A Comparison of Stochastic Optimization Methods for Multi-Reservoir Systems

Abstract

The determination of optimal operations policies for multi-reservoir systems under stochastic inflows is a hard problem. Dynamic Programming (DP) is widely used to solve such problems when the number of reservoirs is small. When there are many reservoirs in the system, the Stochastic Dynamic Programming (SDP) approach is impractical due to the “curse of dimensionality”. Therefore, some approximations have to be used to reduce the dimensionality of the problem. The Aggregation / Decomposition technique is one of the approximate methods used to solve multi-reservoir stochastic optimization problems. Stochastic differential equations can be used to model the dynamics of a multi-reservoir system. Under the assumption of Gaussian inputs, Ito’s stochastic calculus and the automatic formulation of moment equations may be used to derive the equivalent deterministic differential equations for the original stochastic system. These deterministic differential equations describe the evolution of the mean and the variance vector of the state variables of the system, namely, the reservoir storage volumes. Using these equations, optimal operational policies can be derived with the additional use of nonlinear optimization tools. In this paper, the advantages and disadvantages of these two stochastic methods for multi-reservoir problems will be presented.