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Market Models for Studying Congestion Managementin a liberalized Electricity Market
Jean-Samuel Hentz
December 5, 2002
Abstract
This project is set the in the context of the liberalization of the European electricitymarket. We specifically study multi prize zone situations which arise between differentEuropean countries because of congested interconnections.
For the purpose of this study we have developed and implemented a double auction powermarket model, based on the production costs of generators. This market is assumed tobe ideal, so that no specific player is able to exert market power. The particularity of thismodel is to accept power transfer constraints between zones.
Using standard mathematical algorithms (QP and Newton-Raphson), our software opti-mizes production quantities to maximize the society profit.
In a set of two case studies involving the French, Italian and Swiss electricity markets, wedetermine the theoretical transmission link values required to remove the congestions. Inthese cases, we also look at the impact of transmission congestions on electricity prices,consumer profit, producer profit and society profit. We have determined that the removalof congestions, although overall beneficial to society may cause some consumers to payhigher prices. Furthermore our study tends to show that the increase in society profit isvery limited.
The results from our case studies are then used as inputs for valuing a power electronicsdevice known as FACTS, which under some circumstances may increase transmissioncapacities. The valuation carried out, shows that such device has a significant monetaryvalue but a limited impact in removing congestions.
Acknowledgements
First of all, I would like to thankfully acknowledge the support of my supervisor ChristianSchaffner. His advice and discussions guided me throughout this project. I am also verygrateful for the time Dr. Rainer Bacher spent discussing and testing various optimizationmethods. I would also like to thank Prof. Andersson for letting me undertake this projectat the Power Electronics Laboratory of the Swiss Federal Institute of Technology.
Jean-Samuel Hentz
Contents
Abstract I
Acknowledgements II
Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V
1 Introduction 1
2 Basic Economics 3
3 Power Market Overview 8
3.1 Characteristic of the good electricity . . . . . . . . . . . . . . . . . . . . . 8
3.2 Electricity market structure . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.3 Power exchanges in a competitive electricity market . . . . . . . . . . . . . 10
3.3.1 UK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.3.2 Nordic market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4 The Model 13
4.1 Price model as basis for investment decision process . . . . . . . . . . . . . 14
4.2 Various approaches to modeling electricity prices . . . . . . . . . . . . . . . 15
4.3 Characteristics of our model . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.3.1 Model for the loads . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.3.2 Model for the generators . . . . . . . . . . . . . . . . . . . . . . . . 16
4.3.3 Summary of main assumptions . . . . . . . . . . . . . . . . . . . . 18
5 Mathematical Formulation 20
5.1 Basic mathematical formulation . . . . . . . . . . . . . . . . . . . . . . . . 20
5.2 Lagrangean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
IV CONTENTS
5.3 The issue of transmission lines . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.4 Important variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
6 The Software 26
6.1 Program Overall Structure . . . . . . . . . . . . . . . . . . . . . . . . . . 26
6.2 Optimization Engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
6.2.1 Newton-Raphson Method . . . . . . . . . . . . . . . . . . . . . . . 28
6.2.2 QP class B Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
6.3 Module description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
6.3.1 User Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
6.3.2 Graphical Display . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
6.3.3 Scenario Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
6.3.4 Zone Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
6.3.5 Separate Zone Settlement Module . . . . . . . . . . . . . . . . . . . 33
6.4 Excel Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
6.5 Further Software Enhancements . . . . . . . . . . . . . . . . . . . . . . . . 34
7 Case Studies 35
7.1 France-Italy electricity link . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
7.1.1 Choice of simulation parameters . . . . . . . . . . . . . . . . . . . . 36
7.1.2 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
7.2 Valuation of Italy-France FACTS project . . . . . . . . . . . . . . . . . . . 41
7.2.1 Valuation Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
7.2.2 Valuation Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 43
7.2.3 Valuation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
7.3 France-Italy-Switzerland . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
7.3.1 Choice of simulation parameters . . . . . . . . . . . . . . . . . . . . 48
7.3.2 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
8 Conclusion and future work 53
8.1 Project summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
8.2 Suggestions for future work . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Appendix 55
A Software Module Examples 55
CONTENTS V
B France Italy Case Study: Full Set of Parameters and Results 57
B.1 Scenario Input Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
B.2 Matlab Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
B.3 Additional Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
B.4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
B.5 FACTS Project Valuation . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
C France Switzerland Italy Case Study: Full Set of Parameters and Re-sults 65
C.1 Scenario Input Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
C.2 Matlab Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
C.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
C.4 Additional Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Bibliography 75
List of Figures
2.1 Quantity as a function of price . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Consumer Surplus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 Society Profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.1 Main Bottlenecks in the European Union . . . . . . . . . . . . . . . . . . . 9
4.1 Simplified investment decision process . . . . . . . . . . . . . . . . . . . . . 14
6.1 Program Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
6.2 Variable convergence over 5 iterations . . . . . . . . . . . . . . . . . . . . . 28
6.3 Graphical Display . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
6.4 Graphical Display of Scenario . . . . . . . . . . . . . . . . . . . . . . . . . 32
6.5 2 Zone Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
7.1 French and Italian zone prices as a function of interconnection capacity . . 38
7.2 Producer profits as a function of interconnection capacity . . . . . . . . . . 39
7.3 Society profit as a function of interconnection capacity . . . . . . . . . . . 40
7.4 Structure for FACTS project valuation . . . . . . . . . . . . . . . . . . . . 41
7.5 DCF as a function of the cost of borrowing . . . . . . . . . . . . . . . . . . 45
7.6 DCF and IRR as a function of FACTS transmission improvement . . . . . 45
7.7 DCF and ROC as a function of FACTS running costs . . . . . . . . . . . . 46
7.8 ROC and DCF as a function of FACTS transmission improvement . . . . . 46
7.9 Transmission links France-Italy-Switzerland . . . . . . . . . . . . . . . . . 49
7.10 French Swiss and Italian zone prices as a function of link capacity . . . . . 51
7.11 French Swiss and Italian generator profits as a function of link capacity . . 52
7.12 Society profit as a function of link capacity . . . . . . . . . . . . . . . . . . 52
A.1 Scenario Module Example . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
A.2 Various constraints on a tranmission line . . . . . . . . . . . . . . . . . . . 56
A.3 3 Zone Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
LIST OF FIGURES VII
B.1 Marginal cost curves of generators . . . . . . . . . . . . . . . . . . . . . . . 60
B.2 Total cost curves of generators . . . . . . . . . . . . . . . . . . . . . . . . . 60
List of Tables
7.1 Data sources used in the France-Italy case study . . . . . . . . . . . . . . . 36
7.2 Generation costs projections per kWh for 2005-2010 . . . . . . . . . . . . . 37
7.3 Installed production capacity in France and Italy . . . . . . . . . . . . . . 37
7.4 Average hourly consumption in France and Italy . . . . . . . . . . . . . . . 37
7.5 FACTS valuation summary . . . . . . . . . . . . . . . . . . . . . . . . . . 47
7.6 Installed production capacity in Switzerland . . . . . . . . . . . . . . . . . 49
7.7 Hydropower costs projections per kWh for 2005-2010 . . . . . . . . . . . . 49
7.8 Average hourly consumption in Switzerland . . . . . . . . . . . . . . . . . 50
7.9 Congested and Uncongested Electricity Prices . . . . . . . . . . . . . . . . 50
A.1 Separate Zone Settlement . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
Chapter 1
Introduction
Europe, led by the United Kingdom and Nordic countries, has begun the process ofliberalizing its electricity market in the beginning of the 1990’s. This profound change ofmarket structure, from state monopoly to free market, is now spreading to all membersof the European Union. At the Barcelona summit in February 2002, all members haveagreed to a step by step opening of their domestic markets between now and 2004.
In most of the countries where liberalization was introduced, vertically integrated publicutilities that were de facto dominating the market were split to introduce competition.More actors in the electricity generation business, stimulated by market forces have drivencosts down for the consumer. The market for electricity, is now changing rapidly all acrossEurope. The dynamics of change are affecting the various parameters of the whole valuechain. The consequences are far ranging. Cross border mergers and acquisitions havesurged, as national companies have to diversify their sources of revenues. Trading com-panies are now operating on the various European power exchanges, providing liquidityto the market. More and more maintenance services are now out-sourced to pure powerengineering firms.
Despite all these changes, there is presently no common European market for electricity.This is due mostly to limited interconnection capacity between European countries whichper se limit the trade of power. As a consequence of this situation, electricity prices varygreatly from one country to another and each country is to a great extent a separatemarket. From Italy to Finland, consumers theoretically part of the same common marketcan be billed as much as 100% more for one kWh. On the technical side, transmissionsystems are critically congested and since they are managed by natural monopolies, theincentive to build additional cross border transmission capacities is relatively low.
This is the context in which this work is set. The main issue this project will deal with, isthe study of multi-price-zone situations which arise because of congested interconnections.The results from this first study are then used to carry out an attempt to value addi-tional transmission capacity, more specifically using FACTS devices, a technical powerelectronics solution, which in some cases may increase power flows.
The structure of this work is the following: in a first part, the basic economic principleswhich will be used throughout this project will be defined in detail. This will help interpretthe results from the market model. Then, in a second more descriptive part a brief
2 Introduction
overview of the power market will be given. This will to set the scene for the descriptionof the market model which has been developed to study the multi price zone issue. Amathematical problem formulation, as well as a presentation of the software will thenfollow. The last part then covers the results of a series of case studies which have beencarried out as well as a first attempt to value a FACTS project.
This work is at the fine border between economics and engineering. Its main contribu-tion is the software implementation of a pool market model for electricity, for uni- andmulti-zone systems. This model has some very specific features such as the capabilityto introduce transmission constraints between areas. Furthermore a number of financialanalysis tools have been build-in to determine the “value” of transmission constraints andthe “opportunities” for implementing FACTS devices.
Chapter 2
Basic Economics
This work, as its title suggests, deals with markets and economics. Before talking aboutelectricity, in this first very general section we will define the set of economic terms whichwe will use in the rest of our work. This is for the reader to become familiar with these andthen help define the problem mathematically in a later stage. We will first briefly outlinethe fundamentals of pricing and then describe the characteristics of ideal competitivemarkets.
Price
Quantity
D1
P1
Q1
S
D2
P2
Q2
Figure 2.1: Quantity as a function of price
The often quoted objective of economics is to study the allocation of scarce resources. In afree market, exempt of state regulation or intervention, the two categories of participantsinvolved are consumers and producers. Consumers have unlimited wants and satisfy theseby consuming. The goods they acquire to satisfy their needs can be free (such as air),but are more commonly scarce goods which have a price. In the case of electricity, itseems indisputable that the good can be qualified as scarce. A market is defined as theplace, physical or not, where supply and demand meet in order to carry the exchangeof goods. Assuming a perfectly competitive market (we will define this in a later stage),“an equilibrium price is achieved at the point where quantity demanded equals quantity
4 Basic Economics
supplied” 1. In figure 2.1, the point where the supply (S) and demand line (D) meet iscalled the equilibrium price. A change in the demand or supply conditions is representedgraphically by a shift of the respective curve to the right (increase) or to the left (decrease).After a certain time, the market price adjusts to take into account the change in supply ordemand conditions and a new equilibrium point is reached. For simplicity we will assumethat this market clearing process is instantaneous.
Without dwelling on the intricate details of the theory of consumer demand amongstothers, we will now define the key terms: consumer surplus, demand elasticity andproducer surplus.
Price ofGood X
Quantity of Good X
D
MarketPrice
P1
P2
Q1 Q2
ConsumerSurplus
Figure 2.2: Consumer Surplus
When producers sell a good on the market their benefit is clear: it is their profit. Ineconomics this profit is known as producer surplus (PS) . The producer surplus formallyis defined as the difference between the income received by the sale of a good and itsproduction cost. If producers behave rationally, they will only sell goods on the marketif they can derive a profit or producer surplus equal or greater than zero. Underthe assumption of perfect competition, producers adapt their production to demand andprice their goods at a price equal to their short run marginal costs. The marginal cost isdefined as the cost of producing one extra unit. In the case of a fluctuating demand, thismarginal production cost can vary a lot. In the case of electricity producers this explainswhy important price differences exist between peak and off peak hours. Demand is higherat peak time so the demand curve shifts to the right in figure 2.1 from D1 to D2. Thenew equilibrium point is reached at a much higher price.
For the consumers, defining the benefits derived arising from a purchase is more challeng-ing. One could say that the benefit is for example happiness, but since this cannot beaccurately quantified we cannot pursue this thought. What we aim to get is some mon-etary value of the benefit derived by a purchase. Economists have proposed the conceptof consumer surplus. The consumer surplus is defined as the difference between the
1source: [22]
5
value the consumer is prepared to pay and what he actually pays. This is his incentivein participating in the market. The economist George Stigler [22] described it in thisway “When a reflective man buys a crowbar to pry open a treasure chest, he may wellremark to himself that if necessary he would have been willing to pay tenfold the price.”As we can see from figure 2.2, an increase in price from P2 to P1 causes the area definedas the consumer surplus to decrease. We however assume in this explanation that theconsumer behaves rationally, in that he does not purchase any good that has a higherprice on the market than the benefit he would derive from it.
These two concepts of consumer surplus and producer surplus, or in other wordsconsumer profit and producer profit will be of outmost importance in our study sincethey form the main criteria we wish to optimize in our objective function which we willformally define in chapter 5 on p.20.
Price(per unit)
Quantity of Output
D
MarketPrice
Q
ConsumerSurplus
ProducerSurplus
S
Figure 2.3: Society Profit
One last concept we will refer to in the course of our work is the elasticity of demand.This is generally defined as the response of demand to a change in price; more formally“the percentage change in Quantity Q, divided by the percentage change in price P”.Some goods such as bread, or apples have a quite low elasticity of demand. This meansthat consumers will not change greatly their consumption patterns if the price of breadis increased by say 10%. Some consumers might stop consuming bread altogether but onaverage the drop in demand would be minimal (1% to 2%). Other goods such cars forexample have a high elasticity of demand. If the price of a mid market car was raised bythe same 10%, a large percentage of consumers might decide to go for a cheaper model,say 6 to 8%. In the case of electricity, the elasticity of demand in the short run is low.People are unable to change their consumption habits in the short run because it wouldmean either using less the appliances which they have (e.g. microwave, oven, heater,drier), or alternatively investing in new products which consume less power or run onother forms of energy (e.g. gas oven instead of electricity). However, in the longer termas in the case of the two oil shocks in the 1970’s, a sharp rise in fuel prices can significantlyaffect consumption patterns. The oil shocks have lead consumers to seek more efficiency
6 Basic Economics
and habits have changed to encourage energy saving. Good insulation for houses hasbecome a standard features, and the average car today consumes significantly less than25 years ago. In the case of a new significant and prolonged rise of oil or gas certain typesof electricity production means such as solar power or wind power could become viablealternatives.
Under the assumption of perfect competition both consumers and producers have a sur-plus. As we can observe in figure 2.3, we have two areas, the consumer and producersurplus. Consumers and producers being the only economic actors present, they repre-sent the society as a whole. The aggregate of these two surfaces is known as the totalvalue of the market, other terms used by economists are society profit and welfare.
At the beginning of this short economic background introduction the assumption of per-fect competition was made. We will now explain briefly this fundamental assumption.The definition given in [22] by Roy J. Ruffin is the following: “an industry is perfectlycompetitive if firms are price takers and there is free entry”. This dual characteristic hasquite wide ranging consequences. In theory a “price taker” is the reverse of “a price set-ter”. Under the theory of perfect competition, the prices for goods are set by the marketand firms do not posses the power to influence prices otherwise known as “market power”.In reality few markets fall exactly under the previous description. Perfectly competitivemarkets have the following characteristics:
• Many buyers and sellers : this is to prevent firms from coordinating their actionsand identifying specific buyers. This in turn guarantees that no buyer or sellercan influence market prices. In the UK for example, the power market regulatorshave set a lower limit of seven firms generating power in order to be able to have acompetitive market.
• Perfect information: nobody within the market is left out. All participants haveinformation about the price and product specifications. This is true by regulation inthe electricity market. Uniform pricing is applied for retail customers and these areusually aware that large industrial consumers may have a discount. However, it isstill impossible for buyers to federate to get industrial prices for a whole “purchasingpool”.
• Homogeneous product : product specifications are clear and substitutes or competi-tors exist for the product. This is particularly true in the electricity market. Elec-tricity is a uniform product and consumers may switch between suppliers. In thefuture and in some isolated cases today, firms will try to differentiate their prod-ucts by offering for example various power qualities. To cite only a short example,in the semi-conductor industry certain manufacturers have negotiated special con-tracts with power producers for non-interruptible supplies. These contracts containfinancial penalties which power suppliers are obliged to pay if they do not sup-ply the adequate electricity quality. As these contracts only apply to a very smallpercentage of the power sold we can assume that the product sold is homogeneous.
• No entry or exit barriers to the market : firms can enter freely the market to competewith incumbents and exit the market without hindrance. This characteristic ofperfect competition is very debatable in the case of the electricity market. Firstly
7
entry into the market requires usually some sort of government approval whichtakes time and sets additional requirements to participate in the market. Firmshave to invest large sums and since the stranded costs are so high (this is similar tothe airline industry), exiting from the market is a costly move which might meanloosing a large part of these sunken costs. If we take the example of the US electricitymarket the US Department of Energy estimated in 19972 the stranded assets in theUS to be between $72 and $169 billion dollars. This is an extremelly large sum andfurthermore a high percentage of the $400 billion dollars in total asset value.
After these basic economic principles we can start formulating our problem. If we replacethe producers by generators and the consumers by loads and assume perfect competition,these graphs help us explain how the market price for electricity is determined. Allconsumers have marginal cost curves (these are similar to the demand curves D). Allindividual demand curves are then aggregated to obtain one market demand curve. Onthe supply side (generators), all of the marginal supply curves are aggregated to get onemarket supply curve S. The intersection of these two curves (supply S and demand D)is called the market clearing price (MCP), which is the price for electricity under thesemarket conditions. If we assume that transmission is free, or embedded in the productionprice, then this market clearing price is simply the amount paid by the consumer per unitpurchased. In the market model which we have developed (see chapters 4 and 5) our mainaim will be maximizing the value of the market or society profit.
2source: [20] p.27
Chapter 3
Power Market Overview
The objective of this chapter is to describe the various elements of the power marketand its specificities. We will first of all outline the characteristics of electricity, tryingto explain why it is in many ways different from other traded goods, then give a briefoverview of the market structures and power exchanges in Europe.
3.1 Characteristic of the good electricity
In chapter 2 the basic economic principles, which govern the markets for most goods ina free market economy are described. Electricity, is in many ways different from other“conventional”1 goods and has very specific features, which will now be outlined.
Electricity cannot be stored2 on a large scale and therefore production must at all timesof the day meet demand. This is to prevent any significant system failure to occur. As aconsequence of the inability of large scale storage, demand fluctuations between summerperiods and winter periods have significant effects on prices. On top of these seasonalvariations, intra-day variations are also important due to demand patterns. For examplemassive price spike can occur when a significant plant is being taken off the grid. Thisis because an often more costly backup unit has to be switched on immediately. Thesefeatures are specific to electricity, but in many ways similar to air travel. Air transportcannot be stored, price fluctuations are important between high season and low seasonand certain peak times during the day carry significant premiums. In the liberalized airindustry, consumers have however become accustomed to these fluctuations, and knowthat by changing their travel or consumption patterns by choosing for example to traveloff peak they are able to save considerable amounts of money.
The exchange of goods is limited by the technical infrastructure. This is true for anygood but more so for electricity since produced electricity which cannot find its way intothe network is immediately lost.Any system congestion causes trades to be cancelled andprevent players from doing business. In the case of the European market, the EuropeanCommission3 has identified seven main bottlenecks, or critically congested areas across
1we define conventional here as all other goods2with the exception of pumping water up a hill to then turbine it down3source: European Commission, Information and Communication December 2001
3.1 Characteristic of the good electricity 9
Main Bottlenecks:UK/IrelandUK/FranceBelgium/NetherlandsDenmark/GermanyFrance/SpainFrance/ItalyGreece/EU
Figure 3.1: Main Bottlenecks in the European Union
the European Union (see figure 3.1). The parallel with air travel holds again up to acertain extent. Airlines can only open new routes if they are able to get landing slotsat the different airports, which they wish to fly to. Some airports such as Heathrow arecritically congested, which in turn means that capacity cannot be increased. If planescannot be used, their upkeep costs are a net loss to the airline.
Electricity cannot be tracked. The flow of electrons, produced by a generator finds itsway through the network, guided by Kirchoff’s laws, so it is not possible to accuratelydetermine which “path” it follows. This is an important issue in congestion management,but also in billing. For congestion management purposes it makes it difficult for systemoperators to prevent congestion by acting at the root of the problem, and track the gener-ating facility(ies) responsible for congestion at specific points in the network. For billingpurposes, it makes it difficult to charge fairly and accurately the different participants fortheir actual use and congestion of the network.
Losses occur while electricity is transported. As significant amounts of electricity flowthrough the cables, some power is dissipated as heat and as a result the generators haveto produce more electricity than is consumed by the end-users. Losses are a functionof several factors such as loading on a line, the type of line used, the length of lines,so billing customers for the losses their “electricity delivery” has caused is not feasibleyet. Optimizing a system for minimal loss was the objective under former integratedutilities, owning both generation and transmission facilities. In a competitive marketwith generation and transmission being separate economic entities, cost optimization isnow the driving force.
10 Power Market Overview
3.2 Electricity market structure
The electricity market sector is characterized by large stranded fixed costs and high ex-ternalities. This is very similar to the cable networks or the telephone carriers industry.Such a market structure is known as network economics. All participants, consumers andproducers depend exclusively on the network to sell and buy the goods be it electricityor cable TV. The fixed costs are high, however the marginal cost (MC) of delivering (notproducing) an additional unit of electricity are close to nil. As the network is extremelycostly to build and maintain, there is usually little incentive for a many players to owncompeting networks. In all liberalized markets up to now the transmission infrastructurehas remained a so called natural monopoly. In the area of generation, the high invest-ments required to build power plants has lead a few large players to dominate the marketstructure. In Germany three firms control over 50% of the market. This is an oligopolisticstructure, and not a perfectly competitive market as described in chapter 2 of this work.Due to the small number of firms involved, participants do not always behave as “pricetakers” but “strategically”. Strategic behaviour of a firm is characterised by its decisionsbeing dictated by the expected moves of competitors, which affect the two main variablesof prices and quantity. Several papers explore this “strategic” behaviour of firms in theelectricity market, using various established economic theories, such as game theory andthe “Nash equilibrium”. One interesting paper on the subject is [20].
