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UNIVERSIDAD PONTIFICIA COMILLAS DE MADRID

ESCUELA TÉCNICA SUPERIOR DE INGENIERÍA (ICAI)

(Departamento de Organización Industrial)

OPTIMIZACIÓN DE LA EXPLOTACIÓN Y

DE LA PREPARACIÓN DE OFERTAS DE

UNA EMPRESA DE GENERACIÓN DE

ENERGÍA ELÉCTRICA PARA

MERCADOS DE CORTO PLAZO

Tesis para la obtención del grado de Doctor

Directores: Prof. Dr. D. Michel Rivier Abbad

Prof. Dr. D. Mariano Ventosa Rodríguez

Autor: Ing. D. Álvaro Baíllo Moreno

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UNIVERSIDAD PONTIFICIA COMILLAS DE MADRID

ESCUELA TÉCNICA SUPERIOR DE INGENIERÍA (ICAI)

(Departamento de Organización Industrial)

A METHODOLOGY TO DEVELOP OPTIMAL

SCHEDULES AND OFFERING STRATEGIES

FOR A GENERATION COMPANY OPERATING

IN A SHORT-TERM ELECTRICITY MARKET

Tesis para la obtención del grado de Doctor

Directores: Prof. Dr. D. Michel Rivier Abbad

Prof. Dr. D. Mariano Ventosa Rodríguez

Autor: Ing. D. Álvaro Baíllo Moreno

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cumplimiento de los requisitos

académicos; O.M. 17-9-1993, art.9

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“Everything that is really great and inspiring is

created by the individual who can labor in freedom.”

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Acknowledgements

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Acknowledgements

During the development of this doctoral thesis I have benefited from the financial

support of several institutions and from the advice and guidance of a number of people.

Without these contributions this work would never have been possible.

I am indebted to the

Instituto de Investigación Tecnológica

(IIT) of the Universidad

Pontificia Comillas’ Engineering School not only for providing the physical facilities for

the development of this work, but also for an exceptional human and intellectual

environment. It is much easier to climb a wall when you stand on the back of giants. I

am particularly grateful to my two thesis advisors, Professors Michel Rivier and

Mariano Ventosa, and to Professor Andrés Ramos. Their constant support and good

advice has been an essential ingredient for this work. I am also obliged to Professors

Javier García González and Julián Barquín. Their work in this field and their point of

view at particular moments have been two determinant elements of my research.

Additionally, I would like to thank Santiago Cerisola for his extraordinary generosity

when sharing his immense knowledge.

The electric company Iberdrola has played a major role in the development of this

work. From an institutional perspective, Iberdrola has provided a great part of the

funds required during these four years. However, the collaboration between IIT and

Iberdrola goes well beyond this financial support. Many of the ideas included in this

thesis are a result of the valuable feedback and encouragement received during hours of

meetings and discussions. I am grateful to each and every member of the several teams

I have worked with and they know it, but it would take up too much space to mention

them all. I am then forced to reduce my explicit expression of gratitude to the heads of

these teams: Francisco Martínez Córcoles, Ángel Chiarri, Gregorio Relaño and Rodolfo

Martínez.

During the last two years I have also benefited from a scholarship of the Spanish

Ministry of Science and Technology in the program of researchers’ training (Formación

del Personal Investigador, FPI), associated to the research project SEC99 – 0199.

Finally, I want to thank Professors Benjamin F. Hobbs, Yves Smeers, Francisco

Javier Prieto and Ignacio Pérez Arriaga for being part of the Evaluation Committee.

Their questions and suggestions have added significant value to the final version of this

document.

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Si hay algún sentimiento que predomina sobre los demás ahora que ya he defendido

la tesis y todo

parece

haber terminado es el de gratitud. Me considero el hombre más

afortunado del mundo por las personas cuyo apoyo y cariño he tenido el privilegio de

disfrutar durante estos años.

Mis directores de tesis, Mariano y Michel, y Andrés (que ha hecho de tercer director

de tesis) han depositado en mí una confianza que va mucho más allá de lo que yo

pueda merecer. Además han sido y son para mí un ejemplo a seguir, no sólo en el plano

académico, sino también desde el punto de vista humano. Aterrizar en su equipo al

terminar la carrera fue un golpe de suerte. Espero no defraudar sus expectativas en la

nueva etapa que ahora empiezo.

Mi relación con el IIT empezó en el penúltimo año de carrera, con una beca de

colaboración que me ofreció Jaime. Luego David, al dirigirme el proyecto fin de carrera,

me hizo probar el sabor intenso de lo que se cocinaba en aquellos años tanto en el

Instituto como en el sector eléctrico español en general. Gracias a ellos decidí probar la

aventura de hacerme pinche.

Entre los fogones del IIT he disfrutado de la compañía y de la amistad de muchas

personas. Por la tercera planta, en la que han transcurrido la mayor parte de mis horas

en los últimos años, ha pasado mucha gente con la que he compartido

fundamentalmente buenos momentos, que ha sabido aguantarme y de la que he

aprendido mucho. A Santi, además de agradecerle una vez más su ayuda en el terreno

de la programación matemática, le quiero agradecer su generosidad desbordante y su

paciencia conmigo. Estoy convencido de que en menos de un año estaremos celebrando

el final de su tesis. A Toño y Fernando, ahora en Iberdrola, les agradezco su buen

humor infinito y su apoyo en los momentos difíciles. A Jesús le agradezco su entrega

silenciosa y discreta. A Luis y a Ernesto, su cercanía aunque yo a veces ande distraído

y con la cabeza en otra parte. A Rafa, que todos los días me avise para el café, aunque

la mayor parte de las veces no vaya y el resto le diga que voy en cinco minutos. A

Francisco Javier no le voy a agradecer su ayuda en la edición de la tesis, porque

prefiero agradecerle su confianza en mí y que me pregunte de vez en cuando si nos

vamos juntos en metro, ya que he dejado de ir al gimnasio. Le auguro un gran futuro

en Gas Natural. Gracias también a Jordi, a Pablo y a Agustín, a los que he ido

conociendo durante el último año pero que me han visto poco por el aislamiento al que

me ha obligado el tramo final de la tesis. Y gracias también a los muchos que se fueron

y con los que compartí mis momentos de mayor confusión en el Instituto: Alberto,

Óscar, David, Irene, Grego…

Hay además gente repartida por el resto del Instituto con la que he vivido y sigo

viviendo momentos intensos, muchos de ellos relacionados con el desarrollo de nuestras

respectivas tesis: Enrique, Carlos, Pedro, Javier GG, Álvaro... Con frecuencia me han

dejado admirado y estoy seguro de que seguiré aprendiendo cosas de ellos en el futuro.

