But this effect is minor and can be neglected due to the available investment alternatives having similar re-liabilities. These reliabilities are however assumed to be higher than those of the existing power plants and thus are one part of the reason for the reserve capac-ity decreasing in the deterministic model version. In this case wind is assumed to be perfectly predictable and hence does not effect the reserve requirements. The other reason for the decrease in the necessary reserve requirements is due to the decrease in the need for conventional capacities. In case of the stochastic model version, with the intermittency and low predictability of wind taken into account, the reserve requirements increase significantly with the assumed wind deployment. It may be noted that this increase is higher than the increase of demand, so defining the reserve capacity proportional to the overall demand is not sufficient in case of large-scale wind integration.

With the approach considered, the reliability margin of the overall system is constant at 99 % and corresponds to the actual margin in the German system. It can be seen that this leads to a good representation of the historic reserves with the stochastic model version. Higher deviations can be seen in the first years of the time horizon. Those can partly be explained with a higher reliability margin

2000 2004 2008 2012 2016 202015

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Integration Costs of Wind in Germany 99

of the actual system in these years compared to the assumption in this case study. This margin has been reduced in the following years primarily due to the introduction of markets for procuring power systems reserve.

Fig. 9. Reserve capacity: High CO2 price path (left); Low CO2 price path (right)

Figure 10 gives the yearly integration costs of the base wind generation sce-

nario that corresponds to a fraction of 15 % of wind serving demand in 2020. In this study the integration costs are calculated as the difference of the system costs between the stochastic and the deterministic model version. The integra-tion costs then include avoided fuel costs, increased part-load operation, needs for balancing the system, start-up and investment costs (of conventional genera-tion). It can be seen that the integration costs increase over the considered time horizon due to the increasing wind energy deployment. In fact the integration costs greatly depend on the ability of the considered system to dynamically adapt to an increased share of wind generation. A comparison between the high and low CO2 allowance price path again highlights that energy policies can have a major influence on the integration costs. Here the estimated integration costs are lower in case of the assumed high CO2 allowance prices, cf. Figure 10 (left), compared to the low CO2 allowance prices, cf. Figure 10 (right). This is due to the different investments. With the assumed high CO2 allowance prices the variable costs (including the respective fuel and CO2 allowance prices) for coal- and lignite-fired plants increase faster than the variable costs of gas-fired plants. Hence, the investments are dominated by gas-fired combined-cycle plants leading to a higher flexibility of the system; even if wind could be con-sidered to be perfectly predictable. Following this discussion the cost figures in the literature, cf. e.g. [1]-[3] and the references therein, need to be analysed

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Swider and Weber 100

with particular care as often the assumptions leading to the presented results are not sufficiently discussed.

Fig. 10. Yearly integration cost: High CO2 price path (left); Low CO2 price path (right)

Figure 11 gives the integration costs of wind power in the German electric-

ity system over a defined fraction of wind serving demand. To consider the sys-tem adapting to an increased wind generation the results are given for 2020 only. This ensures that the endogenously modelled investments are taken into account. It can be seen that the integration costs greatly depend on the consid-ered CO2 allowance price path and most notably on the fraction of wind serving demand. Thereby lower CO2 allowance prices lead to a decreased value of wind energy in the system and a higher fraction of wind serving demand leads to an increased share of part-load operation of conventional power plants. With the higher investment costs in case of the stochastic model version these effects finally result to comparatively higher integration costs. Such costs are hence often underestimated in static, deterministic electricity market models applied to assess the additional costs of wind integration.

Note that the integration costs estimated in this study do not include costs for grid extensions. But this should not lead to the assumption that they can be neglected; in fact they often cannot. In Germany wind power is predominately installed in the northern part of the country, but the main demand areas are in the southern part. In the future this imbalance is expected to increase due to off-shore wind installations. Those will lead to transmission bottlenecks between the northern and southern parts of the country and hence to the necessity of grid extensions. Integration costs due to such grid extensions can generally be mod-elled in the applied framework if Germany is separated into several sub-regions and an additional decision variable for grid investments is considered.

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Integration Costs of Wind in Germany 101

Fig. 11. Integration cost over wind serving demand: High CO2 price path (left); Low CO2 price path (right)

Figure 12 highlights that the integration costs do not indicate that the overall

system costs are expected to increase. Note that the generally higher investment costs for wind turbines compared to investments in conventional power plants are not considered in this study. This is due to the assumption that wind de-ployment is exogenously given and is assumed to be the result of governmental aid. Taken this assumption into account, the overall system costs decrease over wind serving demand. However, the overall system costs in case of the stochas-tic model version are higher compared to those of the deterministic model ver-sion. In this study this difference is called integration costs.

Fig. 12. System cost over wind serving demand: High CO2 price path (left); Low CO2 price path (right)

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Swider and Weber 102

Figure 13 gives the disaggregated system costs in per cent over wind serv-ing demand. Thereby the irreversible fix costs of endogenous investments (FC irr), reversible fix costs of all installed power plants (FC rev), start-up costs (SC), part-load operation costs (OC part) and full-load operation costs (OC full) of all conventional power plants are respectively given for the deterministic and stochastic model version, cf. Figure 13 (top), and the high and low CO2 allow-ances price paths, cf. Figure 13 (bottom). Notably it can be seen that a higher fraction of wind serving demand in the stochastic model leads to a higher share of part-load operation and start-up costs on the overall system costs. This ex-pected result is due to the higher variability and lower predictability of wind power production as considered in the stochastic model version.

Fig. 13. Disaggregated system costs: High CO2 price path, deterministic model version (top, left); Low CO2 price path, deterministic model version (top, right); High CO2 price path, stochastic model version (bottom, left); Low CO2 price path, stochastic model version (bottom, right)

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Integration Costs of Wind in Germany 103

Figure 14 gives the CO2 emissions over wind serving demand. As expected the CO2 emissions in case of the high CO2 allowance price path are higher than those of the low CO2 allowance price path. Furthermore the CO2 emissions de-crease with the fraction of wind serving demand. Thereby the emissions as es-timated with the stochastic model version are generally lower than those esti-mated with the deterministic model version. At first sight one might assume to get higher emissions due to a higher share of part-load operation and more fre-quent start-ups. However, at closer inspection an opposite effect has to be taken into account. As investments in new thermal power plants are modelled endoge-nously the need for a higher flexibility in the system in the stochastic model version leads to higher investments in gas-fired plants. Those are characterised by lower CO2 emissions.

Fig. 14. CO2 emissions over wind serving demand: High CO2 price path (left); Low CO2 price path (right)

Table 7 finally gives disaggregated integration costs of the base case for the

high and the low CO2 allowance price path respectively. It is first of all impor-tant to note that disaggregated integration costs are hard to determine as e.g. investments in new conventional capacities influence the operation of the over-all system. This means that the reported disaggregated cost figures cannot easily compared to the results of other models considering the changing system opera-tion but no investment decisions. However, the results indicate that the integra-tion costs at lower fractions of wind serving demand are dominated by the changing system operation (higher part-load operation) and at higher fractions of wind serving demand by the changing investment decisions. Comparing the results for the two considered CO2 allowance price paths highlight that the inte-gration costs are lower if the flexibility of the system increases due to energy

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Swider and Weber 104

policies leading to higher CO2 allowance prices. It can be seen that in this case the integration costs due to a fraction of part-load operation and increased start-ups are comparatively lower.

Tab. 7. Disaggregated integration costs, base case (€/MWh)

Year Wind serving demand (%) Operation Investment Sum#

High CO2 allowance price path

2000 2 5.7 0.0 5.7 2005 5 7.9 0.0 7.9 2010 8 4.7 2.7 7.4 2015 12 2.8 5.3 8.1 2020 15 3.1 5.5 8.6

Low CO2 allowance price path

2000 2 5.7 0.0 5.7 2005 5 7.9 0.0 7.9 2010 8 5.1 2.9 8.0 2015 12 3.1 6.5 9.6 2020 15 7.0 3.5 10.5

# Integration costs due to changed system operation and investment decisions.

5. Conclusions

In this paper a stochastic fundamental electricity market model to estimate the additional costs of intermittent wind integration is applied to a German case study. The applied model incorporates the intermittency of wind by a recombin-ing tree following a stochastic approach. The results indicate that the value of intermittent resources is generally overestimated applying a static, deterministic model. Especially the decreasing capacity credit with increasing installed wind capacities cannot sufficiently be modelled. On the one hand the results highlight that next to the explicit consideration of stochastics a model applied to assess the integration costs of intermittent wind should be able to endogenously adapt to an increasing share of intermittent generation, i.e. endogenous investment decision and reserve requirements need to be accounted for. On the other hand the strong dependency on the actual system configuration and its development over time to get sufficient estimates of the integration costs of wind’s intermit-tency has been identified.

The developed approach lends itself to multiple further developments, in-cluding notably the extension to further regions and inclusion of further tech-nologies. But also the rules for deriving optimal investments may be developed

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Integration Costs of Wind in Germany 105

further, contributing to getting even more realistic pictures of the market devel-opments. Subject of currently ongoing research is the incorporation of endoge-nously modelled grid extensions. This may lead to a single model able to esti-mate all major parts of the integration costs of wind’s intermittency.

Acknowledgement

The paper presents results of research financially supported by the European Commission within the projects GreenNet (NNE5/2001/00660) and GreenNet-EU27 (EIE/04/049/S07.38561). Prior versions of this paper have been presented at the IAEE European Conference 2005, Bergen, Norway and at the IEEE PES General Meeting 2006, Montreal, Canada.

References

[1] Auer, H., Stadler, M., Resch, G., Huber, C., Schuster, T., Taus, H., Nielsen, L.H., Twidell, J., Swider, D.J., Cost and Technical Constraints of RES-E Grid Integration. Report of the EU Project: Pushing a Least Cost Integration of Green Electricity into the European Grid [online] <http://www.greennet.at>, Vienna, 2004.

[2] van Werven, M., Beurskens, L., Pierik, J., Integrating Wind Power in EU Electricity Sys-tems. Report of the EU Project: Pushing a Least Cost Integration of Green Electricity into the European Grid [online] <http://www.greennet.at>, Vienna, 2005.