In this work we will assume the market to be perfectly competitive. A consequence of thischoice is that no single player is able to exert significant market power, and that pricingis based on marginal costs. We assume perfect competition because we take the view thatthe aim in liberalizing the European market is not to obtain an oligopolistic structure andthat enough political and legal action should be taken to try to prevent such an event.This view is clearly debatable and not all consumer groups and politicians agree with it.
3.3 Power exchanges in a competitive electricity mar-
ket
Over the past ten years, several national and trans-national markets have emerged inEurope. In 1990 the UK electricity market was liberalized, and a now defunct power poolwas formed so that the various producers could bid centrally. In 1993, the Nordic countriesFinland, Norway and Sweden followed and opened their markets. For the purpose oftrading power and managing congestion a central platform was created known as theNordpool. More recently a string of market places have been launched across Europe. InGermany two market places the LPX4 created in June 2000, and the the EEX5 createdin August 2000 have now merged. France in 2001 launched a market place known asPowernext. Although all these different markets possess their own specificities we donot wish to describe each of them in detail but will outline the main characteristics anddifferences of the most established exchanges.
Exchanges were created in the process of liberalization to ensure:
4Leipzig Power Exchange5European Energy Exchange
3.3 Power exchanges in a competitive electricity market 11
• liquidity
• transparency
Liquidity, which is measured by the volume and number of contracts transacted on anexchange ensures that sufficient supply, meets the demand. An exchange ensures that asufficient number of participants meet so that none of them is able to influence prices 6.
Transparency : trading participants are aware of the price building mechanisms, and allprocedures of doing business on the exchange. Each participant is treated in the sameway, receives the same information so that no asymmetry arises.
Exchanges are usually used for spot transactions, that is transactions settled one dayahead, or one day before delivery and based on future expected demand. Exchangesare an important component in power markets but their importance should not be over-estimated. This is due to two main reasons: firstly transaction volumes are low (1-5%of consumption of the German market, depending on the day), secondly exchanges oftenco-exist with other type of trade systems such as bi-lateral long term contracts (such asin the Nordic markets). It should however be noted that exchanges are the main sourceof price data. This data is then often used for long term contracts. Exchanges, after arather slow start have seen the volume of transaction rise. If most of the transactionswhere conducted over exchanges the value of European wide electricity trading could soarto some 60 billion7 Euros. The recent fall of Enron, which filed for bankruptcy protectionon the in November 2001, has removed a major counterpart (loss of liquidity) and hasbeen a setback for electricity markets in the short term. This could delay by up to a yearsignificant traded volumes on exchanges.
The two markets we will now describe are the most mature markets in Europe, the UK andNordic markets. These two markets possess some significant differences in their structureand way of operating.
3.3.1 UK
The UK market is administered by an independent system operator or ISO, whose taskis to organize both the central exchange called “Power pool” and the electricity dispatch.Mandatory participation for all (large) generators is required and these transmit theirbids to the pool one day ahead. The demand side, is estimated as one fixed quantity, anddoes not bid directly on prices in the auction process. A day-ahead or spot price is thendetermined as the intersection between the highest offer price and the forecasted demand.This price is denoted as the System Marginal Price (SMP). The ISO then purchases therequired quantity to meet the demand forecast at the SMP from the generators and sellsit (with an uplift) to its customers: the regional electricity companies. In the case oftechnical problems or congestion the price paid to the generators is modified (increasedby a capacity payment).
6in economics participants are described as “price takers”7source: Platts 2001, assuming a trade flow of 256 Twh and an average price of Euro 30/MWh
12 Power Market Overview
3.3.2 Nordic market
The Nordic electricity exchange, known as Nordpool, is in many ways more refined sincethe number of its participants is greater and it operates across national borders. Theexchange, also offers a series of additional financial products on its futures market, forthe purpose of hedging and risk management. It operates both a day ahead and an hourahead market. The main differences with the UK power pool is that the participation ofgenerators is not mandatory and that the exchange accepts both sell and purchase bids;this is otherwise known as a double auction model. Both demand and supply meet inthe price building mechanism. This mechanism ensures that demand is price sensitive.One must however beware that only a minority of electricity purchases done in the Nordiccountries is done over this specific exchange and over 60% of transactions are done throughbilateral contracts.
The type of market structure we chose in our simulation is based on the Nordpool. Onemain difference is that generators and loads do not give in discrete bids (which are usuallytransformed into a continuous function as on the LPX8) but bid in directly their marginalcost curve9 .
8source: LPX documentation “Spot Market Concept” p.11 from the 15.10.20019source: Klemperer and Meyer’s supply function equilibrium model 1989
Chapter 4
The Model
In a European Energy market worth some Euro 380 billion1, and progressively movingtowards more competition, valuation of investment opportunities is becoming of criticalimportance. Technically oriented people, amongst which a majority of engineers havepreviously been in charge of both running and planning for new capacity. The focus ofthis planning (and not investing), was to ensure that systems where secure, easy to runand up to technological progress. However this has led to over-design, over- capacity andmajor un-economic and often politically influenced spending of tax payers money. How-ever this has ensured that domestic markets across Europe often have extremely goodcountry specific electricity transportation networks. New market structures and compet-ing companies will bring financiers buying and running electricity assets. It is therefore ofutmost importance for engineers to understand and speak the “cash is king” jargon sinceultimately the two sides of the fence will have to speak to each other. As financial modelsmay seem to engineers as “under developed” or very basic, the opportunity to enhancethese using engineers technical, modeling and analytical skills is immense.
The focus of this part of our work, is to outline the various steps leading to an investmentdecision in the electricity market. In chapter 7 section 7.2 a FACTS project will be valued.We will both draw from literature on the subject but also through the insights gained fromworking for two summers in the financial industry, one in the area of capital markets, theother for in mergers and acquisitions. We will then examine various modeling approaches(literature review), and then specifically show how the tool we have developed fits in thisdecision process. In a later part of our work (chapter 7) p.35, we will illustrate how ourmarket model may be used, by going step by step through two case studies example.Most authors dealing with this subject have nearly exclusively focussed on the issue ofgeneration assets, since this area is already quite well documented we have taken a differentview. We will aim our work at the transmission assets. We think this technical area canpotentially have some “hidden value”, and furthermore benefit from the development ofa new technical solution: FACTS devices.
1source: The Wall Street Journal 06.03.2002
14 The Model
Price Model Future Cash Flowsproject specific
Cost of Capital
Riskfirm specific
project specific
Response ofCompetitors
Impact of projecton prices
Figure 4.1: Simplified investment decision process
4.1 Price model as basis for investment decision pro-
cess
The figure 4.1 [25] describes the usual steps a firm undertakes when it wants to investinto a new project, where a market exists for the product. In the case of the electricitymarket, firms first have to be able to project future prices. This is done by either justlooking at present prices on the spot and futures market, which gives a indication ofprices in the next twelve months. For longer term predictions firm have to build theirown market model. Once prices are determined using a model, usually after a long andcareful decision process about the assumptions to be made and the input parameters,the firms can then start modeling the expect future cash flows (both inflows from theproject and outflows for capital expenditure, wages, taxes etc.). Then the firm has tocarefully calculate its own cost of capital and get information about the current risk freeinterest rate and the risk it associates with a particular project. For determining risk,extensive data is available for specific industries 2. A company may also wish to calculatethe risk factor looking at parameters such as the expected variance of cash flows. Oncemost of these parameters are determined the firm has one number assigned to the valueof its project. It can then take the decision that it fits its own internal criteria. As in acontrol system with a feedback loop the launch of project might have an effect on bothmarket prices or trigger some response amongst competitors. In our work we will notdeal with the response of competitors but will look at the impact of specific investments(specifically those aimed towards removing congestions) on market prices. As we can seefrom this description having a price model, which works is the cornerstone and basis toany evaluation of a project’s economic viability. The aim of our subsequent model is toprovide a simplified yet as realistic and good as possible model for electricity prices in thecase of regional price differences due to transmission constraints.
2The London Business School compiles and amends its database yearly and has historic data for over30 years
4.2 Various approaches to modeling electricity prices 15
The outputs from the price model, are then used as inputs for the project valuation. Inthis case the valuation is carried out under Excel, using a discounted cash flow model.The risks associated with the project will not be calculated, because of the lack of reliabledata for comparison. Rather than extensively explain our approach to valuation, we willcarry out a detailed example in chapter 7 section 7.2 on p.41.
4.2 Various approaches to modeling electricity prices
The purpose of this short section is to give a brief overview of different approaches tomodeling electricity prices. This section should be seen as a short literature review. Forthis purpose we have made use of [25] chapter 5 and [15]. This has been complementedby conversations with the author of the latter work.
A first type of modeling is known quantitative or statistical modeling of electricity prices.The main idea underlining this approach is to try to characterize the past price variationsand get a reasonable model to predict future prices. It is in many ways similar to whatderivatives traders do when trying to price options. In the case of electricity a goodwith high and increasing volatility only limited historical data is available, which makesaccurate modeling extremely difficult. Furthermore this approach does not at all takeinto account the underling characteristics of power production[25].
A second type of modeling is known broadly as “economic equilibrium models”. Kempfertin [13], uses such a model by defining a profit maximizing function for each generator.These generators then bid in a central pool using different strategies to maximize theirown economic function. Maridor in [16] tests out the different strategies which lead toa Cournot equilibrium. It should be noted that such a work drawing heavily on gametheory can give useful predictions under certain circumstances, but as the latter piece ofwork shows most of the price levels obtained after a series of simulations remain highlyunrealistic.
A third approach is the agent-based modeling of electricity prices. We have not enquiredthis area of modeling in detail, but the underlining idea is to characterize mathematicallythe behaviours and relationships between the different actors in the market for a specificgood. By running a certain number of simulations one can look at the successful andun-successful strategies in the market place.
A last approach which Ilic describes in her excellent book [25], is known as the fundamentalmodeling of electricity prices. The proposed method is to find out the key drivers forelectricity prices, be it seasonality (using historical data), or the influence of commodityprices (using oil or gas price information), or any other factor which may influence prices.This is an excellent approach for the basis of risk management, but although in theorythe author is able to describe these main ideas no model seems to have been implemented.This area remains more a collection of mathematically quantified ideas, each tested on itsown, than a complete model.
16 The Model
4.3 Characteristics of our model
The approach we chose in modeling electricity prices is cost based. What we mean bythis is that the inputs required by the model, in order to determine electricity prices,are estimates of the generation costs. Approximates to generation costs can be found byanalyzing pool bids. This has been done for example by Joel Maridor [16], using publiclyavailable data for the UK pool. Another source of generation costs is the analysis ofgeneration company reports. This historic data can only give approximates, is mostlybased on past operating performance and it should be noted that for gas, oil and coalfired power stations the price of electricity generation fluctuates significantly with theprice of the underlining commodities.
The market structure we chose (see section 3.3.2 on p.12) is bilateral otherwise known asdouble auction. On the supply side generators bid-in in their respective cost curves, thedemand being modeled by demand-curves.
4.3.1 Model for the loads
The model for the loads has the following characteristics:
• Loads may be price sensitive or insensitive: loads can be defined as having constantconsumption, as it is the case in the UK power pool, or can be sensitive to changes inprices. Most economists agree that electricity, with its particular characteristics is agood with low embedded price sensitivity3. In all of our simulations we consideredloads to be elastic. This enables us to take into account medium to long termelasticity, rather than short term inelasticity.
• Unlimited number of loads : the model has no restrictions whatsoever on the numberof loads. Loads are treated as negative generators, in other words they consume.We do not consider loads to have embedded fixed costs.
• Seasonality and intra-day variations: through multiple running of the same model4,the possibility exists to model wide variations in demands and the resulting pricespike which exist on exchanges.
4.3.2 Model for the generators
Generators, just like factories producing goods, have a cost associated with the productionof each megawatt. Producing in the most efficient way, involves taking into account ahost of technical factors such as ramp up times for coal generating units, or the narrowproduction ranges in the case of nuclear power plants.
We assume generators to be able to vary production quickly and adapt from one timeinterval to another. Ramp up times are not taken into account. This is a fair assumption
3for definition see chapter 2 p.54scenario tool is described in chapter 6 on p.31
4.3 Characteristics of our model 17
as no markets in commercial operation today takes into account this feature. Generatorscan be constrained and have upper and lower production limits.
This issue of costs in the case of power generation is quite complex. We will first look atthe general cost categories involved in operating generation plants. Then once these costsare defined we will explain how these are taken into account in our model.
Cost Types
• Fixed costs : are usually the result of long term planning. These include interestrepayments, labor (full time - long term contracts), insurances and taxes. Thesecosts do not vary with production and are irrespective of the sale of any power.However they are important when trying to price generated megawatts. Our modeltakes these costs into account. However as explained in chapter 2 the type of costingapplied is marginal costing so fixed costs do not influence pricing.
• Variable costs: as their name indicates are not fixed. In the power business, a fewfactors determine how the volume of variable costs are affected. Mainly these aredetermined by the inputs required to operate a power plant and which depend onproduction quantity. These can be fuel, gas, but also to a lesser extent maintenancecosts in the case of hydroelectric power plants. Variable costs are modeled by aquadratic costs curve for each generator. These are monotonically rising. This is agood approximation to reality. Each type of generator (e.g. oil, gas-fired, nuclear),has a different type of cost curve. For detailed information about the different powerplant cost structures see [24] p.18-22.
The main difference between fixed and variable costs is the time horizon. In thelonger run all fixed costs can be considered as variable. Generally as in otherindustries there is a move towards trying to tie costs with production and revenues.To achieve this, operators have to transform as much as possible their fixed costsinto variable costs. This can be done by subcontracting items such as maintenance,but also shortening the time horizon of so-called long term contracts.
• Start-up costs: this type of cost is a sub category of the variable costs. Start-upcosts are the costs incurred to start the operation of certain specific power stations,mainly coal fired and nuclear power stations. In the case of hydro power plants,diesel or gas powered plants start-up costs are negligible. In our model we haveneglected these start-up costs. Accurate economic simulation including start-upcosts is a whole area on its own, as not only costs but availability of units has tobe taken into account. In our model we do not take into account the availabilityof power plants and assume these to be available during the period simulated. Tosimulate a market with a unit turned off can be done by removing it from the systemaltogether. Determining which unit to turn off and when is a problem category onits own and is known in literature as the “Unit Commitment problem”. This is acomplex mathematical issue as it involves a mixture of cost optimization and binary“state” variables representing the “on” or “off” status [3]. The “Unit Commitmentproblem” is usually a technical rather than economic issue. Existing market modelsused by exchanges do not deal with this issue. Generators can internalize such start-up costs linked to powering up a unit in the bids they offer to the pool. They can
18 The Model
adapt their bidding strategies to insure that the production is always on by givenin bids at a price of zero. This is done by some generators in the UK power pool5.
4.3.3 Summary of main assumptions
The model chosen in this implemententation, is a cost based approach, with a number ofunderlining assumptions. Most of these assumptions have been spelled out in the previouschapters, but this list will act as a useful summary.
Assumptions concerning the market
• Participants are assumed to behave rationally : this assumption described in ch.2 isimportant, and often not spelled out explicitely. It would be extremely difficult andwould not make much sense to describe consumers behaving irrationally. Firms,however, wishing to gain market share or going into some sort of price war, may inthe short run price their goods under their marginal cost. To study such an issueis a whole area on its own, and the objective function is completely different, thistherefore cannot be integrated in this model.
• The market is perfectly competitive: this assumption, also described in ch. 2 maynot apply to the power market in every case. To take into account the “strategicbehaviour” of market players, the user can specify price curves which are abovemarginal costs or decide to take certain units off the grid. Some of the differentstrategies have been analysed in [15] for example. As a result of various strategies,some firms are able to earn above average ptrofits.
• We assume an instantaneous market clearing process.This assumption holds in re-ality as long as electricity is traded on power exchanges. In the case of long termcontracts, the market does not clear immediately as price re-negociations only takeplace at expiration, usually after periods of at least one year.
• We assume no transmission costs: these costs are never included in the marketclearing process. Transmission costs are added ex post as overhead costs usually,based on a number of factors such as delivery zones and transmission volume. Themodel could however be amended to take into account the specific costs of usingcertain power transmission links. Each transmission link would have a cost functionassociated with it.
Assumptions concerning technical issues.
• We assume all powers to be DC : This is because our model used for electricityprices, and not to determine specific power flows. Integrating complex powers wouldrequire to model in detail the network transmission lines and other numerical andmathematical tools such as the AC-OPF would be required. This is not an extensionof the current model but a would represent a whole new model. The AC-OPF was
5source: National Grid Seven Year Statement 1999 Appendix D
4.3 Characteristics of our model 19
experimented in the US market and had to be abandoned because it is a verycomplex model, which usually only produces slightly more accurate results, but istotally unworkable on large scales (with current knowledge) and represents a levelof complexity which economic actors are not ready to take into account.
• We neglect line impedances but replace these by zonal constraints : line impedancescan be added by using the DC-OPF model.
• We assume no losses : losses account for only small amounts of electricity produced.In the Italian market for example losses were about 4.3% of annual producyion6.Losses are usually a function of transmission so these are billed as part of transmis-sion costs as ancilliary services. This issue can be modelled by integrating losses intransmission costs. The drawback of our chosen aproach is that there is no incentivefor reducing losses in allocating production.
6source: preliminary annual report 2001 GMRE
Chapter 5
Mathematical Formulation
After a qualitative description of our model in chapter 4, the aim of this chapter is to givea mathematical problem formulation of the objective function to optimize. This quanti-tative problem formulation will refer extensively to the economic principles described inchapter 2 and make use of the assumptions of chapter 4 section 4.3.3. Firstly the problemwill be described in general terms, then the modeling of transmission lines and constraintswith be dealt with, in more detail.
5.1 Basic mathematical formulation
In our model of an electricity market we have two main actors: generators and loads. Wewish to determine both quantities and prices consumed and produced by each generatorand load, which maximize total welfare. Total welfare is equal to the sum of consumerand producer surplus otherwise known as profit (see chapter 2). We make the simplifyingassumption that we only deal with DC powers and that we have no losses. Generatorsand loads both have continuously differentiable supply and demand functions. Generatorsare defined with convex cost functions.
This problem can mathematically be formulated as:
Maximize W =
m∑i=1
Si(li) +
n∑j=1
πj(gj) (5.1)
Where:
• W is the total Welfare or Society Profit
• m is the total number of loads
• n is the total number of generators
• Si is the consumer surplus of load i
• πj is the producer surplus or profit of generator j
5.1 Basic mathematical formulation 21
• li is the quantity of power consumed by load i
• gj is the quantity of power produced by generator j
We can then rearrange eq.(5.1) by changing the variables of consumer and producersurplus using:
Consumer Surplus S = B − P (5.2)
Producer Surplus or profit π = I − C (5.3)
Where:
• B is the maximum price the consumer is prepared to pay for the good
• P is the actual price paid
• I is the income of the producer (generator)
• C is the cost to the producer (generator’s cost of production)
If we assume zero transmission costs and no taxes then P and I are equal and eq.(5.1)can be re-written as:
Maximize W =
m∑i=1
Bi(li) −n∑
j=1
Cj(gj) (5.4)
This is the objective function which will be optimized. The issue is to find the pointwhich maximizes W . For this problem to be applied to the power market, a number ofconstraints have to be added:
The power balance constraintm∑
i=1
li −n∑
j=1
gj = 0 (5.5)
The generator inequality constraints gminj ≤ gj ≤ gmax
j (5.6)
Note that eq.(5.6) is in fact a set of inequality constraints, as each generator has its ownconstraints.
As soon as we take into account eq.(5.6), we are no longer in an unconstrained optimizationproblem. In our work we will focus on the equality constrained optimization problem,although in a preparatory phase of our project we have also studied the unconstrainedoptimization problem.
22 Mathematical Formulation
5.2 Lagrangean
To solve the problem described in the previous section, the Lagrangean function, a newobjective function, is a powerfull tool to re-formuale this problem. This mathematicalformulation, and its optimal solution (local) has a new set of unknown variables known asLagrange-multipliers λ. No detailed derivation of the optimality conditions will be madeas these can be found in a mathematical textbook (e.g. [2]).
As:
• the variables are continuous and real
• the problem has one objective function W
• there is an equality constraint eq.(5.5)
• we have an inequality or set of inequality constraints eq.(5.6)
We can then rewrite this optimisation problem as a Lagrangean:
L =m∑
i=1
Bi(li)−n∑
j=1
Cj(gj)−λe·( m∑
i=1
li−n∑
j=1
gj
)−µmax
j ·(gj−gmaxj )−µmin
j ·(gminj −gj) (5.7)
Where:
• B is the maximum value the consumer is prepared to pay for a good
• λe is the Lagrange-multiplier for the power balance eq.(5.5)
• µmaxj is the set of Lagrange multipliers associated with the inequality constraints for
the maximas of eq.(5.6)
• µminj is the set of Lagrange multipliers associated with the inequality constraints for
the minimas eq.(5.6)
Mathematically, λe is the Lagrange multiplier associated with the power balance eq.(5.5).This is the sensitivity of the objective function eq.(5.4) with respect to a small change inconsumption. In the bi-lateral unconstrained pool market, simulated in this model, underthe assumptions formulated in chapter 4 section 4.3.3 on p.18 and more generally in mostpower pools λ represents the marginal clearing price or MCP1.
This Lagrange multiplier λe, known as the MCP and its subsequent variations due toconstraints is of central importance in the course of our study. λe is also important as itwill ultimately determine a number of other results such as the turnover of the generators,the price paid by the loads, and by using their respective cost functions the profits of eachactor will be computed.
1see [3] p.85
5.3 The issue of transmission lines 23
From the Kuhn-Tuckers condition of optimality in [12] we can derive the following firstorder conditions:
δBi
δli− λe = 0 (5.8)
−δCj
δgj+ λe − µmax
j − µminj = 0 (5.9)
These optimality conditions have to be fulfilled in order for the solution to be considereda local optimum. In the case of convex, monotonically rising cost curves this optimum isin fact global.
5.3 The issue of transmission lines
In this work, as stated earlier the aim is to investigate the impact of transmission lines,and their congestion on market prices. To do so it is important to simulate these lines, byincluding them in the mathematical problem description. This can be done using a varietyof techniques. The main decision factor in choosing the appropriate modeling techniqueis to determine in what type of application the model results will be used subsequently.Also, the availability of quality input parameters will affect up to which level of detail themodel is of any use.
In this case the model should enable to study the economic or financial “value” of specificnetwork constraints.
