Application of Principal-Component Analysis to Long-Term Reservoir Management

Determining the optimal long-term operating policy of a multireservoir power system requires solution of a stochastic nonlinear programming problem. The paper presents a very efficient procedure for the case where high correlation exists between the reservoirs trajectories and, hence, between the state variables. It consists in performing principal-component analysis (PCA) on the trajectories to find a reduced model of the system. The reduced model is then substituted into the operating problem and the resulting problem is solved by stochastic dynamic programming. The reservoir trajectories on which the PCAs are performed can be obtained by solving the operating problem deterministically for a large number of equally likely flow sequences. The results of applying the manipulation of Quebec's La Grande river, which has five reservoirs, are reported.