This study aims to address the issues of volatile energy access to the active distribution network (ADN), which are the difficulty of frequency regulation, the increased voltage deviation of the ADN, the decrease in operational security and stability, etc. In this study, a two-stage majorization configuration model is established to identify and understand how volatility energy affects a hybrid energy storage system (HESS). The ADN and HESS with lead-acid batteries and supercapacitors (SC) are examined using day forecast data for wind, solar, and load. In this planning stage, the integrated cost, network loss, and node voltage deviation are considered as optimal objectives in a multi-objective optimization model, while the revised multi-objective optimization particle swarm approach is used to solve the initial value of capacity configuration. In the operation stage, optimizing objectives like wind output power fluctuations, the frequency deviation of HESS is used to solve the modified value of the configuration capabilities of the SC, and the output of different types of units in ADN is further optimized by the quantum particle swarm with the addition of a chaotic mechanism. The simulation study is conducted to determine the best configuration result based on case 33 node examples, and the simulation results demonstrate the model’s viability.