Hydro Cascade & Storage Optimisation utilising PLEXOS

2nd Annual Electricity Price Modelling and Forecasting Forum

Tom ForrestSenior Power Market Consultant

Energy Exemplar - Europe

Contents

• Overview of Energy Exemplar & PLEXOS

• Current renewable situation in Europe

• Challenges in modelling hydro assets compared to conventional generation

• Hydro Modelling with PLEXOS

– Exploring different approach's for short vs Long term forecasting?

• Coping with uncertainty in modelling

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OVERVIEW OF ENERGY EXEMPLAR & PLEXOS

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Energy Exemplar

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• Commercial company since 1999 • Focused on development of PLEXOS® Integrated Energy Model

– Continuously enhanced and developed to meet challenges of a changing energy markets and clients modelling requirements

• Over 50 employees serving our global base from five locations:– Adelaide, Australia (Head Office)– London, UK– California, USA (West)– Hartford, USA (East)– Johannesburg, South Africa

• High growth rate of new Customers and Installations at over 30% p.a.• 25% staff with Ph.D. level qualifications spanning Operations Research,

Electrical Engineering, Economics, Mathematics and Statistics

PLEXOS users around the world

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As of February 2015, worldwide installations of PLEXOS exceeded 1,030 at over 170 sites worldwide in 36 countries

19%

53%

7%

9%

6%6%

Consultants

Utilities

Manufactuers (Gen, storages etc)

Energy Regulators/Comissions

Research Institutes

Transmission System/Market Operators

European Region Commercial Client

Breakdown

What is PLEXOS®?

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• Proven power market simulation tool & Integrated Energy Model

• Primarily a modelling tool based around the Fundamentals of the energy market however technicals and stochastics can be integrated also

• Uses cutting-edge linear and Mixed Integer (MIP) programming, optimisationand stochastic techniques

• Uses the same techniques that are used in scheduling, pricing and dispatch models

• Flexible object-oriented design allowing modelling of,

Capacity expansion & investment planning

Market Analysis or Design

Price forecasting and risk analysis

Portfolio Optimisation and valuation

Transmission and Ancillary Services Analysis

Renewable Integration analysis & optimisation

Integrated Electric and Gas System Market Modelling

Co-optimisation of other commodities (Water, Heat etc.)

Simulation and Analysis tools in PLEXOS – Seamless Integration

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LT Plan – Optimal investment

PASA – Optimal reserve share

MT – Resource Allocation

ST – Chronological Unit Commitment

Detailed by-period results

Phase Primary Function & Analysis Main Output Horizon

LT Schedule Generation/Transmission Expansion, Resource Planning, Project viability, Investment analysis, renewable integration

Builds and Retirements 10-50 years

PASA System Outage Scheduling, (Convergent or classical) Monte-Carlo random outages, Regional capacity share

Maintenance Schedule & reliability indices

1-10 years

MT Schedule Hydro-thermal coordination, Long-term Take-or-Pay contracts, Competition analysis & behavior modelling (LRMC recovery, Nash Cournot, RSI, Bertrand), Risk Management

Operating policies 1 year

ST Schedule Day/Week/Hour market simulation, optimal bidding, CCGT analysis, ST risk management, Energy & Ancillary Service optimisation, OPF

Detailed Chronological Operation

1 day – 1 week

RT Schedule Intra-hour market dispatch, Real Time (RT) & Day Ahead (RA) coupling RT economic Dispatch Intra day (down to 1 minute)

Solution from the optimisation task

How does PLEXOS® work?

PLEXOS®Fundamental

Model

Fuel Prices

Energy Demand

Renewable Forecasts

Generation Availability

Input Data Series

Technical Characteristics

• Generator technical properties (heat rate, ramp rates, MSL, start profiles etc.)

• Fuel Constraints • Emission Limits• Interconnector NTCs• System constraints• Ancillary Services

requirements• Market mechanisms

Results

Hourly Price

forecasts

Generation Dispatch

Dispatch Costs

Revenue & P/L

Heat Demand

Fuel Contracts

Water Usage

PLEXOS Engine

Select Solver

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Output & Reporting Options with PLEXOS®

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CURRENT RENEWABLE SITUATION IN EUROPE

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Renewable growth in Europe & unintended consequences

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Annually new installed generation capacity in MW for the EU Region

35GW of new generation installations in 2013• Wind Power 32% (11.2GW)• Solar 31% (11.1GW)

German

Increased Focus: Flexible Generation & Energy Storage solutions

A German study undertaken by Statkraft on how Germany could procure all of its electricity from renewable resources by 2050 identifies Norwegian dams as a realistic way to store large volumes of energy.

