A Repair-Based Improved Whale Optimization Algorithm for Low-Carbon Economic Dispatch of an Islanded Renewable Microgrid

Islanded renewable microgrids must balance power internally, so day-ahead dispatch is affected by wind and photovoltaic variability, battery state-of-charge (SOC) dynamics, demand-response (DR) participation, and emissions from dispatchable generation. This paper proposes a low-carbon economic dispatch model for an islanded photovoltaic–wind-turbine–battery-energy-storage–dispatchable-generator–demand-response (PV-WT-BESS-DG-DR) microgrid. The objective includes fuel, operation and maintenance, BESS degradation, renewable curtailment, load shedding, DR compensation, and carbon-emission costs. A repair-based constraint-handling strategy keeps the search space continuous while enforcing power balance, DG ramping, BESS operating and SOC limits, terminal SOC, and DR constraints. An improved whale optimization algorithm (WOA) is then developed with three modules: diversity enhancement, exploration–exploitation balancing, and local escape and refinement. The method is assessed through base-case dispatch, benchmark comparison, strategy comparison, ablation tests, and sensitivity analysis. In 30 independent runs, the proposed method achieves a mean cost of 2662.96 CNY/day, 4.07% lower than standard WOA, and reduces the standard deviation by 79.72%. Wilcoxon and Friedman tests confirm significant differences from the benchmark algorithms. Sensitivity tests show that higher BESS degradation coefficients and carbon prices increase the accounting cost but do not change the qualitative feasibility of the deterministic dispatch framework.