[3] Gül, T., Stenzel, T., Variability of Wind Power and other Renewables: Management Options and Strategies. Report by the International Energy Agency. [online] <http://www.iea.org>, Paris, 2005.

[4] Grubb, M.J., Value of Variable Sources on Power Systems, IEE Proceedings-C 138(2): 149-165, 1991.

[5] Strbac, G., Quantifying the System Costs of Additional Renewables in 2020. Report with Ilex Energy Consulting. [online] <http://www.dti.gov.uk>, Manchester, 2002.

[6] Hirst, E., Hild, J., The Value of Wind Energy as a Function of Wind Capacity, The Electric-ity Journal 17(6): 11-20, 2004.

[7] DeCarolis, J.F., Keith, D.W., The Economics of Large-Scale Wind Power in a Carbon Con-strained World, Energy Policy 34(4): 395-410, 2006.

[8] Yamin, H., Review on Methods of Generation Scheduling in Electric Power Systems, Elec-tric Power Systems Research 69(2/3): 227-248, 2004.

[9] Schwarz, H.-G., Modernisation of Existing and New Construction of Power Plants in Ger-many: Results of an Optimisation Model, Energy Economics 27(1): 113-137, 2005.

[10] Weber, C., Uncertainty in the Electric Power Industry: Methods and Models for Decision Support, Springer-Verlag, Stuttgart, 2005.

[11] Sontow, J., Energiewirtschaftliche Analyse einer großtechnischen Windstromerzeugung, Institute of Energy Economics and the Rational Use of Energy, Report no. 73, University of Stuttgart, Stuttgart, 2000.

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107

A STOCHASTIC MODEL FOR THE EUROPEAN ELECTRICITY

MARKET AND THE INTEGRATION COSTS FOR WIND POWER

CHRISTOPH WEBER* Chair for Energy Management University of Duisburg-Essen, Germany DERK J. SWIDER Institute of Energy Economics and the Rational Use of Energy University of Stuttgart, Germany

PHILIP VOGEL Chair for Energy Management University of Duisburg-Essen, Germany

Abstract. In this paper a stochastic fundamental electricity market model is presented. The model’s principle is cost minimization by determining the mar-ginal system costs mainly as a function of available generation and transmission capacities, primary energy prices, plant characteristics and electricity demand. The model is then applied to obtain appropriate estimates of the integration costs of wind in an adapting system. Therefore notably reduced efficiencies at part load, start-up costs and reserve power requirements are taken into account. The intermittency of wind is covered by a stochastic recombining tree and the system is considered to adapt on increasing wind integration over time by en-dogenous modelling of investments in thermal power plants. Exemplary results are presented for a European case study.

Keywords: cost minimization; electricity market; fundamental model; stochastic pro-gramming; wind integration cost

______ * To whom correspondence should be addressed. Email: christoph_weber@uni-duisburg-

essen.de

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Weber et al. 108

1. Introduction

With the liberalisation of European electricity markets, the formerly well-defined environment of electricity producers has become subject to increasing uncertainty. With the political will to increase the share of renewables in elec-tricity generation, a further source of uncertainty is getting increasingly impor-tant. This is the fluctuating and intermittent production of many renewables, especially of wind and solar generation. This will influence the performance of the whole system and the increase in uncertainty tends also to add costs to the overall system operation.

In this context, appropriate models are needed to estimate the impact of in-creased uncertainty on system operation and system operation costs, notably to respond to the strong public and scientific interest in the costs of wind integra-tion in electricity systems.

Debates on large-scale wind integration mainly focus on (i) how to estimate the costs of wind’s intermittency and (ii) how to apportion the costs between wind generators and system operators. These aspects are subject to current re-search as may be seen with some recently published reviews [1] – [3]. Within this paper a stochastic approach to determine the changing system operation costs of wind’s intermittency is presented.

Examples of past studies on the integration costs for wind include the stud-ies by Grubb [4], Strbac [5], Hirst and Hild [6] as well as DeCarolis and Keith [7]. All of these studies are based on simulating an electricity system bottom-up. Such models can be expected to be a good choice in order to estimate changing system operation costs due to large-scale wind integration. However they are less suited to analyse the optimal adaptation of the electricity system to increased wind penetration. Conventional electricity system models, such as [8]-[13], determine the optimal system configuration including optimal invest-ment strategies depending on the political and fuel market context. However most of these models are purely deterministic and are thus hardly adequate to cope with the fluctuations of wind energy. Hence, so far no adequate models exist to describe the impact of increased wind energy production on the overall electricity system, including adaptation of generation capacities. Also the Ger-man dena study [14] has not used an integrated modelling approach to deter-mine the impact of increased fluctuating generation on conventional power plant investments and operation.

In order to get an integral approach, a stochastic electricity market model is needed, which describes the fluctuations of wind energy while at the same time allowing for endogenous investment. This paper describes such a model based on a stochastic recombining tree and an optimization of the cost minimal sys-tem operation. Thereby the system is allowed to adapt on increasing wind inte-

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A Stochastic Model for the European Electricity Market 109

gration, fuel price changes, CO2 restrictions etc. by not only modifying the op-eration of the system but also by adapting endogenously investments in conven-tional thermal power plants. The model is applied in a case study to model the European Electricity market. Additionally the changing system operation costs due to large-scale wind integration in this system are estimated. The paper is organized as follows: The principles of the stochastic fundamental electricity market model are described in Section II. Key parameters of the European case study are discussed in Section III. Results obtained with the model for system operation, power plant investments and integration costs for wind energy are given in Section IV. Conclusions and indications for further research are finally drawn in Section V.

2. Model description

Fundamental models basically aim to analyze power markets based on a de-scription of generation, transmission and demand, combining technical and economical aspects. Thus electricity prices are derived from the marginal gen-eration costs plus the impact of other system restrictions such as limited trans-mission capacities, start up costs etc. Basically thereby two types of models may be distinguished. On the one hand short term unit commitment and load dispatch models, which aim at modelling the details of plant and grid operation for single power plant operators or entire grids (for an overview on such models cf. e.g. [15]). These have high time resolution and encompass a detailed model-ling of plant and grid operation restrictions. Capacity investments are usually not treated in these models given that they cover only short time horizons of one day, one week or at most one year. On the other hand long term energy sys-tem or electricity system models aim at analysing the evolution of the electricity system under prespecified scenarios, e.g. on demand growth or emission con-straints (cf. e.g. [16]). In such models typically investment decisions are mod-elled endogenously and the modelling of operational constraints is simplified.

The major innovative contribution of this paper is to provide a system model with endogenous investment while at the same time having a high enough temporal resolution to model fluctuations in wind energy. More over not only the variability of wind energy is taken into account but also its unpre-dictability is modelled using a stochastic recombining tree. Hence in fact the proposed model combines many features of generation scheduling models (unit commitment and load dispatch) with endogenous investment as found typically in energy system models.

In the following first the general approach and the the deterministic version of the model is discussed. This is followed by a discussion of the stochastic ex-tension of the model. Table 1 gives an overview of the symbols used.

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Weber et al. 110

Tab. 1. Symbols used in the model

Variables E Transmission flow OC Operating costs FC Fixed costs Q Production H Storage level S Stochastic stages

L Capacity SC Start-up costs

N Nodes TC Total costs Indices 0 Minimal r Region cyc Cycling pum Pumping

inv investment res Power re-serve

m Marginal s Stochastic Stage n Node stu Start-up new New t Time step

old Old T Final time step

onl Online u Unit type oth other Parameters

a Annuity factor lt Lifetime

d Duration oc Other variable costs

D Energy de-mand sc Specific start-up costs

FC Frequency W Water in-flow

fc Specific fixed costs η Efficiency fp Fuel price ψ Occurring probability i Interest rate ρ Availability lf Load factor τ Transition probability

2.1. Deterministic model

Under the assumption of power markets with efficient information treatment and without market power, the market results will be equivalent to the outcomes

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A Stochastic Model for the European Electricity Market 111

of an optimization undertaken by a fully informed central planner. If electricity demand is treated as price inelastic, welfare maximization is then equivalent to cost minimization in the considered power network. Thus the model minimizes the costs for satisfying a given demand as a function of available generation and transmission capacities, primary energy prices, plant characteristics and possi-ble investments. Thereby also the impact of hydro-storage and start-up costs as well as endogenous investment decisions are taken into account. In the determi-nistic case, the objective function can be written as:

)( ,,,,,, turturturtttur

FCSCOCfdTC ++= ∑∑∑ (1)

The total costs TC to be minimized are hence determined as the sum of op-

erating costs turOC ,, , startup costs turSC ,, and fix costs turFC ,, summed over regions r , unit types u and time segments t . The summands are weighted by the duration td and frequency tf of the corresponding time segment. In the fol-lowing it is assumed that a whole year is represented by a number nD of typical days, composed each of nH time segments.

For the operating costs turOC ,, an affine function of the plant output turQ ,, is assumed. Additionally, the decision variable “capacity currently online”

onlturL ,, is introduced [17]. The capacity online generally forms an upper bound to

the actual output. Multiplied with the minimum load factor, it provides also a lower bound to the output for each power plant (for details see [17]). Hence operating costs can be decomposed in fuel costs for operation at minimum load, fuel costs for incremental output and other variable costs:

turuonl

turuu

turonlturuturm

u

turtur QocLlf

fpLlfQ

fpOC ,,,,0

,,,,,,

,,,, )( ++−=

ηη (2)

In this equation, turfp ,, is the fuel price, m

uη the marginal efficiency for an operating plant and 0

uη the efficiency at the minimum load factor ulf . With 0u

mu ηη > it is less costly to increase the output of an already running plant than

to increase the capacity only. Thus the operators have an incentive to reduce the capacity online. Furthermore other variable costs uoc are included.