Networks with a high number of nodes are usually complex to analyze and constraintswhich influence prices are usually at the boundary between two countries or two largeregions. This is the case for example in the Nordpool2. Models such as the OptimalPower Flow3 are mainly used for technical issues, require extensive computational times,and need a host of parameters such as detailed technical specifications to model existingnetworks. In the “Optimal Power Flow”, the network (with DC powers only) is repre-sented as a matrix which contains values for the various line impedances. This approachhas not been followed because the focus of our approach is the economic use of results,using as input parameters public market data.
The method chosen to model transmission constraints is based on defining import-exportlimits on each zone. This approach is similar to looking at the macro economic flow ofgoods between countries. One country exporting more than it imports has a trade surplus,another importing more than it exports has a trade deficit. This image can be applied toelectricity markets by defining zones which act as seperate “regions” or “countries”, eachwith an import-export value. Intuitively, each zone will import when prices are lower inanother zone and export if it can benefit from re-selling electricity in another area at ahigher price. These limits represent the maximum transmission capacities.
To model these zones mathematically, the initial problem formulation eq.(5.4)is expandedto include these maximum transmission capacities. The initial objective function eq.(5.4)
2for information about these specific zones see www.nordpool.com3see [3] p.37
24 Mathematical Formulation
will be kept, but will be subject to a number of additional constraints, to model import-export limits.
the export constraint∑
i
lzi −∑
j
gzj ≤ E (5.10)
the import constraint∑
i
lzi −∑
j
gzj ≥ I (5.11)
Where:
• E is the export limit or maximum
• I is the import limit or maximum
• the superscript z indicates the zone in which the generator gzj or load lzi is located.
Note that each zone z has import-export constraints, so we have a set of inequalities. Inthis case E and I are the same number with reversed signs; this is because an electricityline has the property to be able to carry as much power in one direction as the other.When we optimize, we however only formulate (z − 1) · 2 import-export constraints. Thelast zone z is known as residual so we do not formulate constraints specifically for thatzone.
We now have a modified Lagrangean:
L =m∑
i=1
Bi(li) −n∑
j=1
Cj(gj) − λe ·( m∑
i=1
li −n∑
j=1
gj
) − µmaxj · (gj − gmax
j ) − µminj
· (gminj − gj) − µz
E ·(( ∑
i lzi −
∑j gz
j
) − Ez)− µz
I ·(Iz − (∑
i lzi −
∑j gz
j
))(5.12)
Using optimization techniques described in chapter 6 section 6.2 p.26, an optimum solutionfor this problem be will computed.
5.4 Important variables
A number of variables will be computed using results from the optimized Lagrangean.
• Zone price: if we are in the uncongested case, only one zone price will apply, thisis defined as the Lagrange multiplier λe of the power balance equation. In thecongested case, each zone z has a separate price which is defined as λe − µz
E − µzI .
• Generator profit : the pricing scheme used to calculate the profits of the generatorsis the following: each generator receives the zone price for the area in which he sellsthe production. This in turn means that exporting generators usually sell theirproduction at two or more different prices. The bulk of their production is usually
5.4 Important variables 25
sold in their own local zone at zone price A, but they also make part of their sales atzone price B or C. To split exports between the different generators we have decidedthat these would be split according to the share of local production. For example agenerator with 60% of the production in his local zone is entitled to make 60% ofthe exports out of that particular zone. The profit for each non exporting generatoris simply defined as the sales price times the quantity minus the production costsfor that specific quantity:
πj = (λe − µzE − µz
I) ∗ gj − Cj(gj) (5.13)
The export out of a zone z is defined as the difference between production locatedin that zone z and the consumption located in the same zone:
Xz =∑
z
g(j) −∑
z
l(i) (5.14)
The fraction of production which a generator is allowed to export is defined as:
fj = g(j)/∑
z
g(j) (5.15)
The profit of an exporting generator (assuming he exports to one zone) located inzone A and exporting to zone B:
πj = (λe − µAE − µA
I ) ∗ (gj − XA ∗ fj) + (λe − µBE − µB
I ) ∗ XA ∗ fj − Cj(gj) (5.16)
This is calculated under Excel in the model.
• consumer profit : is simply defined as the difference between the maximum pricepaid and the actual price (zone price) for a specific quantity. For a load i in locatedin zone z:
Si = Bi(li) − (λe − µzE − µz
I) ∗ (li) (5.17)
Chapter 6
The Software
This chapter aims to give an overview of the different software pieces of the market model,as well as brief comments about the optimization algorithm chosen. The full source codemay be found on the CD.
The aim of the program is quite simple: simulate a market with two types of actors.Generators which produce and loads which consume electricity. Mathematically speakingour program optimizes the cost of generation by allocating production, and maximizesthe social welfare function (see chapter 5). Firstly, the program structure will be outlined,then each module described in more detail.
6.1 Program Overall Structure
The program overall structure can be seen in figure 6.1. The structure is modular to easilyenable further enhancements. The bulk of the optimization part of the program is writtenunder Matlab, the analysis and some of the economic variables are then computed underExcel. This process is enabled by an Excel link which is added to the standard Matlabpackage.
6.2 Optimization Engine
The optimization engine is the heart of the market model. The first issue in any opti-mization problem is to formulate an objective function which is then minimized. In thecase of the market model the objective function is eq.(5.12), a Lagrangean. This functioncontains both equalities and inequalities. In order to apply numerical methods, the in-equalities are re-formulated as equalities. The theory underlining this step can be foundin [2] on p.70.
The optimality conditions for such a problem are known as the Karush-Kuhn-Tuckerconditions, which in fact are a mathematically the first order optimality conditions (see[2] p.75).
In order to optimize the objective function, a set of methods where tested with various
6.2 Optimization Engine 27
Scenario Toolfor multiple runs
Zone Toolfor multiple areas
User Input for:Generators
Loads
Cost Curves arederived automatically
Equations fed intothe optimization
algorithm
Output for Prices,Generator & Load
Consumption &Production
GraphicalRepresentationuni & multi-run
User Input for:Number of Zones
Import/Export Limits
User Input for:Generator Constraints
Constraints fed intothe optimization
algorithm
Constraint equationsderived automatically
Excel Tool
Output for Area Prices,Profits of Participants
with differentpricing mechanisms
FACTS Valuation
Figure 6.1: Program Overview
28 The Software
1 2 3 4 5 6 7 8 9 10-20
0
20
40
60
80
100
120
140
160
Num
eri
cal
Valu
e
Gen
erat
or
1P
roduct
ion
Gen
erat
or
2P
roduct
ion
Load
1C
onsu
mpti
on
Load
2C
onsu
mpti
on
Lm
ult
ipli
erof
pow
ereq
uat
ion
Lm
ult
ipli
erof
gen
erat
or
1li
mit
Lm
ult
ipli
erof
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erat
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mit
Dis
tance
togen
erat
or
1li
mit
Dis
tance
togen
erat
or
2li
mit
Gen
erat
or
3P
roduct
ion
Figure 6.2: Variable convergence over 5 iterations2
degrees of success. The two main methods tried where the Newton-Raphson method andthe QP method. We will not describe these two standard methods in this work, detaileddescription are found in several numerical methods textbooks. Good references can befound in [2].
6.2.1 Newton-Raphson Method
The Newton-Raphson method is particularly suitable to optimize an objective functionwhich is under constrained and possesses equality constraints. This method is a standardoptimization method and has been used for power systems by Handschin and Brosda1 [4]for example. As long as all cost functions of generators are convex, and twice differentiable,the local optimum is in fact a global optimum [2]. For a full description of the algorithmsee [21].
Figure 6.2, shows the rapid convergence of the various variables using a Newton-Raphsonmethod. With a tolerance of 0.0001 the method only takes five iterations to get anoptimum solution, for a set of ten variables. The computation time is under 10 seconds.
However in the course of the refinements of the market model, when introducing a numberof inequality constraints to model the zones, the method was found not to converge onseveral occasions and to optimize production with slightly negative values which does notmake any physical sense. The Newton method was then abandoned although it remained
1confirmed by email exchange with the author2note: each colour represents one iteration
6.3 Module description 29
a perfectly valid tool in the case on a one zone model.
6.2.2 QP class B Method
QP, stands for quadratic programming. This method was chosen, because it relies on theexact optimality conditions being formulated. As stated earlier, generator and load curvesare all second order polynomials, twice differentiable. This enables a perfect problemdefinition, and no need for an second order approximation of cost curves at specific points.The class B method makes use of the Karush Kuhn Tucker optimality conditions3. Thealgorithm requires a re-formulation of the Lagrangean, as well as the addition of a so-calledbarrier function to check that the optimality condition has been reached. The algorithmwas not written as part of this work, as Matlab includes this algorithm known as QPor QUADPROG. Most of the coding is concerned with formulation of the optimalityconditions as input matrices.
This method has given very satisfactory results. It was found that computation timesdropped by around 20% compared to the use of the Newton method. Furthermore thisnumerical method is much better at dealing with inequality constraints. The problemof negative production quantities encountered in some specific cases using the Newton-Raphson method was solved, because the algorithm in itself can have upper and lowerboundary values assigned to the solutions. In all of the case studies this algorithm wasused.
6.3 Module description
We will now describe the various modules of our market model. A full program overviewcan be found in figure 6.1 on p.27.
6.3.1 User Input
Generators
The input parameters for the generators are limited to a number of points representingquantities and costs. On power exchanges, these are known as bids. These are stored intwo matrices. A linear fitting is then done through these points, for each generator. Thiscurve represents the generator marginal cost curve. An example of marginal cost curvescan be seen in appendix B figure B.1 on p.60. Then, a second order polynomial is derivedby integrating the above linear fit. This polynomial is known as the total cost curve.Figure B.2 p.60 is a good example of such curves. The user may also enter a value forthe fixed costs of each generator. These are then added to the total cost curve. Althoughthe current model is not refined to the point that piecewise smooth linear approximationscan be taken into account it is perfectly suitable to enquire on the behaviour of differentactors subject to varying parameters. A similar method was used in commercial operation
3for a full mathematical description see [2] p.128-131
30 The Software
1 2 3 4 50
20
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60
80
100
120
140
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t & In
com
e &
Pro
fit
Generator0 20 40 60 80
0
2
4
6
8
10
12
P [MWh]
incr
emen
tal c
ost (
per
MW
h)
0 20 40 60 800
100
200
300
400
500
P [MWh]
Tot
al c
ost
1 20
0.5
1
1.5
2x 10
4
Max
Pric
e P
aid
/ Cos
t of P
urch
ase
/ Con
sum
er S
urpl
us
Loads
Figure 6.3: Graphical Display
in the now defunct UK Powerpool. The German exchange LPX uses also a very similarmethod4.
The market simulator can have as many generators as the user wishes. The user just hasto specify the total number in the input part of the program.
Generators may have both upper and lower production constraints. A generator can forexample have an upper limit of 500MW defined. The current algorithm has howeversome weaknesses when dealing with lower production constraints. In some cases, it maynot converge.
Loads
Loads are in many ways defined in a similar way to generators. Consumption bids, forquantities and costs are entered by the user. These have negative slopes, because loadsconsume electricity. The slope is otherwise known as sensitivity or price elasticity (seech. 2). From these bids, first a marginal cost curve is computed, by doing a linear fitting,then a total cost curve is derived by integrating the linear fit of the previous bids. In theinput part of the program the total number of loads is defined as numload. This numberis not limited.
6.3.2 Graphical Display
The graphical display of the main program represents a selection of data to the user andis split into 4 separate graphical areas (see figure 6.3). This display is only intended as abrief overview of a simulation run as most of the data actually requires some manipulationunder Excel for the user to exploit it.
4source: LPX documentation from the 15.10.2001
6.3 Module description 31
• In the top left part of the graphical representation we display a group of three bargraphs for each generator. The generator number is on the x-axis of the graphic. Inblue we display the costs of production incurred for the specific quantity generated,in green the income which is defined as quantity generated times market price, thered bar is the profits (difference between income and cost).
• In the top right corner of the graphical representation we display the marginal (orincremental) cost curve for each generator. The marginal cost curve is the curve theuser inputs by giving a set of prices and quantities. The x-axis is the quantity inMWh, the y-axis the price in dollars. Matlab then does a fitting between the givenpoints (which are displayed as red arrows on the graphic) and displays one line foreach generator. All curves are by definition marginally rising.
• In the bottom left corner the graph represents the generator cost curves. Eachgenerator has one curve which is defined as the integral of the marginal cost curve.
• In the bottom right corner of the graphical representation we display a group ofthree bar graphs for each load . The x-axis represents the load number, and they-axis is a monetary value in dollars. The blue bar represents the cost to the load.This concept is related to the price sensitivity of the load which we consider hassome sort of negative cost associated to it. The green bar represents the purchaseof the load in dollars (market price times quantity purchased), and the red barrepresents the loads profit, which is part of the society profit.
6.3.3 Scenario Module
The aim of the scenario module is to simulate variations in demand at different timeperiods. This is an important feature in the case of electricity markets since demand forelectricity unlike other goods varies significantly during the 24 hours of a day. This ismostly due to exogenous factors such as weather. With this module the user is able tosimulate at once n discrete time intervals. Each interval can have a different demandlevel.
Generator cost curves are assumed to remain constant during each simulation period.This is to say that no generator is turned off at a specific period. Furthermore, theconstraints imposed on the generators are the same during each simulation period. The 3Matlab files used for the scenario are scenario.m, inequscenario and lagrange scenario.m.
Scenario.m is the user input file. It has very similar inputs to the main program. This fileis used to define the number of generators, the number of loads as well as their respectivecost curves. In further versions the user input will most probably be done under excel.This is to automate as much as possible both the running and exploitation of data.
Inequscenario.m is a function, which formats the user inputs into polynomials, creates theobjective function to be passed to the optimizer and then returns an optimum solutionfor each iteration. The at the end of the n time periods the user is presented with a briefgraphical summary of the various runs. An example of this graphical output can be seenin figure 6.4.
A short scenario module is included in appendix A on p.55.
32 The Software
1 2 3 4 50
20
40
60
80
100
120
time period
Mar
ket p
rice
(in $
per
MW
h)
1 2 3 4 5200
400
600
800
1000
1200
time period
Tot
al c
onsu
mpt
ion
(in M
Wh)
1 2 3 4 5−200
0
200
400
600
800
time periodTot
al p
rodu
ctio
n (in
MW
h) o
f eac
h ge
nera
tor
Figure 6.4: Graphical Display of Scenario
6.3.4 Zone Module
The aim of the zone module, is to help study the economic impact of transmission con-straints between various regions, here denoted as zones.
Simplified zone tool
The simplified zone tool was implemented in a preliminary phase to study the feasibilityof a multi zone system. The simplified zone tool, enables the user to only define twozones. It is limited in its usability, since the user has to define the zone constraintequations himself. This process will not be described, since is not of much interest and alater program development allows the user to have as many zones as he wishes, withoutmanually deriving the constraint equations. Figure 6.5, gives a good idea of what thezone tool is used for. A short simplified zone tool example is included in appendix A onp.56 for reference.
Automatic Zone Derivation Tool
The aim of the automatic zone derivation model is to give the user the possibility to assigneach generator or load to a specific zone, without manually deriving the zone constraintequations. As in the simple market model, or single zone model, power flows still haveto balance out (power balance eq.(5.5) on p.21), however the user is able to limit theimport/export capacity of each zone, in a way modeling transmission constraints. Atthe end of a run the user is told which zone exports or imports and what quantity. Theprogram has absolutely no constraints on the number of zones defined and zones can haveeither loads or generators or both.
The software derives for n − 1 zones, (n − 1) times 2 inequality constraints, which areformulated as equalities for the purpose of optimization . Each zone has two constraints:one upper and one lower constraint. Both upper and lower constraints are required
6.4 Excel Module 33
LG
1
2 5
L
G
G
3
4
Transmission LineLimit: variable
Zone 1 Zone 2
Figure 6.5: 2 Zone Diagram
because it is impossible to know before hand in which direction the power will flow.Therefore for example a 50MW transmission limit is modeled by two equations. One50MW export limit (+50MW ) on zone 1 and another 50MW import limit on zone 1(−50MW ). The import limit is a negative number because imports are considered aselectricity consumption in a zone.
6.3.5 Separate Zone Settlement Module
The separate zone settlement module calculates what is commonly known as zone prices(see LPX documentation). This tool gives local market prices for each constrained zone,as a global price does not apply anymore. The aim is to recreate in a very simplified way,the effects on prices due to a multi zone system linked with limited transmission capacity.This module also calculates the export and import quantities into and out of each zone.
Separate electricity price zones are a common feature even in liberalized and connectedmarkets. If we look at the EU example, one soon notices that although producers are ableto import electricity from abroad, which in some cases may be produced more cheaply,prices vary across the different countries. Countries which are well connected with fewconstraints such as Switzerland, Austria and Germany are part of the same price zones,however were capacity bottlenecks exist only limited export or import may take place,which in turn leads to zones with different prices.
6.4 Excel Module
Excel is used, to compute a wide number of additional economic indicators for the purposeof data analysis. The choice of excel for mostly financial analysis, is natural since nearlyall of the analysis in any financial institution is done under excel. Excel has a series ofimportant advantages, over an analysis carried under Matlab. First of all, there is no pro-gramming required and wide range of data formatting and calculation can be automated.
34 The Software
Furthermore, build-in tools such as the audit option enable the user to track much moreeasily any mistake. The use of multiple linked sheets gives the user ample space for hidingany calculations and concentrating on the analysis by filtering unnecessary data. Also, forusers requiring external data feeds such as exchange rates or commodity prices, Excel haspowerful link tools to data providers such as Reuters, Bloomberg or Thomson Financial’sDatastream.
Most of the calculations under excel are done by importing the outputs from the opti-mization engine, which is formatted and stored in two matrices. One matrix containsthe production, consumption, costs and location (zone number) of the various generatorsand loads. Then by combining this information with the matrix in which zone prices arestored, profits of consumers and producers are computed. The variations in profits of thedifferent actors in each case is quite important. The reason for looking at profits (totalprofit, change in profit, repartition between generators) of the different participants undervarious conditions, is motivated by the fact that firms change their investment behavioraccording to opportunities to achieve higher profits. In a later stage these profit andincome levels feed into the valuation model which is also under excel, to assess investmentopportunities under various cases.
6.5 Further Software Enhancements
The brief list of further enhancements, is presented here for the purpose of guiding anyother person which would want to continue the market model developed in this work.
• Development of an integrated graphical user interface: one major software enhance-ment would be the ability for the user to define the various input parameters usingpre-defined fields of a graphical interface. The cost bids could be entered usingforms, to limit errors in the bids. Forms here would be ideal because of the stan-dard nature of defining generators. Zone could then be defined by selecting variousgenerators and loads using a drag and drop approach.
• Integration of data feeds: another enhancement would be the ability for the programto accept external data feeds. These could be of several types: bid data, from powerexchanges, but also commodity price data from providers such as Bloomberg. Thiswould enable the program to have generation cost functions which depend on theunderlying commodity. Gas fired generators would have their costs rise wheneverthe cost of gas rises. This could be done by building an import interface under excel.
• Power flows modeled : a new set of constraints would have to be added, to modeltransmission line impedances. This is still a full DC approach. It would enable theuser to introduce the concept of node prices, more detailed than the zone price.However this requires extensive information about the configuration of the networkand would take considerably longer for the user to input data.
Chapter 7
Case Studies
The objective of this chapter is to present a number of different simulations which havebeen conducted using the market model developed. All the simulations are based onreal situations in Europe. The input data, is exclusively from various publicly availablesources.
7.1 France-Italy electricity link
In this section, the transmission link between France and Italy will be studied in detail.This power line is of crucial importance for the Italian market since the Italians are thelargest net importers of electricity in the European Union with 42539 GWh importedin 19991 and have the smallest reserve capacity. For the French incumbent EdF2, theexistence of this transport infrastructure is the key enabler for a large percentage of itselectricity exports. The link is critically congested most of the time, and the lack ofinterconnection capacity leads to a real price isolation of the Italian peninsula from theFrench market. Italian retail customers payed, in 1999 for their electricity, on averagearound 73%3 more than French customers, and industrial customers payed 48%4 morein 2000 than their French counterpart. In such a setting the developed model is veryadequate and a detailed study of the situation, represents a very good opportunity todetermine the impact of the transmission congestion on prices.
In a first section the choice of simulation parameters will be presented, then the analysiswill focus on varying the capacity of the transmission link and determining its effects onmarket prices as well as the profits of the different participants (consumers and producers).Then these results will be used as a basis for determining a theoretical value for theincrease in transmission capacity.
1source: [6] p.92Electricite de France3source: Guide to the Electricity Directive www.europa.eu.int/en/comm/dg17/elec/memor.htm4source: Eurostat European Union Energy and Transport in Figures table 2.5.6
36 Case Studies
7.1.1 Choice of simulation parameters
The choice of accurate and reliable input parameters is a difficult task especially in theopaque sector of electricity production, when the main producer is state owned. This isthe case in both the French and Italian market. In this subsection, we will first brieflydescribe our data sources, then explain and try to outline certain limitations of the choiceof our input data.
The source data used in these simulations are mainly out of two types of sources: firstlyintergovernmental organizations such as the OECD International Energy Agency andEurostat, secondly company reports from firms such as Edf (Electricity de France) orGRTN, the Italian equivalent of the UK Power Grid. The sources are summed up in table7.1.
Data Type SourceElectricity Prices Leipzig Power Exchange (LPX)
PowernextEurostat
Transport Capacity GRTNRTE
Production Capacity EdfEurostat
Production Prices OECD IEAConsumption RTE
GRTN
Table 7.1: Data sources used in the France-Italy case study
The input parameters required by our model and listed in detail in appendix B on p.57. For the production input parameters, the installed capacity was first determined ,taking into account the production mix5. The production mix is an important parameter,because it helps determine the competitiveness in terms of costs of different countries. Thesimplifying assumption to aggregate the different generators of a certain type (nuclear,hydro, thermal) was made. Also, as neither France nor Italy have significant amountof solar or wind power these generators were not taken into account. Furthermore such“green power” is usually able to sell power under the cost of production due to subsidies.Although much of the data about costs is subject to variation and much debate, sinceparameters such as the choice of the depreciation, and the cost of capital can influencerunning costs, and ultimately the cost per MWh, the view taken here was to get goodestimates, as exact data is not publicly available. The table 7.2, represents the productioncosts used as basis for the case study.
