Stochastic modeling and optimization under uncertainty of a hydro power system

Roger Halldin

Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology
2005

ISBN 91-628-6539-0
LUTFMS--1028--2005

Abstract:

Electricity bought and sold on the deregulated Nordic power market is dominated by hydro power. However, hydro power generation is restricted by the amount of water in reservoirs. The inflows to these reservoirs show a yearly cycle and seasonal planning of the production is necessary.

Seasonal planning up to 1.5 years for a power producer in a hydro-thermal system with a regulated river is considered. For a price-taking, risk-averse producer who wants to maximize his profit, the representation of the stochastic variables, i.e. inflows and power price, in the planning algorithm is crucial. The representation of the stochastic variables as scenario trees is the main subject of this thesis.

The inflows to the reservoirs in a river are highly spatially correlated and show temporal autocorrelation, as well. These properties are used to construct scenario trees. By using time series models the autocorrelation is explained and principal component analysis reduce substantially the dimension of the stochastic variables. Since the available amount of water that can be used for power production varies between years due to meteorological reasons the spot price shows large fluctuations. This dependence is used for modeling the power price and power contracts. Altogether, this gives an efficient method to create scenario trees suitable for stochastic programming with few assumptions concerning stochastic properties of the underlying stochastic processes.

Scenario tree generation is the stochastic part in the solution to the seasonal planning problem. A multi-stage stochastic programming model with the inflows to different stations and the power price as stochastic elements has been constructed as well as a program system, SPOT, for obtaining the solution in practice. The different scenario tree generation methods have been evaluated as well as a comparison between the stochastic programming model and a deterministic model.

Key words:
Scenario trees, inflow modeling, principal component analysis, electricity prices, multistage stochastic programs, energy derivatives