Solving power system economic emission dispatch problem under complex constraints via dimension differential learn butterfly optimization algorithm with FDC-based

The economic emission dispatch (EED) aims to minimize the fuel and pollutant emission costs of generator units under various complex constraints. Optimizing the EED problem is of crucial importance for alleviating the current energy and environmental pressures. In this work, nearly all known complex constraints in the EED problem, including the valve-point effect, transmission line power loss, prohibited operating zones, and ramp-rate limits, are taken into account, and an enhanced version of butterfly optimization algorithm (FDCDLBOA) is proposed to solve it. First, a new adaptive fragrance is employed to optimize the instability caused by target differences and improve the convergence performance. Second, the proposed dimension differential learning strategy evolves the position of individuals with the help of superior dimensional information in the population, and this extensive learning exchange can balance global and local search, maintain diversity, and get rid of local optima. Third, the Fitness-Distance-Constraint (FDC) guide selection method is employed for the first time to handle the complex constraints of EED problems, enhancing the ability of individuals to bypass the infeasible search areas. After evaluating the proposed FDCDLBOA on CEC 2022 test suite, it is applied to solve 8 EED cases, encompassing small-, medium- and large-scale systems. Notably, the 280-generator case is the first large-scale test to exceed 200 generators. Compared with 9 representative algorithms, FDCDLBOA performs outstandingly in terms of robustness, improvement index (IF), mean constraint violation (MV), feasibility rate (FR) and Quade multiple comparison, among which IF, MV, FR, and Quade are all employed for evaluating the EED problem for the first time. The presented results confirm that the proposed method effectively enhances the robustness of high-quality solutions and the ability to handle complex constraints, demonstrating strong competitiveness and potential in solving the EED problem.