IN DEGREE PROJECT ELECTRICAL ENGINEERING,SECOND CYCLE, 30 CREDITS

, STOCKHOLM SWEDEN 2017

Probabilistic Life Cycle CostingA Monte Carlo Approach for Distribution System Operators in Sweden

TIM LJUNGGREN

KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF ELECTRICAL ENGINEERING

In memory of my grandfatherHans Ljunggren

1933-10-19 - 2016-11-07

Abstract

Investments in power systems are characterized by large investment costs and uncertainties doto extended time frame. New consumption patterns in the electricity grid, as well as an aginggrid calls for modernization, new solutions and new investments. Components in the electricalsystem is characterized by most of their costs that are caused after their acquisition. One stateof the art method in analyzing investments over long time frames and provide long-term costestimation is life cycle costing (LCC). In LCC a ”cradle to grave”-approach is performed whichenables comparative cost assessment to be made. This thesis reviews the existing literature inprobabilistic life cycle costing and gives a step by step methodology for DSOs to systematicallyaddress uncertainty in cost and technical parameters.

This thesis proposes a Monte Carlo sampling method in combination with a Markov Chainfailure model to model failures is providing a comprehensive method of reaching financial benefitwhen comparing different investment decisions. The model evaluates financial implications andtechnical properties to demonstrate the total cost of components. This thesis analyses a casefor Swedish distribution system operators and their investment in transformers. The proposedmodel includes an all-covering model of costs and incentives. The main conclusion is that prob-abilistic life cycle costing benefits investment decisions and the applied method shows promisingresults in addressing uncertainty and investment risks. The developed PLCC model is used onan investment decision where two transformers are compared. Results shows that PLCC is apowerful tool and could be used in power system applications.

Keywords: Probabilistic life cycle cost, investment decision, Monte Carlo simulation, Markov Chain

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Sammanfattning

Investeringar i kraftsystem kannetecknas av hoga investeringskostnader och osakerheter pa grundav komponenternas langa livslangd. Nya konsumtionsmonster och ett foraldrat elsystem efter-fragar mordenisering, nya losningar och nya investeringar. Komponenter i elnatet karakteriserasav att den storsta delen av kostnader orsakas efter de forvarvats. En framstaende metod for attanalysera investeringar som loper over langa tidsspann och som kan ge en kostnadsestimeringar livscykelkostnadsanalys. Inom livscykelkostnadsanalys tillampas ett fran vaggan till graven-tillvagagangssatt vilket mojliggor jamforelser av kostnader. Denna uppsats granskar existerandeforskning inom probabilistisk livscykelanalys och ger en steg-for-steg-metodik for att en distribu-tionsnatsoperator systematiskt skall kunna adressera osakerheter relaterade till kostnader samttekniska parametrar.

Denna uppsatsen foreslar en Monte Carlo-metod i kombination av en Markovkedja, for attmed en heltackande metod na finansiell jamforbarhet mellan olika investeringsbeslut. Denna upp-satsen analyserar ett fall for en svensk distributionsnatsoperator och dess investering i transfor-matorer. Den foreslagna modellen inkluderar en heltackande modell for kostnader och incitamet.Huvudresultatet fran den foreslagna metoden ar att probabilistisk livscykelkostnadsanalys samtde anvanda metoderna visar lovande resultat for att adressera osakerheter och risker vid inve-steringsbeslut.

Nyckelord: Probabilistisk livscykelkostnad, investeringsbeslut, Monte Carlo-simulering, Markovkedja

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Acknowledgement

First thing first. This thesis would not have been the same without my supervisor Jan HenningJurgensen. You gave me the opportunity to work with this thesis and your always positive at-titude, your enormous patience and support with all of my questions have helped in ways youcannot imagine. Your suggestions and encouragement have always pushed me in the right direc-tion. I would also like to thank my examiner Dr. Patrik Hilber. He has given me great advicealong the way to the completion of this thesis. He kept on asking me questions that made mere-think my initial thoughts and always aimed for the bigger picture.

I would also give a special thanks to Henrik Rinnemo at Ellevio who was a valuable source fromthe industry. He gave me hands-on explanations and from an industry point of view, explainedinvestment decisions and his company’s way of handling investment decisions. I would also liketo express my gratitude to Mats Eriksson at Ellevio who gave me great insight in distributiontransformers. Being given the opportunity to have discussions with someone of your experienceand knowledge is something I am truly grateful for. Furthermore, I want to express my gratit-ude to Elin Grahn who is giving my the permission to use the pictures from the Swedish EnergyMarkets Inspectorate in this thesis.

I would like to give acknowledgement to my classmates Elin, Maria and Nicolina. Without you,there is no way I would have managed to finish my master degree and complete my studies atKTH. Your ability to always being able to bring joy and brighten the longest days, I will alwaysbe thankful for.

Last but not least I want to give a special thanks to my two families. Firstly, the one back homein my hometown. My mom, dad and sister are my true sources of inspiration and I always aimof making them proud. My second family, my basketball team, is always giving me a feeling ofbelonging and brotherhood, in victory and in loss. Thank you.

Stockholm 25th October 2017

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Table of Content

Abstract i

Sammanfattning ii

Acknowledgement iii

List of Figures vi

List of Tables vii

I BACKGROUND 1

1 Introduction 21.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3 Aim and Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.4 Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.5 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Asset Management 72.1 Asset Management in Power Systems . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.3 Maintenance Optimization and Strategies . . . . . . . . . . . . . . . . . . . . . . 82.4 Maintenance Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.5 Condition Monitoring Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3 Failure Rate Basics 113.1 Quantifying Reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.2 Reliability Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.3 Lifetime Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.4 Failure Rate Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.5 Failure Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4 Life Cycle Costing 144.1 What is Life Cycle Costing? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144.2 What is a Life Cycle? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164.3 What is a Cost? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174.4 Net Present Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

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4.5 Internal Rate of Return . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.6 Interest Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.7 Need for Improvement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

5 Probabilistic Life Cycle Costing 205.1 Monte Carlo Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205.2 Methods Assessing Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . 225.3 PLCC Modeling Methods to Handle Uncertainty . . . . . . . . . . . . . . . . . . 235.4 Previous Probabilistic LCC research review . . . . . . . . . . . . . . . . . . . . . 245.5 Cost Identification for PLCC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265.6 Modeling of Repairable Components . . . . . . . . . . . . . . . . . . . . . . . . . 28

6 Regulation of Power Systems 296.1 Revenue Caps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306.2 Performance Regulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306.3 Revenue Cap Regulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306.4 Revenue Cap Regulation in Sweden . . . . . . . . . . . . . . . . . . . . . . . . . . 316.5 Incentives for Swedish DSOs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326.6 Future Changes in the Regulatory Framework . . . . . . . . . . . . . . . . . . . . 35

II MODELS AND RESULTS 36

7 The developed PLCC model 377.1 Different Steps and Requirements of the Model . . . . . . . . . . . . . . . . . . . 38

8 Application of Developed Model 428.1 Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428.2 Economical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458.3 Incentive Regulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 468.4 Outage Cost Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478.5 Effect of Condition Based Maintenance System . . . . . . . . . . . . . . . . . . . 488.6 Fixed-Lifetime Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498.7 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

9 Discussion 529.1 Internalizing of Externalized costs . . . . . . . . . . . . . . . . . . . . . . . . . . 529.2 Regulation and its Relation to Investment Decisions . . . . . . . . . . . . . . . . 52

III Closure 54

10 Conclusions 5510.1 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5510.2 Conclusions From the Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . 5610.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

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List of Figures

2.1 Different types of maintenance strategies . . . . . . . . . . . . . . . . . . . . . . . 9

4.1 The iceberg effect, visualizing total costs . . . . . . . . . . . . . . . . . . . . . . . 15

5.1 Monte Carlo method for repeated sampling . . . . . . . . . . . . . . . . . . . . . 215.2 Two level Monte Carlo simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 225.3 Analytic uncertainty mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235.4 Methods to handle uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245.5 Common sampling methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

6.1 The Swedish revenue cap regulation . . . . . . . . . . . . . . . . . . . . . . . . . 316.2 Incentives for DSOs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326.3 Incentives for DSOs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336.4 Baselines for benchmarking DSOs . . . . . . . . . . . . . . . . . . . . . . . . . . . 336.5 Average performance from benchmarking of all Swedish DSOs . . . . . . . . . . . 34

7.1 Overview of the developed PLCC model . . . . . . . . . . . . . . . . . . . . . . . 37

8.1 Histograms of net present values, combined figure. . . . . . . . . . . . . . . . . . 468.2 Effect of incentive regulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478.3 Effect of outage cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478.4 Effect of outage time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488.5 Condition based maintenance implementation . . . . . . . . . . . . . . . . . . . . 488.6 Fixed-life analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498.7 Sensitivity with respect to interest rate . . . . . . . . . . . . . . . . . . . . . . . . 508.8 Sensitivity with respect to electricity price . . . . . . . . . . . . . . . . . . . . . . 51

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List of Tables

4.1 Different perspectives of life cycles . . . . . . . . . . . . . . . . . . . . . . . . . . 16

5.1 Earlier PLCC studies conducted within different fields of engineering . . . . . . . 255.2 Distributions used in PLCC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

6.1 Cost parameters used in the quality regulation 2016-2019 . . . . . . . . . . . . . 35

8.1 Table describing the two transformers . . . . . . . . . . . . . . . . . . . . . . . . 438.2 Failure statistics for distribution transformers <50kV . . . . . . . . . . . . . . . . 438.3 Cost associated with certain failures . . . . . . . . . . . . . . . . . . . . . . . . . 448.4 Mean and standard deviation of 16 and 20 MVA transformers. . . . . . . . . . . 468.5 Condition based maintenance implementation . . . . . . . . . . . . . . . . . . . . 498.6 Condition based maintenance implementation . . . . . . . . . . . . . . . . . . . . 50

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Part I

BACKGROUND

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Chapter 1

Introduction

This chapter will highlight the research area, motivate scientific context for the thesis, presentthe research questions and highlight the contribution of this thesis.

The electric power sector will within the next decades undergo an enormous transformation.Ever since the UN report Our Common Future [1], led by the earlier Norwegian Prime ministerGro Harlem Brundtland, decarbonisation and climate change have been on the agenda. Multipleinternational agreements such as the Kyoto Protocol (from 1997) and the Paris Agreement (from2016) have been the backbone in the political framework, shaping the path towards a sustainabledevelopment.

The global need for electricity is anticipated to increase by 69% until 2040 [2] and that willimpose a huge challenge to satisfy that growth in demand. The challenges that will follow willinclude the challenges of new technologies, production- and consumption patterns. Simultan-eously as facilitating the increasing demand, efficiency and reliability need to be considered. Itis within the public interest that the electricity is secure, reliable and affordable. In order tofacilitate those needs, a number of challenges of an aging power grid arise. In tomorrow’s powersystem operators need to invest heavily in new technology such as smart grids. According to theInternational Energy Agency (IEA) approximately 500 billion euros is estimated to be investedin the electrical grid until 2030 only in the EU [3]. Without the deployment of new ”smart”technological solutions, the renewal of the grid will become mostly a replacement program onold solutions. Therefore, the electricity grid of tomorrow needs to accommodate high shares ofrenewable energy sources and new flexible grid solutions.

Investments in the power systems are very capital intense and due to the long technical lifetime of the components, optimal investments is a key issue in planning for the power grids oftomorrow. The electricity consumers require needs to be secure, reliable and affordable. Gridowners are regulated to ensure public interests and at the same time facilitate costs and quality(including reliability) towards the company, this at the same time as facilitating its business toa fixed budget constraint, without exploit its market power towards consumers.

Electricity distribution system operators (DSOs) have to handle demanding investment re-quirements during the next years, which will need to not only include integration of renewableenergy sources but also to replace existing equipment in the grid. At the same time the electricalgrid needs to be modernized towards future needs and old components. Also by considering thereliability of components, which is accounting for circa 80% of the customer outage time, DSOs

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can avoid additional penalty costs and also get the possibility to obtain incentives from qualityregulations. To facilitate the total costs during the life cycle of a component, a fully integratedmethod must be considered. Due to uncertainties in input parameters such as interest rate,equipment failure and labour costs, a uniform decision is a difficult task to perform. One toolto analyze the costs of a good or service during its lifetime is through life cycle cost analysis(LCCA).