Besides operation costs, start-up costs may influence the unit-commitment decisions considerably. Again the capacity currently online onl

turL ,, is used, in order to avoid binary variables. Then specific start-up costs usc arise, if the

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Weber et al. 112

capacity online is increased, i.e. if the start-up capacity stuturL ,, gets positive. This

start-up capacity is constrained by

0,,

1,,,,,,

−≥ −

stutur

onltur

onltur

stutur

L

LLL (3)

and will as low as possible, given the costs associated with starts. Thus at least one of these inequalities will be fullfilled with equality. The total start-up costs

tuSC , are then described by:

stuturutur LscSC ,,,, = (4)

In order to take into account the longer term development of the power sys-

tem, investments in new conventional thermal power plants are treated endoge-nously in this model. This reflects that the system will adapt over time to vary-ing exogenous circumstances, e.g. an increased share of wind generation in total production. Hence not only the generation scheduling has to be dealt with, but also the fixed costs turFC ,, enter into the optimization. Thereby the choice among different available investment alternatives with specific investment costs

invufc is modelled using the decision variable of newly build capacity new

turL ,, :

turothu

newtur

invuutur LfcLfcltiaFC ,,,,,, ),( += (5)

To limit the size of the optimization problem, the optimization problem is

formulated for single years under the assumption of myopic expectations. Then the investments are valued using the annuity factor ),( ultia depending on the interest rate i and the lifetime ult . Additionally, also other specific fixed costs

othufc for the total installed power plant capacity turL ,, are taken into account. The key constraint to optimization is that supply and demand have to be

identical in every region r and at every time step t:

∑∑∑ +≥−+ →→u

pumturtr

rtrrtrr

utur QDEEQ ,,,

',',',, )( (6)

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A Stochastic Model for the European Electricity Market 113

Thereby total demand equals the sum of exogenously given domestic de-mand trD , and variable export flows trrE ,'→ , while supply is given by the power production turQ ,, and import flows trrE ,'→ . Moreover, pumping energy

pumturQ ,, has to be added in order to model also pumped hydro storage. The pro-

duction turQ ,, is constrained by the total installed capacity turL ,, multiplied by an availability factor tu ,ρ .

tuturtur LQ ,,,,, ρ≤ (7)

The availability factor depends on the time of the year and accounts for

planned and unplanned outages. Similar capacity constraints are formulated for the pumping energy pum

turQ ,, and for the import and export flows trrE ,'→ . For hydro storage plants, storage constraints need to be considered and the

filling and discharging has to be described. This leads to a storage level equa-tion linking the storage level turH ,, , expressed in energy units, to the storage level 1,, −turH at time step 1−t , the production turQ ,, and the inflow turW ,, for all hydro storage plants.

turturturtur WQHH ,,,,1,,,, +−≤ − (8)

For the pumped storage plants moreover the already introduced pumping

energy pumturQ ,, has to be included, taking into account the so called cycling effi-

ciency cycuη .

pumtur

cycuturturturtur QWQHH ,,,,,,1,,,, η++−≤ − (9)

Additionally, an adequate terminal condition for the water reservoirs has to

be included. One attractive formulation is to require that the final and the initial reservoir level are identical, which can be expressed through the following ini-tial cyclical condition for the hydro plants (thereby the first time step is indi-cated by 1−t and the final time step by Tt = ):

1,,1,,,,1,, ururTurur WQHH +−≤ (10)

and for the pumped storage plants:

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Weber et al. 114

pumur

cycuururTurur QWQHH 1,,1,,1,,,,1,, η++−≤ (11)

Environmental restrictions may be modelled by setting an upper bound EMAX

on the emissions of Greenhouse Gases or other pollutants. With the fuel-based emission coefficient εf we have:

( )MAXEXCMAX

Emr u

onlturu

u

onlturuturm

uuf

ttt EEpLlfLlfQfd ≤−⎟⎟

⎞⎜⎜⎝

⎛+−∑∑∑ ,,0,,,,

1)(1ηη

ε

(12)

Here an upper price limit MAXEmp for the emission price has been introduced

and a corresponding excess emission quantity EEXC. This can be used to model policy processes which effectively limit the prices.

The reserves required in the system to cope with unforeseen variations in load, plant outages and wind fluctuations are described by the requirement that the capacity online has to exceed the actual demand by a certain reserve capac-ity, depending on the maximum demand, the installed wind power and the size of the largest unit:

{ }( )windrruur

resrtr

u

onltur LLDLDL ,max, ,

max,,, +≥∑ (13)

2.2. Stochastic model

In order to cope with the stochastics of intermittent wind generation, the afore-mentioned equations need to be extended. In fact for one typical hour in time, not only one operation mode of the system has to be considered, but different alternative stochastic states depending on the actual wind generation which is far from being predictable. Time segments are thereby grouped into S stochastic stages },...,2,1{ Ss ∈ , that may comprise one or several time segments. For each stage N stochastic states or nodes },...,2,1{ Nn ∈ are distinguished. In this setting, the number of decision variables increases with the power of N, if the decisions are assumed to be path-dependent. This is the curse of dimension-ality of conventional stochastic optimization models.

A way out of this curse of dimensionality is the use of a recombining tree as depicted in Figure 1. All variables are assumed to be node and not path-dependent, thus leading to a computational burden proportional to S times N.

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A Stochastic Model for the European Electricity Market 115

Nevertheless, the stages are required to reduce the resolution of the stochastic representation and thus to limit the computational burden. Fig. 1. Stochastic representation by a recombining tree

Each node in the recombining tree is characterized by the respective value of the stochastic variable and its probability ntsr ),(,ψ (here )(ts indicates that to each time segment t a unique stochastic stage s is associated). Each node 'n at stage s is considered to be coupled with each node 'n at stage 1+s . Thereby transition probabilities ',1, nnssr →+→τ need to be taken into account. They give the probability that a specific stochastic state is expected to follow a specific state on the preceeding stage. To be more specific: In this paper the nodes represent different stochastic states, e. g. low, medium and high wind generation, at a given stochastic stage, i.e. the wind power generation is as-sumed to be constant in the hours comprised by the stochastic stage.

Given that typical days are considered, the transitions at the end of each day should take into account the possibility to switch to a day of the same type and the possibility of a shift from weekend to weekday and vice versa.

The stochastic objective function is here a straightforward extension of the deterministic approach in Eq. (1). The key point is that all decision variables are simultaneously indexed over time t and node n and that the different nodes enter the objective function with their probability ntsr ),(,ψ :

)( ,,,,,,,,,

),(,

nturnturntur

ntsrttntun

FCSCOC

fdTC

++×

= ∑∑∑∑ ψ (14)

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Weber et al. 116

Deterministic “static” equations may easily be transformed into theiri sto-

chastic counterpart by simply adding the index n for the nodes. The capacity, reserve and transmission constraints are examples of such static equations, cf. Eq. (6). They have to be fulfilled in each node at each time step.

However, for dynamic equations, which link different time steps, the ap-proach to be followed is somewhat more complicated. Here the transition prob-abilities have to be taken into account. E. g. start-up capacity is defined as the weighted average over the different transitions

( )

0

1

,,

'',1,,,,,'),()1(,,

''),()1(,,

,,,

−∑

≥ ∑ −→→−→→−

stutur

n

onlntur

onlnturnntstsur

nnntstsur

stuntur

L

LLL ψψ (15)

The weighting is done in order to reflect as exactly as possible the start-up-

costs during the operation. Similarly the reservoir fillings at the end of a time segment t will be deter-

mined by the probability weighted average of the filling levels at all nodes of the prior time segment t-1.

( )

pumtur

cycuturtur

nturnntstsur

nnntstsur

tur

QWQ

HH

,,,,,,

'1,,'),()1(,,

''),()1(,,

,,1

η

ψψ

++−

∑≤ ∑ −→→−

→→− (16)

This is of course only an approximate treatment of the evolvement of reser-voir fillings over the day and the year. Actually, the reservoir level will be a function of exactly the stochastic realisations which occurred in the past and not a function of probability weighted possible occurrences. Yet a precise model-ling of this effect would require the use of a non-recombining tree, leading to the aforementioned curse of dimensionality of stochastic optimisation.

3. Application

For an application of the developed stochastic fundamental electricity market model, key factors to be defined include the regional resolution, time horizon and discount rate, generation capacities and investments, electricity demand and energy policy. Obviously also the considered stochastics are important parame-

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A Stochastic Model for the European Electricity Market 117

ters of the model. They may considerably influence the modelling results and are discussed in the following subsections for a model application to EU-15 plus some Central European States (Poland, Czechia, Slovakia, Hungary).

3.1. Regional resolution

The model is flexible in as far as the regional resolution is concerned. It has been developed to account for several regions (within one country or between neighbouring countries) coupled by defined transmission capacities. In order limit the computational burden, eight regions are modelled in the current ver-sion of the model as shown in Figure 2. Thereby the key regional markets as they are currently emerging in Europe are distinguished and the transmission bottlenecks between these countries are taken into account.

Fig. 2. Regional resolution of the considered model

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Weber et al. 118

3.2. Time resolution, time horizon and discount rate

To limit the computational burden, each year considered is divided into 12 typi-cal days (every two months one typical weekday and weekend) and each day in 12 typical time segments. Moreover all modelling years are computed sepa-rately in a dynamic recursive approach with myopic expectations. Thereby a time horizon until 2020 is considered with 5 year intervals between modelling periods. For an appropriate choice of the discount rate, as needed to model in-vestments, the relevant risks have to be analyzed. These risks result in the un-certainty of the economic competitiveness of the power plant investment in the longer run. Here the discount rate is assumed to be 8 % in real terms, cf. e. g.. [17].

3.3. Generation capacities and investments

All fundamental models depend on the representation of the power plant portfo-lio of the considered system. To reduce the complexity the power plants within this paper are grouped according to the main fuel and vintage. The thermal power plant classes considered are summarised in Table 1. It may be noted that in the case study full- and part-load efficiencies are distinguished, cf. Eq. (2). Additionally may be noted that in the case study distinct availabilities for the two months time periods are assumed, with higher availabilities in the winter months than in the summer months. The lifetime of the considered thermal power plants is assumed to be 35 years and independent of any modernization efforts. The possible choices for the endogenously modelled investments are dependent on available natural resources in the case of lignite and on energy policy in the case of nuclear.

