The volatility and intermittency of renewable energy generation significantly affect the low-carbon economic operation of the power system. To optimize the energy storage capacity for a wind-storage virtual power plant (VPP) while considering carbon trading costs, a multi-objective optimization model is set up that considering the life cycle costs of energy storage, life cycle carbon emission costs, and energy trading costs associated with the higher-level power grid, moreover, a Zoned Parallel Artificial Cooperative Search (ZPACS) algorithm integrated with Pareto-based multi-objective optimization is proposed to overcome the high computational complexity, slow solving efficiency, and the propensity to converge to local optima inherent in traditional mathematical programming methods and multi-objective meta-heuristic optimization algorithms. At last, for a virtual power plant consisting of wind power, variable load, and energy storage equipment, a comparative study is conducted for three different algorithms, namely the proposed ZPACS, the classical Artificial Cooperative Search (ACS), and the Differential Evolution (DE) algorithm for optimizing energy storage capacity, and valuable research conclusions are shown.