Stochastic Linear Programming for Optimal Reservoir Operation: A Case Study

Optimal reservoir operating policy should consider the uncertainty associated with the uncontrolled inflow to the reservoir. In the present study, Stochastic Linear Programming (SLP) model is developed to obtain optimal operating policy for the existing multipurpose reservoir. The objective of the model is to maximise the expected value of the system performance which is the sum of the all performance value times the respective joint probabilities. The decision variables are the probabilities of reservoir release, PR k,i,l,t , which are the joint probabilities of the reservoir release, R k,i,l,t , with an initial reservoir storage volume of S k,t , inflow of Q i,t and the final storage volume of S l,t+1 for a given time period t. The joint probabilities are influenced by the target reservoir storages, releases and the stochastic nature of inflows. This objective is subject to a set of stochastic constraints to maintain continuity. Historic inflow data is used to consider the stochastic nature of inflows in the form of inflow transition probability matrices. A computer program is developed in LINGO (Language for INteractive General Optimisation) to perform stochastic optimisation. The model gives the steady state probabilities of reservoir storage and inflow as output. The model is applied to Hirakud reservoir in Mahanadi river basin of orissa state, India, for development of an optimal reservoir operating policy. The steady state optimal operating policy and its implications are discussed in this paper