This paper presents an improved grey wolf optimization algorithm (IGWOA) for optimal sizing of an isolated photovoltaic (PV), wind turbine (WT), and battery energy storage (BES) hybrid microgrid. To demonstrate the effectiveness of the proposed approach, atmospheric data sets comprising of wind, solar, and temperature of Kaduna International Airport were collected from Nigerian Meteorological Agency while the load demand data was collected from Kaduna International Airport Electricity Distribution Center. The microgrid optimal sizing was formulated as a constrained single objective optimization problem. Constraints including, loss of power supply probability (LPSP), power balance, generation limits and battery state of charge (SOC) were imposed. Three simulation scenarios were considered. Firstly, the target allowable maximum LPSP was fixed at 25% and the algorithm was able to determine the optimal sizing of the hybrid microgrid components and minimize the initial cost from 169,880.00 USD to 112,356.40 USD per annum resulting in 34% savings in cost. Secondly, the effect of the target allowable maximum LPSP variation was investigated, and it was found that the total installed capacity of the system decreases with increase in LPSP thereby decreasing the total cost. Additionally, a novel electricity price index (EPI) was introduced in order to quantify the degree of optimality of the solution. The EPI was found to increase exponentially with increase in LPSP, resulting in an EPI of < 0.05USD/kWh at 20% LPSP. Lastly, to validate the proposed approach, a comparative analysis between the IGWOA and other algorithms was carried out, and the proposed IGWOA proved applicable.