Feasibility of linear decision rules for hydropower scheduling

Linear decision rules is a method for solving multistage stochastic linear programming problems. In this article we consider the feasibility of applying it to the hydropower scheduling problem. In our case, the price-taking producer determines a long-term reservoir management strategy that maximizes the market value of revenues from selling the electricity output in a well-functioning market. Uncertainty is present both in market prices and in reservoir inflows. Traditional methods for this problem suffer from a computing effort that grows exponentially with the number of stages and the number of state variables. The Linear Decision Rules (LDR) approximation is effective at reducing computational complexity, and is well-suited to multistage problems. 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. The approach is demonstrated on four Norwegian hydropower plants.