Scenario reduction and scenario tree construction for power management problems

TLDR

Portfolio and risk management problems of power utilities are modeled by multistage stochastic programs that use scenarios and probabilities for random data such as load, hydro flows, fuel and electricity prices, but the full scenario set is too large, so approximations with fewer scenarios are required. The proposed reduction algorithms determine a subset of the initial scenario 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 bundling similar scenarios. Numerical experience is reported for constructing scenario trees for load and spot market prices in a stochastic portfolio management model of a German utility.

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 complexity and to time limitations this program is often approximated by a model involving a (much) smaller number of scenarios. The proposed reduction algorithms determine a subset of the initial scenario 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 experience is reported for constructing scenario trees for the load and spot market prices entering a stochastic portfolio management model of a German utility.