También he tenido la suerte de dirigir proyectos fin de carrera a personas de gran

valía que luego se han convertido en compañeros: Pedro, Daniel y Santiago (además de

Jesús). Aunque la experiencia del proyecto siempre es dura, creo que no me guardan

rencor. Todos ellos me han apoyado en el último empujón a la tesis, leyéndose

capítulos o participando en cuestiones puntuales de su desarrollo.

Una de las experiencias más gratificantes y que más me ha espoleado en este último

tramo de la tesis ha sido la oportunidad de ser representante de los Investigadores en

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Acknowledgements

Formación junto con Pedro. También en este aspecto me surge un sentimiento de

gratitud por todo lo que me ha permitido aprender, por la nueva perspectiva que me ha

proporcionado tanto del Instituto como de la Universidad y porque mi vocación

universitaria se ha visto reforzada. En particular, quiero agradecer a Miguel Ángel,

Antonio y Michel los esfuerzos que han hecho y siguen haciendo por defender los

intereses de los Investigadores en Formación. Nos han ahorrado mucho trabajo a Pedro

y a mí.

Además de un ambiente agradable, el Instituto pone a disposición de los que en él

trabajamos unos medios técnicos, materiales, formativos y de gestión extraordinarios.

En gran medida son fruto del esfuerzo de un reducido número de personas que no se

limitan a cumplir con su obligación y que nos permiten al resto despreocuparnos y

trabajar de forma mucho más cómoda. Entre estas personas se encuentran Juan Rivier,

Rafa Palacios, Francisco Javier Rubio, José Villar, Efraím Centeno, Begoña Pérez,

Julián Jiménez y Pepe.

Los proyectos de colaboración entre el Instituto e Iberdrola me han dado la

oportunidad de trabajar con dos equipos de gente extraordinaria que han aportado su

visión práctica de los problemas en el desarrollo de esta tesis. Con la gran familia de

PYOFE, (Carlos, Pepe, Manolo, Íñigo, José María, Rafa, Jorge, Alejandro...) he

trabajado durante los cuatro años que llevo en el IIT y debo decir que cuando estoy

con ellos me siento uno más. A ello contribuyó también Antonio, que me ayudó mucho

en mis primeros pasos. En el equipo de ANPRO, con el que he empezado a trabajar

recientemente, tengo la suerte de colaborar con gente que conocí en el Instituto (Toño,

Fernando, Mercedes, Grego) o en PYOFE (Julián, Bárbara, Lucía), así que la

comunicación es natural y fluida. A todos ellos les agradezco el apoyo que he sentido

por su parte y la confianza que en mí han depositado durante estos cuatro años.

Fuera del Instituto también he contado con el ánimo de mucha gente. Mis amigos

del colegio, Salva, Meri, Íñigo, Fernando, Laura, Lourdes, Isa, Paul, Miguel y Myriam,

han contribuido con su buen humor y su presencia a que no perdiera la cabeza en los

momentos más difíciles de estos cuatro años. Les quiero agradecer que hayan sabido

aguantar algunos de mis arranques, mis rarezas y mi insistencia en hablar de fútbol

cuando no tengo ni idea del tema. Para mí la medalla de bronce de Salva es como si

fuera de oro. Siento no haber utilizado la palabra “thunderstriking” durante la defensa,

me faltó valor. Los amigos de la carrera han sufrido mis “desapariciones”, cuando me

he dejado arrastrar por el día a día y no he logrado sacar un minuto para estar con

ellos. A Nacho, Andrés y Antonio les quiero agradecer su gran amistad a pesar de la

distancia.

Quiero dedicar la última parte de estos agradecimientos a mi familia. A Pedro,

Elena y Anna les agradezco los buenos ratos que hemos pasado alrededor de la mesa

tantos sábados y domingos. A Arantxa y Gregorio les agradezco el entusiasmo con que

han seguido el tramo final de mi tesis y esas mañanas de domingo en el Rastro que han

compartido con Paloma y alguna vez conmigo. A Jesús, Elisa y Miguel Ángel les

agradezco su cariño y su apoyo en algunos de los momentos más trascendentales de mi

vida. A mis tíos y primos les quiero pedir disculpas por lo poco que nos vemos, aunque

ya sé que lo de la tesis no vale como excusa. En particular, le agradezco a mi tía Pili su

permanente buen humor.

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Paloma y Moisés han sido para mí una referencia en los últimos años. Me han

acogido en su familia como si fuera un hijo y me han dado todo su cariño y su apoyo

en circunstancias muy difíciles. La ilusión que han puesto en el final de mi tesis me ha

ayudado a terminar con alegría y a disfrutar de esos momentos en los que yo

seguramente me hubiera ofuscado.

A Bego le agradezco que me regalara la corbata de la tesis pero por encima de todo

que me trate como un hermano, incluso cuando digo cosas que a ella le parecen

surrealistas. Para mí ha sido muy importante contar con su apoyo activo en los

momentos críticos de la tesis.

A mis padres les tengo que agradecer todo lo que soy. Ellos han dedicado los mejores

años de sus vidas a mis hermanos y a mí. Se han esforzado y sacrificado por que a

nosotros no nos faltara nunca nada, a pesar de las dificultades que ellos han tenido que

ir superando a lo largo de sus vidas y de lo complicados que hemos salido los tres, cada

uno a nuestra manera. Resulta difícil expresar todo el cariño, orgullo y admiración que

siento por los dos. Jamás llegaré a ser ni la mitad de buen ingeniero que ha sido mi

padre ni la mitad de buena profesora que ha sido mi madre. Y, por supuesto, jamás

llegaré a ser tan buen padre como han sido los dos.

Mi hermano Gonzalo y mi hermana Amparo han vivido muy de cerca esta tesis. Los

dos han tenido el valor de leerse algunos capítulos y me han hecho comentarios que me

han sido de gran ayuda. Además, los dos han sido para mí una luz en el camino. Los

partidos de fútbol organizados por Gonzalo en el colegio y su forma optimista de

entender la vida me han insuflado energías para seguir adelante. La perseverancia de

Amparo y su capacidad para mantener el ritmo a pesar de los altibajos del camino me

han servido de ejemplo en los largos tramos de desierto que se atraviesan durante la

tesis. Sólo quisiera que mi ayuda y mi apoyo les fueran también a ellos realmente

útiles.

