The rapid expansion of renewable energy sources (RES), especially the combination of Solar photovoltaic (PV), wind turbine generating (WTG), and battery energy storage systems (BESS), has sparked significant interest in addressing global warming and climate change issues. These energy sources offer numerous advantages, such as reduced emissions and lower operational costs, but their power output is uncertain. In order to account for fluctuating energy costs, a microgrid with diverse energy sources must schedule BESS charging optimally. The proposed method uses the Artificial Rabbit Optimisation (ARO) algorithm to optimise the charging and discharging schedule for BESS, resulting in a decrease in daily energy costs and an improvement in storage state of health (SOH). The SOH is considered an ageing coefficient for conservative BESS operation in order to extend the battery's lifespan under consistent use. To further validate the effectiveness of the energy management strategy, a fixed pricing scheme and a dynamic pricing scheme are utilised to validate its efficacy. When storage degradation and time-of-use (TOU) tariffs are accounted for, the simulation results of voltage, current, and power profiles over a 24-hour period indicate that the proposed method has the capability to maximise the profitability of a grid-connected PV and WTG-based microgrid.