Implicit stochastic optimization with limited foresight for reservoir systems

Reservoir operation has been described as a multistage stochastic control problem, yet solutions to an explicitly stochastic formulated multi-reservoir operation problem remain problematic. Despite development of new techniques, implicitly stochastic optimization (ISO) models solved using linear programming (LP) remain one of the most readily applicable to the analysis of complex systems. However the attribute of perfect foresight limits the immediate usefulness of such models and hinders the derivation of operating rules for subsequent testing in simulation models. This dissertation presents a modification to the traditional ISO model that overcomes the problem of perfect foresight and incorporates consideration of risk in the prescribed reservoir operation. The proposed method is implemented using sequential runs of an ISO model, where each run has an optimized terminal or carryover storage value function. The time horizon for each run is reduced to a fraction (1/n) of the period-of-analysis. The series of n linked consecutive runs form the optimal operating policy over the entire period-of-analysis. An iterative non-linear search algorithm is used to define the optimal carryover storage value function. Balancing rules are used to reduce the dimensionality of the multi-reservoir operation problem. The method is demonstrated using three case studies: single reservoir operation; single reservoir operation with conjunctive use of groundwater; and multi-reservoir operation. In all three cases the reservoir(s) have the dual purpose of flood control and water conservation. The objective function is to minimize the economic cost of shortage associated with downstream agricultural deliveries. A generalized network flow algorithm with gains is used to find the optimal solution.