Y finalmente quiero dedicar el último párrafo de estos agradecimientos a la persona

más importante de mi vida, Paloma. Ella es el motor de mi vida. Podría empezar y no

terminar de enumerar todos los momentos concretos en que ella ha contribuido

activamente a que esta aventura llegara a buen puerto. Me animó a quedarme en el

Instituto todas las veces que me surgieron las dudas. Me ha dado todo su apoyo y su

amor durante todos estos años en que las cosas han sido difíciles y se ha implicado con

mi familia y mis amigos hasta tal punto que ellos ya prefieren hablar con ella a hablar

conmigo. Ha aguantado las horas que me he pasado delante del ordenador en casa y

mis malos rollos cuando las cosas no terminaban de funcionar. Ha soportado mis

explicaciones relativas al mercado eléctrico y a la programación estocástica multietapa

siempre con una sonrisa. Organizó el aperitivo de celebración de la tesis cuando en la

cafetería de ICADE me dijeron que les era imposible. Como digo, podría seguir hasta el

infinito y me quedaría corto. Y ahora, una vez terminada la tesis, está sufriendo el

difícil transitorio del paso de becario a profesor hasta el punto de preguntarme cuánto

tendría que pagar al Instituto para tener un diez por ciento de mi dedicación. A ella,

que es el mejor regalo que esta vida podría nunca darme, le dedico esta tesis con todo

mi amor.

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Contents

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Contents iii

Table of contents

NOTATION

...

xv

SUMMARY

...xxvii

1.

INTRODUCTION

... 1

1.1

THE REFORM OF THE ELECTRIC POWER INDUSTRY

... 3

1.2

SCOPE AND OBJECTIVES OF THIS THESIS

... 5

1.3

ORGANIZATION OF THIS DOCUMENT... 7

2.

THE ELECTRICITY MARKETPLACE

... 9

2.1

INTRODUCTION...11

2.2

SCHWEPPE’S ELECTRICITY SPOT MARKET

...11

2.3

INFRASTRUCTURE OF THE POWER SYSTEM...12

2.4

INSTITUTIONS

...13

2.4.1

Regulatory authorities...13

2.4.2

Independent system operator (ISO)...14

2.4.3

Market authority...14

2.5

MARKET PARTICIPANTS

...17

2.5.1

The wholesale supply side ...17

2.5.2

The wholesale demand side ...18

2.5.3

Other agents...18

2.6

MARKET MECHANISMS...18

2.6.1

Physical products ...18

2.6.2

Time frames supported by market mechanisms ...20

2.6.3

A characterization of spot market mechanisms...21

2.6.4

Information disclosure ...27

2.7

THE ELECTRICITY MARKETPLACE CONSIDERED IN THIS THESIS

...28

2.7.1

Long-term market mechanisms...30

2.7.2

The spot market as a sequence of market mechanisms...30

2.7.3

Spot market mechanisms as auctions...31

2.7.4

Offers and bids ...31

2.7.5

Market clearing, pricing and settlement ...31

2.8

CONCLUSION...33

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3.

MODELING COMPETITION IN WHOLESALE ELECTRICITY MARKETS

... 37

3.1

INTRODUCTION

... 39

3.2

MODELS THAT INCLUDE AN EXPLICIT REPRESENTATION OF EACH

GENERATION COMPANY

... 39

3.2.1

Equilibrium models... 40

3.2.2

Simulation models ... 53

3.2.3

Conclusion ... 56

3.3

MODELS THAT FOCUS ON A SPECIFIC GENERATION COMPANY

... 56

3.3.1

Models that assume that prices are exogenously fixed ... 57

3.3.2

Models that express the price of electricity as a function of the

company’s decisions... 59

3.4

THE DEMAND SIDE

... 63

3.5

THE MODEL CONSIDERED IN THIS THESIS: AN OVERVIEW

... 63

3.5.1

A model based on residual demand curves... 63

3.5.2

A model that explicitly considers uncertainty... 64

3.5.3

A model that decides offering strategies... 65

3.5.4

A model that takes the company’s portfolio into account... 65

3.5.5

A model that can be adapted to the case of an energy service provider .. 65

3.5.6

Summary of modeling challenges ... 65

3.6

CONCLUSION... 67

3.7

REFERENCES

... 68

4.

A MODEL TO DEVELOP OPTIMAL OFFERS FOR AN ELECTRICITY SPOT

MARKET

... 73

4.1

INTRODUCTION

... 75

4.2

MODELING THE SPOT MARKET

... 75

4.2.1

Residual demand curves and revenue functions ... 76

4.2.2

Sources of uncertainty in a multiunit double auction ... 77

4.2.3

Choosing the right model to represent uncertainty... 78

4.2.4

Probability distributions with finite support ... 80

4.2.5

Implications for the development of optimal offering strategies ... 81

4.2.6

Correlation between different auctions... 83

4.2.7

A multistage stochastic programming problem ... 85

4.2.8

A representation based on spot-market scenario trees... 86

4.2.9

The influence of zonal pricing... 92

4.2.10Building the scenario tree ... 93

4.3

MODELING THE PORTFOLIO OF A GENERATION COMPANY

... 93

4.3.1

Generating units... 94

4.3.2

Forward contracts ... 97

4.3.3

Options...100

4.3.4

The value of the company’s market share...103

4.4

THE CASE OF AN ENERGY SERVICE PROVIDER

...104

4.4.1

The short-term problem of an energy service provider ...104

4.4.2

The portfolio of an energy service provider...105

4.4.3

The spot market from the perspective of an ESP...105

4.5

PROBLEM STATEMENT...106

4.5.1

Objective function ...106

4.5.2

Constraints...107

4.6

CONCLUSION...109

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Contents v

5.

