Increasing integration of intermittent highly penetrated renewable energy sources (RESs) into electric distribution network (DN), coupled with variable load demands, introduces significant operational challenges related to voltage deviation, voltage stability, and power losses. To address these issues, this study proposes a new methodology for optimal integration of RESs, specifically photovoltaic (PV) and wind turbine (WT) generation, alongside hybrid energy storage systems (HESS) within the DN based on a recently developed Artificial Protozoa Optimizer (APO). The HESS employs a combination of longduration gravity energy-storage (GES) and short-duration supercapacitor (SC) energy-storage. This method simultaneously optimizes allocation and operation of these components to minimize voltage deviations and power losses while enhancing voltage stability. The approach is validated and tested on the IEEE 33-bus DN, using a voltage-dependent time-varying mixed load model and variable solar irradiance wind speed. Results demonstrate that the combined deployment of RES and HESS can effectively minimize power loss by 46.1 % and voltage deviation by 64.7 %, as well as improve voltage stability by 7.42 %, leading to a significant enhancement of DN performance.