Application of optimisation methods to electricity production problems

This thesis deals with application of optimisation methods based on linear and mixed-integer linear programming to various problems in the power sector related to electricity production. The thesis goal is to test the applicability of such methods to formulating and solving various instances from the class of real-world electricity production problems, and to find the advantages and disadvantages associated with using these methods. Introductory chapters describe the main characteristics of power markets, including the historical and regulatory context. Fundamental properties of power markets on both demand and supply side are also described, both from a real-world and a modelling point of view. Benefits of optimisation and modelling are discussed, in particular the solution feasibility and optimality as well as insights gained from sensitivity analysis which is often difficult to replicate with the original system. In the core of the thesis, optimisation techniques are applied to three case studies, each of which deals with a specific problem arising during electricity production. In the first problem, the profit of gas-fired power plant in Slovakia from selling power on the day-ahead market is maximised. The model is set up using both technical and commercial constraints. The second problem deals with the problem of representing a two-dimensional production function which primarily arises for a hydro generator with large variations in the level of its reservoir. Several representations of the original function using piecewise linear subsets are presented, compared, and characterised by their computational intensity both theoretically and practically. In the third problem, the prices on the German day-ahead market in 2011 are modelled. Contrary to the previous two models, the model does not capture an optimisation problem faced by a single producer, but incorporates a large subset of the whole market instead. Consequently the model is formed out of generic constraints relevant to all power plants whose parameters are estimated. By combining information about the aggregate availability of power plants with the estimated efficiencies a full supply curve for each day is created. Different scenarios are analysed to test the impact of uncertain inputs such as unknown or estimated constraints. The choice of the investigated problems stems from the attempt to cover electricity production problems from the point of view of multiple criteria. The three investigated electricity production problems span a broad range from the decisions of a single power plant to the modelling a power market as a whole. Formulations of the production function with different level of detail are presented ranging from a simple linear relationship to several bivariate function formulations. While each problem answers a specific question, they all illustrate the ease with which various electricity production problems can solved using optimisation methods based on linear and mixed-integer linear programming. This is mainly due to the ability of these methods to approximate even non-linear functions and constraints over non-convex domains and find global solutions in reasonable time. Moreover, models formulated with these methods allow sensitivity and scenario analyses to be carried out easily as is illustrated in each of the case studies.