This thesis will provide a method were Monte Carlo simulations are used to address life cyclecosts of components in the power system domain considering uncertainties and risks.

1.1 Overview

Reliability & Maintenance

Reliability and maintenance have a central role for today’s network operators. In Sweden in 2013,the costs of power outages were estimated to approximately 140 million euros [4]. The regulatoryframework also gives incentives to DSOs that prioritize reliability and in addition, costs areavoided which results in a double reward. Maintenance is related to reliability by the meansthat maintenance precludes failures. In the context of asset management and maximization ofproperty/asset value, the reliability is related to a risk and is depending on the desired reliabilitylevel and an appropriate balance between budget constraints and acceptable risk.

In the 1960s, an approach to assess cost efficient maintenance strategies. The methodwas called Reliability Centered Maintenance (RCM) and was further developed by professorLina Bertling Tjernberg at KTH, to what is known as Reliability-Centered Asset Maintenance(RCAM) [5, 6]. The method provides a link between system reliability and maintenance effortbut also links together maintenance costs and reliability, which will be further discussed in thisthesis and will be considered in the built in the probabilistic life cycle model.

Condition estimation & monitoring

Condition monitoring provides a different approach compared to classical maintenance strategies(preventive and corrective maintenance). By assessing a components condition with sensorsand measurements, maintenance is only carried out when a condition of the measured value(s)is fulfilled and passes through a pre-defined threshold [7]. Condition monitoring can also beused to justify if a component can be operated at higher loading or needs a lower loading toavoid or postpone maintenance [8]. Previous research within the area shows great potential, forexample [7] shows when considering the individual degradation of components to show whichcomponents have an increased failure rate. It is shown by [9] that it is feasible to estimate thefailure mechanism by measuring physical quantities and by such measurements make maintenancedecisions. A review of methods for condition based monitoring is presented in [8], and [10]presents a detailed step by step walk through for condition based maintenance approach includingdata acquisition and data processing methods.

Life Cycle Costing

Life cycle costing (LCC) is a method used for assessing the total cost for an investment throughits whole life cycle. LCC has a major draw-back it has inherited because of the long term planningin infrastructure projects an uncertainties tied to LCC has questioned the methods credibility[11]. LCC is popular in many contexts, especially in environmental issues were environmentaldamages are given monetary values [11]. This attribute can also be used for societal costs, were

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there is a discrepancy between costs that a company actually pays, and cost of the damagethat the company is causing. An illustrative example for power systems are outage costs were ablack-out is causing way much higher costs than accounted for.

Life cycle costing has evolved to be able to handle uncertainties when applying probabilisticmethods such as Monte Carlo simulations. By using a systematic approach to assess the un-certainties and use methods for connecting key parameters and attributes of a component or asystem such as reliability and regulatory framework, a full picture of the total costs of a life cyclecan be found. In literature this is known as probabilistic life cycle costing (PLCC). However, thePLCC calculations are sensitive to the assumptions and input parameters chosen which requiresa well defined methodology and approach for using the method. By using PLCC one can achievea quantification of risks in terms of standard deviation.

Economic regulation of Power Systems

Since the beginning of the 1980s, the traditional power systems in the world have been verticallyintegrated. That means that one actor on the market has the responsibility of generation,transmission and distribution. However, this is no longer the case. Market platforms havedeveloped were electrical wholesale and retail markets have been introduced to allow competitionon the production side in the system. On the other hand the monopoly has remained on thegrid itself (including both the transmission and the distribution grid). This demands for specificregulations and planning to achieve an efficient system were the economic regulation of themarket steers towards effectiveness [12]. The scope of the regulation is according to [13] to:

• Design the rules for steering the actors on the market towards the objectives (defined bythe regulator)

• Adopt appropriate structure to the power industry market. To operate efficiently, theelectricity market needs a business structure were a sufficient number of competitors arepresent to establish conditions to a certain level of competitiveness.

• Apply appropriate supervision of market participants, meaning that the regulator needs tomonitor, take legal action, penalize to assure that the effectiveness and rules of the marketis maintained.

The concerns of the regulator, according to Perrez-Arriaga, typically includes concerns re-garding consumer price, tariffs, environmental impact, market structure and market power, in-vestment volumes, economic and financial efficiency [13]. In other words the regulator aims toremove market power, assure acceptable levels of investments, reduce the environmental impactand ensure that companies offer the lowest possible price without risking the companies to gobankrupt in the long run. This thesis will provide a method for how to carry out investmentdecisions for distribution system operators (DSOs). The thesis will focus on the regulatory frame-work and with aspects to life cycle costs (LCC) were uncertainties regarding cost distributionsand reliability will be considered.

The regulation of the revenues for a DSO will traditionally be set by the principle cost-of-service (also called rate-of-return) regulation. Cost-of-service means that the company willprovide an investment plan and an estimate of their future operation costs that the regulatorycommission will either accept or reject (known as a negotiation processes). Costs will thereafterbe distributed among the users of the electrical network and show up on their tariff payment ontheir electricity bill.

A more modern way of regulating the revenues is to apply a cap for the revenues and thenallow DSOs to increase their revenues if certain targets regarding improved efficiency or other

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optional compensation drivers such as adjustment factors for changes in demand, distributedgeneration penetration etc are reached [14].

1.2 Motivation

The need for assessment tools for evaluating investments decisions is an important task for eachcompany and especially for companies in the electricity sector. Investments in that sector arecapital intense and they generally have long lead times and are characterized by uncertaintiesregarding costs in many forms. During long lifetimes of components, the operational costs willcontribute greatly to the total costs. Grid owners (DSOs) are regulated by the means that theirrevenues have a cap as well as a regulatory framework trying to send incentives to encourageefficient long-term investments to achieve a more efficient system and at the same time promotereliability. If investors are not well informed of the uncertainties, non-optimal decisions mightbe taken. This will affect the overall economics of the company, leading to higher grid tariffs forcustomers as well as inefficient utilization of capital. Therefore it is necessary to develop newtools that could be used to assess uncertainties in investment decisions. One approach is to usea probabilistic method that can limit the scope of the uncertainty and provide a more efficientinformation base that avoids misguided decisions.

1.3 Aim and Scope

This thesis will provide a framework for a probabilistic life cycle cost model that can be used forassessing individual components or whole system costs. It will relate stochastic parameters suchas reliability and address it to the aggregated costs for a component. This is accomplished byaddress the whole life cycle of components in an electrical network.

Q.1 How to model probabilistic life cycle costs in a deregulated power system?

Q.2 What potential sources of uncertainties exist in LCC?

Q.2.a What methods are appropriate to address uncertainties in LCC calculations?

Q.2.b How can the impact of uncertainties be quantified?

1.4 Contribution

To be able to answer the above mentioned research questions a comprehensive literature studyhas been preformed and a probabilistic life cycle cost model has been developed. The PCCA-method is applicable also to other systems than electrical ones and is one of the most powerfultools when it comes to addressing uncertainty and risks for investment decisions.

1.5 Thesis Outline

Chapter 1 - Presents the background, limitations and research questions.

Chapter 2 - Presents an introduction to asset management.

Chapter 3 - Provides a theoretical background of reliability, common distributions andreliability indices.

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Chapter 4 - Provides a literature review of life cycle costing.

Chapter 5 - Presents how a probabilistic approach of LCC and how uncertainty in inputparameters are addressed. In addition, a literature review of PLCC is presented.

Chapter 6 - Presents how the studied impact of power system regulations are affectinginvestment decisions.

Chapter 7 - Presents the developed model to assess investments with uncertain parameters.

Chapter 8 - Presents the quantitative results from the developed models.

Chapter 9 - Discusses the findings of the thesis.

Chapter 10 - Concludes the findings of the thesis and presents future directions for research.

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Chapter 2

Asset Management

This chapter describes the basics of asset management and how it relates to maintenance andreliability. It describes maintenance strategies and provides a basic view of risks and uncertaintiesin the power system.

Asset management is in the context of electrical power systems mostly related to physical com-ponents that have a long technical lifetime (typical in the range of 20-50 years), but assets couldalso include capital, equipment (physical assets), employees, customer base, brands or corporatestructure [15]. Asset management tries to answer the question when and where actions shouldtake place. The aim of the asset management is to ”in an optimal way fulfill the organizationsgoals considering risk” [15]. Asset management has a central position at each electricity distri-bution company or grid owner. Asset management is the overall decision tool trying to maximizethe value (minimize the costs) for each component in the electrical network to obtain the mostefficient use of resources as possible.

2.1 Asset Management in Power Systems

Electrical power systems consist of thousands of components such as cables, over head lines,transformers, breakers, substations and additional communication technologies. The electricalsystem is very capital intense and for example in Sweden the reliability of the system is governedby law. Therefore, there is a great need for system operators to operate as efficiently as possible.Investments in the electrical network are characterized by long lead times, long planning periodsfor installed components as well as extensive planning for grid expansion. The electrical grid isconstantly aging while a higher demand for reliability is today more critical than ever. The gridwas not built with a ”grand master plan” and is constantly changing. Poor target incentives,overcapacity, low rate of return and inefficient decisions are examples of grid issues. To overcomethese challenges, asset management is used to improve the asset’s life cycle, reduce risks involvedwith the operation of the asset and utilize the asset as economically as possible.

The interest in analyzing power systems on a distribution level is increasing and has receivedmore attention lately. Traditionally, research in transmission level has been more common dueto the more capital intense nature of high voltage equipment. Also the severity of faults ontransmission level may lead to cascade events and catastrophic consequences for the whole systemwhile outages on distribution level is only affecting locally. The reason for the increasing attention

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on the distribution level of power systems has to do with stronger incentives and performanceregulation [16]. On a transmission level, the cost for a single component is much more expensivethan in the distribution system case, which calls for individual observations of the state of thecomponent. For distribution systems a statistical or stochastic approach is more common werethe asset is represented by a model rather than actual measurements [17]. A reliability analysison a distribution level may enlighten and demonstrate advantages of reinforcements in the grid,indicating which components that need more maintenance attention, prove advantages of differentmaintenance strategies and to fulfill laws and regulations.

2.2 Reliability

Reliability in a power system describes by the systems overall ability to maintain its systemgoals. These goals are usually split up into two sub-goals, namely adequacy and security [18].Adequacy can be seen as the static condition of having sufficient facilities in the system to beable to sustain the balance between load demand and generation supply. Security, on the otherhand, refers to the ability of the system to withstand system disturbances such as a generatortrip or a short circuit [18]. According to Kundur et. al, reliability is defined as follows [19]:

”Reliability, in a bulk power electric system, is the degree to which the performance ofthe elements of that system results in power being delivered to consumers within ac-cepted standards and in the amount desired. The degree of reliability may be measuredby the frequency, duration, and magnitude of adverse effects on consumer service”

2.3 Maintenance Optimization and Strategies

To be able to maintain adequate system function, maintenance is required. Physical componentsare subjected to ware and tare due to electrical and mechanical stress. Maintenance managementis accordingly to Nilsson defined as [20]:

”Is a concept including features of how the effect of maintenance on components andsystems could influence on system function and tools and methods for how to performmaintenance”.

Maintenance is a process which consumes time and resources to gain reliability (or restorereliability). This process can be viewed as the maintained component is restored to a stateat higher functional level as before the failure. It exists a variety of different approaches tomaintenance management. Maintenance optimization is the trade-off between preventive andcorrective maintenance. To satisfy the DSO’s customers, it needs to provide available componentsand at the same time minimize the costs. The goal is to reduce the risk of failure in the systembut at the same time satisfy a revenue demand. The optimization process could be designedto optimize for other specifications than those above mentioned. For example reliability couldbe the main objective to maximize. This could for instance be the case for a TSO (which hasmuch higher demands of reliability than a common DSO). Within the topic of maintenanceoptimization also the prioritization process within a system is included [21]. For example; ifa certain budget constraint exists, where should the DSO focus its efforts on to gain maximalmarginal efficiency?

