Application of principal component analysis to long‐term reservoir management

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Abstract
Determining the optimal long‐term operating policy of a multireservoir power system requires solution of a stochastic nonlinear programing problem. For small systems the solution can be found by dynamic programing, but for large systems, no direct solution method exists yet, so that one must resort to mathematical manipulations to solve the problem. This paper presents a very efficient procedure for the case where high correlation exists between the reservoirs' trajectories and hence between the state variables. The procedure consists of 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 programing. The reservoir trajectories on which the PCA is 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 to Quebec's La Grande river, which has five reservoirs, are reported.