Limitations identified to be overcome:• Regulations around reservoir ramp rates (1cm

per hour vs 5cm per hour required)• Size of storages need to be increased to

30GW• Transmission Line capacity upgrades required

into Germany

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Typical Nordic Region Merit Order

• Approximately 50% of all European hydro reservoir capacity is situated in Norway

• The share of hydro power in Norway was 97% in 2012

CR Olsen. (2013, Jan- Can Norway be Europe's "green battery"? [Online]. http://www.cedren.no/News/Article/tabid/3599/ArticleId/1079/CanNorway-be-Europe-s-green-battery.aspx

Increased Focus: Flexible Generation & Energy Storage solutions

• Other storage options have also been explored:– Compressed Air Energy Storage (CAES) – Air is

pumped into underground salt caverns and the compressed air is then released through a generator to generate when required. High build cost however at 1,000 €/kW Becoming closer to commercialisation

– Battery Storage – numerous technologies flow, liquid metal, Ni-Cd & Lithium-ion Many technologies still lack commercial viability Limited life span of batteries Potential safety hazard

– Power to Gas, Electric Vehicles (EV), hydrogen….

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CHALLENGES IN HYDRO MODELLING VS CONVENTIONAL GENERATION

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What Hydro generators can we model?

• There are generally three types of hydro plants we want to model: – Regulated or Storage hydroelectricity, based on reservoirs

that function as “batteries” Storing water inflow from rain and melting snow in large dams, giving the decision maker some extent of freedom regarding the timing of generation

– Run-of-river hydroelectricity, which offers little or no storage possibilities. Such power plants are often used in coherence with reservoirs upstream

– Pumped storage, which can be used for load balancing and shifting. Water is pumped from lower elevation reservoirs to higher elevation reservoirs during low priced hours, and can thus be used for generation and sold during high priced hours

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The Hydro-Thermal Modelling Problem

• Mathematical formulation of a hydro & thermal problem is more complex than a pure thermal system:

– Hydro power plants have the option of storing water if there is a storage attached to them so there is hydraulic temporal coupling

– Natural inflows are uncertain and can be hard to forecast accurately over a long horizon

– Cascade or Run-of-River systems can be complex to optimise due to the decisions taken along the chain

– There may be some specific water usage policies and constraints.

– Operation co-ordination is more complex due to high variety of constraints.• Minimum flow constraints

• Storage ramp constraints

• Minimum Operating Levels

– While water is cost-free but its opportunity cost is fundamental

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If water is free how can we decide when to use it optimally?

• A typical conventional generators SRMC can be broken down into:– SRMC = (Fuel Price x Marginal Heat Rate) + VOM Charge + Emission Cost+ UoS Charge

• But with water being free how can we value it?– We need to determine the value of water (or more commonly called Water Value) which will

vary depending on the expected value of the water in storage– Therefore our objective is to plan the operation of the storage so as to maximise the expected

value of production over time

• Should we,1. Use the water for generation and sell the power to a known price today?2. Keep it in the reservoir and store it for generation and sale at a later stage?

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Option 1 Option 2

The Importance of Storage Management & Optimisation

• The Water Value can be seen as the fictitious marginal generation cost, and is linked to the asset owner’s evaluation of the future revenue opportunity

• Large storages give asset owners flexibility as to when to generate vs when to store

• Short term releases however need to be managed by looking over a longer period of many months or even years for optimal storage management.

• Usually have monthly or yearly targets then these are then decomposed back into a daily running schedule.

– In PLEXOS this process is done via a 2 step process called decomposition utilising 2 phases of PLEXOS in sequence

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Norway: Typical water inflows vs Demand in a year

Large imbalances generally occur between the occurrence of peak demand and peak inflow

HYDRO MODELLING APPROACHES WITH PLEXOS

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Hydro-Thermal Co-ordination Problem

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• The hydro-thermal coordination problem aims to minimise the expected value of thermal generation over a forecast horizon (T) subject to constraints on availability of hydro generation and storage.

Hydro Modelling in PLEXOS

• Modeller can choose between 3 hydro model settings depending on data available:– Energy (Storages volume in GWh, releases and inflows

represented in MWs)– Level (Storage volume in 1000m3, releases and inflows

represented in cumecs)– Volume (Storage volume in CMD, releases and inflows

represented in cumecs)

• Environmental constraints such as minimum releases or storage ramp constraints can be modelled

• Manual storage targets (optional) • Generator efficiency curves and storage head

effects• Natural Inflow forecast

211 cumec = 3,600 cubic meter per hour 1 Cumec Day (CMD) = 24 Cumecs or 86,400 cubic meters

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An example Hydro System setup incorporated into PLEXOS

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1 Week Simulation Horizon – Hourly Intervals Daily Chronology

