Optimal operation of reservoirs by stochastic programming

A model for optimal multi-period operation of a multi-reservoir system with uncertain inflows and water demands is formulated and solved by the Finite Generation Algorithm. Uncertainties are considered in chance constraints and in penalties due to deviations from meeting demand and reservoir level targets. The penalty functions are linear-quadratic, can be imposed on deviations in one or both directions from the target, and are easily fitted to data by selection of parameters. The stochastic variables are assigned discrete probability distributions. The primal (optimal operation) problem is solved by formulating the dual and then finding its optimum (which is proven to be global for the conditions specified) via a sequence of linear-quadratic deterministic optimization problems of controlled size. The method is demonstrated for a three-reservoir two-period problem. Sensitivity analysis with respect to parameter values is presented. Stochastic simulation is used, to augment the information given by the optimal solution.