THE DEVELOPMENT OF A SOLUTION STRATEGY

...113

5.1

INTRODUCTION... 115

5.2

A SEQUENCE OF TWO-STAGE STOCHASTIC PROGRAMS

... 116

5.2.1

The relative importance of market mechanisms... 116

5.2.2

A compact formulation for a two-stage program ... 117

5.2.3

A numerical example... 119

5.2.4

The weekly stochastic unit-commitment problem ... 122

5.3

ANALYSIS OF THE PROBLEM STRUCTURE

... 124

5.3.1

Complicating variables ... 124

5.3.2

Complicating constraints... 126

5.4

A BENDERS’

DECOMPOSITION APPROACH TO SOLVE THE TWO-STAGE PROGRAM

... 127

5.4.1

Benders’ decomposition algorithm... 128

5.4.2

Application to the two-stage program ... 132

5.4.3

The presence of binary variables in the subproblem ... 134

5.4.4

Numerical example ... 135

5.4.5

Separability of the master problem... 137

5.4.6

Numerical example ... 140

5.4.7

Advantages and disadvantages of Benders’ decomposition for the

two-stage program... 141

5.5

A LAGRANGIAN RELAXATION APPROACH TO SOLVE THE TWO-STAGE

PROGRAM

... 142

5.5.1

The Lagrangian dual problem ... 143

5.5.2

An outer-linearization method to solve the dual problem... 148

5.5.3

A numerical example... 151

5.5.4

Advantages of the LR approach for the two-stage program... 153

5.6

LAGRANGIAN RELAXATION AND THE WEEKLY UNIT-COMMITMENT

PROBLEM... 154

5.6.1

An overview ... 154

5.6.2

Mathematical formulation ... 155

5.6.3

Advantages and disadvantages... 157

5.7

CONCLUSION... 157

5.8

REFERENCES

... 159

6.

COMPUTATIONAL RESULTS

...161

6.1

INTRODUCTION... 163

6.2

OFFERING STRATEGIES FOR THE DAY-AHEAD MARKET... 163

6.2.1

A five-scenario case ... 164

6.2.2

An eleven-scenario case ... 169

6.2.3

Sensitivity analysis ... 177

6.2.4

Conclusions ... 184

6.3

WEEKLY UNIT-COMMITMENT SCHEDULES UNDER SPOT MARKET

UNCERTAINTY... 185

6.2.5

A 16-scenario case ... 185

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7.

CONCLUSIONS, CONTRIBUTIONS AND FUTURE RESEARCH

... 195

7.1

SUMMARY AND CONCLUSIONS

...197

7.2

ORIGINAL CONTRIBUTIONS

...200

7.2.1

Methodological contribution ...200

7.2.2

Modeling contributions...200

7.2.3

Algorithmic contributions...201

7.3

FUTURE RESEARCH

...202

7.3.1

Modeling advances...202

7.3.2

Algorithmic improvements...203

7.4

REFERENCES

...204

A.

MODELING THE ELECTRICITY SPOT MARKET THROUGH RESIDUAL

DEMAND CURVES

... 205

A.1

INTRODUCTION

...207

A.2

BASIC CONCEPTS

...207

A.2.1

The idea of residual demand in microeconomic theory...207

A.2.2

The residual demand approach in a repetitive sealed-bid multiunit

double auction ...209

A.2.3

From the residual demand curve to the revenue function ...210

A.3

REPRESENTING RESIDUAL DEMAND CURVES IN A MIP PROBLEM

...211

A.3.1

Piecewise linear approximation of offer curves, bid curves and

residual demand curves...212

A.3.2

Piecewise linear approximations of revenue functions ...214

A.3.3

Dealing with non-concave revenue functions...216

A.4

CONCLUSION...217

A.5

REFERENCES

...218

B.

A PROCEDURE TO BUILD SPOT MARKET SCENARIO TREES

... 219

B.1

INTRODUCTION

...221

B.2

THE DECISION PROCESS OF A COMPANY IN THE SPOT MARKET

...221

B.3

EXPLANATORY VARIABLES

...223

B.4

DAY-TYPE IDENTIFICATION BY CLUSTERING TECHNIQUES

...224

B.4.1

An example of the construction of the scenario structure for the

day-ahead market problem ...224

B.4.2

An example of the construction of the scenario structure for the

adjustment market problem...226

B.5

RELEVANT VS. SIGNIFICANT RESULTS...227

B.6

AN EXTENSION TO OBTAIN WEEKLY SPOT MARKET SCENARIOS...228

B.7

CONCLUSION...231

B.8

REFERENCES

...233

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Contents vii

C.

INPUT DATA FOR THE STUDY CASES

...235

C.1

INTRODUCTION... 237

C.2

GENERATION UNITS’ DATA

... 237

C.3

THE SPOT MARKET SESSIONS OF STUDY

... 238

C.3.1

Daily cases... 238

C.3.2

Weekly cases... 240

C.4

SPOT MARKET DATA FOR THE TWO-STAGE STOCHASTIC PROBLEMS

... 243

C.4.1

Two-scenario case... 243

C.4.1.1

Clustering analysis ...243

C.4.1.2

Relevant historic spot market data for the current spot

market session...244

C.4.2

Five-scenario case ... 246

C.4.3

Eleven-scenario case ... 247

C.5

SPOT MARKET DATA FOR THE WEEKLY STOCHASTIC UC PROBLEM... 248

C.5.1

16-scenario case ... 249

C.6

CONCLUSION... 250

C.7

REFERENCES

... 252

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Index of figures

Figure 2.1. Market mechanisms... 29

Figure 2.2. Sequence of spot market mechanisms. ... 30

Figure 2.3. Market clearing for a certain hour... 32

Figure 2.4. Intersection of the aggregate offer and demand curves. ... 32

Figure 2.5. Price discovery. ... 33

Figure 3.1. Models oriented to develop optimal short-term strategies: a graphic

characterization. ... 66

Figure 4.1. A residual demand curve and the corresponding revenue function. ... 76

Figure 4.2. The concept of market distribution function. ... 78

Figure 4.3. The influence of considering an inadequate probability distribution. ... 79

Figure 4.4. Possible future residual demand realizations based on historic data... 80

Figure 4.5. The shape of the offer curve between two consecutive residual

demand realizations is irrelevant... 81

Figure 4.6.