Total System Cost - $3.1m

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1 Week Simulation Horizon – Hourly Intervals Weekly Chronology

Total System Cost - $2.8m

Simulation and Analysis tools in PLEXOS – Seamless Integration

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LT Plan – Optimal investment

PASA – Optimal reserve share

MT – Resource Allocation

ST – Chronological Unit Commitment

Detailed by-period results

Phase Primary Function & Analysis Main Output Horizon

LT Schedule Generation/Transmission Expansion, Resource Planning, Project viability, Investment analysis, renewable integration

Builds and Retirements 10-50 years

PASA System Outage Scheduling, (Convergent or classical) Monte-Carlo random outages, Regional capacity share

Maintenance Schedule & reliability indices

1-10 years

MT Schedule Hydro-thermal coordination, Long-term Take-or-Pay contracts, Competition analysis & behavior modelling (LRMC recovery, Nash Cournot, RSI, Bertrand), Risk Management

Operating policies 1 year

ST Schedule Day/Week/Hour market simulation, optimal bidding, CCGT analysis, ST risk management, Energy & Ancillary Service optimisation, OPF

Detailed Chronological Operation

1 day – 1 week

RT Schedule Intra-hour market dispatch, Real Time (RT) & Day Ahead (RA) coupling RT economic Dispatch Intra day (down to 1 minute)

Modelling months, years or a multi-year horizon

• The Medium Term (MT) Phase of PLEXOS addresses the key limitation of modelling large horizons in a single chronological step

• Long time horizons are a challenge because they imply that the simulator must optimise decisions spanning weeks, months and years and simultaneously optimise decisions in the short-term (at an hour or minutely resolution)

• Consider the simulation of a single year, one might think that we 'simply' make a mathematical program that includes all 8760 (or 8784) hours of the year and solve it in one giant step, but unfortunately this is usually computationally impossible.

• So we need a way of optimizing medium and long-term constraints and commercial decisions while still simulating in relatively small time steps– Multi-Phase 2 stage run 1st Phase => MT --Results--> 2nd Phase => ST

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MT – ST Decomposition• MT Phase runs first using a reduced

chronology (e.g. Using Load Duration Curves)

• The red line in the chart right shows the Storage End Volume results from MT Schedule as one-value-per-month.

• The continuous upper envelope of the area in the chart shows the synthesized chronology based on the LDC block-by-block release/inflow results mapped back to hours.

• This chronology map can provide a reasonable trajectory for ST Schedule to follow down even to an hourly resolution (though in this case a daily ST Schedule step is as finer resolution as seem sensible).

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MT to ST Decomposition

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ST Schedule daily levels now roughly match MT schedules monthly storage trajectory

The end volume from each LDC block out of MT Schedule has been used to set target end storage volumes* for each ST Schedule step

*Water Values derived from the MT Phase can also be Decomposed down to the ST as an alternative to storage targets

COPING WITH UNCERTAINTY IN MODELLING

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Coping with Uncertainty

4 March, 2015 Energy Exemplar 30

• PLEXOS offers three distinct approaches to coping with uncertainty: – Scenario analysis – Monte Carlo simulation – Stochastic optimisation

• In PLEXOS any parameter can easily have uncertainty applied to it. Common parameters to undertake analysis of include: – Load growth and load shapes – Fuel and emission prices – Hydro inflows and wind generation or speeds– Technology cost trends

• These parameters (Variables) can also be correlated– A high wind generation/speed might be associated with a high demand sample

• Fix perfect foresight issue

– Monte Carlo simulation can tell us what the optimal decision is for each of a number of possible outcomes assuming perfect foresight for each scenario independently;

– It cannot answer the question: What decision should I make now given the uncertainty in all the possible inputs?

• Stochastic Programming

– The goal of SO is to find a decision that is feasible for all (or almost all) the possible data instances and maximise the expectation of some function of the decisions and the random variables

• PLEXOS uses scenario-wise decomposition and can be configured to run in either a two-stage or multi-stage stochastic optimisation

Stochastic Optimisation (SO)

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Hydro-thermal Coordination:Today’s decisions have impact on the future

In a Hydrothermal system water release is relevant to determine the dispatch operations

Present Period

High releases of water

Low releases of water

High Inflow

Low Inflow

High Inflow

Low Inflow

Future period

- Low thermal generation - Low cost of future supply

Future period consequences

- Low dam levels- High cost for future supply of energy- Probably unserved energy

- Spill of water- Low future cost- Present cost could be lower

- Water available in future periods to face dry season - Unserved energy is avoided

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4 March, 2015 Energy Exemplar 33

Monthly Scenario- 10 Possible Inflow Forecasts

10 Inflow Forecast Samples

Min, Max & Mean of adjacent - 10 Inflow Samples

10 Inflow Samples - Monte Carlo (MT Schedule)

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Lake Adelaide – End Volume Lake Brisbane – End Volume

