Stochastic dynamic programming for hydropower reservoir operations with multiple local optima

Multiple optima seriously confine the solution accuracy of stochastic dynamic programming (SDP) for non-concave maximization models of reservoir operation. To address the problem, a two-stage optimization algorithm combining traversing and search is proposed to obtain an optimal decision at each state combination. Single or multiple promising regions where a local optimal solution may exist are identified through coarse traversing in the whole feasible region, and a local search algorithm is used to local optimization in each promising region. Energy maximization model is used to analyze the multiple optima problem and test the method. In the model, quadratic and concave penalty functions are used to address the total power constraint for smaller shortages and fewer shortage periods respectively. The total power constraint increases the probability of multiple local optima existence and intensifies the difficulty in finding optimal decisions. The proposed model and method are applied to the cascaded reservoir system on middle-lower Lancang River in China. Numerical results show that the total power constraint is well addressed, the computing time can be reduced by more than 50% using the two-stage algorithm in getting operating rules with similar performance comparing to only traversing, and the multi-point search algorithm is superior to traversing and single point search in solving the proposed model.