Stochastic unit commitment in hydro-thermal power production planning

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 03-2002, 20

MSC 2000

90C15 Stochastic programming

90C90 Applications of mathematical programming

90C11 Mixed integer programming

We present a mixed-integer multistage stochastic programming model for the short term unit commitment of a hydro-thermal power system under uncertainty in load, inflow to reservoirs, and prices for fuel and delivery contracts. The model is implemented for uncertain load and tested on realistic data from a German power utility. Load scenario trees are generated by a procedure consisting of two steps: (i) Simulation of load scenarios using an explicit respresentation of the load distribution and (ii) construction of a tree out of these scenarios. The dimension of the corresponding mixed-integer programs ranges up to 200,000 binary and 350,000 continuous variables. The model is solved by a Lagrangian-based decomposition strategy exploiting the loose coupling structure. Solving the Lagrangian dual by a proximal bundle method leads to a successive decomposition into single unit subproblems, which are solved by specific algorithms. Finally, Lagrangian heuristics are used to construct nearly optimal first stage decisions.

Keywords:Stochastic programming, unit commitment, Lagrangian relaxation, bundle methods, scenario tree generation