(q p, )

pairs must constitute an increasing offer curve. ... 81

Figure 4.7. Four types of residual demand curves for a company in the Spanish

day-ahead market. ... 83

Figure 4.8. Corresponding types of residual demand curves in the 1

st

session of

the adjustment market... 84

Figure 4.9. The decision process of a generation company in the spot market... 85

Figure 4.10. Two scenarios in a scenario tree. ... 86

Figure 4.11. The case of a single auction. ... 87

Figure 4.12. Two residual demand scenarios for one auction. ... 87

Figure 4.13. The case of several simultaneous auctions. ... 88

Figure 4.14. Two day-ahead market scenarios. ... 89

Figure 4.15. The case of several market mechanisms. ... 90

Figure 4.16. Two spot market scenarios. ... 91

Figure 4.17. A compact representation of the two-stage two-scenario tree. ... 92

Figure 4.18. The influence of a bilateral physical contract on the residual

demand. ... 99

Figure 4.19. A residual offer curve and the corresponding cost function... 106

Figure 5.1. A simplified version of the decision process from the perspective of the

day-ahead market. ... 116

Figure 5.2. The scenario structure for each of the two-stage stochastic programs... 117

Figure 5.3. Hourly market-share value for the two-scenario case. ... 119

Figure 5.4. Hourly offers for the day-ahead market and the adjustment market. ... 120

Figure 5.5. Hourly generation and pumping schedules for the units owned by the

generation company. ... 120

Figure 5.6. Detail of the offers decided for the 21

st

hourly auction of the

day-ahead market. ... 121

Figure 5.7. Detail of the offers decided for the 21

st

hourly auction of the

adjustment market... 121

Figure 5.8. The decision process from the perspective of a whole week... 123

Figure 5.9. The matrix structure of the mathematical programs. ... 125

(25)

Contents ix

Figure 5.10. Benders’ decomposition exploits the presence of complicating

variables. ...126

Figure 5.11. The relaxation of complicating constraints yields smaller

subproblems...127

Figure 5.12. Linearization of the adjustment-market residual demand curve. ...135

Figure 5.13. Evolution of the objective function in Benders’ algorithm...136

Figure 5.14. Evolution of the subproblem’s objective function in Benders’

algorithm. ...137

Figure 5.15. Dual variables corresponding to the energy balance equation...137

Figure 5.16. Matrix structure of one real two-stage program. ...143

Figure 5.17. A representation of the effect of Lagrangian relaxation on the

two-stage problem. ...147

Figure 5.18. The algorithm used to solve the dual problem. ...150

Figure 5.19. Evolution of Cerisola’s first phase. ...151

Figure 5.20. Evolution of Cerisola’s second phase. ...151

Figure 5.21. Infeasibilities due to the dualization of the energy balance equation. ...152

Figure 5.22. Value of the Lagrange multipliers. ...152

Figure 5.23. Evolution of the LR algorithm with dynamic feasibility region. ...153

Figure 5.24. A representation of the effect of Lagrangian relaxation on the weekly

problem. ...154

Figure 6.1. The solution process for a realistic two-stage problem...165

Figure 6.2. Offers for the five-scenario case. ...166

Figure 6.3. Offers for the 12

th

hourly auction of the day-ahead market in the

five-scenario case. ...167

Figure 6.4. Detail of the offers for the 12

th

hourly auction of the day-ahead

market in the five-scenario case. ...167

Figure 6.5. Offers for the 5

th

hourly auction of the day-ahead market in the

five-scenario case. ...167

Figure 6.6. Detail of the offers for the 5

th

hourly auction of the day-ahead market

in the five-scenario case. ...168

Figure 6.7. Offers for the 12

th

hourly auction of the adjustment market in the

five-scenario case...168

Figure 6.8. Detail of the offers for the

12th

hourly auction of the adjustment

market in the five-scenario case. ...168

Figure 6.9. Offers for the 5

th

hourly auction of the adjustment market in the

five-scenario case. ...169

Figure 6.10. Detail of the offers for the

5th

hourly auction of the adjustment

market in the five-scenario case. ...169

Figure 6.11. Offers for the 24 hourly auctions in the eleven-scenario case. ...172

Figure 6.12. Offers for the 12

th

hourly auction in the eleven-scenario case...172

Figure 6.13. Detail of the offers for the 12

th

hourly auction in the eleven-scenario

case...172

Figure 6.14. Offers for the 5

th

hourly auction in the eleven-scenario case...173

Figure 6.15. Detail of the offers for the 5

th

hourly auction in the eleven-scenario

(26)

Figure 6.16. A comparison of the offers developed by the model and the real

offers for the 12

th

hourly auction. ... 174

Figure 6.17. A comparison of the offers developed by the model and the real

offers for the 12

th

hourly auction. ... 174

Figure 6.18. Influence of the non-decreasing constraints on the offers for the 12

th

hourly auction... 175

Figure 6.19. Influence of the number of scenarios on the offers for the 12

th

hourly

auction... 175

Figure 6.20. Influence of the number of scenarios on the offers for the 5

th

hourly

auction... 176

Figure 6.21. Influence of the number of scenarios on the expected results. ... 176

Figure 6.22. Influence of the market-share value on the expected day-ahead

market results . ... 177

Figure 6.24. Influence of market-share value on the offers for the 12

th

hourly

auction... 178

Figure 6.26. Influence of market-share value on the offers for the 5

th

hourly

auction... 178

Figure 6.28. Influence of hydro reserves on the expected day-ahead market results

. ... 179

Figure 6.30. Influence of hydro reserves on the offers for the 12

th

hourly auction. ... 180

Figure 6.32. Influence of hydro reserves on the offers for the 5

th

hourly auction. ... 180

Figure 6.34. Influence of units’ availability on the expected day-ahead market

results. ... 181

Figure 6.36. Influence of units’ availability on the offers for the 12

th

hourly

auction... 182

Figure 6.38. Influence of units’ availability on the offers for the 5

th

hourly

auction... 182

Figure 6.40. Influence of a contract for differences on the expected day-ahead

market results. ... 183

Figure 6.41. Influence of a contract for differences on the offers for the 12

th

hourly

auction... 184

Figure 6.42. Evolution of the LR algorithm for the weekly stochastic problem. ... 185

Figure 6.44. Energy sold by the company in the day-ahead market for each

weekly scenario. ... 185

Figure 6.46. Tree constituted by the company’s sales in the day-ahead market. ... 186

Figure 6.48. Detail of the day-ahead market company’s sales for the two nodes

corresponding to Tuesday. ... 187

Figure 6.50. Day-ahead market clearing prices for each scenario. ... 187

Figure 6.52. Detail of the day-ahead market clearing prices for the two nodes

corresponding to Tuesday. ... 188

Figure 6.54. Company’s sales in the adjustment market. ... 188

Figure 6.56. Adjustment market clearing prices for each scenario. ... 188

Figure 6.57. Scenario tree for the startup and shutdown of unit G24... 191

Figure 6.59. Hydro energy used in each node of the scenario tree in GWh... 191

Figure A.1. Residual demand function for the price leader 1 ... 208

(27)

Contents xi

Figure A.2. The effect of considering the residual demand discrete probability

distribution...209

Figure A.3. Aggregate offer and bid curves for a double auction. ...210

Figure A.4. The relationship between revenue and residual demand...211

Figure A.5. A residual demand curve and the corresponding revenue function. ...211