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2.4 Maintenance Basics

The goal of a power system is to operate at an availability at 100%, this is however not the-oretically possible due to the stochasticity of failures in physical components in the electricalnetwork [18]. Maintenance have a central role for optimizing the reliability of a power system. Awell-balanced maintenance strategy can both boost the reliability and at the same time keep thetotal costs for operating the system low. This will benefit the DSO as they will have lower costs,and also the customers as they will experience higher availability (and lower grid tariffs). Otherrelations, such as economic growth is highly linked to low outage times [22]. For example in In-dia, the low reliability of the electricity grid is costing billions of dollars in loss of gross domesticproduct (GDP) [23]. This means that direct societal benefits will be achieved. Different researchregarding maintenance with various approaches have been done; [15] have investigated the op-timal relation between the costs of maintenance and reliability, and [7] looks into characteristicsindividual components using measurements.

Based on [24] different types of maintenance classifications can be identified. They are builtupon the two main concepts preventive maintenance and corrective maintenance:

1. Preventive maintenance

Preventive maintenance (PM) is when performing maintenance on a working component toprevent future failures. This could include a maintenance schedule that is based on previousknowledge of when to replace of preform service (such as lubrication or replacement) ofcomponents.

(a) Age-based maintenanceThis method have a predefined time of when the maintenance should occur. This couldfor example be years in service, number of cycles performed or kilometers driven. Theplanned maintenance does not care about the actual status of the component, themaintenance will occur anyway.

Figure 2.1: Different types of maintenance strategies

(b) Clock-based maintenanceIn this method a predefined time is specified when maintenance should occur.

(c) Condition-based maintenanceThe maintenance is carried out if physical parameters of a component is exceeding itsvalue (threshold). This means that the technician will either perform certain test todetermine the actual quality of the component or sensors will provide measurementsto decide the condition of the component. Condition-based maintenance is also knownby the name predictive maintenance.

(d) Opportunity maintenanceMaintenance is preformed when an opportunity is given. For example could this takeplace in advance when an unplanned opportunity is given.

9

2. Corrective maintenanceThis method of maintenance is also known as breakdown maintenance or run-to-failuremaintenance. And as the name tells, maintenance is preformed only as a component goesfrom working state to failure state. This maintenance approach usually includes that thefaulty component is replaced by a new working component.

3. Failure-finding maintenanceThis special type of maintenance method is performed on working components to look forhidden failures.

2.5 Condition Monitoring Systems

Condition monitoring systems or CMS is a maintenance strategy that requires that the conditionof the asset is known. Maintenance is then only conducted when a certain threshold is passed,meaning that only repair and service is carried out when needed. The CMS combines three steps[10]:

1. Data Acquisition, obtain relevant data through various sensors to measure temperature,pressure, moisture etc.

2. Data Processing, analyze the signals collected. This includes process the signals inalgorithms, noise reduction, etc.

3. Maintenance Decision-making, in this step diagnostics and prognostics takes place.Diagnostics aims to categorize and identify the error by detect, isolate and identify it whileon the other hand prognostics tries to predict errors before they occur. Methods such asartificial intelligence (AI) and complex decision aiding algorithms then can be used to takethe correct measures to identified faults.

Future trends in CMS are involving soft computing techniques and machine learning. Com-mon present techniques are genetic algorithms (GA), artificial neural network (ANN) and fuzzylogic (FL) [25]. On a system level, deep learning and machine learning algorithms can be incor-porated to deal with systems of high complexity. An implementation of soft computing in assetmanagement will according to [26] may improve decision-making process due to the high amountof uncertainty and the possibility to enhance the tractability and performance of maintenancedecisions.

The improved dynamic of soft computing compared to traditional methods can also be bene-ficial when it comes to data analysis of event data, condition monitoring data for prognostics anddiagnostics [10]. Pattern recognition and fault detection are areas where artificial intelligenceapproaches can in the future be beneficial for telling when faults are about to happen and limitthe damages when a fault occurs. [10].

10

Chapter 3

Failure Rate Basics

This chapter introduces basics about failure rates and models to describe the lifetime of compon-ents.

3.1 Quantifying Reliability

The reliability of an electrical network is at high priority. Due to the stochastic nature of failures,it is a very hard task to show how an electrical network is really reliable. Various methods try-ing to explain reliability exist, traditionally analytically or numerically. Statistic measures andso-called reliability indices is one way to interpret the reliability of a system by expected valuesof failures and mathematical models. The downside of this statistical deterministic approach isthat it does not reflect on the stochastic nature of component failures [18]. The reliability indicesusing expected values can sometimes be misleading. This may be illustrated by an example.If one rolls a dice one time, the expected value is (1+2+3+4+5+6)/6=3.5. Firstly, that is anumber that does not exist on the original dice, and secondly, there is no guarantee that it willhappen just because it is expected ; the method just provides a weighted average from a number ofprobabilities. Modern computational methods such as Monte Carlo methods or Markov Chainswhich are much more sophisticated catch the random behaviour of components providing thereliability analysis with a distribution as results. The results obtained from hundreds or thou-sands of Monte Carlo simulations will follow statistical distributions with a mean and a standarddeviation.

The more traditional way of illustrate the reliability of a power system is to use differentindices such as SAIDI (System Average Interruption Duration Index) and SAIFI (System AverageInterruption Frequency Index), see Equations 3.1, 3.2 and 3.3 below:

SAIDI =Total customer interruption time

Total number of customers(3.1)

SAIFI =Sum of customer interruptions

Total number of customers(3.2)

CAIDI =Sum of customer interruptions durations

Total number of customers interruptions(3.3)

The RCAM research group at KTH has developed new importance indices. The developedindices are establishing a link between component reliability and system reliability, a link which

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is challenging due to the robustness of the power system. The research is within the RCAMmethod. There are two different approaches were [15] focuses on finding an optimal balancebetween maintenance and reliability or were most of the maintenance potential exists (on adistribution level) and [27] research focuses on transmission level applications of indices withinthe RCAM framework.

3.2 Reliability Measures

A cumulative density function CDF (see equation below), describes the time D for which acomponent stays in the same state, less than time τ . The number of states can be modeleddifferently but can for simplicity be illustrated with available or unavailable (in service or out ofservice).

Fd = Pr(D ≤ τ) (3.4)

By definition

Fd(0) = 0 (3.5)

Fd(∞) = 1 (3.6)

3.3 Lifetime Distributions

Assume n non-repairable components put into operation at time t=0. The lifetime of how thefailures are distributed can be shown on different statistical distributions. For reliability modelingin general and power systems in particular the exponential distribution is frequently used [24].

Exponential Distribution

The exponential distribution describes a process which in events occur continuously and inde-pendently at a constant average rate [24]. The parametrization of the curve can be described byonly the scale parameter λ. It is from now on assumed that both λ and t are positive numbers.

f(t;λ) = λe−λt (3.7)

The cumulative distribution function is given by Equation 3.8:

F (t;λ) = 1− λe−λt (3.8)

The failure rate function is given by

h(t;λ) =f(t)

R(t)=λe−λt

e−λt= λ (3.9)

Meaning that the expression simplifies to a constant failure rate. A property that is veryuseful for reliability calculations.

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Weibull Distribution

The Weibull distribution can for certain values of the shape parameter α and scale parameter βobtain the above mentioned exponential distribution (for α = 1 and λ = 1/β. The parametrizationfor the probability density function is given as follows (assumed that both the shape and scaleparameters are positive):

f(t;α;β) =

(α

β

)α−1exp

[−(t

β

α)]

(3.10)

The cumulative density function is given by:

F (t;α;β) = 1− exp[−(t

β

α)]

(3.11)

The failure rate function is given by:

h(t;α;β) =α

β

(t

β

)α−1(3.12)

3.4 Failure Rate Applications

In a power system, the use of failure rate is diverse and possible applications are, according to [7] :calculations of component availability, calculate interruption indices for maintenance, schedulingand optimization also applications for input data for system availability is common. For examplewith reliability block diagrams or Markov models.

A component’s availability is defined as follows:

A =µ

λ+ µ(3.13)

were µ is the repair rate in [time/failure] and λ the failure rate in [failure/time]. The unavail-ability of a component is given by:

U =λ

λ+ µ(3.14)

3.5 Failure Models

A Markov chain is a discrete or continuous stochastic process that satisfies the Markov property.This property is known as memorylessness and is represented by that future states are onlydependent on the present state and independent of previous states [24]. A transition matrix P isgiven by the transition probabilities in each row/column that represent a stochastic process.

P =

a00 a01 . . . a0ja10 a11 . . . a1j...

.... . . a1j

ai0 ai1 . . . aij

(3.15)

The transition matrix have the sum of each row equal to one and all transitions are positiveand less than one. This is illustrated by the following two conditions:

Pij ≥ 0 ; ∀i, j ≥ 0 (3.16)

∞∑j=0

Pij = 1; ∀i = 0, 1, 2 . . . (3.17)

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Chapter 4

Life Cycle Costing

This chapter describes the method of life cycle costing. It raises critique for the tool and presentsits advantages.

4.1 What is Life Cycle Costing?

The definition of LCC according to [11] is the following:

A technique which enables comparative cost assessments to be made over a specifiedperiod of time, taking into account that all relevant economic factors both in terms ofinitial costs and future operational costs

Life cycle costing is a tool developed by the U.S Department of Defence during the 1960s [28].LCC assesses the cumulative costs during a life time. There are a number of different ways a LCCcan be used and depending on the purpose of it, its accuracy and scope might vary dependingon the researcher’s aim, purpose and choice of methodology impacts the results [29]. The diverof the development of analyzing life cycle cost was that the industry came to the conclusion thatit is easier to take care of costs before they occur than having to cut costs in later stages. Beforeexplaining more about LCC, a few words of clarification have to be mentioned regarding thedifferent varieties of life cycle tools:

• Life Cycle Assessment (LCA) - Is a procedure used for calculating the environmentalimpact of a product or service. The four steps of LCA are: (1) Goals and scope definition,(2) inventory analysis, (3) impact assessment (4) interpretation.

• Life Cycle Impact Assessment (LCIA) - The whole analysis could be seen as a ”whatdoes it mean”-step in an LCA. This means that the environmental impact of resource flowsare analyzed with respect to their caused environmental damage. This includes strongemphasizes on the system boundaries and on what will be the impact and causes.

• Life Cycle Sustainability Assessment (LCSA) - Evaluation of social, economic andenvironmental impacts in a decision-making process. Sometimes seen as the aggregatedversion of Environmental-LCA (E-LCA), LCC and social-LCA (S-LCA)

• Life Cycle Costing (LCC) - A cradle to grave approach assessing products, services andenvironmental impact with monetary costs.

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• Life Cycle Cost Assessment (LCCA)1 - A systematic approach to identify environ-mental consequences and assigning them monetary values

• Life Cycle Cost Analysis (LCCA)1 - Determines the most cost effective option amongdifferent alternatives. Considers all costs during the lifetime and the costs are usuallyconverted to net present values.

• Probabilistic Life Cycle Cost (PLCC)2 - A method using probability distributions toassess uncertainties connected to costs.

Methods like LCC (or similarly structured methods) have their base in neoclassic economyrests on three fundamental assumptions: (1) People are rational, (2) Individuals maximize theirutility and (3) People are fully informed. This will have implications for how decisions are made.Individuals tend to make non-rational decisions when the decisions are involving uncertaintiesthat involve long time horizons and complex consequences [11]. This has large implicationswhen assessing environmental costs that might happen a long time after the decisions are made,damage might occur in other locations than were they are caused and damage might have acumulative effect on ecosystems and the environment.

The motivation for using a life-time approach to assess total costs for an investment is thatmany costs for components are hidden due to the iceberg effect, see Figure 4.1. Assessing andeliminating costs by design is a vital task to be able to minimizing costs. Simulations could beused to highlight downstream costs and give them proper attention in the case of investmentdecisions or replacement of components. Figure 4.1 shows that many costs are not visible by onlyconsidering the acquisition costs and one should also note that many of the stated categories ofcosts are variable by nature.

Figure 4.1: The iceberg effect, visualizing total costs

The trend in the industry is that investors require financial transparency and risk assessmentson costs and investments. This is a key driver of the risk-based cost management. Uncertaintiesmay lead to non-optimal investments and allocation of resources. Uncertainties may involvechanges in the regulatory framework, market and political reasons (”rules of the game”) withthe fact that physical assets with a long life time will not continuously adopt to the changingsocio-technical regime and the socio-technical landscape [30].

