Stochastic state variable dynamic programing for reservoir systems analysis

Abstract

The concept of state as used in state space modeling, dynamic programing, and Markov chain analysis is used to link these methods together. The random nature of inflows to the system is treated by incorporating a stochastic inflow model directly within the dynamic programing procedure. Transition probabilities found from the resulting stochastic dynamic programing are employed to determine the steady state probability distribution of the state and decision variables. As an example, the methodology is applied to determine operating policies for the proposed Watasheamu Dam in Nevada. Policies developed considering monthly flows as independently distributed or as serially correlated are similar over the normal range of flows but differ for very high and low inflows. Chance constraints applied at each stage of the dynamic programing are shown to limit the steady state probability of the storage being outside its desirable range but reduce the average annual benefits of operation by up to 15%. Computer time requirements compare favorably with those of an equivalent deterministic analysis of the same system.