With the continuous increase of renewable energy penetration, the operation of distribution networks (DN) faces greater volatility and uncertainty. To address this issue, a multi-energy complementary DN simulation model is developed based on benchmark scenarios with varying new energy penetration levels and typical days of four seasons. The model integrates wind turbines (WT), photovoltaic (PV) systems, battery energy storage systems (BESS), and demand response (DR) mechanisms. For different wind and solar penetration scenarios, a multi-objective optimization model is designed, taking life cycle cost (LCC) and voltage deviation as objectives. The model comprehensively considers the coordinated optimization of BESS capacity, power rating, and operational strategies. Several mainstream optimization algorithms are employed to solve and compare the objective functions and key performance indicators. In particular, the transfer rate (TR) and capacity-to-load ratio (CLR) are introduced as core assessment performance indicators for power supply capability. Through multi-scenario simulation, the impacts of BESS on TR, CLR, and voltage quality are systematically analyzed under different renewable energy penetration rates and DR participation levels. The results show that the rational configuration of BESS combined with DR can not only effectively improve the power supply capacity and economic performance under high renewable penetration, but also significantly improve the operational characteristics of the DN. The findings provide theoretical basis and practical reference for BESS planning and power supply capacity assessment in distribution networks with high shares of renewable energy.