A Two-Stage Stochastic Program for Unit Commitment Under Uncertainty in a Hydro-Thermal Power System

We develop a two-stage stochastic programming model with integer first-stage and mixed-integer recourse for solving the unit commitment problem in power generation in the presence of uncertainty of load profiles. The solution methodology rests on a novel scenario decomposition method for stochastic integer programming. This method combines Lagrangian relaxation of non-anticipativity constraints with branch-and-bound. It can be seen as a decomposition algorithm for large-scale mixed-integer linear programs with block-angular structure. With realistic data from a German utility we validate our model and carry out test runs. Sizes of these problems go up to 20.000 integer and 150.000 continuous variables together with up to 180.000 constraints. Subject classifications: Programming, stochastic: Scenario Decomposition of mixedinteger programs. Natural resources, energy: Unit commitment under uncertainty. Unit commitment aims at finding a fuel cost optimal scheduling of start-up/shut-down decisions and operation levels for power generation units over some time horizon. This is a central task in reliable and efficient operation of power systems. Solution strategies for the unit commitment problem are influenced by the power mix of the generation system. In the present paper we consider a hydro-thermal system as it is met with the German power company VEAG Vereinigte Energiewerke AG Berlin. This system comprises conventional coal and gas fired thermal units as well as pumped-storage plants. The latter imply substantial coupling over time of scheduling decisions which, compared with purely thermal systems, further complicates the problem. Mathematically, unit commitment is handled as a large-scale mixed-integer optimization problem. Advances in mathematical methodology, software engineering and hardware have