Variable generation costs are mainly determined by the fuel costs. Those depend on the fuel prices and the efficiency of the respective power plant class. The development of fuel prices over time is assumed to be independent of in-vestments in new power plants, and is given in Table 2 for Germany.

Besides regional fuel price differences are considered based on historical statistics. Table 3 shows the differences retained for the fossil fuels coal and gas. For nuclear no fuel price differences are considered, for lignite, fuel avail-ability is anyhow limited to the regions DAS and EEU.

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A Stochastic Model for the European Electricity Market 119

Tab. 1: Thermal Power Plants

Fuel Technology Vintage Total Capacity EU 15 + 4, year 2000 Investment

Coal Steam Cycle Before 1969 24.8 1970 – 1979 42.2 1980 – 1984 17.4 1985 – 1989 14.2 1990 – 1994 10.4 1995 – 2000 9.8 Since 2001 0 All regions Lignite Steam Cycle Before 1969 6.2 1970 – 1979 13.5 1980 – 1984 6.9 1985 – 1989 6.0 1990 – 1994 0.5 1995 – 2000 5.3 Since 2001 0 DAS, EEU Gas Gas Turbine Before 2000 12.1 & Gas/Oil Since 2001 0 All regions Steam Cycle All 61.4 Combined Cycle Before 2000 26.7 Since 2001 0 All regions Oil Gas Turbine All 6.3 Steam Cycle all 53.9 Nuclear Before 2000 131.9

Since 2001 0Policy depend-ent

Other Ther-mal all 8.3

Tab. 2: Fuel Prices Free Plant (€/MWh)

2000 2005 2010 2015 2020 Nuclear 6.14 6.14 6.14 6.14 6.14 Lignite 3.55 3.69 3.78 3.86 3.95 Coal 6.28 7.94 8.12 8.3 8.49 Gas (BAU-Mix) 14.54 16.69 23.73 28.15 33.15 Gas CO2-Reg) 14.54 16.69 22.19 24.27 26.4 a fuel cycle cost in €/MWhel

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Weber et al. 120

Tab. 3: Regional fuel price differences (€/MWh)

DAS BNL FRA GRI SPP EEU SCA UKI Coal 0 0.11 -0.83 0.4 -1.44 -1.04 0 -0.11 Gas 0 -4.68 0 -1.84 1.22 0 0 -4.14

Besides the thermal power plants focused on so far, hydroelectric power

plants play a considerable role in the European power system. Thereby three classes have to be distinguished: run-of-river plants, hydro storage plants and hydro storage plants with pumping facilities (pumped storage plants). In differ-ence to the thermal power plants the costs of generation do not play such a sig-nificant role for hydro power plants. The characteristics of the considered hydro power plant classes are given in Table 4.

Tab. 4: Existing Hydro Electric Power Plants

Type RR-E HS-E PH-E Fuel type (--) Water Water Water Vintage (--) -- -- -- Net capacity single plant (MW) 5 5 75 Overall capacity (MW) 2421 324 5103 Efficiency (full load) (%) 100 100 100 Availability (winter) (%) 99 70 70 Reliability (%) 100 100 100 Specific start-up costs (€/kW) 0 0 0 Other variable costs (€/MWh) 2.5 2.5 2.5 Fixed operation costs (€/kW) 69 25 25

Wind integration is assumed to be the result of governmental aid and is

hence exogenous to the model. To analyze the costs of wind integration, the scenario depicted in Figure 3 for wind power capacity is considered.

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A Stochastic Model for the European Electricity Market 121

Fig. 3. Installed Wind Capacity

3.4. Electricity demand

Electricity demand is assumed to be price inelastic and is exogenously given. The development over time can be handled by using predefined growth rates as given in Table 5.

Tab. 5: Gross Electricity Demand Provided By Public Plants (TWh)

Demand 2000 Change (%) 2010 Change (%) 2020 DAS 696 1.2 782 0.9 857 BNL 213 2.3 268 2.6 344 FRA 489 2.4 621 2.1 768 SPP 284 3.0 381 2.0 465 GRI 415 3.7 596 3.2 815 EEU 282 2.9 376 3.9 551 SCA 423 1.1 469 1.4 539 UKI 422 2.0 512 2.5 654

Electricity demand can be understood as the sum of demand of all consumer

groups. As an example, values for each typical time segment are given for

0

20

40

60

80

100

120

140

160

180

2000 2005 2010 2015 2020

offshoreonshore

[GW]

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Weber et al. 122

Germany in Figure 4. It may be noted that the electricity demand is also subject to stochastic variations. However, such effects are not taken into account. Fig. 4. Electricity Demand in Germany

3.5. Energy policy

To assess the effects of energy policies on energy system costs and the addi-tional costs of wind integration a total of four scenarios has been considered. They are summarised in Figure 5 and Table 6.

In the following only the scenarios BAU-Mix and CO2-Reg are discussed, since they provide the most contrasting view of energy system evolution and response to challenges of climate change. In the scenario BAU-Mix no further CO2-reduction requirements are assumed, which go beyond those agreed upon in the first phase of the EU-emission trading scheme. Moreover CO2-prices are bounded by above with a decreasing price limit. By contrast, in the CO2-REG scenario, CO2-emisisons are expected to decrease by 20 % between 2000 and 2020 while at the same time a nuclear phase out is established on a Europe-wide scale. Accordingly the CO2-price bound is increasing over time and reaches 70 €/t in the year 2020.

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A Stochastic Model for the European Electricity Market 123

Fig. 5. Scenarios for future energy policy development

Tab. 6: Key characteristics of energy policy scenarios

Scenario BAU-Mix BAU-Gas CO2-Reg CO2-Tech

Nuclear policy current policies continued

current policies continued

Europe-wide phase-out

No restrictions Europe-wide

CO2-targets electricity sec-tor (relative to 2000) 2005 -4% -4% -4% -4% 2020 -4% -10% -20% -20% CO2-price bound 415 3.7 596 3.2 2010 8 10 35 35 2020 2 20 70 70

3.6. Stochastics

Short term fluctuations are of considerable importance for the operation of the electricity system. Therefore in the application wind speed data have been com-bined with aggregated power curves to assess the variability of wind power. This has been done using data from ten weather stations distributed over Ger-many. The time series are used to determine clusters of days with similar wind energy production. Thereby summer, winter and intermediate days are distin-guished and for each six hour period cluster analyzes are carried out to identify a high, medium and low wind case as well as the corresponding probabilities of occurrence and transition. The cases (or nodes to remain in above’s nomencla-

TodayToday

Energy markets under strong CO2-restrictions

Energy markets under strong CO2-restrictions

Business-as-Usual on energy markets

(no or little CO2-restrictions)

Business-as-Usual on energy markets

(no or little CO2-restrictions)

Continuation of current fuel price trends

- BAU-Mix -

Continuation of current fuel price trends

- BAU-Mix -

Natural Gas available at low

cost and in large quantities

- BAU-Gas -

Natural Gas available at low

cost and in large quantities

- BAU-Gas -

Focus on renewables and

energy efficiency

- CO2-Reg -

Focus on renewables and

energy efficiency

- CO2-Reg -

Without technology restrictions

- CO2-Tech -

Without technology restrictions

- CO2-Tech -

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Weber et al. 124

ture of the stochastic modelling approach) give the capacity factor of wind en-ergy production. Multiplied with the installed wind capacity this yields the ac-tual wind generation, hence the capacity factor corresponds to the full-load hours of wind energy production. The on-shore capacity factors are given with the respective node probabilities in Figure 6. Fig. 6. Capacity factor of wind and node probability at typical time segments

Note that the capacity factor over the time horizon depends on the develop-

ment of the on- and off-shore wind installations, i.e. the higher full-load hours of wind production off-shore are considered. Full-load hours of about 1650 hrs and 2850 hrs are respectively considered for on- and off-shore wind.

Besides fluctuations in wind power production also fluctuations in hydro availability have a considerable impact on power system operation, notably for hydro dominated systems like the Scandinavian one. Hence nodes are not only distinguished according to their wind production but also according to the hydro availability. Here two cases are considered: low hydro availability, i.e. a dry year, and medium to high hydro availability. The low hydro availability is con-sidered separately, given that it imposes particular restrictions on the composi-tion of the power system. A case with 20 % less inflow than in an average year is considered here and it is assigned a probability of 20 %. For the water cases, no transition possibility is foreseen within one typical day nor even within one year. Rather they are considered as representing two distinct years. This yields a node and transition structure as depicted in Figure 7.

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A Stochastic Model for the European Electricity Market 125

Fig. 7. Node structure and transition probabilities for the case study.

4. Results

This section covers some major results of the European case study. Figure 8 gives the yearly electricity production in the two scenarios considered with both the deterministic and the stochastic model version. The electricity production increases due to the increase in demand, yet depending on the policy scenario considered, new capacities are mostly built up in coal, lignite and nuclear units (scenario BAU-Mix, Figure 8 (a)) respectively in gas fired units (scenario CO2-REG, Figure 8b)). Thus the investment decisions are strongly dependent on the energy policy scenario considered, even independently of the increase of wind energy production over time. Figure 9 shows the development of wholesale electricity prices over a time horizon until 2020 for the different regions. In the model these prices correspond to the marginal generation costs and may hence be different from the spot market prices historically observed.

day 1, hour 1

.

.

.

.

.

.

.

.

.

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

s s‘...

.

.

.

.

.

.

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

s s‘

day 1, hour 3

day 1, hour 2

day d, hour h

day d, hour h+1

.

.

.

.

.

.

.

.

.

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

s s‘...

.

.

.

.

.

.

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

s s‘

Average to high water

Low water

High wind

Low wind

.

.

.

High wind

Low wind

.

.

.

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Weber et al. 126

a) b) Fig. 8. Power production in the EU 15 + 4 for to different scenarios a) BAU-Mix, b) CO2-REG.

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A Stochastic Model for the European Electricity Market 127

a) b) Fig. 9 Wholesale baseload electricity prices in the EU 15 + 4 for two different scenarios: a) BAU-Mix, b) CO2-REG.

