The extensive integration of distributed renewable energy resources (DRES) can lead to several issues in power grids, particularly in distribution grids, due to their inherent intermittency. This paper presents a stochastic simulation-based approach to estimate the maximum permissible penetration level of DRES and to determine the optimal capacity of centralized battery energy storage systems (BESS) in distribution networks while adhering to technical constraints. The stochastic method creates a wide range of scenarios under various conditions. For each scenario, our proposed approach calculates the maximum allowable penetration level of DRES and the required BESS capacity with different DRES control logics. The maximum allowable penetration level of DRES and the requirements of the BESS capacity are determined by an analysis of various simulation results. This paper's unique contribution lies in equipping distribution system operators (DSOs) with the ability to compare results and select the most appropriate voltage control and power smoothing methods. This aids in mitigating challenges associated with overvoltage and intermittency issues arising from DRES-generated power, thereby enhancing the overall resilience and reliability of the power grid. Case studies that include four voltage control algorithms and three power smoothing methods demonstrate the universality and effectiveness of the proposed approach.