1Author’s note: there is large possibility for confusion due to the same abbreviation2PLCC denotes the method PLCCA denotes the a particular study or application of a PLCC

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Earlier studies when life cycle costing was used have been used to compare different techno-logies or investment alternatives. Examples of LCCA that has been carried out in the field ofelectrical engineering and power systems are; batteries [31], transmission lines [32], transformers[33], wind power systems [34, 20] and Nuclear power [20]. For a system approach, the authorhas looked at [35] who have used a probabilistic approach with different maintenance strategiesfor identifying costs for a distribution network and a transmission network. Moreover, the au-thor has looked at [36] which have used LCC to assess different investment alternatives whenconsidering tariff regulations and a quantitative reliability method.

A Markov Chain model is used in [33] with repeated sampling for calculating life cycle costsfor transformers on transmission level. The proposed method is a good application of how LCCcould be carried out but lacks in the sense that it uses deterministic costs for many of its identifiedcosts and the uncertainty is represented in the model of the costs associated to the different typesof failures in the Markov Model. The identified research gap comes from the previous researchfails to combine models in an adequate manner. Usually failure costs, for example in the case of[33, 32], where stochastic costs are not used in combination of costs that comes from distribution(probabilistic costs), meaning that the proposed models only captures some of the uncertainties.

4.2 What is a Life Cycle?

The term life cycle depends on within which context the term is used and also between differentpurposes of discussion. When speaking about life cycle assessment (LCA) it is common to saythat the assessment should include all environmental impacts from ”cradle to grave”. The lifecycle represents a variable that might vary and not a fixed constant. Furthermore, differentlifetimes might be used for an LCC, namely economic, technical, physical and utility life [11].Economic lifetime is based on an estimate of the profitable time of the good/service, technicallifetime is the time were the good/service technically can preform its objectives, physical lifetimeis the estimated time it is physically possible to use the good/service. Finally the utility life isthe time the good/service can satisfy a minimum level of performance standards [11].Differentlifetime stages for different perspectives are categorized in Table 4.1 based on [28].

Table 4.1: Different perspectives of life cycles

The different approaches aim to categorize stages in a project life cycle. The different stagesare important when it comes to decision support when costs are categorized. It adds to traditionalaccounting methods were short seeing and simplifications drives the business decisions and notas in a whole life cycle were for example research and development costs are seen as periodicalcosts instead of investments with possible pay outs in future time. The full life cycle approachalso leads to optimal investments in a medium long to a long time horizon. In fact a large partof the total costs of a product is caused continuously during its life time such as reparation costsand costs for losses.

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4.3 What is a Cost?

According to [28] a life cycle cost is defined as:

“The total costs that are incurred, or may be incurred, in all stages of the productlife cycle.”

Costs will, in the context of LCCA, be used as a usage or a consumption of a recourse. Thiscould for example be costs of repair or the indirect cost of wear and tare of a component. Costscan then be categorized by which degree they can be quantified.

The quantification of costs is very different in which degree quantifiable. Some for example endup in the balance sheet of accounting and are directly visible. Others might be indirectly causedor dependent on a company’s liabilities. Other are known as externalities. One example couldbe CO2-emissions caused by the production of a product. Even though the company might payCO2-taxes, they might not add up to the total environmental damage caused by the emissions.People tend to take actions when damage is made to the property they own. Ill defined propertyrights makes it hard in a neoclassic economic theory to address the correct resource allocation,this is known as Coase theorem [11]. This leads to that neoclassical theory in general and LCCin particular has difficulties handling items which have no market value assigned and thereforehandles environmental aspects insufficiently [11]. Life cycle costing faces a major challenge whenit comes to where costs should be addressed. This phenomenon is known as an allocation issuewhich means that depending on the chosen system boundary for the LCCA, may lead to invalidresults [37]. To illustrate this issue, consider a product manufactured abroad and then importedto the country were it will be used during the rest of its life cycle. If this product is causingenvironmental damage by CO2-emissions when produced and when being transported, whichactor (seller or buyer) is responsible for the damages caused by the emissions? The buyer mightargue that all costs of production is included in the price of the good, while the seller mightargue that its responsibility is only within its factory walls. The problem is not only due to thecomplex task of internalizing externalities and to assess in which stage (and to which stakeholder)costs should be addressed, but also to the fact that to be able to use LCCA as a tool, one hasto translate a multi-dimensional problem such as environmental damage to a one-dimensionalmonetary unit [11].

4.4 Net Present Value

Net present value (NPV) calculations is a method of comparing cash flows in the future to aninvestment cost today. If one is asked to chose between receiving 100 SEK today or in 10 years,the rational answer is today, due to the time-value of money. Inflation will cause price levels toincrease and thus, one will receive less goods for the money in one year compared to using themtoday. To be able to compare cash flows from different time periods, a discount rate is used. Ifthe discount rate is 10% it is equivalent as saying that the future value (FV) in 1 year of 100SEK today is 110 SEK, see Equation 4.2. While the present value of receiving 110 SEK in oneyear is 100 SEK today, this is called the present value (PV) see Equation 4.1 and Equation 4.2below.

PV =FV

(1 + i)n(4.1)

FV = PV (1 + i)n (4.2)

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By the sum of the difference in costs and incomes ai (were in this definition the value of aiis assumed to be positive when the income is greater than the costs) over all years from year 1to N, the interest rate r and initial investment G, the total NPV can be found, see Equation 4.3below.

NPV = −G+

N∑n=1

ai(1 + r)n

(4.3)

A positive NPV indicates a good investment decision for the chosen discounting rate. Note thatthe same investment could be negative for some values for r and not for others. This imposes arisk that needs to be analyzed with respect to the sensitivity of the investment rate.

4.5 Internal Rate of Return

By using the concept of NPV calculations and set the NPV to zero, its possible to solve forthe rate r. This rate is defined as the internal rate of return IRR and provides another toolfor investment decisions. The IRR provides an interest rate that the investment must be ableto reach a plus minus zero state (break even point). The IRR method should only be usedconsidering whether an investment should take place or not since it only gives an relative answeras a rate, not absolute in monetary terms.

NPV = −G+

N∑n=1

ai(1 + r)n

= 0 (4.4)

4.6 Interest Rates

Interest rates can be seen as the cost of money. When one party borrows money to a fixed interestrate, the money that should be returned at maturity date (final date) is the principal amount plusthe interest. The ratio between the two defines the interest rate. For example, if one borrows100 SEK and agrees to pay 110 SEK one year later, the interest rate is 110/100=1.1 (10%).For investment decisions, the interest pays a key role. An investment is usually not dependingon a fixed rate, instead macro-economic issues such as inflation are changing the economicallandscape and interest rates are therefore usually considered exogenous variables when modelinginvestment decisions.

Nominal interest rates that are subjected to inflation can be converted to real interest rates,meaning that in the formula, it takes into account that the value of money has decreased, see thefollowing equation. These types of considerations can have a huge impact in developing countrieswhere inflation from year to year can be very volatile and in combination with strong economicgrowth also large in magnitude.

1 + rr =1 + rn1 + ri

(4.5)

were rr is the real interest rate, rn the nominal interest rate and ri the inflation.

When dealing with NPV calculations regarding issues about internalization and quantifyingfor example environmental costs in monetary units, a technique called hurdle rates might beapplied [11]. It involves different levels of rates which are categorized depending on if the impactof the environment is known, uncertain or unknown. A different rate can then be applied todifferent costs making significance to the total result and emphasize different costs more than

18

others [11]. This gives the possibility for NPV calculations to catch time dependency of costs.Some costs might be more severe if they occur in the future (and therefore a negative interestrate could affect the economical evaluation of a project involving environmental damage).

4.7 Need for Improvement

Life cycle costing is a popular tool used for assessing different investments and costs, but themethod has a bad reputation due to its complexity and vagueness for specifying the time period,relevant economic factors in terms of initial costs and future costs [11]. LCC as a method inherentlimitations regarding issues that limits the complete outcomes and assumptions, saying that allinformation is known and individuals are rational.

For life cycle costing to be able to come up with unambiguous results proving its superiorityto other methods, it must include possibilities of forecasting costs and handle uncertainty. If thescope of uncertainty quantification is limited, misguided and sub-optimal decisions are obtained[38]. To avoid this, the LCC modeling needs to not simplify relationships for uncertain parametersand instead systematize the identification process of uncertainties and then in later stages performsensitivity analysis rather than obtain causalities that are too simplified and too far of from thecost one tries to represent with the model. This aims for harmonization of methods whichincreases the more the method is used and when more data is available [39].

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Chapter 5

Probabilistic Life Cycle Costing

This chapter describes the probabilistic life cycle costing method and the current state of the art.A short introduction to Monte Carlo simulations is given and a literature overview of previousprobabilistic life cycle costing methods is presented.

In comparison with deterministic methods, the key difference of a PLCC is that there is nopossibility to trace uncertainties in input variables [40]. Furthermore, by not being able toconduct sensitivity analysis that captures the risks of an LCC, the deterministic approach israther limited. By instead using a probabilistic method it is possible to obtain a more nuancedpicture of the total costs giving the decision maker more valuable data and visualization of risksbut also about the input parameters themselves as a sensitivity analysis usually is carried out.Before continuing on the probabilistic approach of LCC (PLCC), a section to introduce MonteCarlo simulations will follow.

5.1 Monte Carlo Simulations

Monte Carlo simulations refers to a mathematical method to solve problems using randomsamples [41]. A straightforward example of an application for Monte Carlo simulation is whencomputing the expected value of a random variable. Instead of solving complex integrals, theMonte Carlo approach is to collect samples and estimate the expected value based on the samples.According to the law of large numbers (Bernoulli’s or Chebyshev’s Theorem), as the number ofsamples increases, the result will converge towards the theoretical distribution value [31]. AMonte Carlo simulation requires a representative distribution for each stochastic parameter,which could be determined by historical data or expert judgment [42]. Monte Carlo simulationsalso has the advantage of being able to incorporate correlated input uncertainties. Moreover, incases of simulations conducted with a strong variance in the input parameters it will be possibleto highlight uncertainties, especially when comparing investment costs across different techno-logies [31]. The relationship (co-variance) among correlated parameters could be both complexand hard to quantify. A weak correlation with large standard deviation will therefore requireeven more computations (samples) to be able to receive required accuracy. The whole processof the Monte Carlo algorithm can be viewed in Figure 5.1 below. The figure is inspired by [40].

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Figure 5.1: Monte Carlo method for repeated sampling [40].

In the context of a power system, various parameters have to be represented within thestochastic model. The uncertainty (stochasticity) means that even though there are some uncer-tainties attached to the parameters, the possible states and components move between states areoften known (or approximated) [43]. A component in an electrical power system, for examplea transformer, it is known by experience that it is very unlikely that it will work continuouslyfor 20 years straight. It’s also very unlikely that it will have a breakdown every day during itis operating period. As mentioned before, the historical data and expert knowledge will be keyinputs to model the uncertainty.

One way of describing PLCC is as a ”regular” LCC associate uncertainty to input parameters.The uncertainty comes in form of statistically distributed parameters and stochastic processessuch as failures. The method not only considers uncertainties today, but it is also possible toconsider uncertainties in the future and how they will affect investment decisions today. A PLCCapproach is one of the best when it comes to both assessing safety, reliability and costs [44]. Anexample of this is [45] that uses an ARIMA (auto-regressive moving average) model to predict themacroeconomic future. It’s shown that economic parameters have larger effect on the evaluationof a project than physical/technical parameters have. By simulating surrounding parameters, aso-called two layer simulation is obtained. This increases the complexity because more variablesare introduced, but if modeled right, more effects of uncertainties can be captured. The figure

21

describing the model is inspired by [45] but in this thesis and context applied as a general formof multilevel Monte Carlo simulation:

Figure 5.2: Two level Monte Carlo simulation [45].