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Weber et al. 128

In the long-run the prices remain constant or even decrease in case of low CO2 reduction goals, cf. Figure 9 (a) and increase continuously in case of high CO2 reduction goals combined with a nuclear phase-out, cf. Figure 9 (b). These results are not substantially affected by the way of modelling of wind genera-tion. This is due to the relatively minor impact of additional wind generation on the marginal power plant in the system.

Yet the modelling affects the total system costs and thus the value attributed to wind energy. Table 8 shows the integration costs of wind energy calculated from the difference in system costs between the stochastic and the deterministic model version.

Tab. 8: Integration costs of wind energy depending on scenario and year (€/MWh)

Year BAU-Mix CO2-REG 2000 1.11 1.11 2005 0.82 0.82 2010 1.23 0.92 2015 1.87 1.18 2020 2.45 2.71

The results are rather low, this certainly partly due to the rather high share

of flexible hydro power in many of the considered regions. Also internal trans-mission bottlenecks within the regions are not considered in this analysis and thus the results have to be considered as a lower bound to the actual integration costs.

Figure 10 shows the value of the wind energy produced for the region DAS in comparison to the baseload price. The difference between the two values can be interpreted as the marginal costs of wind integration. These are substantially higher than the average costs shown in Table 6. But again there is only little difference between the two scenarios, except for the year 2020. I.e. the integra-tion of wind energy is not much facilitated or impeded by the way the remain-ing system is functioning. This is certainly due to two conflicting factors. In the BAU-Mix, investment focuses on slow medium- to base-load plants, which tends to increase the integration costs. On the other hand, the fuel and CO2 costs are low in this scenario, decreasing not only the overall price level but also the price differences between wind and base price.

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A Stochastic Model for the European Electricity Market 129

a) b) Fig. 10. Wholesale baseload electricity prices and value of wind energy in the DAS region for two different scenarios: a) BAU-Mix, b) CO2-REG.

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Weber et al. 130

5. Conclusions

This paper provides an electricity market model which combines a detailed modelling of short term fluctuations with an endogenous treatment of power plant investments. Thereby the stochastics of intermittent wind generation are incorporated by a recombining tree. It can be notably used to estimate the inte-gration costs for wind in an adapting system. The applicability of the proposed approach is shown with a European case study on large-scale wind integration. The results presented indicate that the value of wind is generally overestimated applying a static, deterministic model. The results highlight that next to the ex-plicit consideration of stochastics a model applied to assess the additional costs of intermittent wind integration should be able to endogenously adapt to an in-creasing share of intermittent generation, i.e. endogenous investment decisions and endogenous reserve requirements need to be accounted for. The developed approach lends itself to multiple further developments. Especially the rules for deriving optimal investments may be developed further, contributing to getting even more realistic pictures of the market developments.

Acknowledgement

This paper presents preliminary results of ongoing research financially sup-ported by the European Commission within the project GreenNet-EU27 (EIE/04/049/S07.38561).

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[17] Weber, C., Uncertainty in the Electric Power Industry: Methods and Models for Decision Support. New York et al. 2005.

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133

OPERATIONAL COSTS INDUCED BY FLUCTUATING WIND

POWER PRODUCTION IN GERMANY AND SCANDINAVIA

PETER MEIBOM* System Analysis Department Risoe National Laboratory, Denmark CHRISTOPH WEBER Chair of Energy Management, University Duisburg-Essen, Germany

RÜDIGER BARTH HEIKE BRAND Institute of Energy Economics and the Rational Use of Energy University of Stuttgart, Germany

Abstract. Adding wind power generation in a power system changes the opera-tional patterns of the existing units due to the variability and unpredictability of wind power production. For large amounts of wind power production the ex-pectation is that the operational costs of the other power plants will increase due to more operation time in part-load and more start-ups. The change in opera-tional costs induced by the wind power production can only be calculated by comparing the operational costs in two power system configurations: with wind power production and with alternative production having properties like con-ventional production, i.e. being predictable and less variable. The choice of the characteristics of the alternative production is not straight forward and will therefore influence the operational costs induced by wind power production. This paper presents a method for calculating the change in operational costs due to wind power production using a stochastic optimization model covering the power systems in Germany and the Nordic countries. Two cases of alternative production are used to calculate the change in operational costs namely per-fectly predictable wind power production enabling calculation of the costs con-nected to unpredictability, and constant wind power production enabling calcu-lation of the operational costs connected to variability of wind power produc-

______ * To whom correspondence should be addressed. Email: [email protected]

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Meibom et al. 134

tion. A 2010 case with three different wind power production penetration levels is analysed in the paper.

Keywords: Wind power integration, stochastic optimization, power market model, in-tegration costs

1. Introduction

Due to global warming and increased competition for the usage of fossil fuel resources especially oil and natural gas, alternatives to electricity production based on fossil fuels have to be introduced in large scale in future power sys-tems. Hydropower is an excellent electricity producing technology in terms of operational characteristics, but large-scale hydropower resources in Europe are to a large extent already developed. After hydropower, wind turbines and ther-mal power production based on biomass are presently the most mature and cost effective kind of electricity producing technologies based on renewable energy sources. Therefore a significant growth of installed wind power capacity in Germany, Spain and Denmark has taken place the last couple of years (BTM consult, 2005).

Wind power production is fluctuating i.e. it varies a lot and is only partly predictable. Large scale introduction of wind turbines in a power system will therefore influence the day to day operation of the power system and the future development of the portfolio of power plants and transmission lines in the power system. On the operational side the variability and unpredictability of wind power production will on average cause the other power producing units to change production levels more frequently and with shorter notice, which im-plies more part-load operation and/or more frequent start-ups.

On the investment side increased wind power production will often lead to an increased need for transmission capacity from locations with good wind re-sources to load centres (DENA, 2005). Furthermore wind power production decreases power prices on the day-ahead power markets (e.g. Elspot market on Nord Pool) in that wind power production is bid to the market with very low short-term marginal costs, and it increases the prices for regulating power due to a larger demand for regulating power caused by the wind power production prediction errors (Meibom et al, 2006a). These changes in power price levels will in the long term cause a shift in the selection of future optimal power plant investments, such that relatively to a situation without introduction of wind power, there will be less future investment in base-load plants characterised by high efficiency and high investment cost and more future investments in peak-

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Operational Costs Induced by Fluctuating Wind Power Production 135

load or balancing power plants with lower efficiency, higher operational flexi-bility and lower investment costs.

These changes in the operation and the development in the power system will to some extent decrease the value of wind power expansion for society. The increase in operation and investment costs due to the expansion of wind power, evaluated relatively to some kind of reference case with the wind power production being replaced with more conventional power production are often summarised under the general term of “integration costs”.

Grubb (1991) provides a detailed discussion and quantitative estimates of the additional costs induced by the installation of fluctuating renewables. In the context of optimal policy design, Elsässer (2002) and Fuchs (2003) give results on the costs of increased part-load operation, start-ups and backup costs for wind energy, without much detail however on the calculation methodology. ILEX (2002) discusses the additional costs related to the integration of large amounts of renewables in the British electricity system, following closely the approach developed by Grubb (1991). In the various presentations given at IEA (2004), different approaches to the quantification of integration costs and also corresponding numerical values are given. Auer et al. (2004) provide an over-view of relevant cost components and discuss cost estimates taken from studies in various European countries. Swider and Weber (2004) derive the value of wind energy from an electricity system model, which includes explicitly the stochasticity of wind as well of hydro sources. They tend to define as integra-tion cost the entire difference between the marginal value of wind energy pro-duction and the average system price. Brand et al. (2005) use a stochastic sys-tem operation model to compute two different values for the integration costs – including the impacts of more frequent part-load operation, increased number of start-ups and higher reserves.

These various contributions are characterized as much by a broad variety of numerical results given as by a challenging diversity of methods used. Söder (2005) and Weber (2006) provide an overview of key differences between ap-proaches and their implications.

The objective of this paper is to provide a detailed assessment of the integra-tion cost using the stochastic system model WILMAR Planning Tool, which has been developed to analyse issues of wind power integration in the Nordic countries and Germany. Correspondingly the paper is organised as follows. Section 2 provides an overview of the WILMAR Planning tool and the way wind power fluctuations are dealt within this model. Section 3 then discuss how integration costs of wind power can be assessed in this framework. Section 4 and 5 describe an application of this methodology for the power systems in Germany and the Nordic countries. Section 4 presents the cases analysed and section 5 presents the results. Finally section 6 concludes.

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Meibom et al. 136

2. The Model

A Planning tool enabling model based analysis of wind power integration issues has been developed in the Wilmar project (www.wilmar.risoe.dk). An overview of the sub-models and databases constituting the Planning tool is given in Figure 1.

Fig. 1. Overview of Wilmar Planning tool. The green cylinders are databases, the red parallelo-grams indicate exchange of information between sub models or databases, the blue squares are models. The user shell controlling the execution of the Wilmar Planning tool is shown in black.

The Joint Market model is a linear, stochastic, optimisation model with

wind power production forecasts as the stochastic input parameter, hourly time-resolution and covering several regions interconnected with transmission lines. It has been tested on German and Nordic data. The Joint Market model is documented in detail in (Meibom et al, 2006b; Brand et al, 2004). A model generating scenario trees representing wind power production forecasts has been developed (Barth et al, 2006). Treatment of large hydropower reservoirs requires optimisation of the use of water over a yearly or longer time horizon. Therefore the Joint Market model is combined with another stochastic, optimi-sation model that focus on calculating the option value of stored water depend-ent on the time of year and reservoir filling (Ravn, 2006).

