Generation expansion planning in electricity markets with bilevel mathematical programming techniques

Abstract

In this thesis we develop and analyze mathematical bilevel models for generation expansion planning in liberalized electricity markets.

In particular, in chapter 2 we first provide a literature review on the subject which puts our work in context to the existing state of the art and then we discuss the model hypotheses and other basic concepts which are useful to better understand the rest of the thesis. These introductory sections are followed by the formulation of a basic version of existing single-level models and the newly developed bilevel generation expansion MPEC and EPEC models in order to motivate the question whether the additional modeling effort with respect to the corresponding single-level models actually pays off.

In chapter 3 we provide an answer to this question by carrying out a theoretical analysis of single-level and bilevel generation expansion equilibrium models. The obtained results, which have been proven in a Theorem, show that in general the bilevel model is more realistic than the single-level model because it more adequately represents investment behavior of generation companies in liberalized electricity markets. However, we also demonstrate that under certain circumstances, single-level and bilevel results can coincide and we characterize when this happens.

Since the theoretical framework of chapter 3 underlines that bilevel models are more realistic for generation expansion planning, we now want to derive large-scale versions of such bilevel models. The first step towards formulating a large-scale bilevel equilibrium model, is a bilevel generation expansion optimization model, i.e., an MPEC, which represents the investment decision of one generation company and which is discussed in detail in chapter 4 of this thesis. This model is particularly useful from the point of view of a generation company because it allows to decide and assess investment decisions under an uncertain and highly competitive framework. Moreover, the MPEC model can be extremely useful for solving EPEC models.

In chapter 5 we derive the bilevel generation expansion equilibrium model, formulated as an EPEC. An EPEC arises when simultaneously solving various MPEC models, which have been introduced in the previous chapter. Since these EPEC models are very hard to solve, we also propose an approximation scheme which allows us to arrive at a good solution two orders of magnitude faster than with standard EPEC methods. Chapter 5 concludes the methodological contributions of this thesis.

Chapter 6 summarizes the numerical techniques that have been applied to solve the MPEC and EPEC models that have arisen throughout this thesis and chapter 7 contains some additional numerical examples of interest including real-size case studies. Finally, chapter 8 presents the conclusions, the thesis contributions and future research.