5.2 Methods Assessing Uncertainties

Uncertainties for LCC modeling are caused by ”any lack of knowledge which causes the model-based predictions to differ from reality”[46]. The uncertainties might have two different origins,either from intrinsic randomness in parameters or samples, or from epistemic uncertainties whichare characterized by a lack of knowledge about fundamental phenomena [46]. Different categor-izations of uncertainties are common in the literature for both LCA and LCC. For the first one,the author refers to an extensive review in [47]. For LCC a short summary of uncertainties arepresented based on [47]:

1. Aleatoric and Epistemic Uncertainty - Uncertainties that are inherent and not possibleto eliminate.

2. PMS Uncertainty

• Parameter Uncertainty - refers to uncertainties characterized by empirical inac-curacy, un-representativeness, and lack of data

• Model Uncertainty - refers to assumptions, approximations, or lack of definition.It is introduced by disregarding potentially relevant aspects or parameters of the realworld.

• Scenario Uncertainty - refers to the influence of the researcher and that the LCAis depending on normative choices in the modeling procedure

”Alea” is the Latin word for ”rolling the dice”, which alludes for the randomness in samplesand parameters [47]. This intrinsic randomness cannot be eliminated and originates from lackof knowledge and the only way to reduce it is by introducing more explanatory variables orby increasing the accuracy in the already introduced variables [48]. On the analytic level of

22

uncertainties Ilg states that of all all reviewed articles parameter uncertainty is the most common(see Figure 5.3)[47].

Figure 5.3: Analytic uncertainty mapping, based on values presented in [47].

Not surprisingly, the most common uncertainties included in papers are parameter uncer-tainties. The fundamental of a reliable LCC analysis is high quality of the data. This includesfrequency, quality and accuracy of the data points. Another not so clear uncertainty regardingdata quality found in literature is that data from different sources might increase the uncer-tainty due to the different starting points, approximations and modeling approach [49]. ThePMS uncertainty can further be broken down into smaller categories. Model errors contains thesubcategories: simplification errors (induced by averaging, extrapolation, reduction of numberof variables and functional form of ignoring non-linearities), approximations in computer codingand extrapolation.

Chosen parameters or system boundaries influences the life cycle costing and to be able tocoherency compare different approaches, the same definitions, methodology and system boundarymust be applied [29].

5.3 PLCC Modeling Methods to Handle Uncertainty

For the PLCC method to be able to handle the uncertainty (variance) in input variables, prob-abilistic methods have to be used. A basic point estimate generates a single outcome whileprobabilistic methods generates a spectrum of solutions, representing the risk and spread of theanalysis. The spectrum width is determined by the standard deviation, which is a statisticalmeasure of how disperse the samples are. Therefore, the larger standard deviation, the largerspread of the output values. The different models to deal with uncertainty are presented belowand Figure 5.4 is inspired by [47] and some categories and methods are left out due to spacelimitations.

23

Figure 5.4: Methods to handle uncertainty. Picture is simplified and inspired by [47].

For the applied models that deal with uncertainty, a sensitivity analysis is usually carriedout. The sensitivity analysis tells how the influence of the assumptions regarding the data andmodel approach influences the result. A variety of methods exists. A classic sensitivity analysisvaries one parameter at a time and observes the output of the model. More advanced methodsexist, such as variance based methods, screening or scatter plots. Previous literature also statesthe statistics for which sampling methods are most commonly used, see Figure 5.5 below.

Figure 5.5: Common sampling methods [47].

5.4 Previous Probabilistic LCC research review

Previous research in the area is preformed in various fields of science and engineering. Applic-ations for life cycle costs is of interest for all assets or systems which are capital intense, have

24

reliability requirements and long life times. Therefore, it is an important task to learn from priorresearch and models developed, this is presented in Figure 5.1 below:

Table 5.1: Earlier PLCC studies conducted within different fields of engineering

Zhangs method of incorporate a real-time condition monitoring system to evaluate life cyclecosts is an applied railway application were multiple similarities to the power system are tobe found. For example, the high initial investments and extensive dependence of maintenanceactions are very much related to outages. Failures will lead to high costs and large problemsin the railway networks as well as large penalty costs if the railway company does not fulfilltheir required function [50]. Zhang uses a Petri Net (PN) model which uses different statisticaldistributions for failures but lacks to deal with uncertainties in cost parameters that are notstochastic.

Nasir and Chong uses a deep neural network to train a model to predict life cycle costs whencomparing repair costs and acquisition costs. This method requires a lot of training data, butis a good choice for capturing relationships between input parameters and includes uncertaintyin the input variables but lacks in the sense of using distributions for the different costs. Thisis although compensated for with the fuzzy logic modeling approach [25]. The main strength ofthe deep neural network modeling that could be translated into the power system domain is theability of the model to without much knowledge of the system itself be able to optimize the modelbased on training data. The disadvantage of Nasir and Chong’s research is although that they donot consider a synthetic evaluation of economy and technology. One attempt to solve this issueis done by Biann et al. and they have come up with a comprehensive evaluation of probabilisticanalysis that uses a Monte Carlo method to assess the uncertainties in input parameters, butalso pays specific emphasize to macro economical parameters such as inflation and the modelused also includes a variability in discount rate [51]. This approach gives a valuable insight in apractical application in the power system domain, but the model presented has the disadvantagethat it only uses average data for failures, meaning that a stochastic method to handle failuresis missing.

Battke et al. highlights one of the key aspects to probabilistic life cycle costing: the differencein performance across technologies [31]. With this techno-economic model, life cycle costs fordifferent performances of technology and variation within technologies. This could in the powersystem domain be in used for comparisons between different investment decisions were differenttechnologies results in different life cycle costs. The modeling approach is also possible to use to

25

represent the variability within ”same” technology or between different manufacturers.Zhu et al. provides an extensive methodology for assessing costs when comparing a ground

source heat pump. They consider the regulatory framework and incentives in the probabilisticapproach [52]. The research lacks in the way that there is no systematic way of deciding distri-bution functions and their relation to the sensitivity of the output.

Vithayasrichareon et al. show a practical example of correlation between uncertain para-meters using multivariate lognormal distributions between different fuels and highlights the im-portance of the standard deviation in the output (LCC results)[42]. The results are directlyapplicable to many investment decisions where correlation between input parameters are presentand by generating multivariate distribution, underlying correlations between variables can becaptured.

Frangopol et al. combines a deterioration model and a decision model by combining a MarkovDecision Process (MDP) with a Monte Carlo model to optimize maintenance and at the sametime minimize the total life cycle cost. The model used includes distributed input parametersand a renewal process and a deterioration process.

5.5 Cost Identification for PLCC

For costs to be fairly compared, a uniform framework has to be developed. The life cycle costingapproach accommodates all costs regarding acquisition, operation & maintenance, replacement,disposal and recycling [53].

The costs are the core of the PLCC, the estimation methods used for assessing the inputuncertainties to the correct distributions determine the accuracy of the whole PLCC analysis[45]. Quantifying the input parameters could be a difficult task, but Saltelli and Tarantoladescribe in their paper that the quantification of the input uncertainty can be based on sixmethods; measurements, estimates, expert judgment, physical bounds, output from simulationsand analogies to similar simulation input [54]. Costs are categorized in deterministic costs thatare fixed costs origin from the owner of the asses specific choices. For example inspection period,re-investments or other fixed costs/point estimates [17]. The other group of costs are stochasticcosts that are dependent on the occurrence of an event, often unexpected such as a failure withresulting repair and costs for penalties and/or compensation [17].

Historical costs are not always publicly available but together with expert approximations,good values should be possible to be obtained. The costs are dependent on which manufacturerhave produced the component, in fact it is a matter of quality management at each producingfactory. Also product developments might affect the component lifetime in a good way, but thiswill have effects on the mathematical model. Another important aspect of costs is how they arestatistically distributed. Which distributions are used when modeling will have great impact ofthe final LCC results. Another way to see the assumptions is that when they are incorporated,the risks can be visualized. The term ”cost uncertainty” is in the engineering context consideredto be more widely accepted and suitable, especially when it comes to applications in Monte Carlosimulations [42].

Incorporate risks are challenging, in particular due to the fact that there is often a relationship(correlation) between the uncertain parameters that is not straightforward. The data rely onhigh quality data and long-term forecasts which makes the data uncertainty a key priority whenpreforming life cycle costing analysis [55].

The following section of this thesis about cost estimation characteristics is mostly based on[56], the distinction between cost distribution as either analytic or by simulation.

To determine a cost distribution when historical data is available, this could be done by

26

essentially solving a fitting problem of data points to a distribution. Fitting problems like this andthe selection of appropriate distribution could be handled by software. The proposed distributioncan then be compared with statistical test such as χ2, Kolmogorov-Smirnov or Anderson-Darlingtests [57]. Distributions can either be parametric or non-parametric. The difference is basicallyif the data is given in an ordinal or nominal scale, a non-parametric statistic should be used. Ifthe data is given in interval or ratio scale a more powerful parametric statistic should be used.Non-parametric is useful when historical data is limited and one doesn’t require stiff modelingassumptions [47]. The most frequent distributions used in PLCC in a review from [47] stated inthe table below:

Table 5.2: Distributions used in PLCC [47]

Noteworthy is, according to Ilg, that: the Gaussian distribution is mainly applied when littlehistorical data is available and linear and triangular distributions are usually represented whena questionnaire study is preformed and when the available data is limited [47]. The Weibulldistribution is, as mentioned in section 3.3 useful when dealing with life time data while thePoisson distribution is mainly used for probabilities of occurrence.

The human perception capacity is tested by Miller [58] in how people can assign numbers tothe magnitude of different stimulus. Miller finds that people’s processing capability is rather smalland that judgments between people do not vary that much from person to person. The numberof alternatives for the people in the test ranges from 3 to 15 and most people are in the range of7±2. This tells that it is hard to do estimates that are extreme, both in negative and positivedirection. Meaning that expert judgments are more likely to give specifications/recommendationsin the middle of an interval rather than in the extremes.

The suitability depends on data availability, type of data (tangible, intangible, random, non-random), screened hot-spots, and tested modeling specifications.

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5.6 Modeling of Repairable Components

Failures of components are causing large economic costs. By modeling the failures with respectto accurate data for reliability , it is possible to predict future failures. There are generally threeapproaches to model reliability: black box, grey box and white box models [59]. A black boxmodel is a two state model, were a component can either be functioning or non-functioning. Theprocess can be described (for a non-repairable component) as probability distribution of the timeto failure. For a repairable component the black box process can be described as a stochasticprocess i.e a sequence of probability distributions for successive times to failure. [59]

When the degradation of a component is observable, it is possible to construct a mathematicalmodel that represent the degradation, then the model is considered grey. When a gray box modelexists it can be used for a model physical parameters and environmental conditions. This is inliterature referred as a white box model. The suitability of the chosen failure/degradation isdepending on the data availability and the type of data available (and accessible). This includesdata that is tangible, intangible, random and non-random [60]

Stochastic processes such as Markov models, Brownian motions or gamma processes areexamples of models to represent the sequence of failing components. This is known as degradationmodeling.

By applying a physical approach to model failures, the stress and condition can be modeledexplicitly [9]. This approach is highly linked to condition monitoring (see section 2.5). Byapplying sensors to gain measurements, the maintenance actions will be efficient.

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Chapter 6

Regulation of Power Systems

This chapter describes the economic tools and theory used to analyze investments in an elec-trical power network. Different regulatory models are presented as well as the current Swedishregulation.

DSO operators are natural monopolies and are regulated entities that have to cover their costonly through regulation revenues. Regulatory schemes are deciding the rules for the cost recoveryand sets the business rules for the DSOs. There are different regulatory models around in EU(and the world) which all try to balance the relation between DSOs, consumers and regulatoryinstances. What is driving the regulations over all is the main goal of optimize the utilization ofthe grid. This includes to avoid exploitation of the monopoly market power and aims to increasethe general welfare for the society, both economical and societal. Other aims of the regulationare to drive energy efficiency such as the Energy Efficiency Directive (EED) which will help theEU to reach its 20% energy efficiency target. The target aims to increase all member states’energy efficiency from generation to end consumption [61].

The economical regulation of the DSOs aims to facilitate three main objectives for the networkowners; keep economic viability of the company, deliver at best price for customers as possibleand deliver a high quality of service [62]. Traditionally the whole electricity sector has beena non-competitive market but since the liberalization and unbundling of the wholesale market,introduction of competition have increased the efficiency in over all but on the other hand a needfor regulatory framework to keep competitive parties from exploiting control over monopolyfunctions [63]. In Europe, EU directives are working for a liberalized and open pan-Europeanelectricity market and set rules (but not require implementation). The overall goal of theseEuropean level regulatory framework is to work towards decarbonization and europeanisation[64]. On a national and regional level, these regulations indirectly affect the DSOs regarding forexample harmonization, transparency and price issues.

