Discussion on the monotonicity principle of the two-stage problem in joint optimal operation of cascade hydropower stations

Abstract

The joint optimal dispatching of cascade hydropower stations aims to maximize economic benefits while satisfying various constraints. However, numerous studies have failed to acknowledge the significance of the intrinsic optimization principle and lack discussion on this issue. This study started with a mathematical principle analysis of the optimization problem and studied the optimality principle puzzle of the joint optimal dispatching of cascade hydropower stations. First, a two-stage optimization problem was constructed to describe the relationship between the variation in discharge and the incremental function of the total energy generation of the reservoir. Subsequently, the first and second derivatives of the cascade total generating capacity increment to cascade reservoir discharge variation were derived, and the existence condition of monotonically decreasing the first derivative was proposed. Moreover, the monotonicity principle was proven through numerical simulations by comparing the optimization results of POA and the monotonicity principle coupled IPOA in the cascade hydropower stations operation of the Jinsha River, it was found that in terms of power generation and computational efficiency, IPOA is superior to POA. Finally, using this optimization principle, the optimal operation mode of the two typical cascade reservoirs was analyzed in the case studies. The example results show that the proposed optimal principle can theoretically analyze and clarify the optimal operation mode of cascade reservoirs, and the operation modes of the two typical cascade reservoirs can provide guidance and reference for the operation modes of cascade reservoirs in real life.