Figure A.6. Piecewise linear approximation for residual demand curves. ...212

Figure A.7. PWL approximation for an aggregate offer curve in the Spanish

day-ahead market. ...213

Figure A.8. Auction-clearing price as a function of the agent’s sales in a MIP

model...214

Figure A.9. From a PWL residual demand curve to the corresponding PWL

revenue function. ...215

Figure A.10. Binary variables and the revenue function. ...216

Figure A.11. Concave sections in the revenue function. ...217

Figure B.1. The decision process of a generation company in the spot market...221

Figure B.2. A simplified version of the decision process from the perspective of

the day-ahead market. ...222

Figure B.3. A simplified version of the decision process from the perspective of

the adjustment market. ...222

Figure B.4. The scenario structure for each of the two-stage stochastic programs...223

Figure B.5. Detail of the five clusters obtained in a 17-day case according to their

24 h demand profile. ...225

Figure B.6. Scenario structure for the day-ahead market problem. ...226

Figure B.7. Detail of the four clusters obtained for a 17-day case according to

their 24 h day-ahead market price profile. ...227

Figure B.8. The decision process from the perspective of the weekly

unit-commitment problem...229

Figure B.9. A scenario tree for the weekly unit-commitment problem...231

Figure C.1. Trading volumes and clearing prices on October 24

th

2001. ...238

Figure C.2. Energy sold by the company on October 24

th

2001. ...239

Figure C.3. Energy sold by the company in the day-ahead market on October

24

th

2001. ...239

Figure C.4. Trading volumes and clearing prices from October 22

nd

to October

28

th

2001. ...241

Figure C.5. Energy sold by the company from October 22

nd

to October 28

th

2001. ...241

Figure C.6. Energy sold by the company in the day-ahead market from October

22

nd

to October 28

th

2001...241

Figure C.7. Detail of the four clusters obtained in a 6-day case according to their

24 h demand profile. ...244

Figure C.8. Historic residual demand curves constitute the spot market scenarios...245

Figure C.9. Trading volumes for each of the spot market scenarios ...246

Figure C.10. Detail of the four clusters obtained in a 10-day case according to

their 24 h demand profile...247

Figure C.11. Detail of the four clusters obtained in a 24-day case according to

(28)

Figure C.12. Detail of the five clusters obtained in a 14-day case according to

their 24 h demand profile... 249

Figure C.13. A sixteen-scenario tree for the weekly unit-commitment problem. ... 250

(29)

Contents xiii

Index of tables

Table 2.1. The electricity marketplace considered in this thesis. ... 29

Table 3.1. A characterization of SFE models. ... 51

Table 3.2. A comparison of models oriented to develop optimal short-term

strategies. ... 62

Table 5.1. Attributes of the problems that result from Benders’ decomposition. ...135

Table 5.2. Evolution of Benders’ algorithm during the first 15 iterations. ...136

Table 5.3. Evolution of Benders’ algorithm with slack variables in the

subproblem. ...140

Table 5.4. Evolution of Benders’ algorithm when the master problem is separated

into hourly problems...141

Table 6.1. A comparison of two study cases...164

Table 6.2. Evolution of Benders’ algorithm with the master problem separated

into hourly problems...164

Table 6.3. A comparison of three study cases...170

Table 6.4. Evolution of Benders’ algorithm for the eleven-scenario case...170

Table 6.5. Unit-commitment schedule for the first possible outcome of Tuesday’s

session...189

Table 6.6. Unit-commitment schedule for the second possible outcome of

Tuesday’s session. ...190

Table 6.7. Hydro energy used in each weekly scenario. ...192

Table 6.8. Energy pumped in each weekly scenario...192

Table B.1. Classification of 17 days according to their 24 h demand profile. ...224

Table B.2. Classification of 17 days according to their 24 h day-ahead market

price profile...226

Table B.3. Classification of 21 days into four clusters according to their 24 h

demand profile...230

Table C.1. Characteristics of the thermal units...237

Table C.2. Characteristics of the hydro units...238

Table C.3. Unit-commitment schedule for October 24th 2001...240

Table C.4. Energy sold by the company in the day-ahead market for each type of

unit from October 22

nd

to October 28

th

2001, in MWh. ...242

Table C.5. Hours of startup and shutdown for the company’s thermal units from

October 22

nd

to October 28

th

2001. ...242

Table C.6. Energy produced by the company’s hydro units from October 22

nd

to

October 28

th

2001, in MWh...243

Table C.7. Classification of 5 days according to their 24 h demand profile. ...244

Table C.8. Classification of 10 days according to their 24 h demand profile. ...246

Table C.9. Classification of 24 days according to their 24 h demand profile. ...247

Table C.10. Classification of two weeks into five clusters according to their 24 h

(30)
(31)

Notation

(32)
(33)

Notation xvii

Indices

Symbol Interpretation

c

contract;

g

generating unit;

h

hydro unit;

i

agent; firm;

j

component of a vector;

agent; firm;

k

scenario; possible realization of an uncertain factor;

l

vertex of the set of possible solutions of a linear program;

element of the set of accumulated iterations;

n

hour; hourly auction;

m

stage of a multistage decision process;

market mechanism;

o

option;

p

period of time (day);

t

thermal unit;

ν

hour in which a thermal unit remains offline;

current iteration of an algorithm;

(34)

Sets

Symbol Interpretation

D

C

contracts for differences;

P

C

physical contracts;

H

hydro units;

J

segments used to approximate a curve;

components of a vector;

K

possible realizations of an uncertain factor;

M

market mechanisms;

E

M

market mechanisms in which energy is traded;

R

M

market mechanisms in which reserve is traded;

N

hourly auctions;

P

O

options that are physically settled;

F

O

options that are financially settled;

LPP

O

long put positions that are physically settled;

LPF

O

long put positions that are financially settled;

SCP

O

short call positions that are physically settled;

SCF

O

short call positions that are financially settled;

P

periods (days);

P

nkm

constraints affecting the value of option

o

in the

n

-th hour if market

situation

k

occurs;

Q

g

feasible schedules for generating unit

t

;

Q

mn

feasible outputs for the

n

-th hourly auction of the

m

-th market mechanism;

Q

mnk

feasible outputs for the

n

-th hourly auction of the

m

-th market mechanism

if market situation

k

occurs;

S

supply functions

T

thermal units;

