The power system is the cornerstone of modern industrialized society. Decarbonizing power systems requires balancing electricity costs and supply stability to ensure equal energy access for all consumers. This paper develops a novel power system dispatching model integrating thermal power, wind power, photovoltaic (PV) generation, and energy storage systems (ESS). Monte Carlo simulations are used to analyze how renewable energy and ESS capacity impact costs, carbon emissions, power fluctuations, and renewable energy utilization. A unique feature of this study is the combination of the non-dominated sorting genetic algorithm II (NSGA-II) and the technique for order preference by similarity to an ideal solution (TOPSIS) to optimize and select capacity configurations across three regions. Results indicate that while ESS capacity improves renewable energy utilization, it can also increase fluctuations when renewable utilization is low. The findings highlight the importance of limiting renewable energy capacity to 50% to ensure grid stability. Optimal configurations achieve significant improvements, including the cost reduction of 21.6%–36.8% and the reduction of 5.2%–8.8% in carbon emissions. By examining the effects of component capacity changes and identifying optimal allocation schemes, this study provides actionable insights for decarbonizing power systems while promoting energy equity.