In this work, a strategy is proposed for the optimal placement of a Battery Energy Storage System (BESS) in a power system network for frequency support during a power system contingency. It is an optimization algorithm that considers the best location for the integration of a BESS for a frequency support as the place that will result in a minimum rate of change of frequency (RoCoF) during a power system disturbance. The formulation (which aims at determining the minimum RoCoF during contingency) was based on the inertia constant contributions and active power injections (during contingency) from a mixed power generation sources of conventional power plants (CPPs), wind power plants (WPPs) and a battery energy storage system (BESS). Three different optimization solvers, particle swarm optimization (PSO), Fmincon MATLAB solver, and genetic algorithm (GA)) were used in solving the optimization problem for the purpose of comparing the results obtained in order to choose the minimum RoCoF value among the three optimization solvers. The proposed methodology was tested using two network models namely a modified 12-bus and 53 -bus (Western Cape) test systems each consisting of CPPs, WPPs and BESS as energy sources. Simulation results show that when BESS is placed on its optimal location of bus 61 (using the modified 53-bus Western Cape Network model) the power imbalance due to contingency was reduced to about 38 % of its maximum value of 4791 MW and consequently the system frequency nadir was improved from 49.49 Hz to 49.60 Hz. This is very necessary in order to keep the system frequency from falling beyond the limit that may activate the underfrequency load shedding relays.