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 9162865390
LUTFMS10282005

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 hydrothermal
system with a regulated river is considered. For a pricetaking, riskaverse
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 multistage 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


