Censored‐data correlation and principal component dynamic programming

Abstract

A principal component stochastic dynamic programming algorithm for stochastic multireservoir hydropower system operation optimization was proposed by Saad and Turgeon (1988). The dimension of the state space of the system is reduced by using only the major principal components of the system's state as determined by a principal component analysis of the results of a deterministic optimization. A significant refinement of the procedure is to employ censored‐data principal component analysis. The more sophisticated statistical analysis provides a better model of the full dynamic range of the reservoir system's state, explains more observed variability of the reservoir volumes, and provides more accurate estimates of the statistical description's parameters. In an example presented of a four‐reservoir system, the first component of the censored‐data principal component analysis, for a given month, explained all but 7% of the uncensored system's variability, whereas the standard analysis for the same month left 12% of the observed system's variability unexplained.