U

mnk

constraints affecting the exercise of option

o

in the

n

-th hour if market

situation

k

occurs;

O

V

optimality cuts;

F

V

feasibility cuts;

X

feasible values for the vector of variables

x

;

(35)

Notation xix

Parameters

Symbol Interpretation

,

A B

matrices of coefficients;

b

vector of parameters;

c

vector of costs;

e

vector of 1’s;

t

f

variable fuel cost of thermal unit

t

, in €/Tcal;

h n

i

net inflows received by the reservoir corresponding to hydro unit

h

in hour

n

, in MWh;

g

k

self-consumption coefficient of generating unit

g

, in p.u.;

t

l

ramp-rate limit of thermal unit

t

, in MW/h;

q

M

a large quantity;

p

M

a large price;

t

o

variable O&M cost of thermal unit

t

, in €/MWh;

j

p

j

-th element of a vector of

J

prices;

c n

p

exercise price of contract

c

in hour

n

, in €/MWh;

o n

p

exercise price of option

o

in hour

n

, in €/MWh;

m nk

Q

volume of energy traded in the

n

-th hourly auction of the

m

-th market

mechanism if market situation

k

occurs, in MWh;

l m nk

q

energy sold by the company in the

n

-th hourly auction of the

m

-th market

mechanism in iteration

l

if market situation

k

occurs, in MWh;

c n

q

amount of energy involved in contract

c

in hour

n

, in MWh;

o n

q

amount of energy involved in option

o

in hour

n

, in MWh;

g

q

,

q

g

minimum and maximum gross output of generating unit

g

, in MW;

t

s

start-up cost of thermal unit

t

, in €/startup;

h

w

,

w

h

minimum and maximum storage level of the reservoir corresponding to hydro

unit

h

, in MWh;

0

h

W

available energy in the reservoir corresponding to hydro unit

h

at the

beginning of the planning horizon, in MWh;

t

α

linear term of the heat rate function of thermal unit

t

, in Tcal/MWh;

t

β

intercept of the heat rate function of thermal unit

t

, in Tcal;

γ

Penalizing coefficient, in €/MWh;

j

δ

slope of the residual demand curve in its

j

-th segment;

j

ρ

slope of the revenue function in its

j

-th segment;

k

π

probability of scenario

k

;

t

(36)

Symbol Interpretation

h

η

Performance of the pump-turbine cycle of hydro unit

h

, in p.u.;

l

θ

value of the recourse function in iteration

l

of Benders’ algorithm, in €;

l

ϕ

value of the feasibility function in iteration

l

of Benders’ algorithm;

l

λ

value of the dual variables of the optimality subproblem in iteration

Benders’ algorithm;

l

of

value of the Lagrange multipliers in iteration

l

;

l

µ

value of the Lagrange multipliers in iteration

l

;

l

σ

value of the dual variables of the feasibility problem in iteration

l

of Benders’

algorithm;

m n

σ

value of the company’s market share in the

n

-th hourly auction of the

m

-th

market mechanism, in € per unit;

(37)

Notation xxi

Variables

Symbol Interpretation

B

,

B

i

benefit, in €; benefit obtained by agent

i

, in €;

h

nk

b

energy pumped by hydro unit

h

in hour

n

if market situation

k

occurs, in

MWh;

q

quantity;

p

price;

nk

p

spot price of electricity in hour

n

if market situation

k

occurs, in €/MWh;

o nk

p

value of option

o

in hour

n

if market situation

k

occurs, in €/MWh;

m nk

p

clearing price for the

n

-th hourly auction of the

m

-th market mechanism if

market situation

k

occurs, in €/MWh;

g nk

q

net energy produced by generating unit

g

in hour

n

if market situation

k

occurs, in MWh;

m nk

q

energy sold by the company

g

in the

n

-th hourly auction of the

m

-th

market mechanism if market situation

k

occurs, in MWh;

r

revenue, in €;

g nk

r

amount of reserve provided by generating unit

g

in hour

n

if market

situation

k

occurs, in MW;

h nk

s

energy spilt from the reservoir corresponding to hydro unit

h

in hour

n

if

market situation

k

occurs, in MWh;

t

independent variable;

m jnk

u

binary variable indicating that the

has been reached in the

n

-th hourly auction of the

j

-th element of the residual demand curve

m

-th market mechanism

if market situation

k

occurs;

o nk

u

exercise decision for option

o

in hour

n

if market situation

k

occurs;

t nk

u

commitment state of thermal unit

t

in hour

n

if market situation

k

occurs;

+

v

,

v

vectors of slack variables;

m jnk

v

incremental quantity corresponding to the

demand curve in the

n

-th hourly auction of the

j

-th element of the residual

m

-th market mechanism if

market situation

k

occurs, in MWh;

h nk

w

energy stored in the reservoir corresponding to hydro unit

h

at the end of

hour

n

if market situation

k

occurs, in MWh;

m nkk

x

binary variable indicating the relative position of two possible residual

demand realizations,

k

and

k

, in the

n

-th hourly auction of the

m

-th

market mechanism;

x

,

y

vectors of variables;

t nk

y

start-up decision for thermal unit

t

in hour

n

if market situation

k

occurs;

(38)

Symbol Interpretation

t nk

z

shut-down decision for thermal unit

t

in hour

n

if market situation

k

occurs;

σ

vector of dual variables corresponding to the feasibility problem;

λ

vector of dual variables corresponding to the optimality subproblem;

vector of Lagrange multiplers;

µ

vector of Lagrange multiplers;

(39)

Notation xxiii

Functions

Symbol Interpretation

( )

c q

,

c q

i

( )

cost function, in €; cost function for agent

i

, in €;

( )

c q

,

c q

i

( )

marginal cost function, in €/MWh; cost function for agent

i

, in €/MWh;

(

, ,

)

t t t t nk

c

q u y

operating costs of thermal unit

t

in hour

n

if market situation

k

occurs, in

€;

( )

D p

demand function;

( )

f

x

objective function or part of the objective function;

( )

h x

vector of equality constraints

(

=

0

)

;

( )

g x

vector of inequality constraints

(

0

)

;

( , , )

x

λ

µ

L

Lagrange function;

(

)

m m nk nk

p

q

inverse residual demand function for the

n

-th hourly auction of the

m

-th

market mechanism if market situation

k

occurs, in €/MWh;

( )

p t

,

q t

( )

parametric equations used to represent an offer curve;

( )

r q

revenue function, in €;

( )

R p

residual demand function;

( )

1

R

p

,

p q

( )

inverse residual demand function;

