Modeling of Uncertainty for the Real-Time Management of Power Systems

Nicole Gröwe-Kuska, Matthias P. Nowak, Isabel Wegner

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

MSC 2000

90C15 Stochastic programming

A major issue in the application of multistage stochastic programming to model the cost-optimal generation and trading of electric power is the approximation of the underlying stochastic data processes by tree-structured schemes. We present a methodology for the generation of scenario trees for the stochastic load process from historical load profiles. The statistical modeling of the load process exploits the decomposition of the load process into a daily mean load process and a mean-corrected load series. The probability distribution of the load process over the optimization horizon is derived by using a time series model for the daily mean load process and regression models for the mean-corrected load series. We utilize the explicit representation of the distribution to compute approximate load scenarios and their probabilities. In a final step we reduce the number of load scenarios by a scenario deletion procedure. We report on the application of our approach to the cost-optimal generation of electric power in the hydro-thermal generation system of a German power utility.

Keywords: Multistage stochastic programs, scenario generation, electrical load scenario tree