Multimodal hierarchical distributed multi-objective moth intelligence algorithm for economic dispatch of power systems

The issue of economic dispatch in the context of environmental sustainability is more challenging with the integration of clean energy into the grid and the increase in the size of power systems. Power engineers have a responsibility to seek a novel algorithm that can hierarchically simplify the problem, enhance the diversity of solutions, balance economic and environmental goals, reduce the environmental footprint, and increase economic efficiency. In this paper, a multimodal hierarchical distributed multi-objective moth intelligence algorithm is proposed, combines the hierarchical distributed method with the moth algorithm, introduces the loose equivalence of multimodality, and adopts the Pareto curve partition processing and the extraction of objective points. The proposed method converts the information exchange of the adjacent regions of each layer and the optimization of each layer to be performed in the bottom layer, achieving the coordinated optimization of the whole system through the parallel optimization of the bottom layer regions. The simulation results show that: (1) the computational efficiency is improved. In the 118-bus system, the proposed algorithm reduces 0.13% cost and 5.76% carbon emission than distributed optimization; the proposed algorithm reduces 0.53% cost and 3.81% carbon emission than centralized optimization; (2) the speed of computation is accelerated. In the 1139-bus system, three-layer distributed optimization and two-layer distributed optimization of the proposed algorithm reduce the time by 62.64% and 37.22% than distributed optimization, respectively; (3) the performance metrics of the proposed method demonstrate superiority. •Multimodal hierarchical multi-objective optimization problems are considered.•A multimodal hierarchical multi-objective economic dispatch framework is built.•A multimodal hierarchical distributed multi-objective moth algorithm is proposed.•The gap of multimodal hierarchical intelligent algorithms for optimization is filled.•The algorithm increases the diversity of decision solutions.