Revenues for the DSOs have traditionally been based on either cost-of-service or rate-of-returnscheme. The application of sound and fair regulatory mechanisms is an important foundation ofeach actor in the electrical network. It favors the accessibility, network expansion and investmentsand service quality. A good regulatory framework will enhance the robustness of the relationsbetween DSO, consumer and producer [65].

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6.1 Revenue Caps

Under revenue cap a ceiling is set on the price that the DSO are allowed to charge their customers.This is known as cost-of-service or rate-of-return regulation. As this maximum level of revenues isperiodically re-negotiated, the by the company received rate of return is identified by calculatingthe total costs and from that decide an acceptable level of return on the invested capital. Thelevels of tariffs are from the total costs calculated for the period [13]. If the company managesto reduce costs but there will be re-negotiations during the regulatory period, the system doesnot encourage reduction of losses or a more effective utilization of resources. Consequently, ifthe costs during the regulatory period rise, the rate of return is reduced [65]. This imposes noincentive to exert cost-reducing effort.

6.2 Performance Regulation

In performance regulation, indicators or indices are used for qualitative analysis of the per-formance of the DSOs. From [66] performance, criterion are defined for criteria of performanceindicators are as follows:

1. The improvement of the indicator should be a quantifiable benefit to grid users in particularand the society in general as a whole.

2. The index used should be possible to calculate and determine in an accurate and objectiveway

3. The index should be possible to influence, even to a limited extent by the system operatoror the network operator.

4. The index used should as far as possible be technology neutral.

6.3 Revenue Cap Regulation

In Sweden there is a revenue cap regulation since 2012. The Swedish Market Inspectorate decides(Sv: Energimarknadsinspektionen, Ei) the revenue cap for a time period of four years [4]. Eachperiod includes an incentive for continuous supply. The DSOs will either be rewarded or penalizeddepending on how they perform. Each DSO will individually receive a benchmark level dependingon parameters such as consumer density. This was first introduced during the regulatory periodof 2012-2015 [4]. During the previous regulatory period of 2012-2015 the performance of DSOswas carried out using the statistical indicators SADI and SAFI (see section 3.1) and comparedto historical levels.

The performance-based indicators in Sweden are based on two entities, namely losses andload factor [4]. Losses might affect the DSO’s investment decisions [67]. High losses will increasethe total costs of operating the grid as well as less energy needs to be produced to cover thelosses leading to larger benefits for the society in general [4, 68]. The load factor is determinedby the average power and the peak power in a feeding point of a distribution network. Theratio between the two is considered as an index for how the load point is utilized. The aim in adistribution network is to keep the power flow profiles constant, level off high peak demands andlow load valleys [68]. In Sweden, the load factor is determined by the the ratio between averageload levels and the highest peaks in load (calculated for each day and then the average is usedin the regulation).

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As ohmic losses are proportional to the square of the current, lower peak power flows havea large impact on the total losses in the distribution network. These incentives are rewardinglower losses and a low ratio between peak and average load in the system which implies the timeaspect of the network incitement i.e. it is more beneficial to reduce the losses during peak hours,leading to greater incentives when the grid is at most exposed.

6.4 Revenue Cap Regulation in Sweden

An ex-ante regulation of the network tariffs was introduced in Sweden 2012 and underwentchanges to the second regulatory period 2016-2019, see Figure 6.1. The level of the cap thatlimits how much each DSO can charge their customers are set to be a balance between enoughreturn for the DSO and reasonable tariffs for the customers.

Figure 6.1: The Swedish revenue cap regulation [16].

Figure 6.1 shows an overview of the Swedish revenue cap and one can see that there arethree different parts that decide the revenue cap for the regulatory period, namely controllablecosts, non-controllable costs and asset base. The controllable costs are possible for the DSO toaffect and are related to the operation of the grid. Since the costs are influenceable, the EnergyMarket Inspectorate added an efficiency requirement, described in section 6.5 below. The non-controllable costs are to some extent not influenceable. It could for example constitute of coststo the feeding grid and fees. The asset base consists of two parts, depreciation and return. Theasset base is calculated by the sum of all present purchase values (PPV) and is then used tocalculate the capital costs. The return is sometimes adjusted by incentives (described in section6.5).

The capital cost calculations is for the regulatory period 2016-2019 a real linear method witha depreciation time set to 40 years for current carrying equipment and 10 years for meters andIT.

Capital cost = Dep+Ret =

1LT + LT+1−age

LT ·WACC if age ≤ LT1age + 1

age ·WACC if LT < age ≤ (LT + α)

0 if age > (LT + α)

(6.1)

were,Dep is the depreciation.

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Ret is the return.LT is the depeciation time.α is a constant providing some capital costs α more years after LT. α is 2 years for meters and10 years for other componentsWACC is the weighted average cost of capitalPPV is the present purchase value

6.5 Incentives for Swedish DSOs

In Sweden it is regulated by law that an outage should never last longer than 24 hours, the max-imum number of outages is set to 11 outages per year as well as voltage quality and compensationschemes if the DSOs are not fulfilling their obligations [4]. The regulatory framework aims formaintaining a minimum level of requirements but will provide incentives for DSOs to provide ahigher level of service if it is socioeconomically motivated. During the current regulatory periodof 2016-2019 the customers are categorized in five groups: household, industry, agriculture, com-mercial service and public service. These customer groups are forming input parameters givenin costs of interrupted power (SEK/kW) and cost for interrupted energy (SEK/kWh) with adifferentiation if the interruption is notified in beforehand or not. The indicators used are seenin Figure 6.2 and the equations used for SAIDI and SAIFI is given in equation 3.1 and equation3.2 respectively.

The indicator CEMIn is introduced to reduce the size of the penalty or reward and removethe possibility that some parts of a distribution system will be boosted by only focusing on highdensity areas of customers to the expense of low density areas (see equation 6.2). This is doneby review if CEMI4 (4 is chosen to represent ”good quality”) has worsened or improved andwill always reduce the reward or penalty (and is limited to 25%).

CEMIn =Total number of customers experiencing at least n interruptions

Total number of customers(6.2)

Figure 6.2: Incentives for DSOs [4].

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Figure 6.3: Incentives for DSOs [4].

To be able to base line between average performance between DSOs with different sizes,ownership and geographic conditions the average performance for SAIDI, SAIFI, notified inter-ruptions, un-notified interruptions and for the five customer groups a total number of 20 baselinesare calculated (see figure 6.5).

Figure 6.4: Different base lines for benchmarking DSOs. Examples were baseline A is under-performing and baseline B overperforming respectively [4].

The DSOs in Sweden are categorized by different conditions. Some of the DSOs have verydense customer density while others are very sparse. This implies for the Energy Market In-spectorate to even out the performance between different DSOs. This is done by a regressionmodel, illustrated in Figure 6.5. The DSOs above the red line are using baseline A in Figure6.4 while DSOs below the red line is using their own performance as baseline. See baseline B inFigure 6.4.

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Figure 6.5: Average performance from benchmarking of all Swedish DSOs [16].

The final incentive is the calculated for each DSO in Equation 6.3,

Qy =

5∑k=1

2∑j=1

((SAIDIb,jk − SAIDIo,jk)KE,jk)+((SAIDIb,jk − SAIDIo,jk)KP,jk) ·Pav (6.3)

were,y is the yeark is the five different customer groups (1-5)j is the two categories of interruptions (notified or not)b represents the baselineo represents the outcome during year yKE is the cost parameter given in SEK/kWhKP is the cost parameter given in SEK/kWPav is the average yearly power usage

Pav =Ey,kHy

(6.4)

were, E is the total energy consumption for each customer type k, year y and Hy is the numberof hours during the year y. The next step is to calculate the yearly adjustment depending on thehistorical performance of CEMI4

CEMI4δ,y = CEMI4,b − CEMI4,y (6.5)

were CEMI4δ,y is the yearly adjustment, CEMI4,b is the historical performance and CEMI4,ythe yearly outcome. Qy is limited to ±0.25%. In cases were CEMI4 is affecting the incentivethe final yearly incentive is calculated as follows:

QTy = Qy (1− |CEMI4δ,y|) (6.6)

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During the whole four year regulatory period the total incentive is given by

Qt =

4∑y=1

QTy (6.7)

The cost parameters are given by the following table, specified by the Energy market inspect-orate:

Table 6.1: Cost parameters used in the quality regulation 2016-2019 [16].

6.6 Future Changes in the Regulatory Framework

The current regulation in Sweden will be present between 2016-2019, and after that there is a largeuncertainty of which regulatory framework will be chosen for the upcoming period. The SwedishEnergy Market Inspectorate might adjust how incentives are calculated and re-shape how capitalbases in for electricity grid owners are calculated to provide the, according to them, adequate levelof investment signals, adequacy and reliability [62]. The high penetration of renewable sourcessuch as photovoltaic and wind power as well as the integration of electric vehicles, DSOs needsnew tools to meter, automate and facilitate their grids. These are investment requirements whichno extra incentives are given for today, even though there are new possible business opportunitiesand possibilities for DSOs that chooses to invest in smart grid equipment. Although, these typesof investments are not today included in the regulation (because it is neutral to technology).Innovation incentives might exist in the future, but today it is only possible for DSOs to applyfor pilot projects regarding new technology. For more innovative solutions (investments) to beapproved, regulatory incentives have to be given. For example in Italy, pilot projects are receiving2% extra WACC for smart grid investments [62].

To be able to obtain long-term investments rather than short term optimization the regulationhas to be predictable. DSOs must be able to have a stable and predictable rate of invested money,both to attract investors but also to keep good constant levels of the performance of the grid.Moreover, it is important that the long-term challenges of investments are included in today’sregulatory framework to incorporate the challenges of tomorrow.

Future trends of how the electricity network is regulated is changed and is moving from tra-ditional productivity-oriented towards output-based regulation [69]. The trend is going towardsquality regulation to obtain cost efficiency and long-term time performance.

For assessing life cycle costs, the regulations are of high interest and have a strong influence onthe investments in the grid. Therefore it is a very important factor to consider when calculatingfuture costs or incentives.

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Part II

MODELS AND RESULTS

36

Chapter 7

The developed PLCC model

A Swedish Distribution System Case

This chapter describes the developed life cycle costing model and explains the different modules todescribe the cost contributions during the life cycle of components in a power system.

The developed life cycle costing model provides a quantitative link to the total life cycle costs ofcomponents in a power system. The advantage of the model is that it uses the stochasticity ofreliability for components resulting in capturing the uncertainty and risk. The model considersuncertainties in costs by assessing them as distributions. The model provides the possibility toconsider total societal cost for outages and how the current regulatory framework affects main-tenance strategies in the power sector by using the framework developed in general in Chapter 5and applying the peculiarities of a Swedish distribution system. This means that the developedmodel will emphasize of the regulations today in Sweden but the model can be generalized toother systems or components.

The developed model is illustrated in Figure 7.1;

Figure 7.1: Overview of the developed PLCC model

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7.1 Different Steps and Requirements of the Model

Step 1. Component Decision

The first step is to decide which component or part of the power system to be considered. Thisstep involves gather data about were the component is located in the system, how many cus-tomers will be affected if the component fails, which the investment alternatives to consider areand which the current maintenance strategy is, and also important considerations regarding theenvironment of were the component is installed. How does for example the load level of the nodelook and is the load level expected to rise?

Data needed: Component nameplate information (rated power, rated voltage, no-load losses,max load losses), component location, maintenance strategy, investment alternatives and con-sidered time scale. Load factor, assumed growth or decline in electricity use.

Step 2. Cost Identification

Identify which costs to consider in the model and decide how deep the model needs to be ableto give a representative picture of the scenario. In a minimum the model must consider: capitalinvestment costs, operation and maintenance costs and costs of loss of energy. The easiest wayto obtain the distributions for the different costs is to gather the costs in a histogram and thenfit a distribution to each individual cost [70]. To choose the most appropriate distribution, aKolmogorov-Smirnov test could be used. If no historical data is available or too few data points,other methods such as expert opinions or assuming a PERT1 distribution for the known physicalboundaries could be used.