Combining data from tables 7.2 and 7.3 precise marginal cost curves and total cost curves
5source: Eurostat European Union Energy and Transport in Figures 2001 table 2.4.26source: OECD/IEA NEA 1998, 1997 dollars assumes a discount rate of 5% for nuclear and coal, 30
year lifetime, and 75% load factor7source: DIREM average for 19978source Eurostat: European Union Energy and Transport in Figures 2001 table 2.4.2
7.1 France-Italy electricity link 37
France6 US cents Euro cents7
Nuclear 3.22 2.87Coal 4.64 4.13Gas 4.74 4.22
Table 7.2: Generation costs projections per kWh for 2005-2010
1999 in GW8 France ItalyNuclear 63.2 -Conventional Thermal 26.2 52.4Hydro 25.2 20.4Total 114.6 72.8
Table 7.3: Installed production capacity in France and Italy
for three French and two Italian generators were defined. France has one Nuclear, oneThermal and one Hydro generator, Italy only one Thermal and one Hydro unit. Theexact input parameters can bee found in appendix B. Graphical examples of such costcurves can also be seen in the same appendix B figures B.1 and B.2.
For the loads the choice of parameters was difficult because of the lack of publicly availabledata. For the purpose of the case study, the choice was made to have a price sensitive,with a sensitivity of −0.1, and identical demand curve at each run. The choice of thesensitivity is not arbitrary. It is a bit lower than the one chosen by Green in [11], andrepresents rather a short term than a long term elasticity. This hourly electricity demandfor the French and Italian markets was determined by arbitrarily choosing the month ofMarch and calculating an average hourly consumption. The month of March was chosen,because it neither displays a high winter peak, nor summer slump. Similar results wereobtained using yearly average hourly demands, however only for the French market. Sincethe set of publicly available data for Italy was less complete the choice was made to havea consistent arbitrary data set rather than extensive and incomplete.
Average hourly consumption in GWh9 France ItalyMarch 2001 50,7 34,5
Table 7.4: Average hourly consumption in France and Italy
7.1.2 Simulation results
Using the parameters described in the previous section, a number of simulations were run,varying the interconnection capacities between the French and Italian zones. In the firstrun, the link was set to its existing capacity, that is 2.5GW 10 and the results were very
9source: GRTN for Italy and RTE for France, www.grtn.it and www.rte.fr10source: GRTN
38 Case Studies
promising since prices calculated using the market model, were in many ways similar toreality. First of all the price levels were close to the prices on the market (by 20%), andthe difference between the French zone and the Italian zones were significant: 30%. Thiscan mainly be explained by the un-favorable production mix which the Italian markethas. Table 7.3, illustrates the heavy weighting of Italian generation towards expensivethermal production. Secondly, as in reality, the link between the two zone is criticallycongested, since even with a drop in demand in the Italian zone, there is still a permanentneed for the 2.5GW/h power transfer from the French market.
In a later stage the interconnection capacity was varied and its effects on zone pricesamongst others studied.
2.50
2.70
2.90
3.10
3.30
3.50
3.70
3.90
4.10
2.5 5 7.5 10 12.5 15
Capacity in GW
Pri
ce
(in
10'0
00
Eu
ro/G
Wh
)
French Price
Italian Price
Figure 7.1: French and Italian zone prices as a function of interconnection capacity
Figure 7.1, is a graphical illustration of the results of the market model, when the inter-connection capacity is gradually varied from 2.5GW to 15GW . There is a linear priceconvergence, as long as the same set of generators are operating. As soon as a generatorfrom a different merit order has to increase significantly its production there is no morelinearity in the price convergence. The figure 7.1 shows how this market model may beused to determine the value of the transmission line which have to be build in order tohave a single market price and eliminate the current price zones. One significant result,is that a 20% increase in transmission capacity, to 3GW leads to a drop of 0.67% of theItalian prices, and a slight increase of 0.17% of the French zone price. As a result theexisting price differential is reduced by over 1% point, a small step towards the integrationof a European electricity market.
This market price data, is only one of the parameters which varies with interconnectioncapacity. These price and production variations, in turn have a significant impact onthe profits of the various participants : both consumers and producers. These profitvariations are important to analyze since the main motivator of economic actors is thequest for increased profit. Firstly the producer profits are studied in detail.
7.1 France-Italy electricity link 39
15.00
25.00
35.00
45.00
55.00
65.00
75.00
85.00
2.5 5 7.5 10 12.5 15
GW
10'0
00
of
Eu
ros
Italian Generator ProfitsFrench Generator ProfitsSum of Generator Profits
Figure 7.2: Producer profits as a function of interconnection capacity
Producer profits are calculated for each simulation run. The complete set of data can befound in appendix B. Each run is of a length of one hour, and producers are not assumedto pay any sort of toll to use the transmission link, so this profit figure is an indicativemeasure. Costing for the use of the transmission link was not included, for the simplereason that no data was available concerning that specific cost. Figure 7.2, represents thehourly French and Italian producer profits, as well as the sum of the generator profits.The main trends which can be observed from the following experiments are the following:
• The profits of Italian generators are heavily impacted in the case of a significantlyincrease of the transmission link. Overall profits (sum of all Italian generators),fall by about 11% for a doubling to 5GW of the link capacity. However the mostaffected generators are the thermal generators which have profits drop by 25%.
• Conversely, French generators have significant opportunities to increase profitability.The same doubling of link capacity would lead to a 10% increase in profitability,netting in yearly a turnover increase of over Euro 800m11.
• The total value of profits defined as the sum of Italian and French producer profits,actually slightly declines or remains constant with the removal of the constraint.This is an illustration of the feature of market efficiency. As markets become moreefficient, non performing generators have less possibilities to sell their production.
These results concerning producer profits, could be the source of a detailed investigationon the strategic actions of firms. These results are interesting and the full set can befound in appendix B, however the yardstick defined earlier to measure the effect of atransmission link is the society profit or sum of consumer and producer profits. Figure
11figure derived by own calculation assuming prices and quantities calculated using the market model
40 Case Studies
7.3, shows the variation of society profit with interconnection capacity. It should benoted, that as described in the choice of parameters the demand price sensitivity waschosen to be very low (−0.1). From the results obtained in this case study, there is nosignificant increase of society profit with link capacity. The increase is under 0.1% andcan be considered insignificant. This can be explained by a series of different factors.First of all the increase in consumer profit in the Italian zone due to a drop in pricesis compensated by a decrease in consumer profit in the French zone. The net differenceis therefore close to zero. Also, the total consumer profit drops after going through amaximum for a 12.5GW link. This is compensated by an increase in producer profits.Furthermore as demand is so price insensitive, consumers only very slightly reduce theirconsumption even with important price jumps, in turn they only very slightly consumemore if prices dive.
240.72
240.73
240.74
240.75
240.76
240.77
240.78
240.79
240.80
2.5 5 7.5 10 12.5 15
Interconnection Capacity in GW
So
cie
typ
rofi
tin
millio
nE
uro
s
Figure 7.3: Society profit as a function of interconnection capacity
To conclude the first part of this case study, it can be noted that the shear numberof variables and parameters derived by the market model, make any sort of analysis ofcourse only partial. The data chosen here illustrates only one situation in which this modelcan be used. Some results are however very interesting. In the case of the Italian Frenchinterconnection, very small increases in link capacity, have significant impact on the profitsof French and Italian generators, but an important price differential remains between thetwo zones, even with significant transmission capacity. Total price convergence is onlyobtained with a theoretical link of 14.5GW . In reality building a link of such capacityis impossible because of its huge costs and a number of additional technical issues whichwould arise. The total value of the society profit, the yardstick or objective function whichis optimized does not vary by over 0.1% over the range of link capacities.
7.2 Valuation of Italy-France FACTS project 41
7.2 Valuation of Italy-France FACTS project
From the conclusions of the previous section, it has been shown that a slight increase intransmission capacity leads to some price changes and to profit redistribution. As genera-tors in low price zones usually benefit greatly from exports, they might consider investingin a FACTS device, which can under some circumstances increase significantly the in-terconnection capacities. According to recent research conducted by Christian Schaffnerand prof. Goran Andersson in [23], a FACTS power electronics device should increase thetransmission capacity of the France-Italy electricity link. The purpose of this section isusing earlier results from our market model to assess the financial viability of a specificproject and then to give a critical appraisal of an investment in such a project. We willboth make use of theoretical models, but also draw on experience from working in aninvestment bank.
To value a project, one first of all has to set a suitable framework to determine the benefitsderived from this potential investment. The benefits, considered here as the intrinsic valueof a project is defined here as its ability to generate cash. The key issue in any valuationis to accurately be able to forecast future cash flows. Getting the numbers right is muchmore a case of carefully choosing realistic parameters than heavy intensive calculations.
In the FACTS project, the first issue was to isolate the FACTS device to measure thevalue of installing such a solution. The mechanism used in this case is known as a SpecialPurpose Vehicle or S.P.V. This company is a separate legal entity from the power producer,which by law should not operate directly in the area of transmission. The FACTS S.P.V.is fully owned by the power producer but has a negligible capital. This structure enablesthe power producer to make efficient use of its own equity base and by demonstratingthat the project is a high cash generator, the SPV can borrow the full amount it needsto fund the project.
FACTS S.P.V.Power
Producer Ltd.(in low price zone)
Customer(in high price zone)
Power SalePowerre-sale
Payment athigh zoneprice
}
100% owned by powerproducer
Figure 7.4: Structure for FACTS project valuation
In the chosen framework, which is outlined in figure 7.4 the power producer located inFrance (low price zone) wishing to export his electricity sells his production at productioncost to the FACTS operator, which then re-sells the same electricity in the Italian zone,at a higher zone price. The benefit derived is clear: once the FACTS operator has soldpower to the Italian producer and received the cash amounts, ultimately, after deductingoperating costs there remains a surplus.
42 Case Studies
7.2.1 Valuation Method
The method used to carry out the valuation is known as the Enterprise DCF12 model.This method was chosen because it is the most widely used in practice. Furthermore it isvery suitable for this specific project because in the case of a debt only financed companyonly little financial market sensitive information is required.
We will first explain the main ideas of the model used, then a brief overview and discussionof the different parameters for the valuation will be given, finally the results presented.
According to established theory the value of an investment is simply equal to the futurebenefits minus the costs. Copeland in [9] defines the value of operations as the “discountedvalue of expected future free cash flows”. Free cash flows is the total cash amount availableto debt and equity holders. A formal definition:“free cash flow is equal to the after taxoperating earnings of the company, plus noncash charges, less investments in operatingworking capital, property, plant and equipment and other assets” [9].
The value of future cash flows has to be discounted to take into account the opportunitycost associated with investing in this specific project. In practice the future cash flowsare split into two periods. A first period, of some five to ten years, which usually can bemore accurately forecasted, a second period, of indefinite length known as the “continuingvalue”. For this specific project the decision was made to assume that the FACTS wouldhave a limited lifetime of ten years (T = 10) and a continuing value of zero. This is a fairassumption because it seems probable that part or all of the technical device would haveto be replaced after that time.
For calculating the cash flows, the following formula was used[9]:
V alue =T∑
t=1
(NOP(t) + NCI(t)
DF(t)
) − I (7.1)
• T is the total project duration, here 10 years.
• DF stands for discount factor. The discount factor is different for each year t andgrows with the years.
• NOP stands for Net Operating Profit
• NCI stands for non cash items (mainly depreciatation)
• I is the initial investment
To simplify the choice of the discount factor the project is assumed to be financed entirelythrough debt. In the case of a mix between debt and equity the choice of a realisticdiscount factor is complicated by the fact that the WACC13 has to be computed. AsEdF, the French operator is not yet a quoted company it does not make sense to calculatea WACC, as the cost of equity cannot be determined. In a 100% debt financed project
12Discounted Cash Flow13Weighted Average Cost of Capital
7.2 Valuation of Italy-France FACTS project 43
the discount factor is calculated for each year of the project lifetime. The formula usedis the following:
DF(t) = (COB ∗ (1 − TR))t (7.2)
• COB stands for Cost of Borrowing
• TR stands for tax rate. Interest expenses are in most cases tax deductible, whichreduces the cost of borrowing.
The discount factor chosen for the valuation can be found in the summary valuation table7.5 on p.47, or alternatively in Appendix B.
7.2.2 Valuation Parameters
A certain number of parameters where chosen as fixed, others have been varied, for thepurpose of sensitivity analysis .
• FACTS enhancement : the FACTS device was assumed to increase the link capacityby 10%, in the base case. This figure is was chosen based the results in [19], whichis a study of FACTS devices.
• Project lifetime: this was chosen to be ten years. As a FACTS is a power electron-ics device, assuming a longer life time would be risky. This value of ten years isconsidered as conservative, because is could well be that the device still functionsafter that time period. However it should be noted that the forecast of cash flowsover long periods of times is a very difficult task. The value of the equipment at theend of the project lifetime of the project is set to zero. This is known as the salvagevalue. Again this assumption is conservative.
• Project utilization: it is assumed that the device is to be used 80% of the timesix months of the year and 100% during the remaining six months. Each yearwas assumed to be of 362.25 days. This utilization assumes that the device fullyfunctions half of the year.
• Risk free interest rate: this was chosen to be equal to the ten year yield of theUS government bonds on the 02.04.200214 and is equal to 5.42%. This approach isrecommended by Copeland in [8] on p.192.
• Cost of borrowing : is assumed to be 1% over the risk free interest rates whichamounts to 6.42% in the base case. Investments in utilities are usually viewed as lowrisk, so any bond issued by such a company would only have a slight premium overgovernment bonds. In 1988 McKinsey calculated the risk premiums by industry15
and found out that electric utilities had amongst the lowest premiums (less that0.5%).
14source: Dow Jones15source: [9] p.228 exhibit 10.11
44 Case Studies
• Cost of running the link : this was assumed to be 5% of gross turnover, in the basecase. As no similar projects are in commercial operation today, this parameter isan educated guess.
• Initial investment : this was assumed to be 80 million Euro. This assumption is aproxy for the total investment and break up as follow:
Cost Type Amount in million EurosLand and Infrastructure 5Research and Development 10Administrative and Legal 5Device 60
These cost estimates were derived using as basis a the Hydro-Quebec interconnectionproject between Quebec and new England. This project is described in [17] onp.324-327.
• Sales price and cost of sales: these two parameters are inputs from the marketmodel. The impact of the link on zone prices are taken fully into account. Notethat the cost of sales is the sum of two cost types. First of all the cost of producingthe electricity only (around 66%)16, on top of this cost a running cost for the linkis added which amounts to 5% of sales in the base case.
• Corporate tax rate: this was assumed to be 37%17, this was the average corporatetax rate in 2001 in France for large corporations.
• Working capital : this was assumed to 20 million Euros plus a variable part equalto 5% of revenues. This assumption is considered high as it amounts to over 25% ofthe initial investment. The working capital is the cash required for the project tofunction, to pay wages and other expenses before the revenues flow in. The workingcapital is usually high in the first years of a project but then decreases over time asthe project is then financed only through internal cash flows.
• Growth rates: revenues were assumed to drop significantly with time. This is totake into account the initial drop in electricity prices which has been observed inliberalized electricity markets such sa the UK or Norway. A drop in revenues of7.5% the first year 5% in the second 4% in the third and 1% in the fifth year wasassumed.
7.2.3 Valuation Results
Table 7.5 p.47 is a summary of the project valuation which was carried out with the basecase parameters. The negative cash flows in year three is explained by an important callfor working capital combined with a sharp drop of revenues. The important cash inflow
16source: from own calculations based on company reports17source: French ministry of finance website
7.2 Valuation of Italy-France FACTS project 45
0
5
10
15
20
25
30
35
40
45
50
DC
Fin
Eu
rom
5.42% 5.92% 6.42% 6.92% 7.42% 7.92%
Cost of borrowing
Figure 7.5: DCF as a function of the cost of borrowing
8.31
26.22
61.73
44.13
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
0% 2% 4% 6% 8% 10% 12% 14% 16%
FACTS transmission improvement
Inte
rna
lR
ate
of
Re
turn
Figure 7.6: DCF and IRR as a function of FACTS transmission improvement
46 Case Studies
37.50
24.46
30.98
44.13
50.55
5.0%
7.0%
9.0%
11.0%
13.0%
15.0%
17.0%
19.0%
0% 2% 4% 6% 8% 10% 12%
Expenses to run the link as a % of revenue
RO
C
Figure 7.7: DCF and ROC as a function of FACTS running costs
8.31
26.22
61.73
44.13
0%
5%
10%
15%
20%
25%
0% 2% 4% 6% 8% 10% 12% 14% 16%
FACTS transmission improvement
Re
turn
on
Ca
pit
al
Figure 7.8: ROC and DCF as a function of FACTS transmission improvement
7.2 Valuation of Italy-France FACTS project 47
Year Free Cash Flow Discount Factor Present value of FCF(Euro million) (4.04%) ( Euro million)
1 32.43 1.04 31.172 31.72 1.08 29.33 -1.6 1.13 -1.464 14.18 1.17 12.105 13.97 1.22 11.466 13.94 1.27 10.997 13.94 1.32 10.628 13.94 1.37 10.159 13.94 1.43 9.7610 29.70 1.49 19.98Continuing value 0.00 0.00 0.00Total enterprise value 144.02Minus: Value of Debt 100.00Equity Value 44.02
Table 7.5: FACTS valuation summary
in year ten is due to the project end, which means that the working capital flows back.The salvageable fraction of the working capital is set to 25%.
From this base case, a number of parameters where varied and their effect on the projectvaluation will be presented. It should be noted that in figures 7.6, 7.7 and 7.8 on pages45-46 the circle area represents the DCF amount.
The first effect which was investigated was the influence of the borrowing on the enterpriseDCF. As can be seen in figure 7.5, the variation from the base case (which is displayedin dark) is only moderate. This can be explained by the tax benefits which reduce signif-icantly the impact of borrowing on the bottom line. The cost of borrowing is thereforeonly a moderate to low influence factor in such a heavy cash generating project. A 1%point increase in the cost of borrowing leads to a valuation drop of 2 million Euros. Thecost of borrowing does not affect the ROC because the ROC is an internal measure basedon earnings before interest and tax. As interest rates vary over time, such an analysisis important to determine if the project might be at risk in the case of an interest rateincrease. In this specific project interest rates are a low risk factor.
The sensitivity of the DCF as well as the ROC18 was also tested by varying the estimatedtransmission capacity enhancements. In figure 7.8, the size of the bubble indicates theproject value in million Euros for a specific transmission improvement. The base case indark blue is for am improvement of 10%. From this set of experiments it can be notedthat the DCF and ROC are very sensitive to any drop in FACTS performance. A 10%figure for the FACTS performance (our base case) is the lower limit for the project toremain financially attractive. Bellow this figure the ROC drops to under 15% which isusually considered as the limit for investing in a project19. This analysis demonstrates the
18Earnings before interest and tax divided by the book value of assets19source: conversations with bankers
48 Case Studies
need for a perfectly functioning technical solution. If the FACTS device does not have areliability of 95%, or does not work at full capacity the project is financially at risk.
In the experiments displayed in figure 7.7 the effects on the project valuation of theFACTS running costs as a percentage of revenue were studied. The relationship betweenthese two parameters is linear. A 1% drop in margin has an impact of 3.15 million Euroson the project value (assuming all other parameters set to the base case). An increasein running costs due to higher maintenance expenses than expected could therefore makethe project unattractive. If running costs run over 5% of revenues it does not seem wiseto make the investment. Once the exact running costs are determined, it would be veryimportant to determine the factors which can influence these and assess their probabilityof occurence. This would help determine the risk associated with a rise in running costs.
To conclude this section on valuation, it can be noted that the total project value isbetween 30 and 45 million Euros depending on the assumptions. This figure is howeververy sensitive to two parameters namely the running costs and the performance of theFACTS device. As the project is a high cash generator the impact of the borrowing rateonly affects slightly the valuation. This valuation should be seen as a framework andgood results can only be obtained if the costs of FACTS devices, which are not yet incommercial operation, are known. Unfortunately exact figures are not publicly availableso some approximations had to be made.
7.3 France-Italy-Switzerland
The purpose of this case study is to investigate the power trades between France, Switzer-land and Italy. In the course of our preliminary research it was found that Switzerlandacts as a very important power transporter. Nearly all of the power flows between Franceand Switzerland are on a long term contract basis, so the flows between the French andSwiss market will not be investigated. These two markets are assumed to be coupled asthe link between France and Switzerland has a higher capacity than the average totalSwiss consumption20. Some days during the year (mainly in winter), hourly transfersexceed 7.5GWh.
7.3.1 Choice of simulation parameters
The simulation parameters as well as the general approach for the French and Italianmarkets remain the same as in the previous case study (see section 7.1), so these will notbe outlined again. Figure 7.9 gives a graphical overview of the situation which will bemodeled.
The data sources for the Swiss electricity production are mainly from two sources. Fordata concerning electricity production as well as installed capacity we used data from theSwiss Federal Office for Energy. The production data used can be found in table 7.6. Forproduction cost data we made use of a recently published detailed study entitled “Impactof the new Swiss electricity law on the competitiveness of hydropower” [10]. This paper
20source: www.rte-fr.com
7.3 France-Italy-Switzerland 49
Coupled Markets
2.5GW
3.3GW
Figure 7.9: Transmission links France-Italy-Switzerland
analyzes in detail the breakdown of the cost structure of the 46 pure electricity producersover the course over the years 1990 to 199921. As this study is purely historical and doesnot make cost projections for the years 2005 to 2010, we used it as a basis but made someadjustments to take into account the fact that the two sets of data were different. Thegenerator variable costs were used as the basis for our input data22. Capital costs are afunction of depreciation and amortization, which will be to a large extent fully expendedduring the years 2005 to 2010, so these have only been taken into account at 10% of theircurrent value. The production costs (after adjustments) are presented in table 7.7
2000 in GW SwitzerlandNuclear 3.2Conventional Thermal23 0.79Hydro 13.13Total 17.16
Table 7.6: Installed production capacity in Switzerland
Switzerland Euro centsHydropower 2.31-4.62
Table 7.7: Hydropower costs projections per kWh for 2005-2010
Using this data the Swiss production was modeled as three separate generators: onenuclear, one thermal and and one large hydro generator. The cost characteristics forthe nuclear and thermal generators were kept identical to the France-Italy case study.For exact Matlab input parameters see Appendix C. The demand as before was chosen
21using the annual reports of the years 1990, 1995, 1997, 199922source: [10] p.7 Figure 223note that this also includes other generation types
50 Case Studies
arbitrarily as the average electricity consumption for the month of March (see table 7.8). Itshould be noted that the Swiss power consumption is fairly low compared to the Frenchconsumption for example. On an average day the Swiss total demand is about eighttimes lower than the French. This in turns has an effect on the Swiss ability to export orinfluence prices.
Average hourly consumption in GWh24 SwitzerlandMarch 2001 6,54
Table 7.8: Average hourly consumption in Switzerland
7.3.2 Simulation results
The parameters described in section were used as inputs for the market model. Two setsof experiments were carried out. In a first set we varied the link between France andItaly, keeping the Swiss-Italy link constant. In a second set we varied the link betweenSwitzerland and Italy and kept the French-Italian link constant. The results from thefirst set will be fully presented, the other set can be found in Appendix C.
