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
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
cumplimiento de los requisitos
académicos; O.M. 17-9-1993, art.9
“Everything that is really great and inspiring is
created by the individual who can labor in freedom.”
Acknowledgements
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.
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
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.
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.
Contents
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
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
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... 1545.6.1
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... 1856.2.5
A 16-scenario case ... 185
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
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
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
stsession 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
sthourly auction of the
day-ahead market. ... 121
Figure 5.7. Detail of the offers decided for the 21
sthourly 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
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
thhourly auction of the day-ahead market in the
five-scenario case. ...167
Figure 6.4. Detail of the offers for the 12
thhourly auction of the day-ahead
market in the five-scenario case. ...167
Figure 6.5. Offers for the 5
thhourly auction of the day-ahead market in the
five-scenario case. ...167
Figure 6.6. Detail of the offers for the 5
thhourly auction of the day-ahead market
in the five-scenario case. ...168
Figure 6.7. Offers for the 12
thhourly auction of the adjustment market in the
five-scenario case...168
Figure 6.8. Detail of the offers for the
12thhourly auction of the adjustment
market in the five-scenario case. ...168
Figure 6.9. Offers for the 5
thhourly auction of the adjustment market in the
five-scenario case. ...169
Figure 6.10. Detail of the offers for the
5thhourly 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
thhourly auction in the eleven-scenario case...172
Figure 6.13. Detail of the offers for the 12
thhourly auction in the eleven-scenario
case...172
Figure 6.14. Offers for the 5
thhourly auction in the eleven-scenario case...173
Figure 6.15. Detail of the offers for the 5
thhourly auction in the eleven-scenario
Figure 6.16. A comparison of the offers developed by the model and the real
offers for the 12
thhourly auction. ... 174
Figure 6.17. A comparison of the offers developed by the model and the real
offers for the 12
thhourly auction. ... 174
Figure 6.18. Influence of the non-decreasing constraints on the offers for the 12
thhourly auction... 175
Figure 6.19. Influence of the number of scenarios on the offers for the 12
thhourly
auction... 175
Figure 6.20. Influence of the number of scenarios on the offers for the 5
thhourly
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
thhourly
auction... 178
Figure 6.26. Influence of market-share value on the offers for the 5
thhourly
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
thhourly auction. ... 180
Figure 6.32. Influence of hydro reserves on the offers for the 5
thhourly 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
thhourly
auction... 182
Figure 6.38. Influence of units’ availability on the offers for the 5
thhourly
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
thhourly
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
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
th2001. ...238
Figure C.2. Energy sold by the company on October 24
th2001. ...239
Figure C.3. Energy sold by the company in the day-ahead market on October
24
th2001. ...239
Figure C.4. Trading volumes and clearing prices from October 22
ndto October
28
th2001. ...241
Figure C.5. Energy sold by the company from October 22
ndto October 28
th2001. ...241
Figure C.6. Energy sold by the company in the day-ahead market from October
22
ndto October 28
th2001...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
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
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
ndto October 28
th2001, in MWh. ...242
Table C.5. Hours of startup and shutdown for the company’s thermal units from
October 22
ndto October 28
th2001. ...242
Table C.6. Energy produced by the company’s hydro units from October 22
ndto
October 28
th2001, 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
Notation
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;
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
nkmconstraints affecting the value of option
o
in the
n
-th hour if market
situation
k
occurs;
Q
gfeasible schedules for generating unit
t
;
Q
mnfeasible outputs for the
n
-th hourly auction of the
m
-th market mechanism;
Q
mnkfeasible 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
mnkconstraints 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
;
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
gminimum and maximum gross output of generating unit
g
, in MW;
t
s
start-up cost of thermal unit
t
, in €/startup;
h
w
,
w
hminimum 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
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
;
lσ
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;
Notation xxi
Variables
Symbol Interpretation
B
,
B
ibenefit, in €; benefit obtained by agent
i
, in €;
hnk
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;
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;
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;
( )
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;
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;
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;
Summary
Summary xxix