For costs to be fairly compared, a uniform framework has to be developed. Different invest-ment alternatives have to have the same costs and assumptions for an analysis to be conducted.To asses the life cycle costs in an investment decision, the following costs are considered:

• Capital investment costThis includes the initial acquisition cost, cost of construction, administration and manage-ment.

• Operation and maintenance costOperation and maintenance costs are including all costs needed for the component tofunction and operate in a safe manner. This includes costs for operate the component,costs for personnel doing maintenance inspection, cost of spare parts and costs of repair.

• Cost of loss of energyThese are the ohmic thermal losses occurring in the network caused by the component.Depending on the component type, the loss-level is different, but differences are also causedby how heavily loaded the component is and of its physical state.

• Outage costThe cost a DSO has to pay to the customers when interrupting the power. The outage costis described by Equation 7.1 and is an approximate form (found in [71]) of the regulatorycompensation scheme described in [16]:

Outage cost = LF · Prated · λ · Toutage (7.1)

1a family of probability distributions that are defined by maximum, minimum and most likely value

38

were, LF is the load factor, Prated is the rated power of the transformer, λ is the electricityprice for the corresponding customer compensation scheme and Toutage is the outage time.It is in the model assumed that the distribution transformers are only serving residentialloads and each outage is unnoticed, see Figure 6.1.

The developed PLCC model applies to calculate different costs during a life cycle of a com-ponent. The model output is a frequency distribution of calculated NPV that are annualized bya discount rate, expressed in a monetary unit today. The life cycle cost function models costsas positive and incentives as negative. There will be no considerations to incomes and thus, thegoal is to minimize the costs in the NPV function. The life time of the model is the technical lifetime of the studied component. The mathematical representation of the NPV function is shownin Figure 7.2 below.

LCC = Capex+

N∑n=1

Outagei +Maintenancei + Lossesi − Incentivesi(1 + r)n

(7.2)

Data needed: Historical data for costs. Costs to be considered in the most basic evaluationmethod: operational costs, maintenance costs, acquisition cost and outage cost.

Step 3. Decide Model for External Economical Parameters

For the PLCC to be able to capture economical movements on a macroeconomical level, inflationfor example could be be modeled with an ARIMA model.

By fitting an auto-regressive model to the historical data a good approximation can be ob-tained. Other approaches could be to fit a distribution for the parameters and then with thesame procedure as for cost, randomly pick a number from the obtained distribution.

Data needed: Inflation rate (or historical inflation rate), discount rate and electricity pricemodel.

Step 4. Decide Failure Model

The failure model will capture the stochasticity of failures of the component. When conditionbased maintenance is used it is highly advisable to use a random process model or a stochasticcontinuous time models such as Brownian motion or Wiener process. These failure models canbe trained to represent real world data and scenarios. Another approach is to model the failureswith a Markov chain. That model could be used in a simple way were only two states are present(working and non-working states). The model is also possible to model other states and couldbe expanded depending on the data available. In this stage, assumptions regarding how thecomponent behaves after a failure occurs may be important, depending on if the chosen failuremodel approach considers a repairable component or if all failures leads to the end-of-life-state.

For DSOs that have access to extensive historical data for failures and failure types it isrecommended to use a Markov chain. Data will be Weibull-fitted and parameters to the distri-bution will be obtained. The values will the be used to build the transition matrix for the Markovchain. Other possibilities when measurements at site are present, is to use different stochasticprocesses such as the gamma process or a Brownian motion, due to their ability to representphysical systems [72].

Data needed: failure rate, failure frequency and historical failure data. Optional: failure rateover time.

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Step 5. Model of Condition Improvement

The maintenance strategy of the component will represent different costs for different main-tenance actions. In this step one has to choose to either ignore the increase in reliability if acomponent is refurbished, or another maintenance action should be performed. Other approachesis to decide a fixed value for each maintenance action or represent the component health with arandom improvement.

There are two different ways how a DSO might implement a probabilistic model to assess theimpact of different maintenance models. This is by either model the condition, assuming fixed orvariable conditioning improvement or using a CMS to measure the actual condition of the asset.

1. Modeled ImprovementThis includes a modeling approach in both ends of the method. Mathematical modelsrepresent both the decoration and failure modeling of the asset as well as the modelingrepresentation of the condition improvement. By obtaining good estimation models, theimpact of every maintenance action can be determined, leading to a more effective main-tenance schedule.

2. Fixed ImprovementSame as above with the difference that maintenance actions are assumed to be fixed. Onecommon modeling approach is to use either ”as good as new” or ”as bad as old”. The basicassumption is that the results lies in the range between the two states

Data needed: Mathematical representation of condition improvement.

Step 6. Model of Regulatory Framework

The current regulation where incentives and costs are added to the total cost function. Consider-ations must be taken regarding how different actions are punished or promoted by the regulations.The regulations might be formulated on a system level where the whole system performance isevaluated and not on a component level. It is therefore important to make correct assumptionshow individual component performance should be represented in a regulation that is based onthe whole system performance of the DSO.

Revenue Cap Regulation

The revenue cap regulation in Sweden is described in section 6.4. The key aspect for a DSOto consider is the capital cost calculation method for which the depreciation time is set to 40years. Practically this means that equipment older than this age will not contribute to the returnallowed for the DSO.

Loss reduction

The Swedish regulations for distribution systems are described in section 6.3. The revenue capregulation is described by two parts, one for the adjusted incentives and one for the allowedreturns. Based on the regulation scheme in today (between 2016 and 2019), the mathematicalmodel of the regulation scheme is defined as follows:

Loss evaluation = (P0ref − P0 + LF 2 · PLref− PL) · λ · T (7.3)

40

were P0ref is the reference no load loss, P0 the no load losses, LF is the load factor, PLrefthe

max load losses, PL the max load losses and λ the electricity price and T the number of hoursthe transformer is running.

As stated in [67], the energy loss model is a conservative assumption due to it only considersresistive heat losses. In reality one uses the difference in energy fed at the feeding point and theenergy withdrawn at the load point [67].

The incentives regarding losses is a function of the total losses for a DSO. In this model, thelosses are derived from the losses of the typical transformer. The values used as reference pointis an assumed already installed transformer. The reduction of losses is then compared relativelyto this transformer.

Data needed: Mathematical representation of punishments and incentives.

Step 7. Choose Sampling Method

There exists a variety of different sampling methods. One of the easiest ones to use is MonteCarlo simulation where random numbers are used to generate different parameters in each iter-ation, and after a large number of simulations a histogram of costs can be generated and fromthat, conclusions can be drawn. If the computing power is demanding, other sampling methodscould be used, were Latin Hypercube is the second most common method, after Monte Carlosimulations.

Step 8. Results

When a distribution of life cycle costs are obtained one must be able to equally compare thedifferent investment alternatives. This is for example done with calculating the annuity of thenet present value. The annuity used is preferably the mean of the obtained LCC result andannualized with the average life time. This gives an approximate value for the annualized lifecycle costs and makes it possible to compare investment alternatives with different time horizons.

Step 9. Sensitivity Analysis (Recommended)

After a well-performed PLCC analysis the input parameters must be analyzed to evaluate howdifferent individual variables are affecting the final result. This could be done with scenariosimulation or vary parameters in a pre-determined manner and observe the outcome.

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Chapter 8

Application of Developed Model

This chapter describes the result of a conducted case study and summarizes results from thesimulations

The aim is to apply the developed PLCC model to analyze and apply it to an investment decision.The application of the developed model is versatile and applicable for many different components,but will here focus on life cycle costs for transformers. The results obtained are dependent onthe specific choices of transformer types, network data and of the different cases applied to thesimulation.

8.1 Setting

The developed model compares two different transformers, one that is 16 MVA and one 20 MVA.The goal is to investigate how the different characteristics of the two transformers are reflectedin the life cycle cost of them both. The main question that will be answered is if it is a goodinvestment decision to choose a smaller transformer with lower initial investment cost which runsat a higher loading compared to a transformer that is over-sized in capacity and has a higherinitial cost. The transformer takes a large portion of the initial investment and plays a crucialrole when it comes to the reliability and continuity of supply of the power system. Outages resultin large costs and loss of income. Taking a life cycle perspective of the investment and analyzingthe stochasticity and uncertainty of the two transformers could show huge insight for investorsand provide guidance of how to select transformer for grid expansion (or replacement).

Transformers are in general categorized by a long service life and are traditionally very reliable,but the impact of outages and failures might get costly. The following table illustrates the twotransformers that will be analyzed, see the table below.

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Table 8.1: Table describing the two transformers [73].

8.1.1 Failure Statistics Used

As mentioned before, transformers are a very reliable components in the power system. Whena failure occurs, the consequences could be devastated. Both for the component itself but alsofor the system as a whole. The failure statistics used in this case study is based on [74], seeTable 8.2. The failures for distribution transformers are presented below and is used as inputparameters to the PLCC model:

Table 8.2: Failure statistics for distribution transformers <50kV [74].

The two transformers are expected to have a weibull distributed lifetime with an expected life-time of 40 years for both transformers. The assumed shape parameter of the weibull distributionis in both cases 2.8.

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8.1.2 Costs used

Failure costsWhen the Markov Chain iterates through the years of the transformer’s life, it will sometimesreach a faulty state. This state is associated with certain cost, earlier mentioned as stochasticcosts. See table below and following section about the description of the PLCC-algorithm.

Table 8.3: Cost associated with certain failures

Inspection costsOther costs assumed are that every 5th year an inspection of the transformer takes place. Duringthis inspection the DSO investigates the state of the components by visual inspection. The costof this inspection is set to 10 000 SEK.

Cost of loss of energyThe cost of loss of energy is calculated by using Equation 7.3. The load factor LF is set to 0.57for the 16 MVA transformer. Since the 20 MVA transformer has 20% larger rated power, it isassumed that the load factor will decrease equivalently. This is comparable values of load factorsused in [4] where an average of 0.5 during the day. The electricity price λ is assumed to be 0.455SEK. The yearly total cost of loss of energy is then assumed to follow a normal distribution witha standard deviation of 10% of its mean.

Outage costThe outage cost is calculated by Equation 7.1. Here the load factor LF is assumed to be 0.4in the 20 MVA case and 0.6 in the 16 MVA case, Prated is the rated power of the transformer(20 and 16 MVA), the electricity price λ is also here assumed to be 2.00 SEK and the outagetime Toutage is set to 10 minutes. The outage cost is calculated from assuming a penalty cost ofenergy not served.

8.1.3 Incentives Used

The incentives used in the PLCC model is calculated from Equation 7.3. The values chosen forλ and T are set to 0.455 SEK and 8760 hours. Also here the load factor LF is set to 0.5 forcomparison reasons and the incentive is half of the value of the loss valuation.

8.1.4 CBM used

Condition based maintenance and failure detection is not common to be used at distributionlevel in power systems. At transmission level on the other hand, CBM is common. This thesisrelies on the assumption that the same type of failures will detected as for transmission leveltransformers. It is also assumed that the same type of sensors is possible to use, making aconversion of costs from transmission level components to distribution level components. The

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initial costs for the sensors, IT system and setup is set to 80 000 SEK and a yearly cost of 2500SEK for analyzing the results. The used fault tree uses have the same probabilities as in [75].The used statistics used for detection of errors in windings will 85% be detected and of the 15%that not will be detected, catastrophic failures will occur at 80% of the time while minor faultswill appear at 20% [75].

8.1.5 Description of PLCC-algorithm

Considering the regulation model, failure model, maintenance model, input of uncertainties andeconomic parameters, the probabilistic life cycle cost model is formulated. Each net presentvalue is described in Equation 7.2.

1. Generate n transformer lifetimes

2. Simulate n Markov chains of long length

3. Cut each Markov chain at the lifetime value of each corresponding transformer by settingthe state of the chain to ”end of life”.

4. Generate a cost distribution from a Monte Carlo simulation. Iterate through all chains.Assign costs and incentives for every year and to the different states.

5. Repeat for all transformer types

8.2 Economical Results

The following section will show the histogram of the PLCC performed on the two transformertypes. The net present values are shown below.