The first run, using the existing link values, we obtained three different zone prices forSwitzerland, Italy and France. These are summed up in table 7.9
France Switzerland ItalyCongested 2.97 3.11 3.61Uncongested 3.09 3.09 3.09Variation (%) +4.2 -0.45 -14.3
Table 7.9: Congested and Uncongested Electricity Prices
The price levels obtained were close to reality. Both French and Swiss producers arecompetitive and the Italian market with two links one of 2.5GW, the other of 3.3GW fullyuses its import capacity. The high Italian price zone makes the link critically congested.However the addition of the Swiss link, compared to the previous case study brings Italianprices down by 7%. Swiss imports impact Italian prices, but this impact is moderate dueto the fairly small Swiss production capacity.
In figure 7.10, the convergence of zone prices due to the removal of transmission conges-tions is displayed. A France-Italy link of 13GW leads to a uni price zone situation (nocongestion). In the uncongested case (see table 7.9), Swiss market prices drop by some0.45%, French prices increase by 4.2% and the bulk of the decrease is in Italy with a14.3% decrease. Italian consumer would therefore be the biggest beneficiaries of such alink. The small drop in Swiss prices is explained by a reduction of 0.08GW/h of Swissproduction. This drop is is caused by Swiss exports being substituted by cheaper Frenchproduction. The construction of such a link would however be extremely costly and is
24source: Swiss Federal Office for Energy, www.strom.ch
7.3 France-Italy-Switzerland 51
2.50
2.70
2.90
3.10
3.30
3.50
3.70
2.5 5 7.5 10 12.5 15
France-Italy link capacity in GW
Pri
ce
(in
10'0
00
Eu
ro/G
Wh
)
French PriceItalian PriceSw iss Price
Figure 7.10: French Swiss and Italian zone prices as a function of link capacity
cannot be foreseen in the near future. These are very similar results to the two zone casestudy which was carried out earlier.
Although zone prices are important they are not the only parameter which has to betaken into account to be able to get a full view of the situation. Usually the investment innew transmission capacity is either driven by technical or financial motives. The increaseof the Italy-France link has effects on the profits of all the generators in the market. Ascan be observed in figure 7.11, our experiments show that the total value of the generatorprofits decreases steadily with the removal of the congestion. This steady decrease isdifferent from what was observed in the previous case study (see 7.2 on p.39). In thethree zone case the market is more efficient, so we do not see the profit increase observedin the previous case study.
These results show how some actors in the economy actually benefit from congestions.The removal of the France-Italy congestion would cost Italian generators one third oftheir profits. Some of the un-economic production facilities would have to be temporarilyremoved from the grid. Overall, most of the profits are actually redistributed amongstthe different participants.
Figure 7.12, shows the evolution of the society profit, that is the total value of consumerand producer surplus as a function of interconnection capacity. The society profit in-creases steadily with link capacity. This shows that congestions actually carry a socialcost. Congestions enable resources to be allocated to less economic generators, whichdrive consumer prices higher. In turn, high generator profits for un-economic units aresustainable because the lack of link capacity limits competition. It should however benoted that the increase in society profit is very small (less than 0.1%), from the congestedto totally uncongested situation. For a complete assessment of the situation a cost benefitanalysis would have to be carried out, by estimating precisely the costs of building sucha link.
52 Case Studies
0
20
40
60
80
100
2.5 5 7.5 10 12.5 15
France-Italy link capacity in GW
10'0
00
of
Eu
ros
Italian Generator ProfitsFrench Generator ProfitsSw iss Generator ProfitsSum of Generator Profits
Figure 7.11: French Swiss and Italian generator profits as a function of link capacity
187.1
187.2
187.3
2.5 5 7.5 10 12.5 15
France-Italy link capacity in GW
So
cie
typ
rofi
tin
millio
nE
uro
s
Figure 7.12: Society profit as a function of link capacity
Chapter 8
Conclusion and future work
In this project multi price zone situations which arise from congested interconnections havebeen studied extensively. In the conclusion of this work which is split in two distinctiveparts we will first give a brief summary of the work undertaken. In a second part we willoutline areas of improvement and further research.
8.1 Project summary
In a time of rapid change in the European market for electricity cross border trading israpidly surging. As a consequence transmission networks are critically congested.
The description of the power market in chapter 3 shows how different countries to intro-duce more competition in the electricity sector have implemented various market modelsfor their power exchanges. The bi-lateral power pool is now the most widely adoptedacross Europe.
The model we developed in chapter 4 is a double auction market model in which generatorsbid in their respective cost functions and loads are modeled as price sensitive. Each actor(load or generator), is assigned to a specific zone and power transmissions are limitedbetween these.
This problem was formulated mathematically in chapter 5 as a constrained Lagrangeanobjective function, which was optimized in the software we developed using Newton-Raphson and Quadratic Programming methods.
To illustrate the working of our software and study specific congested transmission linkswe undertook a series of case studies in chapter 7 involving the French, Swiss and Italianelectricity market. We were able to determine how producers and consumers were im-pacted by the presence or absence of constraints. The overall impact on society which wechose to measure using what economists define as “society profit” was determined. Wefound out that although congestions have a social cost, by our measures this cost is small.
Finally we undertook the valuation of a FACTS project specifically between the Frenchand Italian markets, which would enable increased power trades between the two markets.The opportunity for an investment in such a project was validated through this analysis.
54 Conclusion and future work
8.2 Suggestions for future work
The topics studied in the course of this project could be extended and the model enhancedin several ways. We would like to suggest just a few specific areas of future work.
• model the market as “imperfect”. Perfect competition would no longer be assumed.The model could take into account the strategic behaviour of firms which arise in“oligopolistic” situations. Firms no longer bid-in the market their cost functions butwould amend these, by manipulating the supply, to try to achieve above averageprofits. This would extensively draw on the theories developed by Cournot.
• model the network architecture. This enhancement would make power flows morerealistic and be a first step in taking into account losses in power trades. Thiswould require the implementation of a so called AC or DC optimal power flow.The optimization could be done using an interior point quadratic programmingalgorithm.
• apply this model to determine the economic impact of congestions in other industries.This model has been developed, such that it can easily be adapted to study othertypes of congestions. One type of congestion which could be studied, using thismodel is the congestions of specific airports. This model could then be used todetermine the specific value of a landing slot.
Appendix A
Software Module Examples
Scenario Module example
In the following short example the scenario tool will be used to simulate and analyze largejumps in prices due to varying demand.
The scenario example is based on 5 periods. Generators 1 and 2 both have generationconstraints. Generator 1 has a production limit of 150MW and generator 2 has a pro-duction limit of 200MW . Generator 1, the cheapest among the 3 is always running at itsmaximum whereas generator 2 only hits his generation limits in periods 1, 4, and 5. Thevariable output of generators with different cost functions has a clear influence on pricesas can be observed in figure A.1.
Simplified Zone Tool example
Figure A.2 is the result of an implementation using the simplified zone tool. It enables theuser to define one constraint in the transmission system and study its effects on productionquantities, and one of the two zone prices.
Period 1 Period 2 Period 3 Period 4 Period 5
Generator 1 production in MW 150 149 149 150 150
Generator 2 production in MW 200 53 53 200 200
Generator 3 production in MW 660 -2 -2 233 423
Load 1 consumption in MW 505 100 100 292 386
Load 2 consumption in MW 505 100 100 292 386
Price paid in $ 101 10 10 42 69
Total Consumption 1010 201 200 583 773
Consumption variations t to t+1 -80.1% -0.3% 190.9% 32.5%
Price variations t to t+1 -90.1% -0.1% 325.2% 61.7%
Scenario Module Example
Figure A.1: Scenario Module Example
56 Software Module Examples
Transmission line limit 80.0 100.0 110.0 no limit 85.0 87.0 88.0
Generator 1 100.0 100.0 100.0 100.0 100.0 100.0 100.0
Generator 2 100.0 100.0 100.0 100.0 100.0 100.0 100.0
Generator 3 176.5 192.6 192.6 192.6 181.5 183.4 184.4Load 1 180.0 196.3 196.3 196.3 185.0 187.0 188.0
Load 2 196.5 196.3 196.3 196.3 196.5 196.4 196.4
Price paid in $
Analysis at various constraints upon a transmission line
Figure A.2: Various constraints on a tranmission line
constrained
Zone Price
($)
Generator Prod
Costs
Production
(MW)
Consumption
(MW)
Import / Export
(MW)
26.84$ Low 247 197 50
28.40$ Medium 209 197 12
28.40$ High 135 197 -62unconstrained
Zone Price Generator Prod Production Consumption Import / Export
27.70$ Low 262 197 64
27.70$ Medium 200 197 3
27.70$ High 130 197 -68
Figure A.3: 3 Zone Example
Separate Zone Settlement Module example
To illustrate this module we chose a 3-zone model. We have limited the export of zonesone and two but have not constrained any of the generators. We now wish to look atprice variations in each zone due to the effect of zonal constraints.
Zone 1 Zone 2 Zone 3Generation Cheapest Moderate ExpensiveConsumption 200 200 200Export Limit 50 100 not defined
Table A.1: Separate Zone Settlement
One can see in figure A.3 that the constraints imposed zones 1 and 2 have effects onthe zone prices (zone 1 has a zone price decrease in the constrained case, zone 2 and 3have price increases. Furthermore generators vary their production. In the unconstrainedcase, cheaper generators are able to export most of their production (this is the case ofthe generator in zone 1). One should note that as generators are unconstrained there isabsolutely no risk that consumers cannot be delivered. Transmission in this example isnot for the purpose of quality of service but only for trade.
Appendix B
France Italy Case Study: Full Set ofParameters and Results
B.1 Scenario Input Data
B.2 Matlab Parameters
B.3 Additional Graphs
B.4 Simulation Results
B.5 FACTS Project Valuation
58 France Italy Case Study: Full Set of Parameters and Results
1)
19
99
Pro
du
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nca
pa
city
(in
GW
)2)
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AN
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B.5 FACTS Project Valuation 59
Note
s
1)
this
inclu
des
som
eexport
from
the
avera
ge
hourly
export
calc
ula
tion
Fra
nce
2)
2)
Nucle
ar
Genera
tor
13
)assum
es
am
ix50%
coal,
50%
gas
Pnval(in
GW
h)
047.4
63.2
4)
costs
for
hydro
are
opport
unity
co
sts
dC
nval(in
10'0
00
ofE
uro
s)
2.4
42.8
73.3
05
)
6)
assum
ea
price
sensitiv
ity
of-0
.1
3)
Therm
al
Genera
tor
27
)assum
e85%
availa
bili
tyfo
rnucle
ar
genera
tors
Pnval(in
GW
h)
019.6
526.2
8)
assum
e100%
availa
bili
tyfo
rth
erm
algenera
tors
5)
dC
nval(in
10'0
00
ofE
uro
s)
3.1
34.1
76.2
69
)assum
e70%
availa
bili
tyfo
rhydro
genera
tors
(weath
er
para
mete
r)
4)
Hydro
Genera
tor
3P
nval(in
GW
h)
018.9
25.2
dC
nval(in
10'0
00
ofE
uro
s)
12
5
Italy
3)
Therm
al
Genera
tor
4
Pnval(in
GW
h)
039.3
52.4
5)
dC
nval(in
10'0
00
ofE
uro
s)
3.1
34.1
76.2
6
4)
Hydro
Genera
tor
5P
nval(in
GW
h)
015.3
20.4
dC
nval(in
10'0
00
ofE
uro
s)
12
5
Max
pro
duction
7)
Genera
tor
153.7
28
)G
enera
tor
226.2
9)
Genera
tor
317.6
4
8)
Genera
tor
49
)G
enera
tor
5
Fra
nce
1)
Pnval(in
GW
h)
50
60
dC
nval(in
10'0
00
ofE
uro
s)
102
2
Italy
Pnval(in
GW
h)
25
35
dC
nval(in
10'0
00
ofE
uro
s)
102
2
60 France Italy Case Study: Full Set of Parameters and Results
0 10
20
30
40
50
60
700
24
68
10
12
P [MWh]
incr
em
en
talc
ost
(pe
rM
Wh
)
Generator Marginal Cost CurvesFrance Italy Scenario
Nuclear Generator
Hydro Generator
Thermal Generator
Figure B.1: Marginal cost curves of generators
0 10
20
30
40
50
60
700
50
10
01
50
20
02
50
30
03
50
40
04
50
P [Mwh]
Tota
lco
st
Generator Total Cost CurvesFrance Italy Scenario
Figure B.2: Total cost curves of generators
B.5 FACTS Project Valuation 61
Fra
nc
eIt
aly
Sc
en
ari
oR
es
ult
s
Pro
du
cti
on
/C
on
su
mp
tio
n
inG
W
Zo
ne
Ma
xp
ric
e
pa
id
Inc
om
e
ind
icta
tor
Inc
om
eS
tate
me
nt
Ge
ne
rato
r1
Inc
om
eS
tate
me
nt
Ge
ne
rato
r2
Inc
om
e
Sta
tem
en
t
Ge
ne
rato
r3
To
tal
Zo
ne
1In
co
me
Sta
tem
en
t
Ge
ne
rato
r4
Inc
om
e
Sta
tem
en
t
Ge
ne
rato
r5
Lo
ad
1L
oa
d2
Co
ns
um
er
su
rplu
s
Lin
ko
f2
.50
GW
.M
ark
et
sh
are
of
loca
lp
rod
uctio
n7
2.2
%0
.6%
27
.2%
10
0.0
%M
ark
et
sh
are
of
loca
lp
rod
uctio
n5
5.8
%4
4.2
%1
00
.0%
Ge
ne
rato
r1
45
.03
1.0
01
21
.12
13
3.8
6To
talP
rod
uctio
n(in
GW
h)
45
.03
0.3
91
6.9
86
2.4
0To
talP
rod
uctio
n(in
GW
h)
18
.03
14
.28
32
.31
Ge
ne
rato
r2
0.3
91
.00
1.1
61
.17
Exp
ort
ed
Pro
du
ctio
n1
.80
0.0
20
.68
2.5
0E
xp
ort
ed
Pro
du
ctio
n0
.00
0.0
00
.00
Ge
ne
rato
r3
16
.98
1.0
03
1.1
15
0.4
70
0
Lo
ad
1-5
9.9
01
.00
-18
119
.76
-17
8.0
6L
oca
lS
ale
s1
28
.50
1.1
24
8.4
41
78
.06
Lo
ca
lS
ale
s6
9.7
45
5.2
31
24
.97
Ge
ne
rato
r4
18
.03
2.0
06
1.2
86
9.7
4N
et
Exp
ort
Sa
les
6.9
80
.06
2.6
39
.67
Ne
tE
xp
ort
Sa
les
0.0
00
.00
0.0
0
Ge
ne
rato
r5
14
.28
2.0
02
6.8
05
5.2
3To
talS
ale
s(in
10
'00
0e
uro
s)
13
5.4
71
.18
51
.08
18
7.7
3To
talS
ale
s(in
10
'00
0e
uro
s)
69
.74
55
.23
12
4.9
7
Lo
ad
2-3
4.8
12
.00
-61
94
.45
-13
4.6
4P
rod
uctio
nC
osts
-12
1.1
2-1
.16
-31
.11
-15
3.4
0P
rod
uctio
nC
osts
-61
.28
-26
.80
-88
.08
Gro
ss
Pro
fit
14
.35
0.0
21
9.9
73
4.3
4G
ross
Pro
fit
8.4
62
8.4
33
6.8
91
79
41
.69
60
59
.81
24
00
1.5
0
12
Zo
ne
Pri
ce
s2
.97
25
60
71
3.8
67
57
Lin
ko
f2
.75
GW
.M
ark
et
sh
are
of
loca
lp
rod
uctio
n7
2.2
%0
.7%
27
.1%
10
0.0
%M
ark
et
sh
are
of
loca
lp
rod
uctio
n5
5.5
%4
4.5
%1
00
.0%
Ge
ne
rato
r1
45
.24
1.0
01
21
.74
13
4.5
9To
talP
rod
uctio
n(in
GW
h)
45
.24
0.4
21
7.0
06
2.6
5To
talP
rod
uctio
n(in
GW
h)
17
.78
14
.28
32
.06
Ge
ne
rato
r2
0.4
21
.00
1.2
41
.24
Exp
ort
ed
Pro
du
ctio
n1
.99
0.0
20
.75
2.7
5E
xp
ort
ed
Pro
du
ctio
n0
.00
0.0
00
.00
Ge
ne
rato
r3
17
.00
1.0
03
1.1
75
0.5
70
0
Lo
ad
1-5
9.9
01
.00
-18
119
.76
-17
8.2
2L
oca
lS
ale
s1
28
.68
1.1
94
8.3
51
78
.22
Lo
ca
lS
ale
s6
8.5
55
5.0
41
23
.60
Ge
ne
rato
r4
17
.78
2.0
06
0.3
26
8.5
5N
et
Exp
ort
Sa
les
7.6
50
.07
2.8
81
0.6
0N
et
Exp
ort
Sa
les
0.0
00
.00
0.0
0
Ge
ne
rato
r5
14
.28
2.0
02
6.8
05
5.0
4To
talS
ale
s(in
10
'00
0e
uro
s)
13
6.3
31
.26
51
.22
18
8.8
2To
talS
ale
s(in
10
'00
0e
uro
s)
68
.55
55
.04
12
3.6
0
Lo
ad
2-3
4.8
12
.00
-61
94
.46
-13
4.2
0P
rod
uctio
nC
osts
-12
1.7
4-1
.24
-31
.17
-15
4.1
4P
rod
uctio
nC
osts
-60
.32
-26
.80
-87
.12
Gro
ss
Pro
fit
14
.60
0.0
32
0.0
63
4.6
8G
ross
Pro
fit
8.2
32
8.2
43
6.4
71
79
41
.54
60
60
.26
24
00
1.8
0
12
Zo
ne
Pri
ce
s2
.97
51
45
04
3.8
54
62
4
Lin
ko
f3
.00
GW
.M
ark
et
sh
are
of
loca
lp
rod
uctio
n7
2.2
%0
.7%
27
.1%
10
0.0
%M
ark
et
sh
are
of
loca
lp
rod
uctio
n5
5.1
%4
4.9
%1
00
.0%
Ge
ne
rato
r1
45
.44
1.0
01
22
.35
13
5.3
2To
talP
rod
uctio
n(in
GW
h)
45
.44
0.4
41
7.0
26
2.9
0To
talP
rod
uctio
n(in
GW
h)
17
.54
14
.28
31
.82
Ge
ne
rato
r2
0.4
41
.00
1.3
11
.32
Exp
ort
ed
Pro
du
ctio
n2
.17
0.0
20
.81
3.0
0E
xp
ort
ed
Pro
du
ctio
n0
.00
0.0
00
.00
Ge
ne
rato
r3
17
.02
1.0
03
1.2
25
0.6
70
0
Lo
ad
1-5
9.9
01
.00
-18
119
.76
-17
8.3
7L
oca
lS
ale
s1
28
.86
1.2
64
8.2
51
78
.37
Lo
ca
lS
ale
s6
7.3
75
4.8
61
22
.23
Ge
ne
rato
r4
17
.54
2.0
05
9.3
66
7.3
7N
et
Exp
ort
Sa
les
8.3
30
.08
3.1
211
.53
Ne
tE
xp
ort
Sa
les
0.0
00
.00
0.0
0
Ge
ne
rato
r5
14
.28
2.0
02
6.8
05
4.8
6To
talS
ale
s(in
10
'00
0e
uro
s)
13
7.1
91
.34
51
.37
18
9.9
0To
talS
ale
s(in
10
'00
0e
uro
s)
67
.37
54
.86
12
2.2
3
Lo
ad
2-3
4.8
22
.00
-61
94
.46
-13
3.7
5P
rod
uctio
nC
osts
-12
2.3
5-1
.31
-31
.22
-15
4.8
8P
rod
uctio
nC
osts
-59
.36
-26
.80
-86
.17
Gro
ss
Pro
fit
14
.84
0.0
32
0.1
53
5.0
2G
ross
Pro
fit
8.0
02
8.0
63
6.0
61
79
41
.38
60
60
.71
24
00
2.0
9
12
Zo
ne
Pri
ce
s2
.97
77
29
36
3.8
41
67
7
Lin
ko
f4
.00
GW
.M
ark
et
sh
are
of
loca
lp
rod
uctio
n7
2.4
%0
.8%
26
.7%
10
0.0
%M
ark
et
sh
are
of
loca
lp
rod
uctio
n5
3.7
%4
6.3
%1
00
.0%
Ge
ne
rato
r1
46
.27
1.0
01
24
.80
13
8.2
5To
talP
rod
uctio
n(in
GW
h)
46
.27
0.5
41
7.0
96
3.9
0To
talP
rod
uctio
n(in
GW
h)
16
.54
14
.28
30
.82
Ge
ne
rato
r2
0.5
41
.00
1.6
01
.62
Exp
ort
ed
Pro
du
ctio
n2
.90
0.0
31
.07
4.0
0E
xp
ort
ed
Pro
du
ctio
n0
.00
0.0
00
.00
Ge
ne
rato
r3
17
.09
1.0
03
1.4
55
1.0
70
0
Lo
ad
1-5
9.9
01
.00
-18
119
.75
-17
8.9
9L
oca
lS
ale
s1
29
.59
1.5
24
7.8
81
78
.99
Lo
ca
lS
ale
s6
2.6
95
4.1
211
6.8
1
Ge
ne
rato
r4
16
.54
2.0
05
5.5
76
2.6
9N
et
Exp
ort
Sa
les
10
.98
0.1
34
.06
15
.16
Ne
tE
xp
ort
Sa
les
0.0
00
.00
0.0
0
Ge
ne
rato
r5
14
.28
2.0
02
6.8
05
4.1
2To
talS
ale
s(in
10
'00
0e
uro
s)
14
0.5
71
.65
51
.93
19
4.1
5To
talS
ale
s(in
10
'00
0e
uro
s)
62
.69
54
.12
116
.81
Lo
ad
2-3
4.8
22
.00
-61
94
.48
-13
1.9
7P
rod
uctio
nC
osts
-12
4.8
0-1
.60
-31
.45
-15
7.8
6P
rod
uctio
nC
osts
-55
.57
-26
.80
-82
.37
Gro
ss
Pro
fit
15
.77
0.0
42
0.4
83
6.2
9G
ross
Pro
fit
7.1
22
7.3
23
4.4
41
79
40
.76
60
62
.51
24
00
3.2
8
12
Zo
ne
Pri
ce
s2
.98
80
66
67
3.7
89
89
2
Lin
ko
f5
.00
GW
.M
ark
et
sh
are
of
loca
lp
rod
uctio
n7
2.6
%1
.0%
26
.5%
10
0.0
%M
ark
et
sh
are
of
loca
lp
rod
uctio
n5
2.1
%4
7.9
%1
00
.0%
Ge
ne
rato
r1
47
.09
1.0
01
27
.27
14
1.1
9To
talP
rod
uctio
n(in
GW
h)
47
.09
0.6
41
7.1
76
4.9
0To
talP
rod
uctio
n(in
GW
h)
15
.55
14
.28
29
.83
Ge
ne
rato
r2
0.6
41
.00
1.9
01
.92
Exp
ort
ed
Pro
du
ctio
n3
.63
0.0
51
.32
5.0
0E
xp
ort
ed
Pro
du
ctio
n0
.00
0.0
00
.00
Ge
ne
rato
r3
17
.17
1.0
03
1.6
85
1.4
80
0
Lo
ad
1-5
9.9
01
.00
-18
119
.75
-17
9.6
0L
oca
lIn
co
me
13
0.3
11
.77
47
.52
17
9.6
0L
oca
lS
ale
s5
8.1
15
3.3
811
1.4
9
Ge
ne
rato
r4
15
.55
2.0
05
1.8
25
8.1
1N
et
Exp
ort
Inco
me
13
.56
0.1
84
.94
18
.69
Ne
tE
xp
ort
Sa
les
0.0
00
.00
0.0
0
Ge
ne
rato
r5
14
.28
2.0
02
6.8
05
3.3
8To
talIn
co
me
(in
10
'00
0e
uro
s)
14
3.8
81
.96
52
.46
19
8.3
0To
talS
ale
s(in
10
'00
0e
uro
s)
58
.11
53
.38
111
.49
Lo
ad
2-3
4.8
32
.00
-61
94
.50
-13
0.1
8P
rod
uctio
nC
osts
-12
7.2
7-1
.90
-31
.68
-16
0.8
5P
rod
uctio
nC
osts
-51
.82
-26
.80
-78
.63
Gro
ss
Pro
fit
16
.61
0.0
62
0.7
83
7.4
4G
ross
Pro
fit
6.2
92
6.5
83
2.8
71
79
40
.15
60
64
.32
24
00
4.4
6
12
Zo
ne
Pri
ce
s2
.99
84
03
97
3.7
38
10
6
62 France Italy Case Study: Full Set of Parameters and Results
Lin
kof
6.0
0G
W.