In order to analyse adequately the market impacts of wind power it is essen-tial to model explicitly the stochastic behaviour of wind generation and to take the forecast errors into account. In an ideal, efficient market setting, all power

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Operational Costs Induced by Fluctuating Wind Power Production 137

plant operators will take into account the prediction uncertainty when deciding on the unit commitment and dispatch. This will lead to changes in the power plant operation compared to an operation scheduling based on deterministic expectations, since the cost functions for power production are usually non-linear and not separable in time. E.g. even without fluctuating wind power, start-up costs and reduced part-load efficiency lead to a trade-off for power plant operation in low demand situations, i.e. notably during the night. Either the power plant operator chooses to shut down some power plants during the night to save fuel costs while operating the remaining plants at full output and hence optimal efficiency. Or he operates a larger number of power plants at part load in order to avoid start-up costs in the next morning. This trade-off is modi-fied if the next increase in demand is not known with (almost) certainty. So in an ideal world, where information is gathered and processed at no cost, power plant operators will anticipate possible future wind developments and adjust their power plant operation accordingly. The Joint Market model describes such an ideal and efficient market operation by using a stochastic linear program-ming model, which depicts ‘real world optimization’ on the power market on an hourly basis with rolling planning. With efficient markets, i.e. also without mar-ket power, the market results will correspond to the outcomes of a system-wide optimization as described in the following. The cost and price effects derived for the integration of wind energy in this model should then provide a lower bound to the magnitude of these effects in the real, imperfect world.

In a liberalized market environment it is possible not only to change the unit commitment and dispatch, but even to trade electricity at different markets. The Joint Market model analyses power markets based on an hourly description of generation, transmission and demand, combining the technical and economical aspects, and it derives hourly electricity market prices from marginal system operation costs. This is done on the basis of an optimisation of the unit com-mitment and dispatch taking into account the trading activities of the different actors on the considered energy markets. In this model four electricity markets and one market for heat are included: 1. A day-ahead market for physical delivery of electricity where the Nord Pool

spot market is taken as the starting point. This market is cleared at 12 o’clock for the following day and is called the day-ahead market. The nomi-nal electricity demand is given exogenously.

2. An intra-day market for handling deviations between expected production agreed upon the day-ahead market and the realized values of production in the actual operation hour. Regulating power can be traded up to one hour before delivery. In the present version of the Joint Market model the de-

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Meibom et al. 138

mand for regulating power is only caused by the forecast errors connected to the wind power production.

3. A day-ahead market for automatically activated reserve power (frequency activated or load-flow activated). The demand for these ancillary services is determined exogenously to the model.

4. An intra-day market for positive secondary reserve power (minute reserve) mainly to meet the N-1 criterion and to cover the most extreme wind power forecast scenarios that are neglected by the scenario reduction process. Hence, the demand for this market is given exogenously to the model.

5. Due to the interactions of CHP plants with the day-ahead and the intra-day market, intra-day markets for district heating and process heat are also in-cluded in the model. Thereby the heat demand is given exogenously.

2.1. Objective Function and Restrictions

The objective function in the Joint Market model minimises the operation costs in the whole system, as we have assumed fixed electricity demands for this study. It considers the operation and start-up costs of condensing and CHP plants and the operation costs of heat boilers. Power production costs of hydro reservoir plants are modelled through water values, which are calculated with the help of the long-term model (Ravn, 2006)..

The model is defined as a stochastic linear programming model (Birge and Louveaux, 2000), (Kall and Wallace, 1994). The stochastic part is presented by a scenario tree for possible wind power generation forecasts for the individual hours. The technical consequences of the consideration of the stochastic behav-iour of the wind power generation is the partitioning of the decision variables for power output, for the transmitted power and for the loading of electricity and heat storages: one part describes the different quantities at the day-ahead market (thus they are fixed and do not vary for different scenarios). The other part describes contributions at the intra-day-market both for up- and down-regulation. The latter consequently depends on the scenarios. So for the power output of the unit group i at time t in scenario s we find

−+ −+= tsitsiAHEADDAY

titsi PPPP ,,,,_

,,, . The variable AHEAD_DAYt,iP denotes the energy sold

at the day-ahead market that has to be fixed the day before. +tsiP ,, and −

tsiP ,, de-note the positive and negative contributions to the intra-day market. The deci-sion variables for the transmitted power and the loading of electricity and heat storages are defined accordingly.

Further the model is defined as a multi-regional model. Each country is sub-divided into different regions, and the regions are further sub-divided into dif-ferent areas. Thus, regional concentrations of installed wind power capacity,

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Operational Costs Induced by Fluctuating Wind Power Production 139

regions with comparable low demand and occurring bottlenecks between the model regions can be considered. The subdivision into areas allows separate district heating grids within regions.

The capacity restrictions for electricity producing units are defined for maximum and minimum electric power output. As the model is defined as a multi-regional model, capacity restrictions of transmission lines have to be met as well. Transmission loss is considered to be proportional to the amount of electricity transmitted.

Start-up costs may considerably influence unit commitment decisions of plant operators. In order to avoid that units are always kept online, one has to account for the fact that the efficiency at part load is usually lower than at full load. In typical unit commitment models, the restrictions for start-up costs, re-duced part-load efficiency and start-up times include integer variables. How-ever, this is hardly feasible for a model representing several countries. There-fore an approximation due to Weber (2004) modelling the restrictions in a lin-ear way by introducing an additional decision variable “Capacity online” has been used.

The flexibility of the unit dispatch is restricted by the use of lead times that describe the start-up times of conventional power plants. Hence, the model is constrained to make decisions whether to bring additional conventional capacity online before the precise wind power production is known.

Dispatch of heat generating units like CHP plants and heat boilers at the lo-cal heat markets is optimised as well. In order to represent individual district heating grids, the model regions are accordingly subdivided into heating areas. CHP plants are distinguished between extraction-condensing units and back-pressure units. The PQ-charts (electric power versus thermal power charts) show the possible operation modes of the CHP plants representing the possible combinations of electric power and thermal power produced. These technical restrictions require additional equations.

2.2. Rolling Planning

It is not possible and reasonable to cover the whole simulated time period of for instance two weeks with only one single scenario tree. Therefore the model uses the multi-stage recursion approach with rolling planning (Buchanan et al, 2001). In stochastic multi-stage recourse models, there exist two types of deci-sions: decisions that have to be taken immediately and decisions that can be postponed. The first kind of decisions is called “root decisions”, as they have to be decided “here and now” and before the uncertain future is known. The sec-ond kind of decisions taken after some of the uncertain parameters are known is called “recourse decisions”. These “recourse decisions” can start actions which

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Meibom et al. 140

might possibly revise the first decisions. In the case of a power system with wind power, the power generators have to decide on the amount of electricity they want to sell at the day-ahead market before the precise wind power produc-tion is known (root decision). In most European countries this decision has to be taken at least 12-36 hours before the delivery period. And as the wind power prediction is not very accurate, recourse actions are necessary in most cases when the delivery period is in the near future and the wind power forecast be-comes more and more accurate (recourse decisions).

In general, new information arrives on a continuous basis and provides up-dated information about wind power production and forecasts, the operational status of other production and storage units, the operational status of the trans-mission grid, heat and electricity demand and updated information about day-ahead and regulating power market prices. Hence, an hourly basis for updating information would be most adequate. However, stochastic optimisation models quickly become intractable, since the total number of scenarios has a double exponential dependency in the sense that a model with k+1 stages, m stochastic parameters, and n scenarios for each parameter (at each stage) leads to a sce-nario tree with a total of kmns = scenarios (assuming that scenario reduction techniques are not applied). It is therefore necessary to simplify the information arrival and decision structure in a stochastic model. Hence, the model steps forward in time using rolling planning with a 3 hour step holding the individual hours. This decision structure is illustrated in Figure 2 showing the scenario tree for four planning periods covering half a day. For each planning period a three-stage, stochastic optimisation problem is solved having a deterministic first stage covering 3 hours, a stochastic second stage with five scenarios covering 3 hours, and a stochastic third stage with 10 scenarios covering a variable number of hours according to the rolling planning period in question (in this way the determination of the shadow values is eased). In the planning period 1 the amount of power sold or bought from the day-ahead market is determined. In the subsequent replanning periods the variables standing for the amounts of power sold or bought on the day-ahead market are fixed to the values found in planning period 1, such that the obligations on the day-ahead market are taken into account when the optimisation of the intra-day trading takes place.

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Operational Costs Induced by Fluctuating Wind Power Production 141

12 15 18 21 00 03 00

Rolling planning period 1

Rolling planning period 2

Rolling planning period 3

Rolling planning period 4

Stage 1 Stage 2 Stage 3

12 15 18 21 00 03 00

Rolling planning period 1

Rolling planning period 2

Rolling planning period 3

Rolling planning period 4

Stage 1 Stage 2 Stage 3

12 15 18 21 00 03 0012 15 18 21 00 03 0012 15 18 21 00 03 00

Rolling planning period 1

Rolling planning period 2

Rolling planning period 3

Rolling planning period 4

Stage 1 Stage 2 Stage 3

Fig. 2. Illustration of the rolling planning and the decision structure in each planning period within half a day.

2.3. Scenario creation and scenario reduction

The inclusion of the uncertainty about the future wind power production in the optimisation model is considered by using a scenario tree. The scenario tree represents wind power production forecasts with different forecast horizons cor-responding to each step in the optimisation period. For a given forecast horizon the scenarios of wind power production forecasts in the scenario tree is repre-

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Meibom et al. 142

sented as a number of wind power production outcomes with associated prob-abilities, i.e. as a discrete distribution of future wind power production levels. The construction of this scenario tree is carried out in two steps: 1. Modelling of the wind speed forecast error and the simulation of the distrib-

uted wind power forecast scenarios, whose first values of the root node are identical.

2. Reduction of the wind power forecast scenarios to the scenario tree with three stages. In the following these steps are described in more detail.

2.3.1. Modelling the wind power forecast data process

The generation of wind power forecast scenarios is based on time-series of measured wind speed and of historical forecast errors of wind speed predic-tions. The increasing trend of the wind speed forecast error with rising forecast horizon is reproduced using multidimensional Auto Regressive Moving Aver-age (ARMA) time-series:

1)(kZβ(k)Z1)(kXα(k)X WFWFWFWFWFWF −++−= (1)

where XWF(k) is the wind speed error and ZWF(k) is the random variable with given standard deviation in the forecast hour k for the wind power farm WF (XWF(0) = 0 and ZWF(0) = 0, given αWF and βWF). The random variables ZWF(k) are normally distributed and created by Monte Carlo simulations result-ing in a predefined large number of scenarios of the wind speed forecast error. Thereby the correlation between the forecast errors at spatial distributed wind power farms is considered following the approach of (Söder, 2004). For exam-ple, data analysis from Sweden (Figure 3) shows that the closer the stations, the higher are the correlations between forecast errors and that the correlation be-tween different stations increases with forecast lengths.

