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

**Abstract**

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*