Reliability-based Optimal Design and Operation of Cascade Hydraulically-Coupled Hydropower Reservoir Systems

Optimal design and operation of a cascade hydropower reservoir system accounting for the reliability level of the system’s firm energy is a complex, difficult-to-solve problem in terms of both the problem formulation and its solution approach. This study dealt with the reliability-based optimal design and operation of cascade hydropower reservoirs considering hydraulic coupling between the tail-race of the upstream powerplant and the water elevation at downstream reservoir. The formulation of the resulting optimization model was a nonlinear, nonconvex program (NLP) which by accounting for the reliability level of energy production and the hydraulic coupling it became a mixed integer NLP (MINLP). The resulted MINLP, which was an NP-hard (nonpolynomial deterministic-hard) problem, was solved by both classical and evolutionary optimization algorithms and their performances were tested in Karoon2-Karoon3 cascade hydropower system as a real case study. Since the number of binary variables was large and the nonlinear part of the MINLP was nonconvex, classical gradient-based algorithms were unable to solve the problem. However, particle swarm optimization (PSO) algorithm, a metaheuristic optimization algorithm, fulfilled to find near optimal good solutions to the problem. This was made possible by the help of incremental generating of feasible solutions, which satisfy the equality constraints of balance equations and the system operation characteristics during the low-flow periods.