(

)

m m nk nk

r

q

revenue function for the

n

-th hourly auction of the

m

-th market mechanism

if market situation

k

occurs, in €;

( )

S p

supply function;

( , )

w

λ

µ

dual function;

( , )

q p

ψ

market distribution function;

( )

θ

x

recourse function;

( )

θ

x

approximation of the recourse function by an outer linearization;

( )

(40)

Acronyms

Symbol Interpretation

AGC

automatic generation control;

APX

Automated Power Exchange; Amsterdam Power Exchange;

CAISO

California Independent System Operator;

CALPX

California Power Exchange;

CAMMESA

Compañía Administradora del Mercado Mayorista de Electricidad (Marker

Operator, Argentina);

CCGT

combined-cycle gas turbine;

CDEC

Centro de Despacho Económico de Cargas (Load Dispatch Center, Chile);

CfDs

contract for differences;

CSF

conjectured supply functions;

CV conjectural

variation;

DCR

demand curve for release;

DCS

demand curve for water in storage;

DP dynamic

programming;

DSP

dual of the subproblem;

DSPF

dual of the feasibility problem;

E&W

England and Wales;

ECNZ

Electricity Corporation of New Zealand;

EEX

European Energy Exchange (Frankfurt);

EMCO/M-Co Electricity Market Company (New Zealand);

EMF

Energy Modeling Forum;

ESP

Energy Service Provider;

EU European

Union;

GA genetic

algorithms;

GAMS

General Algebraic Modeling Language;

GME

Gestore del Mercato Elettrico (Market Operator, Italy);

GNE

generalized Nash equilibrium;

GRTN

Gestore della Rete di Transmissione Nazionale (ISO and TSO, Italy);

GS

subproblem corresponding to a certain generation unit;

HHI Hirschman-Herfindahl

Index;

IEA

International Energy Agency;

(41)

Notation xxv

Symbol Interpretation

IPE

International Petroleum Exchange;

ISO

Independent System Operator;

LP linear

programming;

LPX

Leipzig Power Exchange;

LR Lagrangian

relaxation;

MCP

mixed complementarity problem;

MD

master dual problem;

MDF

market distribution function;

MEM

Mercado Eléctrico Mayorista (Wholesale Electricity Market, Argentina);

MIP

mixed linear-integer programming;

MO Market

Operator;

MP master

problem;

MPEC

mathematical programming with equilibrium constraints;

MS1

subproblem corresponding to the first market mechanism;

MS2

subproblem corresponding to the second market mechanism;

NEMMCO

National Electricity Market Management Company Ltd.

NETA

New Electricity Trading Arrangements;

NGC

National Grid Company;

OASIS

Open Access Same Time Information System;

OFGEM

Office and Gas and Electricity Markets;

OMEL

Compañía Operadora del Mercado Eléctrico (Market Operator, Spain);

OO ordinal

optimization;

OPF

optimal power flow;

OPS

subproblem corresponding to options that are financially settled;

OTC

over the counter;

P primal

problem;

PBC

physical bilateral contract;

PC personal

computer;

PJM

Interconnection formed by Pennsylvania, New Jersey, Maryland, Delaware,

Virginia and the District of Columbia;

PWL Piecewise

linear;

(42)

Symbol Interpretation

QVI quasi-variational

inequalities;

REE

Red Eléctrica de España (ISO and TSO, Spain);

SC scheduling

coordinator;

SDDP

stochastic dual dynamic programming;

SFE

supply function equilibrium;

SMP

system marginal price;

SP subproblem;

SPF feasibility

problem;

TSO

Transmisión System Operator;

TSP two-stage

program;

UKPX

UK Power Exchange;

US United

States;

VI variational

inequalities;

VPX

Victoria Power Exchange;

(43)

Summary

(44)
(45)

Summary xxix

This thesis addresses the problem of developing an optimal offering strategy for a

generation company operating in an electricity spot market, an issue of the maximum

relevance due to the process of regulatory reforms that the worldwide power industry

has experienced in recent years.

Nevertheless, the idea of constructing optimal offers for an electricity spot market is

too general to be developed in a straightforward manner. The variety of spot market

designs that can be found throughout the world is so wide that it is impossible to

propose a general methodology valid for them all. Therefore, this thesis will commence

with an overview of the most relevant spot market designs currently in operation.

Based on this description and analysis, the rules that govern the spot market assumed

in this thesis will be clearly defined.

The search for an optimal offering strategy requires evaluating the expected benefit

of any candidate strategy. In particular, a generation company must be able to

estimate the revenues that it expects to obtain in the spot market. This implies

modeling the rivals’ behavior, given that rivals exert a direct influence on the spot

price of electricity. Among the variety of models that have been recently proposed to

represent competition in wholesale electricity markets, this thesis should adopt the

approach that best adapts to its general objective. As a result of a literature survey, a

representation based on residual demand curves and revenue functions will be used to

calculate the outcome of the hourly auctions that constitute the spot market of study.

Uncertainty with respect to rivals’ behavior is at the root of the development of any

offering strategy. It is because of this uncertainty that a generation company gets

involved in a decision process more complex than simply choosing a single price for all

its output or a specific level of production. However, not every representation of this

uncertainty is equally amenable in order to search for an optimal offering strategy. In

this thesis, uncertainty about the strategies followed both by rivals and by wholesale

buyers in each of the hourly auctions that constitute the spot market will be

represented by assuming that the probability distribution of the corresponding residual

demand curve has finite support. In other words, it will be assumed that each hourly

auction has a limited number of possible outcomes. Given that the spot market of

study consists of a sequence of auctions, this approach will yield a representation of the

spot market in the form of a multistage stochastic program. It will be shown that this

representation is valid not only for the case of a generation company, but also for other

agents operating in a spot market such as energy service providers.

The previous multistage stochastic programming framework will be enriched with a

detailed model of the company’s portfolio. This model will consider each of the

company’s generation units, including their production costs and technical constraints.

It will also take into account the obligations assumed by the company in previous

market mechanisms, such as futures or options markets.

Although this thesis focuses on the development of strategies for market mechanisms

that operate on a daily basis, the main objective of a generation company is the

maximization of its long-term profit. Hence, we should include some sort of guideline in

our methodology, so as to orient its results toward this long-term objective. With this

purpose, an explicit valuation of the market share obtained by the company in the spot

market will be suggested in order to correct the myopic incentive that a generation

company has to reduce its sales and increase the spot price of electricity. We will

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