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Operational Costs Induced by Fluctuating Wind Power Production 143

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0 5 10 15 20 25 30

Wind speed (m/s)

Pow

er (p

er u

nit)

(kW

/m2)

Single Multiple

In order to derive the wind power forecast from the wind speed forecast for

each region, technological aspects of the wind power stations located in the considered region are needed. Additionally, their spatial distribution within each region has to be taken into account. This yields an aggregation of the power generation in each region by smoothing the power curves (Figure 4).

Fig. 4. A standard normalised power curve (‘Single’) and the corresponding smoothed power curve (‘Multiple’). Source: (Norgard et al., 2004).

+ Maglarp – Bösarp

(15 km) O Maglarp – Sturup

(26 km) + Näsudden – Ringhals

(370 km)

Fig. 3. Correlation between forecast errors for different pairs of stations (Söder, 2004).

0 5 10 15 20 25 300

0.2

0.4

0.6

0.8

1

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Meibom et al. 144

2.3.2. Scenario reduction

In order to keep computation times small for models representing a trans-national market with a huge number of generating units, only significantly less scenarios than the scenarios created before by the Monte Carlo simulations can be used. Simply generating a very small number of scenarios by Monte Carlo simulations is not wanted since less scenarios cannot represent the distribution of wind speed forecast errors adequately. Hence, the aim is to loose only a minimum of information by the reduction process applied to the whole set of scenarios. As the current version of the scenario reduction algorithm reduces the standard deviation of the original generated scenarios, the most extreme wind power forecast scenarios have to be considered by the secondary reserve power market.

Fig. 5. Example for the backward scenario reduction heuristic. Source: modified figure from (Gröwe-Kuska et al., 2001)

Two steps are necessary for the scenario reduction: first, the pure number of

scenarios has to be reduced. Afterwards, based on the remaining scenarios that still form a one-stage tree, a multi-stage scenario tree is constructed by deleting inner nodes and creating branching within the scenario tree. Therefore a step-wise backward scenario reduction algorithm based on the approach of (Dupacova et al., 2003) is used: the original scenario tree is modified through bundling similar scenarios or part of scenarios. Bundling two scenarios or parts

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Operational Costs Induced by Fluctuating Wind Power Production 145

of scenarios means deleting the one (or the part of the scenario) with the lower probability and adding its probabilities to the remaining one (Figure 5). As a measure for the similarity of different scenarios, the Kantorovich distance be-tween two scenarios is used.

The scenario creation and reduction is carried out with different modules that are implemented in Matlab® to the so called Scenario Tree Tool. The Sce-nario Tree Tool is documented in (Barth et al., 2006).

3. Calculation of integration costs of wind power

The general term of integration costs is coined to designate additional costs of integrating something new into a pre-existent system. In the context relevant here, the pre-existent system is a power system, which consists basically of generators, transmission lines and consumers, distributed over a certain geo-graphical area. The new things are novel generation technologies, based on other than conventional energy transformation processes. In principle integra-tion costs could also be calculated for non-renewable technologies, be them novel or conventional (cf. also Söder 2004) – yet this is not the object of this paper.

3.1. General Approach

For a precise definition of integration costs, it is essential to distinguish them from additional system costs caused by the imposition of a certain amount of renewables generation (cf. Weber 2006). Integration costs are commonly under-stood as the difference between some expected cost savings through renewables and the actual ones. Yet this not operational as long as the cost savings “which would be expected” are not precisely defined.

Along the lines taken by Weber (2006) we therefore define integration costs as the difference in the cost savings induced by the renewables in the conven-tional system compared to the cost savings through some alternative (new) gen-eration. Thereby for both technologies, investment costs are disregarded (or assumed to be of same height).

This can be written formally:

*,

*Re, AltAddnAddInt CCC −= (2)

Thereby C*Add,Ren designates the optimal system costs for the system includ-

ing wind power (or generally renewables). Analogously C*Add,Alt refers to the

optimal costs for the system including the alternative generation technology instead. Here reference is made to an optimal system, because the system has in

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Meibom et al. 146

general possibilities to adapt to new requirements (c.f. Weber 2006). E.g. with the introduction of wind energy, gas turbines may be used more frequently to compensate for fluctuations in wind. In the context of WILMAR, only adapta-tions in the operation of the generation technologies are considered here.* Ad-aptation of the remaining generation park, e.g. through increased investment in flexible gas-fired technologies is not considered here.

Obviously the integration costs are in this setting always dependent on the definition of a hypothetical technology alternative and will depend on the choice of the reference technology.

Put in another way:

*,

*Re, AltAddIntnAdd CCC += (3)

The additional system costs resulting from imposing a renewables target can be decomposed in the so-called integration costs and the additional costs when targeting the same objective with an alternative technology.

Among the integration costs, different categories can be distinguished (cf. Auer 2005, Weber 2006). Notably grid connection and grid extension cost arise as a consequence of the uneven spatial distribution of wind power production (cf. also DENA 2005). Yet these shall not be considered in detail in the follow-ing. Rather the focus is on the costs related to the fact that wind power, simi-larly to solar energy, is fluctuating by nature. These fluctuations cause addi-tional costs for increased reserves, higher shares of part-load operations etc. Correspondingly the integration costs may be derived by comparing wind power integration to the integration of a (hypothetical) technology, which pro-vides the same energy output but at a constant rate over all the year.

For further insights, two categories of integration costs may be distin-guished: • Costs of unpredictability (or partial predictability)

These are the additional costs occurring when comparing the system with wind to one with a hypothetical technology having same, time-varying out-put but perfect predictability. These costs, taken with the opposite sign, cor-respond to the value of perfect information, commonly referred to in the stochastic programming literature (e.g. Birge, Louveaux 1997). Formally they may be written

*

,*

, PredAddRenAddUnpred CCC −= (4)

______ * Price-flexible demand is foreseen in the WILMAR model, but is not used in this application.

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Operational Costs Induced by Fluctuating Wind Power Production 147

Thereby the costs C*Add,Pred are the costs associated with a system with time-

varying wind input but without uncertainty about the future wind input. • Costs of variability

These are then the costs associated with the fact that wind power generation is varying over time and that this will require increased use of expensive generation technologies to compensate for wind drops etc, even if wind generation were perfectly predictable. It is thus computed by comparing the costs of the system with the predictable wind power with the costs of the system with a hypothetical technology delivering the same energy output at a perfectly constant rate:

*

,*

, ConstAddPredAddVariab CCC −= (5)

C*Add,Const are here the optimal costs associated with time-varying wind input

but without uncertainty about the future wind input. Overall we get for the integration costs:

*

,*

Re, ConstAddnAddIntVariabInt CCCCC −=+= (6)

For computing the integration costs and its components it is hence necessary to make three model runs: 1. a model run with stochastic wind power feed-in and corresponding uncer-

tainty, delivering C*Add,Ren

2. a model run with deterministic but time-varying wind power feed-in, deliv-ering C*

Add,Pred 3. a model run with constant equivalent power feed-in, delivering C*

Add,Const If wind power is the only source of uncertainty in the model, the second and

third model run are deterministic ones, limiting consequently considerably the computational burden.

3.2. Calculating Integration costs by region

Besides computing wind power integration costs for the overall system, also a decomposition by region is of interest – especially in order to analyse whether and to what extent the integration cost depend on regional specificities – e.g. the share of hydro power.

The difficulty is that the overall system costs are not the sum of independent system costs for the different regions. Rather the regions are interconnected through interconnection capacities and the system costs occurring in one region depend on the power flows to neighbouring regions. When doing the model

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Meibom et al. 148

runs for computing integration costs, these power flows may be dependent on the type of model run carried out. If no correction for changing interregional flows is done, integration costs may rapidly become negative in regions which are increasing their net imports in the stochastic modeling compared to the de-terministic versions.

In order to avoid such difficulties an approximative approach is taken, which is illustrated in the following for the most simple setup: two regions (r and r’) connected with one transmission line.

i: model run index, i∈(Ren,Pred,Const) r,r’: region index t: hour index pi(r,t): price on the intraday-market in region r and hour t. xi(r,r’,t): export of power from region r to region r’ in hour t. The intraday-market power price in region r in hour t is equal to the variable

production costs on the marginal power plant in the region (or in the case of price flexible demand, either the marginal production costs or the willingness-to-pay of the marginal consumer). A lower bound on the saved operational costs due to net import in a region is the intraday-power price times the net import in MWh, because the import replaces power production within the region having marginal production costs that are higher or equal to the intraday-market price. Likewise an upper bound on the increase in operational costs due to net export in a region is the intraday-market price times the net export, because the net export is produced on power plants with marginal production costs lower or equal to the intraday-market price.

When comparing two cases it is important to clarify, that it is only the change in power flow from one case to the other that is to be taken into account. E.g. if in two cases the import into region r in hour t is 6000 MW, no correction of the operational costs of the region should be made although the intraday price can be different between the two cases. The reason is twofold: • As the import is the same in the two cases, the difference in operational

costs between the two cases already reflects the integration costs of wind power for a region with a specific transmission capacity available.

• Intraday prices are marginal values, i.e. in theory they only apply for very small changes from the present situation. Therefore we should only use them on the difference in transmission between two cases. When the net export from region r is higher in case i1 than in case i2, the op-

erational costs in case i1 have to be decreased by the increase in net export from case i1 to case i2 valued at the average of the intraday-power price in the two

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Operational Costs Induced by Fluctuating Wind Power Production 149

cases (corresponding to the average of the marginal production costs in the two cases). The use of the average of the power price in the two cases has the ad-vantage that the correction provides the same results (with opposite sign) if case i1 is subtracted from i2 than if i2 is subtracted from i1.

