A constrained state formulation for the stochastic control of multireservoir systems

A new formulation is presented for the analysis of multireservoir systems, based on the development of first and second moment expressions for the stochastic storage state variables. These expressions give explicit consideration to the maximum and minimum storage bounds in the reservoir system, a feature not incorporated in some existing formulations based on traditional control theory. Using this analysis, expected values of the storage states, variances of storage, release policies, reliability levels, and failure probabilities (useful information in the context of reservoir operations and design) can be obtained from a nonlinear programming solution. The approach does not involve any discretization of the system variables. The results for the means and standard deviations of the storage states for a multireservoir system compare favorably with those obtained from simulation.