Long Term Hydropower Scheduling under Price and Inflow Uncertainty: A Linear Decision Rules Approach

Abstract

This thesis takes the perspective of a hydropower producer facing the task of determining a long term reservoir management strategy that maximizes the expected market value of production. This task is complicated by the uncertainty in future electricity price and inflow. Linear Stochastic Programming and Stochastic Dynamic Programming are traditionally used for solving these type of problems. The size of these problems grows exponentially with the number of stages and the number of state variables, respectively. Hence the problems may become computationally cumbersome. In this thesis, a multistage stochastic scheduling model is developed based on the Linear Decision Rules (LDR) approximation. This approximation is effective at reducing computational complexity, and permits scalability to multistage models (Kuhn et al., 2011). By restricting the decision variables to be affine functions of the realisations of the uncertain parameters, the original intractable problem is transformed into a tractable one with short computational time. In order to estimate the loss of optimality incurred by the complexity reduction, the approximation is applied to both the primal version and the dual version of the problem. The approach is demonstrated on four Norwegian hydropower plants, and is proven to give an acceptable trade-off between accuracy and tractability. It is shown that both the length of the scheduling horizon considered and the relation between the size of the reservoirs, the amount and distribution of inflow and the production capacity of the power stations affect the reservoir management strategies.