An efficient mathematical-based optimization method to optimize multi-hydropower operating rules

Optimizing hydropower multi-reservoir systems requires both effective operating rules and efficient optimization techniques. The main contribution of this paper is offering a unique approach that elegantly combines two important parts: creating an efficient optimization method and developing hydropower operating rules. In this regard, a nonlinear rule curve (NLRC) and a linear rule curve (LRC), are tailored for the coordination of a hydropower multi-reservoir system (HMRS) in Iran. To optimize operating rules, the study fabricates a novel algorithm termed the multi-operator weighted mean of vectors (MINFO). The algorithm combines a powerful global search strategy (GSS) that thoroughly searches the solution space with an efficient local search (LS), striking a balance between solution diversity and convergence speed. To fine-tune this balance, an adaptive parameter-tuning strategy is applied. Furthermore, the active-set sequential quadratic programming (ASQP) serves as a localized escaping operator to enhance the algorithm's convergence speed. The effectiveness of the proposed MINFO algorithm is first evaluated through a nonlinear five-reservoir problem. The findings indicate that the MINFO algorithm outperforms a set of 14 distinct optimization methods. Subsequently, the MINFO algorithm is applied to identify optimal NLRC and LRC for a six-reservoir hydropower system. The results underscore the superiority of optimized NLRC, yielding a potential power augmentation of up to 17 % in comparison to the LRC approach. In summation, this study constitutes a seminal contribution by cultivating an efficient rule curve framework for the management of HMRSs.