With the promotion and application of renewable energy sources such as wind and solar power, which effectively reduce carbon emissions, the intermittency and volatility of these renewable sources impact power quality and stability. Energy storage systems, with their rapid charge and discharge capabilities and ease of construction, can smooth out fluctuations in renewable energy output, reduce wind and solar curtailment, improve supply reliability, and support the achievement of carbon neutrality goals. Therefore, a multi-objective optimization scheme for energy storage capacity is proposed in this paper. For proposed scheme, a multi-objective optimization model for energy storage capacity under low-carbon constraints is first set up, then, the Non-Dominated Sorting Artificial Cooperative Search (NSACS) algorithm is integrated with Pareto evaluation to generate the Pareto front, moreover, the composite weighted technique for order preference by similarity to ideal solution (CW-TOPSIS) is proposed to determine the optimal solution on the Pareto front. At last, case studies demonstrate that the proposed scheme is able to automatically determine the optimal energy storage capacity effectively and achieve synergistic optimization of energy storage economic efficiency, reliability, and carbon reduction.