Mark
etsh
are
oflo
cal p
roduct
ion
72.7
%1.1
%26.2
%100.0
%M
ark
etsh
are
oflo
cal p
roduct
ion
50.5
%49.5
%100.0
%
Genera
tor
147.9
11.0
0129.7
4144.1
6To
tal P
roduct
ion
(in
GW
h)
47.9
10.7
417.2
565.9
0To
tal P
roduct
ion
(in
GW
h)
14.5
514.2
828.8
3
Genera
tor
20.7
41.0
02.2
02.2
3E
xport
ed
Pro
duct
ion
4.3
60.0
71.5
76.0
0E
xport
ed
Pro
duct
ion
0.0
00.0
00.0
0
Genera
tor
317.2
51.0
031.9
251.8
90
0
Load
1-5
9.9
01.0
0-1
811
9.7
5-1
80.2
2Loca
l Sale
s131.0
32.0
247.1
7180.2
2Loca
l Sale
s53.6
452.6
4106.2
8
Genera
tor
414.5
52.0
048.1
353.6
4N
etE
xport
Sale
s16.0
80.2
55.7
922.1
2N
etE
xport
Sale
s0.0
00.0
00.0
0
Genera
tor
514.2
82.0
026.8
052.6
4To
tal S
ale
s(in
10
'000
euro
s)147.1
12.2
752.9
6202.3
4To
tal S
ale
s(in
10
'000
euro
s)53.6
452.6
4106.2
8
Load
2-3
4.8
32.0
0-6
194.5
2-1
28.4
0P
roduct
ion
Cost
s-1
29.7
4-2
.20
-31.9
2-1
63.8
5P
roduct
ion
Cost
s-4
8.1
3-2
6.8
0-7
4.9
3G
ross
Pro
fit17.3
70.0
721.0
438.4
9G
ross
Pro
fit5.5
125.8
431.3
517939.5
36066.1
224005.6
5
12
Zo
ne
Pri
ces
3.0
0874127
3.6
8632
Lin
kof
7.0
0G
W.
Mark
etsh
are
oflo
cal p
roduct
ion
72.8
%1.3
%25.9
%100.0
%M
ark
etsh
are
oflo
cal p
roduct
ion
48.7
%51.3
%100.0
%
Genera
tor
148.7
41.0
0132.2
2147.1
4To
tal P
roduct
ion
(in
GW
h)
48.7
40.8
417.3
266.9
0To
tal P
roduct
ion
(in
GW
h)
13.5
614.2
827.8
4
Genera
tor
20.8
41.0
02.5
02.5
3E
xport
ed
Pro
duct
ion
5.1
00.0
91.8
17.0
0E
xport
ed
Pro
duct
ion
0.0
00.0
00.0
0
Genera
tor
317.3
21.0
032.1
552.3
00
0
Load
1-5
9.9
01.0
0-1
811
9.7
4-1
80.8
4Loca
l Sale
s131.7
42.2
746.8
3180.8
4Loca
l Inco
me
49.2
751.9
0101.1
7
Genera
tor
413.5
62.0
044.4
949.2
7N
etE
xport
Sale
s18.5
30.3
26.5
925.4
4N
etE
xport
Inco
me
0.0
00.0
00.0
0
Genera
tor
514.2
82.0
026.8
051.9
0To
tal S
ale
s(in
10
'000
euro
s)150.2
72.5
953.4
2206.2
8To
tal I
nco
me
(in
10
'000
euro
s)49.2
751.9
0101.1
7
Load
2-3
4.8
42.0
0-6
194.5
4-1
26.6
1P
roduct
ion
Cost
s-1
32.2
2-2
.50
-32.1
5-1
66.8
6P
roduct
ion
Cost
s-4
4.4
9-2
6.8
0-7
1.2
9G
ross
Pro
fit18.0
60.0
921.2
739.4
2G
ross
Pro
fit4.7
825.1
029.8
817938.9
16067.9
224006.8
3
12
Zo
ne
Pri
ces
3.0
1907857
3.6
34535
Lin
kof
10.0
0G
W.
Mark
etsh
are
oflo
cal p
roduct
ion
73.3
%1.6
%25.1
%100.0
%M
ark
etsh
are
oflo
cal p
roduct
ion
42.5
%57.5
%100.0
%
Genera
tor
151.2
0410203
1139.7
107
156.1
771438
Tota
l Pro
duct
ion
(in
GW
h)
51.2
01.1
417.5
569.8
9To
tal P
roduct
ion
(in
GW
h)
10.5
714.2
824.8
5
Genera
tor
21.1
361244
13.3
97908
3.4
6528221
Exp
ort
ed
Pro
duct
ion
7.3
30.1
62.5
110.0
0E
xport
ed
Pro
duct
ion
0.0
00.0
00.0
0
Genera
tor
317.5
5476452
132.8
4846
53.5
4362004
0
Load
1-5
9.8
9499095
1-1
811
9.7
3-1
82.6
851413
Loca
l Sale
s133.8
32.9
745.8
8182.6
9Loca
l Sale
s36.7
849.6
886.4
6
Genera
tor
410.5
720822
233.8
7308
36.7
8215552
NetE
xport
Sale
s25.4
90.5
78.7
434.7
9N
etE
xport
Sale
s0.0
00.0
00.0
0
Genera
tor
514.2
82
26.8
0246
49.6
8266145
Tota
l Sale
s(in
10
'000
euro
s)159.3
23.5
454.6
2217.4
8To
tal S
ale
s(in
10
'000
euro
s)36.7
849.6
886.4
6
Load
2-3
4.8
520822
2-6
194.5
95
-121.2
565967
Pro
duct
ion
Cost
s-1
39.7
1-3
.40
-32.8
5-1
75.9
6P
roduct
ion
Cost
s-3
3.8
7-2
6.8
0-6
0.6
8G
ross
Pro
fit19.6
10.1
421.7
741.5
2G
ross
Pro
fit2.9
122.8
825.7
917937.0
56073.3
424010.3
9
12
Zo
ne
Pri
ces
3.0
5009047
3.4
79178
Lin
kof
12.0
0G
W.
Mark
etsh
are
oflo
cal p
roduct
ion
73.6
%1.9
%24.5
%100.0
%M
ark
etsh
are
oflo
cal p
roduct
ion
37.5
%62.5
%100.0
%
Genera
tor
152.9
1130648
1144.9
362
162.5
188993
Tota
l Pro
duct
ion
(in
GW
h)
52.9
11.3
417.6
471.8
9To
tal P
roduct
ion
(in
GW
h)
8.5
814.2
822.8
6
Genera
tor
21.3
41540074
14.0
26647
4.1
20586519
Exp
ort
ed
Pro
duct
ion
8.8
30.2
22.9
412.0
0E
xport
ed
Pro
duct
ion
0.0
00.0
00.0
0
Genera
tor
317.6
41
33.1
0892
54.1
8186724
0
Load
1-5
9.8
9284656
1-1
811
9.7
3-1
83.9
6294
Loca
l Sale
s135.3
93.4
345.1
4183.9
6Loca
l Sale
s28.9
748.2
077.1
7
Genera
tor
48.5
82439328
227.0
5379
28.9
7093988
NetE
xport
Sale
s29.8
10.7
69.9
440.5
1N
etE
xport
Sale
s0.0
00.0
00.0
0
Genera
tor
514.2
82
26.8
0246
48.2
0366398
Tota
l Sale
s(in
10
'000
euro
s)165.2
04.1
955.0
8224.4
7To
tal S
ale
s(in
10
'000
euro
s)28.9
748.2
077.1
7
Load
2-3
4.8
6243933
2-6
194.6
3-1
17.6
818845
Pro
duct
ion
Cost
s-1
44.9
4-4
.03
-33.1
1-1
82.0
7P
roduct
ion
Cost
s-2
7.0
5-2
6.8
0-5
3.8
6G
ross
Pro
fit20.2
70.1
621.9
742.4
0G
ross
Pro
fit1.9
221.4
023.3
217935.7
76076.9
524012.7
1
12
Zo
ne
Pri
ces
3.0
7153442
3.3
75607
Genera
tor
1Lin
kof
15.0
0G
W.
Mark
etsh
are
oflo
cal p
roduct
ion
72.2
%4.1
%23.7
%100.0
%M
ark
etsh
are
oflo
cal p
roduct
ion
29.9
%70.1
%100.0
%
Genera
tor
253.7
21
147.4
242
174.3
850819
Tota
l Pro
duct
ion
(in
GW
h)
53.7
23.0
117.6
474.3
7To
tal P
roduct
ion
(in
GW
h)
6.1
014.2
820.3
8
Genera
tor
33.0
14555298
19.3
11468
9.7
85805517
Exp
ort
ed
Pro
duct
ion
10.4
70.5
93.4
414.5
0E
xport
ed
Pro
duct
ion
0.0
00.0
00.0
0
Load
117.6
41
33.1
0892
57.2
62711
17
0
Genera
tor
4-5
9.8
7538146
1-1
811
9.6
7-1
94.3
665915
Loca
l Sale
s140.3
97.8
846.1
0194.3
7Loca
l Sale
s19.7
946.3
666.1
4
Genera
tor
56.0
96207614
218.8
2214
19.7
894204
NetE
xport
Sale
s34.0
01.9
111
.16
47.0
7N
etE
xport
Sale
s0.0
00.0
00.0
0
Load
214.2
82
26.8
0246
46.3
5552809
Tota
l Sale
s(in
10
'000
euro
s)174.3
99.7
957.2
6241.4
3To
tal S
ale
s(in
10
'000
euro
s)19.7
946.3
666.1
4
-34.8
7538146
2-6
194.6
73
-113.2
119555
Pro
duct
ion
Cost
s-1
47.4
2-9
.31
-33.1
1-1
89.8
4P
roduct
ion
Cost
s-1
8.8
2-2
6.8
0-4
5.6
2G
ross
Pro
fit26.9
60.4
724.1
551.5
9G
ross
Pro
fit0.9
719.5
520.5
217925.3
16081.4
624006.7
7
12
Zo
ne
Pri
ces
3.2
4618544
3.2
46185
B.5 FACTS Project Valuation 63
Wit
hFA
CT
S
(lin
ko
f
Wit
ho
ut
(lin
ko
f2
,5G
W)
Pro
jec
tR
ev
en
ue
sIn
Eu
ros
As
su
mp
tio
ns
INP
UT
SH
EE
T:
US
ER
EN
TE
RS
AL
LB
OL
DN
UM
BE
RS
INIT
IAL
INV
ES
TM
EN
TC
AS
HF
LO
WD
ETA
ILS
DIS
CO
UN
TR
AT
E
4)
Initia
lIn
ve
stm
en
t=8
0'0
00
'00
0.0
0�
Re
ve
nu
es
inye
ar
1=
73
'47
3'1
87
.23
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pp
roa
ch
(1:D
ire
ct;
2:C
AP
M)=
2
Op
po
rtu
nity
co
st
(if
an
y)=
-�
Va
r.E
xp
en
se
sa
s%
of
Re
v=
72
%1
.D
isco
un
tra
te=
10
%
Life
tim
eo
fth
ein
ve
stm
en
t1
0F
ixe
de
xp
en
se
sin
ye
ar
1=
03
)2
a.
Be
ta0
.9
Sa
lva
ge
Va
lue
at
en
do
fp
roje
ct=
$0
Ta
xra
teo
nn
et
inco
me
=3
7%
1)
b.
Ris
kle
ss
rate
=5
.42
%
De
pre
c.
me
tho
d(1
:St.
line
;2:D
DB
)=1
Ifyo
ud
on
ot
ha
ve
the
bre
akd
ow
no
ffixe
da
nd
va
ria
ble
2)
c.
Ma
rke
trisk
pre
miu
m=
6.5
0%
Ta
xC
red
it(if
an
y)=
0%
exp
en
se
s,
inp
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the
en
tire
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as
a%
of
reve
nu
es.
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De
bt
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=1
00
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%
Oth
er
inve
st.
(no
n-d
ep
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ble
)=0
e.
Co
st
of
Bo
rro
win
g=
6.4
2%
Dis
co
un
tra
teu
se
d=
4.0
4%
WO
RK
ING
CA
PIT
AL
Initia
lIn
ve
stm
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tin
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rk.
Ca
p=
80
'00
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00
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Wo
rkin
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ap
it ala
s%
of
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v=
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lva
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ab
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nd
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GR
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12
34
56
78
91
0
Re
ve
nu
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Do
no
te
nte
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.00
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.00
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%
Fix
ed
Exp
en
se
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on
ot
en
ter
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0.0
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0.0
0%
0.0
0%
0.0
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De
fau
lt:T
he
fixe
de
xp
en
se
gro
wth
rate
isse
te
qu
alto
the
gro
wth
rate
inre
ve
nu
es
by
de
fau
lt.
YE
AR
64 France Italy Case Study: Full Set of Parameters and Results
01
23
45
67
89
10
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stm
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00
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0.0
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73
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Inv
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BO
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DE
PR
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Bo
ok
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lue
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gin
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No
tes
1)
U.S
.1
0y
yie
ldo
nth
e2
,04
,20
02
:a
pp
roa
ch
reco
mm
en
din
Co
pe
lan
dp
.19
2
3)
Ed
fis
no
ttr
ad
ed
so
this
ca
nn
ot
be
co
mp
ute
d
4)
assu
me
da
FA
CT
Sco
sts
Appendix C
France Switzerland Italy Case Study:Full Set of Parameters and Results
C.1 Scenario Input Data
C.2 Matlab Parameters
C.3 Simulation Results
C.4 Additional Graphs
66 France Switzerland Italy Case Study: Full Set of Parameters and Results
Fra
nce
Sw
itzerl
an
dIt
aly
Scen
ari
oD
ata
Ele
ctr
icD
ata
Eco
no
mic
Data
1)
1999
Pro
duction
capacity
(in
GW
)/2000
for
Sw
itzerland
2)
Ele
ctr
icity
prices
for
industr
yin
euro
/100kW
h11
)F
rance
Italy
Sw
itzerland
Fra
nce
Italy
Nucle
ar
63.2
-3.2
1998
4.9
7.2
6C
onventT
herm
al
26.2
52.4
0.7
91999
5.0
36.7
Hydro
25.2
20.4
13.1
72000
5.1
57.0
7Tota
l11
4.6
72.8
17.1
69)
Pro
jecte
dcosts
ofopera
tion
2005-2
010
for
Fra
nce
3)
Siz
eofth
ein
terc
onnection
toItaly
(in
GW
)c$
cE
uro
Win
ter
2.5
3.3
Nucle
ar
3.2
22.8
7S
um
mer
2.2
2.9
Coal
4.6
44.1
3
Gas
4.7
44.2
24)
Tra
fic
on
the
Italy
-Fra
nce
link
(in
GW
hper
month
)m
ax
theor.
