Evaluation of the parameterization-simulation-optimization approach for the control of reservoir systems

Most common methods used in optimal control of reservoir systems require a large number of control variables, which are typically the sequences of releases from all reservoirs and for all time steps of the control period. In contrast, the less widespread parameterization-simulation-optimization (PSO) method is a low-dimensional method. It uses a handful of control variables, which are parameters of a simple rule that is valid through the entire control period and determines the releases from different reservoirs at each time step. The parameterization of the rule is linked to simulation of the reservoir system, which enables the calculation of a performance measure of the system for given parameter values, and nonlinear optimization, which enables determination of the optimal parameter values. To evaluate the PSO method and, particularly, to investigate whether the radical reduction of the number of control variables might lead to inferior solutions or not, we compare it to two alternative methods. These methods, namely the high-dimensional perfect foresight method and the simplified 'equivalent reservoir' method that merges the reservoir system into a single hypothetical reservoir, determine 'benchmark' performance measures for the comparison. The comparison is done both theoretically and by investigation of the results of the PSO against the benchmark methods in a large variety of test problems. 41 test problems for a hypothetical system of two reservoirs are constructed and solved for comparison. These refer to different objectives (maximization of reliable yield, minimization of cost, maximization of energy production), water uses (irrigation, water supply, energy production), characteristics of the reservoir system and hydrological scenarios. The investigation shows that PSO yields solutions that are not inferior to those of the benchmark methods and, simultaneously, it has several theoretical, computational and practical advantages.