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Figure 8.1: Histograms of net present values, combined figure.

The mean and standard deviation is illustrated in the following table:

Table 8.4: Mean and standard deviation of 16 and 20 MVA transformers.

The results shows that the 20 MVA transformer in average is cheaper to install than th 16MVA. It also has a lower standard deviation, meaning that the risks and uncertainties associatedto the investment are lower in the 20 MVA case.

8.3 Incentive Regulation

The incentives sent by the current regulation is, as stated before, giving double incentive in thesense of reduced cost for covering loss of energy and economic compensation for reducing thelosses. The impact of the incentive is visible as a shift of the NPVs towards lover values.

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Figure 8.2: Effect of incentive regulation. The incentive is increased from 0 to 200 per cent.100%-level means the level as of today.

8.4 Outage Cost Effects

Traditionally in urban areas a distribution transformer could be fed from two different locations.That means that if one cable is having a fault, the power can be re-routed and the outage willonly last a short period of time, while if there is a fault or failure in a rural area the distributiontransformer is replaced by one from the DSOs stock.

The outage cost are the cause of the extreme spikes in costs that occur. Because there is ahigh outage cost associated with a failure and the failures occur rarely, once a failure occurs thecosts for the energy not served is large. The outage cost is one of the largest reasons for thespread in the histograms of NPV. If no failure occurs, all the sampled data is located around themean but as soon a failure happens, the cost associated with it are making a large impact of thestandard deviation (and variance) of the samples.

By analyzing the impact of the outage time, the 16MVA transformer is used as an example.The outage time is varied from 10 minutes to two hours, this to illustrate the impact of theoutage time, see Figure 8.3 below:

Figure 8.3: Effect of outage cost

If the cost of compensation (i.e the cost the DSO need to pay in compensation is varied from0 to 20 SEK. The cost of energy not served (ENS) is highly correlated to an increase in life

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cycle costs, visible in the figure below. Note that the figure is smoothed to better illustrate therelationship.

Figure 8.4: Effect of outage time

8.5 Effect of Condition Based Maintenance System

When implementing a CMB system it exists a initial cost of the acquisition of the sensors andmeasurement systems. Also an annual cost of analyzing the newly obtained data will be present.By implementing a CMB one can detect some failures that otherwise would have caused severedamage or end-of-life for the component. This implies that some of the stochastic costs areavoided, but are on the other hand traded for known costs of acquiring the CBM system and theanalysis of the data.

Figure 8.5: Condition based maintenance implementation

There is no clear and obvious difference between Figure 8.5 and Figure 8.1, but when analyzing

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the details, illustrated in the following table, differences of having CBM is visible.

Table 8.5: Condition based maintenance implementation

It can be concluded that a CBM is not a good investment. The overall increase in meanNPV is not compensated by a sufficient reduction in large failures. This concludes that theinitial cost of CBM plus its costs for analysis, does not outweigh the benefits (a lower net presentvalue). For a DSO it could be of interest to have the information of the status and health oftheir components. This might also help them to reduce costs from unnecessary maintenance andin a better manner plan for the decommissioning of the transformer in its end-of-life.

8.6 Fixed-Lifetime Scenario

Instead of assuming a Weibull distributed lifetime of the transformers, a fixed lifetime is assumedto 40 years. This means that the ”natural death” of the transformer occurs at 40 years of service.But the possibility of an end-of-life failure still exist which means that some of the samples willhave a lifetime shorter than 40 years due to a catastrophic failure.

Figure 8.6: Fixed-life analysis. All samples are assumed to have a fixed lifetime of 40 years.

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Table 8.6: Condition based maintenance implementation

The standard deviation reduces significantly since all transformers have the same amount ofworking years. This means that each sample gathers almost the same cost troughout its lifetime.

8.7 Sensitivity Analysis

In this section the results from the perspective of a conducted sensitivity analysis is presented.The the input parameter is varied and the average value of the NPV for that Monte Carlosimulation is presented.

8.7.1 Discount Rate

By varying the discount rate from -5% to 15% one can clearly see the dependency of howimportant the interest rate is for performing NPV calculations. By assuming first a high negativerate, which means that one values money with a higher value in the future than today, thereis both a steep slope but also significantly higher NPV values for more negative values of thediscount rate. The reason for this can be seen as pure mathematical by observing the NPVequation, but by also analyzing large cash flows in the future there will be large implicationsdepending on the assumed value for discount rate. It can be concluded that the choice of discountrate has a very strong dependency in deciding whether an investment it profitable or not.

Figure 8.7: Sensitivity with respect to interest rate

8.7.2 Electricity Price

The electricity price is important for calculating the value of losses. In this sensitivity analysisone can clearly see a linear relationship between the NPV and the electricity price. This wasexpected since the transformer is operating at all time during one year which means that a cost of

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loss of energy will always be present. The following illustration shows how the NPV is changingwhen the electricity price is varied.

Figure 8.8: Sensitivity with respect to electricity price

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Chapter 9

Discussion

This chapter provides a discussion for the findings in the case study.

9.1 Internalizing of Externalized costs

The costs rationalized in the model are highly dependent on the costs parameters and cost levelsused. This is depending on whether all costs are internalized in the model. Depending on whichperspective of costs the model tries to explain, the costs will vary. The different approachescould origin from costs affecting the customers, costs affecting the DSO or costs for the societyas a whole (socioeconomic costs). This phenomenon is best illustrated with an example. Outagecosts should aim to represent the costs an outage is causing. However there is a gap betweenwhat a DSO pays in penalty and what the cost of an outage actually is. The outage cost issometimes high, for example when large factories are involved with long restart times. The caseis different for a supermarket for example where the costs will not be high for short outages butafter a certain threshold in time, food will be destroyed if the electricity is not back on-line. Itis a hard task quantifying the ”correct” value for the compensation scheme but progress is madetowards a closer link to actual causes.

9.2 Regulation and its Relation to Investment Decisions

Because of that the losses are calculated on a component level, which means that only certainparts of the system are analyzed, is a fair simplification for individual investments and compar-isons between different investment alternatives that incorporate the regulatory framework. Inreality, a DSO can decide to install a high performance component that reduces the losses, but ona system level the losses might increase due to new consumption patterns, higher consumptionetc. The same reasoning is true fore the incentives for reliability improvements. Particular oc-currences of failures might be reduced when investing in new components but if no considerationis taken on reliability as a whole, individual investments will only have a marginal effect. It isstill to remember that each component is a part of the aggregated system and the performanceof the system. For DSOs to achieve the most use of their limited money, reliability importanceindices can be used to diversify maintenance efforts and gain better understanding of systemperformance.

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An interesting parallel is when investment decisions on component level (such as the analysisin this thesis when life cycle costs are analyzed) are compared to infrastructure investments andupgrades are compared and one can draw conclusions how the regulatory framework is affectingdifferent areas/aspects of the electrical network. Huang found that the incentive for load factorincrease does impact the network infrastructure investment, but the incentive for loss reductiondoes not. This is also true for investment decisions for transformers were a DSO in no way canaffect the load factor [67].

Another interesting aspect is the replacement criteria for a transformers. Since bushings andtap-changers are replaceable the only reason for replacing a transformer due to age is caused byinsulation decoration and problems with the paper/oil insulation. Otherwise a transformer ispossible to refurbish either on- or off-site. In practice this means that a DSO is forced to replacea working transformer older than 40 years due to current regulation. However, the trend amongDSOs is that no replacement of working transformers is carried out except when a new stationis built and the DSO usually replaces all components as well as feeding cables/lines. The otheralternative for a replacement is when tree poles and over head lines are replaced to protect thegrid from storms, meaning that the transformers located on poles are also replaced.

It should be denoted that the PLCC analysis and method is site dependent and depends on thecharacteristics of the particular location in the grid as well as the characteristics of the usage of thecomponent. It is previously shown that within a large population of components (transformersfor example) a variety of performance across the population is present [7]. The uncertainty ofthe analysis is preferably measured in the standard deviation of the generated cost distributioncurve, but as stated in [55], high investment costs and monetary gains of energy savings incapital intense investment decisions still seem rather limited by investors due to simplificationsin input parameters. This is also illustrated by incorporating many different uncertainties anddistribution for costs, it is a very complex task to investigate whether a certain input parametergives a significant influence on the end result. It can in the obtained results be seen thatfor example to compare the effect of losses when uncertainties exists, they hide beneath otheruncertain (stochastic) parameters such as outage costs.

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Part III

Closure

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Chapter 10

Conclusions

This chapter presents the conclusion of the thesis as well as the concluding remarks of the earlierpresented research questions. The chapter also identifies future research directions.

10.1 Concluding Remarks

In this thesis a PLCC model is presented which uses a Monte Carlo sampling method in combin-ation with a Markov Chain failure model which is then applied to distribution system operatorsapparatus and transformers in particular. The proposed model quantifies the total cost througha life cycle of a component and includes the incentives and regulatory punishment costs. Themodel generates a spectrum of net present values that for different technologies or settings,makes it possible to compare investments and reach understanding about the uncertainty andrisks attached to the investment.

R.1 How to model probabilistic life cycle costs in a deregulated power system?There exists a variety of options for modeling life cycle costs. It is shown with the casestudy that a combination of different tools such as Markov Chains, Monte Carlo samplingand degradation modeling is proven to capture uncertainties of investments.

R.2 What potential sources of uncertainties exists in LCC?

R.2.a What methods are appropriate to address uncertainties in LCC calcula-tions?Firstly, the uncertainty must be categorized and identified. The core of addressingthe uncertainty is to analyze the size of the standard deviation and also to compareit to the sensitivity analysis. Depending on the type of uncertainty, the addressing ofit will look different. The uncertainty is characterized differently depending on if it isregarding the model or the data. The proposed PLCC captures stochastic uncertaintywith a Markov Chain Model and uncertainty that comes in the form of input data,multiple distributions is used to capture the variability of the input parameters.

R.2.b How can uncertainties impact be quantified?Uncertainty can be viewed as a standard deviation or a probability that an extremevalue will occur. Both of these representations are tied together. The process ofquantification is done by using: simulations, expert judgment or historical data to

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assess costs. Methods such as Kolmogorov-Smirnov can be used to find appropriatedistribution for the costs which then is possible to quantify the uncertainty.

10.2 Conclusions From the Case Study

When comparing the two transformer types that a DSO that has to choose between, either ofthe two has to make a choice that is not completely obvious. The uncertainty in the case study,illustrated by the spread (standard deviation) of the net present values shows that the probabilitythat either of the two types is for sure a cheaper option can be rejected. The sensitivities ofimportant parameters are indicating how sensitive the model is to changes and variability. Outof them, the DSO can make predictions about the future and analyze how such changes willaffect their investment decision. The developed model proves that it is suitable for power systemapplications, and a life cycle approach for costs is favorable when comparing different investments.

From the case study one can conclude that the definitive answer to which transformer is thebetter alternative is not completely obvious. The fixed age analysis showed an advantage for themore expensive 20 MVA transformer. This can partly be explained by that the load factor in the20 MVA case is lower since the load is assumed to be the same in the different cases but sincethe the rated power is 20% higher in the 20 MVA case, it operates at lower levels of load (as apercentage of maximum power). Even since the absolute terms of no-load losses and max-loadlosses are higher, the total losses over a life cycle is lower. This has a big impact of the result.

10.3 Future Work

Uncertainties is not a unique feature of LCC but it is present in all forecasting methods. Whena life cycle perspective is assumed and if the scope of the analysis is to narrow, it might forcemisguided decisions. No general consensus exists for systematically categorizing and assessinguncertainties. For PLCC to be accepted in the power system domain, a broader collaborationbetween the industry, researches and regulatory institutions must be present. Building modelsthat predict the future is highly dependent on accurate and available data. To be able tobuild more exact models, the link between mathematical representation and physical healthmust be linked closer together. This can be obtained by the use of sensors and CBM-systems.For the PLCC model to provide a robust estimation for decision makers, a system perspectiveof quantifying costs from a life cycle point of view must be taken, this because many of theregulatory incentives are based on system performance and not individual components. Thismeans that a larger picture and a holistic point of view will be shown and a higher degree of costeffectiveness will be acquired.

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