Q. What is our optimal storage trajectory for the next 1 week?

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Lake Adelaide – End Volume Lake Brisbane – End Volume

10 Inflow Samples – Stochastic Optimisation (MT Schedule)

• Gives the generation scheduler a single trajectory to target for each storage• Allows us to reassess our decisions again after a week - possibly with new forecasts• Allows Managers and planners can defend their storage operating decisions with conviction

Concluding Remarks and Summary• Flexible generation & ‘battery’ like storage is becoming increasingly

important as countries increase non-flexible renewable capacity (wind & solar) due to investment and production subsidies

• Understanding the physical characteristics of each technology and how it will operate in the chosen energy market will help guide initial investment and optimal operation & dispatch

• Fundamental modelling software can assist in forecasting the optimal operation of a hydro storage over numerous time horizons in a competitive market environment

• Uncertainty in inflow forecasts (or any other forecasted input) can be taken into consideration in results by using Monte Carlo approach's or Stochastic Optimisation

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Thank you for your time and the opportunity

Tom ForrestSenior Power Market Consultant

tom.forrest@energyexemplar.com

www.energyexemplar.com

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APPENDIX

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PLEXOS Optimisation Methods

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• Linear Relaxation - The integer restriction on unit commitment is relaxed so unit commitment can occur in non-integer increments. Unit start up variables are still included in the formulation but can take non-integer values in the optimal solution. This option is the fastest to solve but can distort the pricing outcome as well as the dispatch because semi-fixed costs (start cost and unit no-load cost) can be marginal and involved in price setting

• Rounded Relaxation - The RR algorithm integerizes the unit commitment decisions in a multi-pass optimization. The result is an integer solution. The RR can be faster than a full integer optimal solution because it uses a finite number of passes of linear programming rather than integer programming.

• Integer Optimal - The unit commitment problem is solved as a mixed-integer program (MIP). MIP solvers are based on the Branch and Bound algorithm, complemented by heuristics designed to reduce the search space without comprising solution quality. Branch and Bound does not have predicable run time like linear programming. It is difficult in all but trivial cases toprove optimality and guarantee that the integer-optimal solution is found. Instead the algorithm relies on a number of stopping criteria that can be user defined in determining unit on and off states.

• Dynamic Programming - Dynamic programming (DP) is a technique that is well suited to the unit commitment problem because it directly resolves the min up time and min down time constraints, and over long horizons. Its weakness is in the way unit commit is decomposed so that units are dispatched individually. Thus if all units in the system were dispatched using dynamic programming it would be difficult to converge on a solution where system-wide demand was met exactly, and where any other system-wide or group constraint such as fuel or emission limits were obeyed. For certain classes of generator though DP can be fast and highly effective. The DP is most suited to units with a high capacity factor, and if applied to all units in the system is likely to produce significant under/over generation. Thus you must carefully select units for which the DP is applied e.g. high capacity factor plant with long min up time or min down time values are most suitable.

• Stochastic Programing - The goal of SO is to find some policy that is feasible for all (or almost all) of the possible data instances and maximize the expectation of some function of the decisions and the random variables

Stochastic Optimisation Theory• The most widely applied and studied stochastic programming

models are two-stage linear programs• Here the decision maker takes some action in the first stage,

after which a random event occurs affecting the outcome of the first-stage decision

• A recourse or new decision can then be made in the second stage that compensates for any bad effects that might have been experienced as a result of the first-stage decision

• The optimal policy from such a model is a single first-stage policy and a collection of recourse decisions (a decision rule) defining which second-stage action should be taken in response to each random outcome

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Stochastic Optimisation Theory• This decision framework is conveniently

visualized though a scenario tree. • The nodes represent states of the problem at a

particular instant: where the decisions are made.

• In the first node, called “The Root”, the first stage decisions are made.

• The nodes connected to the root node are the second stage nodes and represents the points where the second stages decisions are made.

• The number of nodes in the last stage equals the number of scenarios. The branches are different realizations of the random variables.

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Stage 0 Stage 1 Stage 2

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1st stage 2nd stage 3rd stageRoot

Node

Node

No information is revealed in this node

two leaves means that the random variable can take two different outcomes, so for the period between root and 1st

stage there are two different realizations of the random variable.

Time

A stage means that new information is revealed and a new decision can be made based on the current state of the stage. In this case two branches per node means that the random variable can take two different values from the state defined in node.

Four different nodes in one stage means that four different decisions can be taken between this stage and the next one.

At 3rd stage there are eight possible outcomes from root to 3rd stage.

Multi-Stage Stochastic Optimisation