Stochastic Unit Commitment in Hydro-Thermal Power Production Planning

Economic needs and the ongoing liberalization of European electricity markets stimulate the interest of power utilities in developing models and optimization techniques for the generation and trading of electric power under uncertainty. Utilities participating in deregulated markets observe increasing uncertainty in load (i.e., demand for electric power) and prices for fuel and electricity on spot and contract markets. The mismatched power between actual and predicted demand may be supplied by the power system or by trading activities. The competitive environment forces the utilities to rate alternatives within a few minutes. In this chapter, we describe a mathematical model for optimal short term operation and trading of a hydro-thermal based electric utility, which is usually called unit commitment problem because of the important role of the commitment or on/off decisions. Furthermore, we present a methodology for modelling the stochastic data process in form of a scenario tree and report on a Lagrangian-based decomposition strategy for solving the optimization model. We also provide some numerical experience obtained from test runs on realistic data from the German utility Vereinigte Energiewerke AG (VEAG). The optimization model has emerged from a collaboration with engineers of VEAG. For our tests we use a configuration of the VEAG system consisting of 25 (coal-fired, gas-burning) thermal units and seven pumped storage hydro units. Its total capacity is about 13,000 megawatts (MW), including a hydro capacity of 1,700 MW; the peak loads of the system are about 8,600 MW. In contrast to other hydro-thermal based utilities the amount of installed pumped storage capacity enables the inclusion of pumped storage plants into the optimization. It is an additional feature of the VEAG system that, for a weekly planning period, inflows to reservoirs are negligible. There is a growing number of contributions to stochastic power system optimization with emphasis on modelling aspects and solution methods. For stochastic models including commitment decisions see Bacaud et al. (2001), Bogensperger (1999), Carøe and Schultz (1998), Carpentier et al. (1996), Conejo et al. (1999), Dentcheva and Römisch (1998), Gröwe∗Institute of Mathematics, Humboldt-University Berlin, 10099 Berlin, Germany ([email protected], [email protected]).