Scenario Trees for Inlfow Modelling in Stochastic Optimisation for Energy Planning

Roger Halldin

Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,

ISSN 1404-028X
The Nordic countries Norway, Sweden, Finland and Denmark have formed a deregulated power market. Electricity bought and sold on this market is dominated by hydro power. However, hydro power generation is restricted by the amount of water in reservoirs. The inflow to these reservoirs shows a yearly cycle and seasonal planning of the production is necessary.
Seasonal planning for a fictive power producer in a hydro-thermal system with two regulated rivers is considered. This planning stretches up to 1.5 years ahead with a minimum time resolution of one week. For a price-taking, risk-averse producer who wants to maximise his profit, the representation of the stochastic variables, i.e. inflows and power price, in the planning algorithm is crucial. A multi-stage stochastic programming model with the inflows to different stations and the power
price as stochastic elements has previously been constructed. The representation of the stochastic variables as scenario trees is the subject of this thesis.
The inflows to the reservoirs in the two rivers 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. In the scenario tree construction estimated moments of the relevant stochastic variables are used. 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 trees, inflow modeling, principal component analysis