Extract nonlinear operating rules of multi-reservoir systems using an efficient optimization method.

Hydropower plants are known as major renewable energy sources, usually used to meet energy demand during peak periods. The performance of hydropower reservoir systems is mainly affected by their operating rules, thus, optimizing these rules results in higher and/or more reliable energy production. Due to the complex nonlinear, nonconvex, and multivariable characteristics of the hydropower system equations, deriving the operating rules of these systems remains a challenging issue in multi-reservoir systems optimization. This study develops a self-adaptive teaching learning-based algorithm with differential evolution (SATLDE) to derive reliable and precise operating rules for multi-reservoir hydropower systems. The main novelty of SATLDE is its enhanced teaching and learning mechanism with three significant improvements: (i) a ranking probability mechanism is introduced to select the learner or teacher stage adaptively; (ii) at the teacher stage, the teaching mechanism is redefined based on learners' performance/level; and (iii) at the learner stage, an effective mutation operator with adaptive control parameters is proposed to boost exploration ability. The proposed SATLDE algorithm is applied to the ten-reservoir benchmark systems and a real-world hydropower system in Iran. The results illustrate that the SATLDE achieves superior precision and reliability to other methods. Moreover, results show that SATLDE can increase the total power generation by up to 23.70% compared to other advanced optimization methods. Therefore, this study develops an efficient tool to extract optimal operating rules for the mentioned systems.