1800
2376
10)
Avera
ge
exchange
rate
for
1997
actu
al
1500
1969
Euro
/Dolla
r0.8
89832292
5)
Avera
ge
Reserv
ecapacity
in%
Fra
nce
Italy
n.a
.5.6
7)
Fre
nch
Dem
and
for
2001
inM
Wh
12)
Sw
iss
Dem
and
for
2001
inM
Wh
Avera
ge
Day
Avera
ge
Hour
Month
Avera
ge
Day
Avera
ge
Hour
January
1372024.0
57167.7
Marc
h4869000
157064.5
6544.3
5484
Febru
ary
1324527.2
55188.6
Marc
h1217475.4
50728.1
April
1197874.9
49911
.5M
ay
1071859.8
44660.8
Note
s
June
1059825.9
44159.4
1)
so
urc
eE
uro
sta
t:E
uro
pe
an
Un
ion
En
erg
y&
Tra
nsp
ort
inF
igu
res
tab
le2
.4.2
July
1057178.1
44049.1
2)
so
urc
eE
uro
sta
t:E
uro
pe
an
Un
ion
En
erg
y&
Tra
nsp
ort
inF
igu
res
tab
le2
.5.6
August
1000563.7
41690.2
3)
so
urc
eG
RT
N:
Ge
sto
reR
ete
Tra
sm
issio
ne
Na
zio
na
le2
00
1a
ctivity
rep
ort
p.1
2
Septe
mber
1104844.2
46035.2
4)
so
urc
eG
RT
N:
Ge
sto
reR
ete
Tra
sm
issio
ne
Na
zio
na
le2
00
1a
ctivity
rep
ort
Octo
ber
1139335.7
47472.3
5)
so
urc
eE
uro
pe
an
Co
mm
issio
nIn
fra
str
uctu
reth
ee
ne
rgy
dim
en
sio
np
.7
Novem
ber
1348581.9
56190.9
6)
so
urc
e:
OE
CD
/IE
AN
EA
19
98
Dis
co
un
tra
te5
%fo
rn
ucle
ar
&co
al,
75
%lo
ad
facto
r
Decem
ber
1462396.2
60933.2
7)
so
urc
eR
TE
8)
so
urc
eG
RT
N:
Ge
sto
reR
ete
Tra
sm
issio
ne
Na
zio
na
le2
00
0sta
tistics
8)
Italia
nD
em
and
for
2000
inM
Wh
9)
so
urc
e:
in1
99
7U
Sd
olla
rsO
EC
D/I
EA
NE
A1
99
8D
isco
un
tra
te5
%fo
rn
ucle
ar
&co
al,
75
%lo
ad
facto
r
Avera
ge
Day
Avera
ge
hour
10)
so
urc
eD
IRE
M
Marc
h828096.8
34504.0
11)
so
urc
e:
Sw
iss
Fe
de
rall
Offic
eo
fE
ne
rgy
Be
rn2
00
0
12)
so
urc
e:
BF
E2
00
1
Siz
eofth
ein
terc
onnection
toS
witzerland
(in
GW
)13)
so
urc
e:
ww
w.r
te-f
r.co
mo
nth
e2
3.0
4.0
2
Win
ter
3.3
Sum
mer
C.4 Additional Graphs 67
Matl
ab
Para
mete
rs
Gen
era
tor
Para
mete
rsN
ote
s
1)
this
inclu
des
som
eexport
from
the
avera
ge
hourly
export
calc
ula
tion
Fra
nce
2)
2)
Nucle
ar
Genera
tor
13
)assum
es
am
ix50%
coal,
50%
gas
Pnval(in
GW
h)
047.4
63.2
4)
costs
for
hydro
are
opport
unity
costs
dC
nval(in
10
'000
ofE
uro
s)
2.4
42.8
73.3
05
)
6)
assum
ea
price
sensitiv
ity
of-0
.1
3)
Therm
al
Genera
tor
27
)assum
e85%
availa
bili
tyfo
rnucle
ar
genera
tors
Pnval(in
GW
h)
019.6
526.2
8)
assum
e100%
availa
bili
tyfo
rth
erm
algenera
tors
5)
dC
nval(in
10
'000
ofE
uro
s)
3.1
34.1
76.2
69
)assum
e70%
availa
bili
tyfo
rhydro
genera
tors
(weath
er
para
mete
r)
data
from
CS
FB
stu
dy
from
1997
adju
ste
dfo
rpro
jections
4)
Hydro
Genera
tor
3
Pnval(in
GW
h)
018.9
25.2
Gen
era
tor
Co
nstr
ain
ts
dC
nval(in
10
'000
ofE
uro
s)
12
5M
ax
pro
duction
7)
Genera
tor
153.7
2
Italy
8)
Genera
tor
226.2
3)
Therm
al
Genera
tor
49
)G
enera
tor
317.6
4
Pnval(in
GW
h)
039.3
52.4
8)
Genera
tor
452.4
5)
dC
nval(in
10
'000
ofE
uro
s)
3.1
34.1
76.2
69
)G
enera
tor
520.4
7)
Genera
tor
62.7
2
4)
Hydro
Genera
tor
58
)G
enera
tor
70.7
9
Pnval(in
GW
h)
015.3
20.4
9)
Genera
tor
89.2
19
dC
nval(in
10
'000
ofE
uro
s)
12
5
Sw
itzerland
Dem
an
dP
ara
mete
rs
2)
Nucle
ar
Genera
tor
6
Pnval(in
GW
h)
02.4
3.2
Fra
nce
dC
nval(in
10
'000
ofE
uro
s)
2.4
42.8
73.3
01
)P
nval(in
GW
h)
50
60
dC
nval(in
10
'000
ofE
uro
s)
102
2
3)
Therm
al
Genera
tor
7
Pnval(in
GW
h)
00.5
90.7
9Italy
5)
dC
nval(in
10
'000
ofE
uro
s)
3.1
34.1
76.2
6P
nval(in
GW
h)
25
35
dC
nval(in
10
'000
ofE
uro
s)
102
2
10
)H
ydro
Genera
tor
8
Pnval(in
GW
h)
09.8
813.1
7S
witzerland
dC
nval(in
10
'000
ofE
uro
s)
2.2
02.3
14.6
2P
nval(in
GW
h)
67
dC
nval(in
10
'000
ofE
uro
s)
12
2
68 France Switzerland Italy Case Study: Full Set of Parameters and Results
Fra
nce
Italy
Lin
kC
apacity
2.5
2.7
53
4.5
6.5
810
14
Sw
itzerland
Italy
Lin
kC
apacity
3.3
3.3
3.3
3.3
3.3
3.3
3.3
3.3
Fre
nch
Price
2.9
72.9
82.9
82.9
93.0
13.0
33.0
53.1
0
Sw
iss
Price
3.1
13.1
13.1
13.1
13.1
13.1
13.1
13.1
0
Italia
nP
rice
3.6
13.6
03.5
93.5
13.4
23.3
43.2
43.1
0
Lin
kC
apacity
2.5
2.7
53
4.5
6.5
810
14
Tota
lC
onsum
er
Surp
lus
18650
18650
18651
18651
18652
18654
18656
18658
Fre
nch
Genera
tor
Pro
fits
34
34
34
35
36
37
38
39
Sw
iss
Genera
tor
Pro
fits
77
77
76
66
Italia
nG
enera
tor
Pro
fit s
29
29
29
28
27
24
23
20
Sum
ofG
enera
tor
Pro
fit s
70
70
70
70
69
68
67
66
Tota
lS
ocie
tyP
rofit(m
)187.2
187.2
187.2
187.2
187.2
187.2
187.2
187.2
Fra
nce
Italy
Lin
kC
apacity
2.5
2.5
2.5
2.5
2.5
Sw
itzerland
Italy
Lin
kC
apacity
3.3
3.5
45
6
Fre
nch
Price
2.9
72.9
72.9
72.9
72.9
7
Sw
iss
Price
3.1
13.1
53.2
33.4
03.5
0
Italia
nP
rice
3.6
13.6
03.5
83.5
33.5
0
158
174
190
206
222
Lin
kC
apacity
3.3
3.5
45
6
Tota
lC
onsum
er
Surp
lus
18650
18650
18651
18651
18651
Fre
nch
Genera
tor
Pro
fit s
34
34
34
33
33
Sw
iss
Genera
tor
Pro
fits
77
89
10
Italia
nG
enera
tor
Pro
fit s
29
29
28
27
26
Sum
ofG
enera
tor
Pro
fit s
70
70
70
70
69
Tota
lS
ocie
tyP
rofit(m
)187.2
187.2
187.2
187.2
187.2
C.4 Additional Graphs 69
Pro
du
cti
on
/C
on
su
mp
tio
n
inG
W
Zo
ne
Pro
du
cti
on
Co
st
Inc
om
e
ind
icta
tor
Inc
om
eS
tate
me
nt
Ge
ne
rato
r1
Inc
om
eS
tate
me
nt
Ge
ne
rato
r2
Inco
me
Sta
tem
en
t
Ge
ne
rato
r3
To
tal
Zo
ne
1In
co
me
Sta
tem
en
t
Ge
ne
rato
r4
Inc
om
e
Sta
tem
en
t
Ge
ne
rato
r5
Inc
om
e
Sta
tem
en
t
Ge
ne
rato
r6
To
talZ
on
e2
Lin
ko
f2
.50
GW
.3
.30
GW
.M
ark
et
sh
are
oflo
ca
lp
rod
.7
2.2
%0
.6%
27
.2%
10
0.0
%M
ark
etsh
are
of
loca
lp
rod
.2
8.0
%0
.5%
71
.5%
10
0.0
%
Ge
ne
rato
r1
45
.03
1.0
01
21
.12
13
3.8
6To
talP
rod
uctio
n(in
GW
h)
45
.03
0.3
91
6.9
86
2.4
0To
talP
rod
uctio
n(in
GW
h)
2.7
20
.05
6.9
69
.73
Ge
ne
rato
r2
0.3
91
.00
1.1
61
.17
Exp
ort
ed
Pro
du
ctio
n1
.80
0.0
20
.68
2.5
0E
xp
ort
ed
Pro
du
ctio
n0
.92
0.0
22
.36
3.3
0
Ge
ne
rato
r3
16
.98
1.0
03
1.1
15
0.4
70
Lo
ad
1-5
9.9
01
.00
-18
119
.76
-17
8.0
6L
oca
lS
ale
s1
28
.50
1.1
24
8.4
41
78
.06
Lo
ca
lS
ale
s5
.59
0.1
11
4.3
02
0.0
0
Ge
ne
rato
r4
2.7
22
.00
7.4
68
.46
Ne
tE
xp
ort
Sa
les
6.5
20
.06
2.4
69
.03
Ne
tE
xp
ort
Sa
les
3.3
30
.07
8.5
211
.92
Ge
ne
rato
r5
0.0
52
.00
0.1
60
.17
To
talS
ale
s(x
10
'00
0e
uro
s)
13
5.0
21
.18
50
.90
18
7.1
0To
talS
ale
s(x
10
'00
0e
uro
s)
8.9
30
.17
22
.83
31
.93
Ge
ne
rato
r6
6.9
62
.00
17
.20
21
.64
Pro
du
ctio
nC
osts
-12
1.1
2-1
.16
-31
.11
-15
3.4
0P
rod
uctio
nC
osts
-7.4
6-0
.16
-17
.20
-24
.82
Ge
ne
rato
r7
13
.15
3.0
04
3.0
04
7.5
0
Ge
ne
rato
r8
14
.28
3.0
02
6.8
05
1.6
0
Lo
ad
3-3
3.2
33
.00
-62
1.8
4-1
20
.05
2.9
72
56
07
14
3.1
114
511
63
3.6
13
14
01
29
Lin
ko
f2
.75
GW
.3
.30
GW
.M
ark
et
sh
are
of
loca
lp
rod
.7
2.2
%0
.7%
27
.1%
10
0.0
%M
ark
etsh
are
of
loca
lp
rod
.28.0
%0
.5%
71
.5%
10
0.0
%
Ge
ne
rato
r1
45
.24
1.0
01
21
.74
13
4.5
9To
talP
rod
uctio
n(in
GW
h)
45
.24
0.4
21
7.0
06
2.6
5To
talP
rod
uctio
n(in
GW
h)
2.7
20
.05
6.9
69
.73
Ge
ne
rato
r2
0.4
21
.00
1.2
41
.24
Exp
ort
ed
Pro
du
ctio
n1
.99
0.0
20
.75
2.7
5E
xp
ort
ed
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du
ctio
n0
.92
0.0
22
.36
3.3
0
Ge
ne
rato
r3
17
.00
1.0
03
1.1
75
0.5
70
Lo
ad
1-5
9.9
01
.00
-18
119
.76
-17
8.2
2L
oca
lS
ale
s1
28
.68
1.1
94
8.3
51
78
.22
Lo
ca
lS
ale
s5
.59
0.1
11
4.3
02
0.0
0
Ge
ne
rato
r4
2.7
22
.00
7.4
68
.46
Ne
tE
xp
ort
Sa
les
7.1
50
.07
2.6
99
.90
Ne
tE
xp
ort
Sa
les
3.3
20
.06
8.5
011
.88
Ge
ne
rato
r5
0.0
52
.00
0.1
60
.17
To
talS
ale
s(x
10
'00
0e
uro
s)
13
5.8
31
.26
51
.03
18
8.1
2To
talS
ale
s(x
10
'00
0e
uro
s)
8.9
10
.17
22
.80
31
.89
Ge
ne
rato
r6
6.9
62
.00
17
.20
21
.64
Pro
du
ctio
nC
osts
-12
1.7
4-1
.24
-31
.17
-15
4.1
4P
rod
uctio
nC
osts
-7.4
6-0
.16
-17
.20
-24
.82
Ge
ne
rato
r7
12
.91
3.0
04
2.1
54
6.4
8
Ge
ne
rato
r8
14
.28
3.0
02
6.8
05
1.4
2
Lo
ad
3-3
3.2
43
.00
-62
1.8
9-1
19
.69
2.9
75
14
50
39
3.1
114
511
63
3.6
00
83
1151
Lin
ko
f3
.00
GW
.3
.30
GW
.M
ark
et
sh
are
of
loca
lp
rod
.7
2.2
%0
.7%
27
.1%
10
0.0
%M
ark
etsh
are
oflo
ca
lp
rod
.2
8.0
%0
.5%
71.5
%1
00
.0%
Ge
ne
rato
r1
45
.44
1.0
01
22
.35
13
5.3
2To
talP
rod
uctio
n(in
GW
h)
45
.44
0.4
41
7.0
26
2.9
0To
talP
rod
uctio
n(in
GW
h)
2.7
20
.05
6.9
69
.73
Ge
ne
rato
r2
0.4
41
.00
1.3
11
.32
Exp
ort
ed
Pro
du
ctio
n2
.17
0.0
20
.81
3.0
0E
xp
ort
ed
Pro
du
ctio
n0
.92
0.0
22
.36
3.3
0
Ge
ne
rato
r3
17
.02
1.0
03
1.2
25
0.6
70
Lo
ad
1-5
9.9
01
.00
-18
119
.76
-17
8.3
7L
oca
lS
ale
s1
28
.86
1.2
64
8.2
51
78
.37
Lo
ca
lS
ale
s5
.59
0.1
11
4.3
02
0.0
0
Ge
ne
rato
r4
2.7
22
.00
7.4
68
.46
Ne
tE
xp
ort
Sa
les
7.7
80
.08
2.9
11
0.7
7N
et
Exp
ort
Sa
les
3.3
10
.06
8.4
711
.84
Ge
ne
rato
r5
0.0
52
.00
0.1
60
.17
To
talS
ale
s(x
10
'00
0e
uro
s)
13
6.6
41
.33
51
.16
18
9.1
4To
talS
ale
s(x
10
'00
0e
uro
s)
8.9
00
.17
22
.77
31
.85
Ge
ne
rato
r6
6.9
62
.00
17
.20
21
.64
Pro
du
ctio
nC
osts
-12
2.3
5-1
.31
-31
.22
-15
4.8
8P
rod
uctio
nC
osts
-7.4
6-0
.16
-17
.20
-24
.82
Ge
ne
rato
r7
12
.67
3.0
04
1.3
04
5.4
8
Ge
ne
rato
r8
14
.28
3.0
02
6.8
05
1.2
4
Lo
ad
3-3
3.2
53
.00
-62
1.9
4-1
19
.33
2.9
77
72
93
65
3.1
114
511
63
3.5
88
52
21
73
Lin
ko
f3
.50
GW
.3
.30
Ma
rke
tsh
are
oflo
ca
lp
rod
.7
2.3
%0
.8%
26
.9%
10
0.0
%M
ark
et
sh
are
oflo
ca
lp
rod
.2
8.0
%0
.5%
71
.5%
10
0.0
%
Ge
ne
rato
r1
45
.85
1.0
01
23
.57
13
6.7
8To
talP
rod
uctio
n(in
GW
h)
45
.85
0.4
91
7.0
56
3.4
0To
talP
rod
uctio
n(in
GW
h)
2.7
20
.05
6.9
69
.73
Ge
ne
rato
r2
0.4
91
.00
1.4
61
.47
Exp
ort
ed
Pro
du
ctio
n2
.53
0.0
30
.94
3.5
0E
xp
ort
ed
Pro
du
ctio
n0
.92
0.0
22
.36
3.3
0
Ge
ne
rato
r3
17
.05
1.0
03
1.3
45
0.8
70
Lo
ad
1-5
9.9
01
.00
-18
119
.76
-17
8.6
8L
oca
lS
ale
s1
29
.23
1.3
94
8.0
61
78
.68
Lo
ca
lS
ale
s5
.59
0.1
11
4.3
02
0.0
0
Ge
ne
rato
r4
2.7
22
.00
7.4
68
.46
Ne
tE
xp
ort
Sa
les
9.0
20
.10
3.3
61
2.4
7N
et
Exp
ort
Sa
les
3.2
90
.06
8.4
111
.76
Ge
ne
rato
r5
0.0
52
.00
0.1
60
.17
To
talS
ale
s(x
10
'00
0e
uro
s)
13
8.2
51
.48
51
.42
19
1.1
5To
talS
ale
s(x
10
'00
0e
uro
s)
8.8
80
.17
22
.71
31
.76
Ge
ne
rato
r6
6.9
62
.00
17
.20
21
.64
Pro
du
ctio
nC
osts
-12
3.5
7-1
.46
-31
.34
-15
6.3
7P
rod
uctio
nC
osts
-7.4
6-0
.16
-17
.20
-24
.82
Ge
ne
rato
r7
12
.20
3.0
03
9.6
04
3.4
8
Ge
ne
rato
r8
14
.28
3.0
02
6.8
05
0.8
9
Lo
ad
3-3
3.2
83
.00
-62
2.0
3-1
18
.61
2.9
82
89
80
15
3.1
114
511
63
3.5
63
90
42
16
Lin
ko
f4
.50
GW
.3
.30
GW
.M
ark
et
sh
are
oflo
ca
lp
rod
.7
2.5
%0
.9%
26
.6%
10
0.0
%M
ark
et
sh
are
oflo
ca
lp
rod
.2
8.0
%0
.5%
71
.5%
10
0.0
%
Ge
ne
rato
r1
46
.68
1.0
01
26
.03
13
9.7
2To
talP
rod
uctio
n(in
GW
h)
46
.68
0.5
91
7.1
36
4.4
0To
talP
rod
uctio
n(in
GW
h)
2.7
20
.05
6.9
69
.73
Ge
ne
rato
r2
0.5
91
.00
1.7
51
.77
Exp
ort
ed
Pro
du
ctio
n3
.26
0.0
41
.20
4.5
0E
xp
ort
ed
Pro
du
ctio
n0
.92
0.0
22.3
63
.30
Ge
ne
rato
r3
17
.13
1.0
03
1.5
75
1.2
80
Lo
ad
1-5
9.9
01
.00
-18
119
.75
-17
9.3
0L
oca
lS
ale
s1
29
.95
1.6
54
7.7
01
79
.30
Lo
ca
lS
ale
s5
.59
0.1
11
4.3
02
0.0
0
Ge
ne
rato
r4
2.7
22
.00
7.4
68
.46
Ne
tE
xp
ort
Sa
les
11.4
60
.15
4.2
11
5.8
2N
etE
xp
ort
Sa
les
3.2
40
.06
8.2
911
.60
Ge
ne
rato
r5
0.0
52
.00
0.1
60
.17
To
talS
ale
s(x
10
'00
0e
uro
s)
14
1.4
21
.79
51
.90
19
5.1
1To
talS
ale
s(x
10
'00
0e
uro
s)
8.8
40
.17
22
.59
31
.60
70 France Switzerland Italy Case Study: Full Set of Parameters and Results
Ge
ne
rato
r6
6.9
62
.00
17
.20
21
.64
Pro
du
ctio
nC
osts
-12
6.0
3-1
.75
-31
.57
-15
9.3
6P
rod
uctio
nC
osts
-7.4
6-0
.16
-17
.20
-24
.82
Ge
ne
rato
r7
11.2
53
.00
36
.26
39
.55
Ge
ne
rato
r8
14
.28
3.0
02
6.8
05
0.1
9
Lo
ad
3-3
3.3
33
.00
-62
2.2
2-1
17
.16
2.9
93
23
53
17
3.1
114
511
63
3.5
14
66
83
03
Lin
ko
f6
.50
GW
.3
.30
GW
.M
ark
et
sh
are
of
loca
lp
rod
.7
2.8
%1
.2%
26
.0%
10
0.0
%M
ark
et
sh
are
of
loca
lp
rod
.2
8.0
%0
.5%
71
.5%
10
0.0
%
Ge
ne
rato
r1
48
.32
1.0
01
30
.98
14
5.6
4To
talP
rod
uctio
n(in
GW
h)
48
.32
0.7
91
7.2
96
6.4
0To
talP
rod
uctio
n(in
GW
h)
2.7
20
.05
6.9
69
.73
Ge
ne
rato
r2
0.7
91
.00
2.3
52
.38
Exp
ort
ed
Pro
du
ctio
n4
.73
0.0
81
.69
6.5
0E
xp
ort
ed
Pro
du
ctio
n0
.92
0.0
22
.36
3.3
0
Ge
ne
rato
r3
17
.29
1.0
03
2.0
35
2.1
00
Lo
ad
1-5
9.9
01
.00
-18
119
.75
-18
0.5
3L
oca
lS
ale
s1
31
.39
2.1
54
7.0
01
80
.53
Lo
ca
lS
ale
s5
.59
0.1
11
4.3
02
0.0
0
Ge
ne
rato
r4
2.7
22
.00
7.4
68
.46
Ne
tE
xp
ort
Sa
les
16
.16
0.2
65
.78
22
.21
Ne
tE
xp
ort
Sa
les
3.1
50
.06
8.0
611
.27
Ge
ne
rato
r5
0.0
52
.00
0.1
60
.17
To
talS
ale
s(x
10
'00
0e
uro
s)
14
7.5
52
.41
52
.78
20
2.7
3To
talS
ale
s(x
10
'00
0e
uro
s)
8.7
40
.17
22
.36
31
.28
Ge
ne
rato
r6
6.9
62
.00
17
.20
21
.64
Pro
du
ctio
nC
osts
-13
0.9
8-2
.35
-32
.03
-16
5.3
6P
rod
uctio
nC
osts
-7.4
6-0
.16
-17
.20
-24
.82
Ge
ne
rato
r7
9.3
63
.00
29
.70
31
.98
Ge
ne
rato
r8
14
.28
3.0
02
6.8
04
8.7
8
Lo
ad
3-3
3.4
43
.00
-62
2.6
0-1
14
.25
3.0
13
90
99
19
3.1
114
511
63
3.4
16
19
64
77
Lin
ko
f8
.00
GW
.3
.30
GW
.M
ark
et
sh
are
of
loca
lp
rod
.7
3.0
%1
.4%
25
.6%
10
0.0
%M
ark
et
sh
are
of
loca
lp
rod
.2
8.0
%0
.5%
71
.5%
10
0.0
%
Ge
ne
rato
r1
49
.56
1.0
01
34
.71
15
0.1
3To
talP
rod
uctio
n(in
GW
h)
49
.56
0.9
41
7.4
06
7.9
0To
talP
rod
uctio
n(in
GW
h)
2.7
20
.05
6.9
69
.73
Ge
ne
rato
r2
0.9
41
.00
2.8
02
.84
Exp
ort
ed
Pro
du
ctio
n5
.84
0.1
12
.05
8.0
0E
xp
ort
ed
Pro
du
ctio
n0
.92
0.0
22
.36
3.3
0
Ge
ne
rato
r3
17
.40
1.0
03
2.3
85
2.7
10
Lo
ad
1-5
9.9
01
.00
-18
119
.74
-18
1.4
5L
oca
lS
ale
s1
32
.44
2.5
14
6.5
01
81
.45
Lo
ca
lS
ale
s5
.59
0.1
11
4.3
02
0.0
0
Ge
ne
rato
r4
2.7
22
.00
7.4
68
.46
Ne
tE
xp
ort
Sa
les
19
.52
0.3
76
.85
26
.74
Ne
tE
xp
ort
Sa
les
3.0
80
.06
7.8
911
.03
Ge
ne
rato
r5
0.0
52
.00
0.1
60
.17
To
talS
ale
s(x
10
'00
0e
uro
s)
15
1.9
62
.88
53
.36
20
8.1
9To
talS
ale
s(x
10
'00
0e
uro
s)
8.6
80
.17
22
.19
31
.03
Ge
ne
rato
r6
6.9
62
.00
17
.20
21
.64
Pro
du
ctio
nC
osts
-13
4.7
1-2
.80
-32
.38
-16
9.8
8P
rod
uctio
nC
osts
-7.4
6-0
.16
-17
.20
-24
.82
Ge
ne
rato
r7
7.9
43
.00
24
.91
26
.55
Ge
ne
rato
r8
14
.28
3.0
02
6.8
04
7.7
3
Lo
ad
3-3
3.5
23
.00
-62
2.8
7-1
12
.05
3.0
29
41
58
71
3.1
114
511
63
3.3
42
34
26
08
Lin
ko
f1
0.0
0G
W.
3.3
0G
W.
Ma
rke
tsh
are
of
loca
lp
rod
.7
3.3
%1
.6%
25
.1%
10
0.0
%M
ark
et
sh
are
of
loca
lp
rod
.2
8.0
%0
.5%
71
.5%
10
0.0
%
Ge
ne
rato
r1
51
.20
1.0
01
39
.71
15
6.1
8To
talP
rod
uctio
n(in
GW
h)
51
.20
1.1
41
7.5
56
9.8
9To
talP
rod
uctio
n(in
GW
h)
2.7
20
.05
6.9
69
.73
Ge
ne
rato
r2
1.1
41
.00
3.4
03
.47
Exp
ort
ed
Pro
du
ctio
n7
.33
0.1
62
.51
10
.00
Exp
ort
ed
Pro
du
ctio
n0
.92
0.0
22
.36
3.3
0
Ge
ne
rato
r3
17
.55
1.0
03
2.8
55
3.5
40
Lo
ad
1-5
9.8
91
.00
-18
119
.73
-18
2.6
9L
oca
lS
ale
s1
33
.83
2.9
74
5.8
81
82
.69
Lo
ca
lS
ale
s5
.59
0.1
11
4.3
02
0.0
0
Ge
ne
rato
r4
2.7
22
.00
7.4
68
.46
Ne
tE
xp
ort
Sa
les
23
.76
0.5
38
.15
32
.44
Ne
tE
xp
ort
Sa
les
2.9
90
.06
7.6
51
0.7
0
Ge
ne
rato
r5
0.0
52
.00
0.1
60
.17
To
talS
ale
s(x
10
'00
0e
uro
s)
15
7.6
03
.50
54
.03
21
5.1
2To
talS
ale
s(x
10
'00
0e
uro
s)
8.5
90
.17
21
.95
30
.71
Ge
ne
rato
r6
6.9
62
.00
17
.20
21
.64
Pro
du
ctio
nC
osts
-13
9.7
1-3
.40
-32
.85
-17
5.9
6P
rod
uctio
nC
osts
-7.4
6-0
.16
-17
.20
-24
.82
Ge
ne
rato
r7
6.0
53
.00
18
.68
19
.63
Ge
ne
rato
r8
14
.28
3.0
02
6.8
04
6.3
2
Lo
ad
3-3
3.6
33
.00
-62
3.2
3-1
09
.10
3.0
50
09
04
73
3.1
114
511
63
3.2
43
87
07
81
Lin
ko
f1
4.0
0G
W.