Likewise when the net import into region r is higher in case i1 than in case i2, the operational costs in case i1 should be increased with the increase in net import from case i1 to case i2 times the average of the intraday-power price in the two cases.

The correction to the operational costs in each region can be summarized as follows: • Net exports are higher in case i1 than in case i2, i.e.

xi1(r,r’,t)- xi1(r’,r,t)> xi2(r,r’,t)- xi2(r’,r,t) ⇒ Operational costs of region r in case i1 are decreased by: ½* (pi1(r,t)+pi2(r,t))*(xi1(r,r’,t)- xi1(r’,r,t)-( xi2(r,r’,t)- xi2r’,r,t)))

• Net imports are higher in case i1 than in case i2, i.e. xi1(r’,r,t)- xi1(r,r’,t)> xi2(r’,r,t)- xi2(r,r’,t) ⇒ Operational costs of region r in case i1 are increased by: ½* (pi1(r,t)+pi2(r,t))*( xi1(r’,r,t)- xi1(r,r’,t)-( xi2(r’,r,t)- xi2(r,,r’,t))) The approach is easily generalised to a region with transmission lines to

several surrounding regions by summing over r’ in the expressions above. In this study the approach is used to separate integration costs between countries. Therefore only changes in transmission between regions belonging to different countries are corrected for.

4. Case descriptions

The power system configuration taken as basis here is a projection of the pre-sent power system configuration in Germany and in the Nordic countries to 2010 by introducing investments in power plants and transmission lines that are already decided today and scheduled to be online in 2010, and by removing power plants that have been announced to be decommissioned before 2010.

The 2010 system also includes planned transmission lines between Eastern and Western Denmark (Storebælt), Finland and Sweden (Fennoskan2) and North East and North West of Germany. Power plant investments are mainly gas in Germany and Norway, nuclear and wood in Finland, upgrade of existing nuclear power plants in Sweden, and very little investment in Denmark.

This base scenario for the development of the power system until 2010 is supplemented with three scenarios for the development in installed wind power capacity in 2010:

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Meibom et al. 150

4. Base: For all countries a “most likely” forecast of wind power capacities in 2010 is used based on estimations by the authors and estimations in (DENA, 2005; BTM consult 2005).

5. 10%: For Denmark and Germany: Forecasted wind power capacities for 2015 (equal to cover approximately 29 % and ca. 11 % of the annual elec-tricity demand, respectively). For Finland, Norway and Sweden: Wind power capacities equal to cover 10 % of the annual electricity demand.

6. 20%: For Denmark and Germany: Same development as the 10% wind case. For Finland, Norway and Sweden: Wind power capacities equal to cover 20 % of the annual electricity demand. The Base wind case expresses a reasonable growth in installed wind power

capacity until 2010, where as the 10% and 20% wind cases represent unrealistic strong growth rates of installed wind power capacity in Norway, Sweden, and Finland in the period 2005-2010, and a high growth scenario but still more plausible amount of wind power in Denmark and Germany. Although not plau-sible developments within this short time period, the 10% and 20% wind cases are interesting when studying the change in operational costs due to large-scale wind power integration. Figure 6 shows the installed wind power capacity per region in each of the wind power capacity development scenarios. The wind profiles used are based on 2001 wind power production and wind speed data.

Fig. 6. Installed wind power capacity in each region in the three wind power capacity develop-ment scenarios.

CO2 allowance price is set to be 17 €/MWh. The fossil fuel price scenario

implies a continuation of the present high price levels with fuel oil, natural gas

02000400060008000

100001200014000160001800020000

DE_CS

DE_NE

DE_NW

DK_EDK_W FI_R

NO_MNO_N

NO_SSE_M

SE_NSE_S

Cap

acity

[MW

]

Base 10% 20%

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Operational Costs Induced by Fluctuating Wind Power Production 151

and coal prices being respectively 6.16, 6.16 and 2.25 Euro2002/GJ. All coun-tries share the same fuel prices. The assumptions behind the base power system scenario in 2010 are documented in (Meibom et al 2006 c).

The operational integration costs of wind power production disregarding in-vestments are analysed using the three wind power case mentioned above, but running the Wilmar Planning tool for five selected weeks. These five weeks are selected using a scenario reduction technique with the hourly wind power pro-duction, electricity demand and heat demand taken as input parameters, because these input parameters are judged as the most important for the variation in wind power integration costs between weeks. The selected weeks are supposed to be the best representative weeks of a year with regard to the variation in these input parameters. It is necessary to use selected weeks due to the long calcula-tion times associated with stochastic optimization.

As discussed in section 3, the integration costs are divided into two groups: 1. System operation costs due to forecast errors, which are analysed by com-

paring the system operations costs in the stochastic simulation with the sys-tem costs in a Wilmar Planning tool simulation with perfect foresight, i.e. perfectly predictable wind power production.

2. System operation costs due to variability, which are analysed by comparing the system operations costs in the perfect foresight simulation with the sys-tem costs in a Wilmar Planning tool simulation with constant wind power production within each week.

5. Results

Figure 7 shows the results for the three wind power cases and aggregated over all countries. The results are not entirely comparable between the cases due to the uncertainty introduced by only using five selected weeks. The main conclu-sion is that wind power integration costs are increasing with increasing share of wind power production capacity in the power systems as expected. The base wind case has very low costs associated with partial predictability and negative costs associated with variability. The negative costs express that in the base case, the wind power variations are positively correlated with the electricity demand. The results for wind case 10% and 20% show that the costs of being variable is larger than the costs connected to being partially unpredictable. So the time periods with low loads and large amounts of wind power production generate more costs than the balancing costs due to forecast errors. One reason for this is that the regulating hydropower production has very low balancing costs, and that the modeled balancing market is extremely efficient (in effect the

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Meibom et al. 152

perfect balancing market). In reality balancing costs would be higher due to transaction costs and in some cases market power.

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Base 10% 20%

Eur

o/M

Wh

Win

d

Costs partial predictability Costs variability

Fig. 7. Increase in system operation costs per MWh wind power production when comparing system cost in a model run with constant weekly average wind power production with a perfect foresight model run (Costs variability), and when comparing system costs in a stochastic model run with a perfect foresight run (Costs partial predictability).

Figure 8 shows the wind power integration costs (sum of costs due to partial

predictability and costs due to variability) divided on countries for each of the three wind cases. The division on countries has been done by making correc-tions to the system operation costs when the net export between two countries changed between model runs as explained in section 3.2. Obviously wind inte-gration costs are highest in the thermally dominated German system, whereas they are lowest in the hydro dominated Norwegian system.

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Operational Costs Induced by Fluctuating Wind Power Production 153

-1

-0.5

0

0.5

1

1.5

2

2.5

3

Germany Denmark Finland Norway Sweden

Eur

o/M

Wh

Win

d

Base 10% 20%

Fig. 8. Increase in system operation costs per MWh wind power production for the three wind cases and divided on countries.

Inspired by an approach suggested by Lennart Söder, the ratio between av-

erage wind power production and the sum of transmission capacity to other model countries and the average power demand has been determined, as shown in Table 1. This so-called wind power impact ratio is interpreted as an indicator of how much wind power production is present in each country, because wind power production has to be either consumed domestically or exported to other countries in the model.

Tab. 1. The ratio between the average wind power production in each wind case and the sum of the transmission capacity to other countries included in the model and the average power demand.

Country Transmission ca-pacity to other model regions [MW]

Base 10% 20%

Denmark 5050 0.12 0.11 0.09 Finland 2300 0.01 0.11 0.21 Germany 1720 0.08 0.09 0.09 Norway 4220 0.02 0.09 0.15 Sweden 8110 0.01 0.06 0.11

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Meibom et al. 154

Combining the information in Figure 8 and Table 1 the following observa-tions can be drawn: 1. The wind power integration costs are lower in hydro dominated countries

(especially Norway) compared to thermal production dominated countries (Germany, Denmark). The reason is that hydropower production has very low part-load operation and start-up costs and that hydro-dominated systems are generally not constrained in regulating capacity.

2. The wind power integration costs increases when a neighboring country gets more wind power. Germany and Denmark have the same amount of in-stalled wind power capacity in wind case 10% and 20%, but because the ex-port possibilities become less attractive, due to the increased amounts of wind power capacity in Finland, Norway and Sweden, the integration costs of Germany and Denmark increase from wind case 10% to 20%.

3. Germany has the highest integration costs although their ratio in Table 1 is among the lowest. The reason is that the wind power capacity is very un-evenly distributed within Germany with the model region North-western Germany having a wind impact ration of 0.31 in wind case 10% and 20% (not shown in Table 1).

4. Denmark has the highest share of wind power among the countries, but also excellent transmission possibilities to neighboring countries compared with e.g. Finland. Therefore the wind power integration costs of Denmark are lower than those of Finland in wind case 20%.

6. Conclusions

This paper discuss the issues related to the calculation of wind power integra-tion costs and pinpoint that wind power integration costs always depend on the choice of a reference case to which the system costs with wind power are com-pared. The choice of the characteristics of the reference case is not straight for-ward. A methodology for calculation of integration costs by comparison of three different model runs: with stochastic wind power, with perfectly predict-able wind power, and with constant wind power production has been proposed. The method distinguishes between integration costs related to partial predict-ability and to variability.

A linear, stochastic optimisation model covering the Nordic countries and Germany has been presented. The model is able to quantify the integration costs related to variability and to partial predictability. The latter is only possible in models treating wind power production as a stochastic input parameter. Only operational integration costs can be calculated with the model, i.e. integration

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Operational Costs Induced by Fluctuating Wind Power Production 155

costs related to grid extensions and changes in a future power generation portfo-lio are not included in the study.

A base scenario for the power system configuration in 2010 in Germany and the Nordic countries has been supplemented by three wind power capacity cases, and country-wise wind power integration costs have been calculated for each case. Results confirm expectations, i.e. integration costs are lower in hydro dominated systems compared to thermally dominated, and integration costs are higher in power systems having a relatively larger ratio between wind power production and the sum of average power demand and transmission capacity to neighboring regions. Interestingly integration costs increase in countries with constant wind power production when neighboring countries experience in-creased wind power capacities.

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