1Scenario Reduction and Scenario Tree Construction for Power Management Problems

Abstract — Portfolio and risk management problems of power utilities may be modeled by multistage stochastic programs. These models use a set of scenarios and corresponding probabilities to model the multivariate random data process (electrical load, stream flows to hydro units, and fuel and electricity prices). For most practical problems the optimization problem that contains all possible scenarios is too large. Due to computational complex-ity and to time limitations this program is often approximated by a model involving a (much) smaller number of scenarios. The pro-posed reduction algorithms determine a subset of the initial sce-nario set and assign new probabilities to the preserved scenarios. The scenario tree construction algorithms successively reduce the number of nodes of a fan of individual scenarios by modifying the tree structure and by bundling similar scenarios. Numerical ex-perience is reported for constructing scenario trees for the load and spot market prices entering a stochastic portfolio management model of a German utility. Index Terms — Stochastic programming, scenario reduction, scenario tree construction. I