3.3
0G
W.
Ma
rke
tsh
are
of
loca
lp
rod
.7
3.6
%2
.2%
24
.2%
10
0.0
%M
ark
et
sh
are
of
loca
lp
rod
.2
8.2
%0
.5%
71
.3%
10
0.0
%
Ge
ne
rato
r1
53
.72
1.0
01
47
.42
16
6.3
9To
talP
rod
uctio
n(in
GW
h)
53
.72
1.5
91
7.6
47
2.9
5To
talP
rod
uctio
n(in
GW
h)
2.7
20
.05
6.8
89
.65
Ge
ne
rato
r2
1.5
91
.00
4.7
94
.92
Exp
ort
ed
Pro
du
ctio
n9
.62
0.2
83
.16
13
.06
Exp
ort
ed
Pro
du
ctio
n0
.91
0.0
22
.29
3.2
2
Ge
ne
rato
r3
17
.64
1.0
03
3.1
15
4.6
40
Lo
ad
1-5
9.8
91
.00
-18
119
.72
-18
5.5
0L
oca
lS
ale
s1
36
.60
4.0
44
4.8
61
85
.50
Lo
ca
lS
ale
s5
.62
0.1
01
4.2
01
9.9
2
Ge
ne
rato
r4
2.7
22
.00
7.4
68
.42
Ne
tE
xp
ort
Sa
les
29
.79
0.8
89
.78
40
.45
Ne
tE
xp
ort
Sa
les
2.8
10
.05
7.1
19
.97
Ge
ne
rato
r5
0.0
52
.00
0.1
50
.15
To
talS
ale
s(x
10
'00
0e
uro
s)
16
6.3
94
.92
54
.64
22
5.9
5To
talS
ale
s(x
10'0
00
eu
ros)
8.4
20
.15
21
.31
29
.88
Ge
ne
rato
r6
6.8
82
.00
16
.96
21
.31
Pro
du
ctio
nC
osts
-14
7.4
2-4
.79
-33
.11
-18
5.3
2P
rod
uctio
nC
osts
-7.4
6-0
.15
-16
.96
-24
.57
Ge
ne
rato
r7
3.2
43
.00
9.7
51
0.0
3
Ge
ne
rato
r8
14
.28
3.0
02
6.8
04
4.2
3
Lo
ad
3-3
3.7
93
.00
-62
3.7
4-1
04
.67
3.0
97
33
74
06
3.0
97
33
74
06
3.0
97
33
74
06
# 5
Lin
ko
f2
.50
GW
.3
.30
GW
.M
ark
et
sh
are
of
loca
lp
rod
.7
2.2
%0
.6%
27
.2%
10
0.0
%M
ark
et
sh
are
of
loca
lp
rod
.2
8.0
%0
.5%
71
.5%
10
0.0
%
Ge
ne
rato
r1
45
.03
1.0
01
21
.12
13
3.8
6To
talP
rod
uctio
n(in
GW
h)
45
.03
0.3
91
6.9
86
2.4
0To
talP
rod
uctio
n(in
GW
h)
2.7
20
.05
6.9
69
.73
Ge
ne
rato
r2
0.3
91
.00
1.1
61
.17
Exp
ort
ed
Pro
du
ctio
n1
.80
0.0
20
.68
2.5
0E
xp
ort
ed
Pro
du
ctio
n0
.92
0.0
22
.36
3.3
0
Ge
ne
rato
r3
16
.98
1.0
03
1.1
15
0.4
70
Lo
ad
1-5
9.9
01
.00
-18
119
.76
-17
8.0
6L
oca
lS
ale
s1
28
.50
1.1
24
8.4
41
78
.06
Lo
ca
lS
ale
s5
.59
0.1
11
4.3
02
0.0
0
Ge
ne
rato
r4
2.7
22
.00
7.4
68
.46
Ne
tE
xp
ort
Sa
les
6.5
20
.06
2.4
69
.03
Ne
tE
xp
ort
Sa
les
3.3
30
.07
8.5
211
.92
C.4 Additional Graphs 71
Genera
tor
50.0
52.0
00.1
60.1
7Tota
lS
ale
s(x
10'0
00
euro
s)
135.0
21.1
850.9
0187.1
0Tota
lS
ale
s(x
10'0
00
euro
s)
8.9
30.1
722.8
331.9
3
Genera
tor
66.9
62.0
017.2
021.6
4P
roduction
Costs
-121.1
2-1
.16
-31.1
1-1
53.4
0P
roduction
Costs
-7.4
6-0
.16
-17.2
0-2
4.8
2
Genera
tor
713.1
53.0
043.0
047.5
0
Genera
tor
814.2
83.0
026.8
051.6
0
Load
3-3
3.2
33.0
0-6
21.8
4-1
20.0
5
2.9
72560714
3.1
114511
63
3.6
13140129
Lin
kof
2.5
0G
W.
3.5
0G
W.
Mark
et
share
oflo
calpro
d.
72.2
%0.6
%27.2
%100.0
%M
ark
et
share
oflo
calpro
d.
27.4
%0.6
%72.0
%100.0
%
Genera
tor
145.0
31.0
0121.1
2133.8
6Tota
lP
roduction
(in
GW
h)
45.0
30.3
916.9
862.4
0Tota
lP
roduction
(in
GW
h)
2.7
20.0
67.1
49.9
3
Genera
tor
20.3
91.0
01.1
61.1
7E
xport
ed
Pro
duction
1.8
00.0
20.6
82.5
0E
xport
ed
Pro
duction
0.9
60.0
22.5
23.5
0
Genera
tor
316.9
81.0
031.1
150.4
70
Load
1-5
9.9
01.0
0-1
811
9.7
6-1
78.0
6LocalS
ale
s128.5
01.1
248.4
4178.0
6LocalS
ale
s5.5
40.1
314.5
520.2
1
Genera
tor
42.7
22.0
07.4
68.5
6N
etE
xport
Sale
s6.5
00.0
62.4
59.0
1N
etE
xport
Sale
s3.4
60.0
89.0
812.6
1
Genera
tor
50.0
62.0
00.1
90.2
0Tota
lS
ale
s(x
10'0
00
euro
s)
135.0
01.1
850.9
0187.0
7Tota
lS
ale
s(x
10'0
00
euro
s)
9.0
00.2
123.6
232.8
2
Genera
tor
67.1
42.0
017.7
822.4
7P
roduction
Costs
-121.1
2-1
.16
-31.1
1-1
53.4
0P
roduction
Costs
-7.4
6-0
.19
-17.7
8-2
5.4
4
Genera
tor
712.9
63.0
042.3
246.6
9
Genera
tor
814.2
83.0
026.8
051.4
6
Load
3-3
3.2
43.0
0-6
21.8
8-1
19.7
6
2.9
72560714
3.1
45750633
3.6
03292947
Lin
kof
2.5
0G
W.
4.0
0G
W.
Mark
et
share
oflo
calpro
d.
72.2
%0.6
%27.2
%100.0
%M
ark
et
share
oflo
calpro
d.
26.1
%0.8
%73.0
%100.0
%
Genera
tor
145.0
31.0
0121.1
2133.8
6Tota
lP
roduction
(in
GW
h)
45.0
30.3
916.9
862.4
0Tota
lP
roduction
(in
GW
h)
2.7
20.0
97.6
110.4
2
Genera
tor
20.3
91.0
01.1
61.1
7E
xport
ed
Pro
duction
1.8
00.0
20.6
82.5
0E
xport
ed
Pro
duction
1.0
40.0
32.9
24.0
0
Genera
tor
316.9
81.0
031.1
150.4
70
Load
1-5
9.9
01.0
0-1
811
9.7
6-1
78.0
6LocalS
ale
s128.5
01.1
248.4
4178.0
6LocalS
ale
s5.4
10.1
715.1
520.7
4
Genera
tor
42.7
22.0
07.4
68.7
9N
etE
xport
Sale
s6.4
60.0
62.4
38.9
5N
etE
xport
Sale
s3.7
40.1
210.4
614.3
1
Genera
tor
50.0
92.0
00.2
70.2
8Tota
lS
ale
s(x
10'0
00
euro
s)
134.9
51.1
850.8
8187.0
1Tota
lS
ale
s(x
10'0
00
euro
s)
9.1
50.3
025.6
035.0
5
Genera
tor
67.6
12.0
019.2
724.5
9P
roduction
Costs
-121.1
2-1
.16
-31.1
1-1
53.4
0P
roduction
Costs
-7.4
6-0
.27
-19.2
7-2
7.0
0
Genera
tor
712.4
83.0
040.6
244.6
7
Genera
tor
814.2
83.0
026.8
051.1
0
Load
3-3
3.2
63.0
0-6
21.9
7-1
19.0
4
2.9
72560714
3.2
31499308
3.5
7867499
Lin
kof
2.5
0G
W.
5.0
0G
W.
Mark
et
share
oflo
calpro
d.
72.2
%0.6
%27.2
%100.0
%M
ark
et
share
oflo
calpro
d.
23.9
%1.2
%74.9
%100.0
%
Genera
tor
145.0
31.0
0121.1
2133.8
6Tota
lP
roduction
(in
GW
h)
45.0
30.3
916.9
862.4
0Tota
lP
roduction
(in
GW
h)
2.7
20.1
48.5
411
.40
Genera
tor
20.3
91.0
01.1
61.1
7E
xport
ed
Pro
duction
1.8
00.0
20.6
82.5
0E
xport
ed
Pro
duction
1.1
90.0
63.7
55.0
0
Genera
tor
316.9
81.0
031.1
150.4
70
Load
1-5
9.9
01.0
0-1
811
9.7
6-1
78.0
6LocalS
ale
s128.5
01.1
248.4
4178.0
6LocalS
ale
s5.2
00.2
616.3
221.7
8
Genera
tor
42.7
22.0
07.4
69.2
6N
etE
xport
Sale
s6.3
70.0
62.4
08.8
2N
etE
xport
Sale
s4.2
10.2
113.2
217.6
5
Genera
tor
50.1
42.0
00.4
30.4
7Tota
lS
ale
s(x
10'0
00
euro
s)
134.8
61.1
850.8
5186.8
9Tota
lS
ale
s(x
10'0
00
euro
s)
9.4
10.4
829.5
439.4
3
Genera
tor
68.5
42.0
022.3
729.0
7P
roduction
Costs
-121.1
2-1
.16
-31.1
1-1
53.4
0P
roduction
Costs
-7.4
6-0
.43
-22.3
7-3
0.2
6
Genera
tor
711
.54
3.0
037.2
640.7
2
Genera
tor
814.2
83.0
026.8
050.4
0
Load
3-3
3.3
23.0
0-6
22.1
7-1
17.5
9
2.9
72560714
3.4
02996657
3.5
29439077
Lin
kof
2.5
0G
W.
6.0
0G
W.
Mark
et
share
oflo
calpro
d.
72.2
%0.6
%27.2
%100.0
%M
ark
et
share
oflo
calpro
d.
22.7
%1.4
%75.9
%100.0
%
Genera
tor
145.0
31.0
0121.1
2133.8
6Tota
lP
roduction
(in
GW
h)
45.0
30.3
916.9
862.4
0Tota
lP
roduction
(in
GW
h)
2.7
20.1
79.0
811
.96
Genera
tor
20.3
91.0
01.1
61.1
7E
xport
ed
Pro
duction
1.8
00.0
20.6
82.5
0E
xport
ed
Pro
duction
1.2
70.0
84.2
35.5
7
Genera
tor
316.9
81.0
031.1
150.4
70
Load
1-5
9.9
01.0
0-1
811
9.7
6-1
78.0
6LocalS
ale
s128.5
01.1
248.4
4178.0
6LocalS
ale
s5.0
90.3
116.9
822.3
7
Genera
tor
42.7
22.0
07.4
69.5
2N
etE
xport
Sale
s6.3
20.0
62.3
88.7
5N
etE
xport
Sale
s4.4
40.2
714.8
119.5
1
Genera
tor
50.1
72.0
00.5
30.5
8Tota
lS
ale
s(x
10'0
00
euro
s)
134.8
11.1
850.8
3186.8
2Tota
lS
ale
s(x
10'0
00
euro
s)
9.5
20.5
831.7
841.8
8
Genera
tor
69.0
82.0
024.2
131.7
8P
roduction
Costs
-121.1
2-1
.16
-31.1
1-1
53.4
0P
roduction
Costs
-7.4
6-0
.53
-24.2
1-3
2.2
1
Genera
tor
711
.00
3.0
035.3
538.5
0
Genera
tor
814.2
83.0
026.8
050.0
0
Load
3-3
3.3
53.0
0-6
22.2
8-1
16.7
6
2.9
72560714
3.5
01235317
3.5
01235317
72 France Switzerland Italy Case Study: Full Set of Parameters and Results
Inc
om
e
Sta
tem
en
t
Ge
ne
rato
r7
Inc
om
e
Sta
tem
en
t
Ge
ne
rato
r8
To
tal
Zo
ne
3L
oa
d1
Lo
ad
2L
oa
d3
Co
ns
um
e
rs
urp
lus
Ma
rke
tsh
are
of
loca
lp
rod
.4
7.9
%5
2.1
%1
00
.0%
To
talP
rod
uctio
n(in
GW
h)
13
.15
14
.28
27
.43
Exp
ort
ed
Pro
du
ctio
n0
.00
0.0
00
.00
Lo
ca
lS
ale
s4
7.5
05
1.6
09
9.0
9
Ne
tE
xp
ort
Sa
les
0.0
00
.00
0.0
0
To
talS
ale
s(x
10
'00
0e
uro
s)
47
.50
51
.60
99
.09
Pro
du
ctio
nC
osts
-43
.00
-26
.80
-69
.80
Ma
rke
tsh
are
of
loca
lp
rod
.4
7.5
%5
2.5
%1
00
.0%
To
talP
rod
uctio
n(in
GW
h)
12
.91
14
.28
27
.19
Exp
ort
ed
Pro
du
ctio
n0
.00
0.0
00
.00
Lo
ca
lS
ale
s4
6.4
85
1.4
29
7.9
0
Ne
tE
xp
ort
Sa
les
0.0
00
.00
0.0
0
To
talS
ale
s(x
10
'00
0e
uro
s)
46
.48
51
.42
97
.90
Pro
du
ctio
nC
osts
-42
.15
-26
.80
-68
.95
Ma
rke
tsh
are
of
loca
lp
rod
.4
7.0
%5
3.0
%1
00
.0%
To
talP
rod
uctio
n(in
GW
h)
12
.67
14
.28
26
.95
Exp
ort
ed
Pro
du
ctio
n0
.00
0.0
00
.00
Lo
ca
lS
ale
s4
5.4
85
1.2
49
6.7
2
Ne
tE
xp
ort
Sa
les
0.0
00
.00
0.0
0
To
talS
ale
s(x
10
'00
0e
uro
s)
45
.48
51
.24
96
.72
Pro
du
ctio
nC
osts
-41
.30
-26
.80
-68
.10
Ma
rke
tsh
are
of
loca
lp
rod
.4
6.1
%5
3.9
%1
00
.0%
To
talP
rod
uctio
n(in
GW
h)
12
.20
14
.28
26
.48
Exp
ort
ed
Pro
du
ctio
n0
.00
0.0
00
.00
Lo
ca
lS
ale
s4
3.4
85
0.8
99
4.3
7
Ne
tE
xp
ort
Sa
les
0.0
00
.00
0.0
0
To
talS
ale
s(x
10
'00
0e
uro
s)
43
.48
50
.89
94
.37
Pro
du
ctio
nC
osts
-39
.60
-26
.80
-66
.41
Ma
rke
tsh
are
of
loca
lp
rod
.4
4.1
%5
5.9
%1
00
.0%
To
talP
rod
uctio
n(in
GW
h)
11.2
51
4.2
82
5.5
3
Exp
ort
ed
Pro
du
ctio
n0
.00
0.0
00
.00
Lo
ca
lS
ale
s3
9.5
55
0.1
98
9.7
4
Ne
tE
xp
ort
Sa
les
0.0
00
.00
0.0
0
To
talS
ale
s(x
10
'00
0e
uro
s)
39
.55
50
.19
89
.74
Pro
du
ctio
nC
osts
-36
.26
-26
.80
-63
.06
Ma
rke
tsh
are
of
loca
lp
rod
.3
9.6
%6
0.4
%1
00
.0%
To
talP
rod
uctio
n(in
GW
h)
9.3
61
4.2
82
3.6
4
Exp
ort
ed
Pro
du
ctio
n0
.00
0.0
00
.00
Lo
ca
lS
ale
s3
1.9
84
8.7
88
0.7
7
Ne
tE
xp
ort
Sa
les
0.0
00
.00
0.0
0
To
talS
ale
s(x
10
'00
0e
uro
s)
31
.98
48
.78
80
.77
Pro
du
ctio
nC
osts
-29
.70
-26
.80
-56
.50
Ma
rke
tsh
are
of
loca
lp
rod
.3
5.7
%6
4.3
%1
00
.0%
To
talP
rod
uctio
n(in
GW
h)
7.9
41
4.2
82
2.2
2
Exp
ort
ed
Pro
du
ctio
n0
.00
0.0
00
.00
Lo
ca
lS
ale
s2
6.5
54
7.7
37
4.2
8
Ne
tE
xp
ort
Sa
les
0.0
00
.00
0.0
0
To
talS
ale
s(x
10
'00
0e
uro
s)
26
.55
47
.73
74
.28
Pro
du
ctio
nC
osts
-24
.91
-26
.80
-51
.71
Ma
rke
tsh
are
of
loca
lp
rod
.2
9.8
%7
0.2
%1
00
.0%
To
talP
rod
uctio
n(in
GW
h)
6.0
51
4.2
82
0.3
3
Exp
ort
ed
Pro
du
ctio
n0
.00
0.0
00
.00
Lo
ca
lS
ale
s1
9.6
34
6.3
26
5.9
5
Ne
tE
xp
ort
Sa
les
0.0
00
.00
0.0
0
To
talS
ale
s(x
10
'00
0e
uro
s)
19
.63
46
.32
65
.95
Pro
du
ctio
nC
osts
-18
.68
-26
.80
-45
.48
Ma
rke
tsh
are
of
loca
lp
rod
.1
8.5
%8
1.5
%1
00
.0%
To
talP
rod
uctio
n(in
GW
h)
3.2
41
4.2
81
7.5
2
Exp
ort
ed
Pro
du
ctio
n0
.00
0.0
00
.00
Lo
ca
lS
ale
s1
0.0
34
4.2
35
4.2
6
Ne
tE
xp
ort
Sa
les
0.0
00
.00
0.0
0
To
talS
ale
s(x
10
'00
0e
uro
s)
10
.03
44
.23
54
.26
Pro
du
ctio
nC
osts
-9.7
5-2
6.8
0-3
6.5
6
Ma
rke
tsh
are
of
loca
lp
rod
.4
7.9
%5
2.1
%1
00
.0%
To
talP
rod
uctio
n(in
GW
h)
13
.15
14
.28
27
.43
Exp
ort
ed
Pro
du
ctio
n0
.00
0.0
00
.00
Lo
ca
lS
ale
s4
7.5
05
1.6
09
9.0
9
Ne
tE
xp
ort
Sa
les
0.0
00
.00
0.0
0
C.4 Additional Graphs 73
Tota
lS
ale
s(x
10
'000
euro
s)
47.5
051.6
099.0
9
Pro
duction
Costs
-43.0
0-2
6.8
0-6
9.8
0
Mark
etshare
oflo
calpro
d.
47.6
%52.4
%100.0
%
Tota
lP
roduction
(in
GW
h)
12.9
614.2
827.2
4
Export
ed
Pro
duction
0.0
00.0
00.0
0
LocalS
ale
s46.6
951.4
698.1
4
NetE
xport
Sale
s0.0
00.0
00.0
0
Tota
lS
ale
s(x
10
'000
euro
s)
46.6
951.4
698.1
4
Pro
duction
Costs
-42.3
2-2
6.8
0-6
9.1
2
Mark
etshare
oflo
calpro
d.
46.6
%53.4
%100.0
%
Tota
lP
roduction
(in
GW
h)
12.4
814.2
826.7
6
Export
ed
Pro
duction
0.0
00.0
00.0
0
LocalS
ale
s44.6
751.1
095.7
8
NetE
xport
Sale
s0.0
00.0
00.0
0
Tota
lS
ale
s(x
10
'000
euro
s)
44.6
751.1
095.7
8
Pro
duction
Costs
-40.6
2-2
6.8
0-6
7.4
2
Mark
etshare
oflo
calpro
d.
44.7
%55.3
%100.0
%
Tota
lP
roduction
(in
GW
h)
11.5
414.2
825.8
2
Export
ed
Pro
duction
0.0
00.0
00.0
0
LocalS
ale
s40.7
250.4
091.1
2
NetE
xport
Sale
s0.0
00.0
00.0
0
Tota
lS
ale
s(x
10
'000
euro
s)
40.7
250.4
091.1
2
Pro
duction
Costs
-37.2
6-2
6.8
0-6
4.0
6
Mark
etshare
oflo
calpro
d.
43.5
%56.5
%100.0
%
Tota
lP
roduction
(in
GW
h)
11.0
014.2
825.2
8
Export
ed
Pro
duction
0.0
00.0
00.0
0
LocalS
ale
s38.5
050.0
088.5
0
NetE
xport
Sale
s0.0
00.0
00.0
0
Tota
lS
ale
s(x
10
'000
euro
s)
38.5
050.0
088.5
0
Pro
duction
Costs
-35.3
5-2
6.8
0-6
2.1
5
2.50
2.70
2.90
3.10
3.30
3.50
3.70
3.90
3.3 3.8 4.3 4.8 5.3 5.8
Switzerland-Italy link capacity in GW
Pri
ce
(in
10'0
00
Eu
ro/G
Wh
)
French PriceItalian PriceSw iss Price
74 France Switzerland Italy Case Study: Full Set of Parameters and Results
0
20
40
60
80
100
3.3 3.8 4.3 4.8 5.3 5.8
Switzerland-Italy link capacity in GW
10'0
00
of
Eu
ros
Italian Generator ProfitsFrench Generator ProfitsSw iss Generator ProfitsSum of Generator Profits
187.1
187.2
187.3
3.3 3.8 4.3 4.8 5.3 5.8
Sw itzerland-Italy link capacity in GW
So
cie
typ
rofi
tin
millio
nE
uro
s
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