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This article develops, implements, and tests a method for selecting the locations and sizes of battery storage systems (BSSs) for power systems with distributed power generation. The developed method is based on calculating the coherency index for each bus to determine its contribution to the frequency of the center of inertia (COI) during and post a transient event. Once the coherency index is calculated for all buses, the principle component analysis (PCA) is used to identify the buses with consistent low values of the coherency index. These buses are considered as candidate locations for BSSs. In addition, the lowest values of the coherency index are used to determine the required sizes of BSSs to be connected at the buses with low contributions to the frequency of the COI. The performance of the PCA with COI (PCA-COI) method is evaluated for the Barbados power system for various transient events. Performance results show that BSSs (selected using the proposed method) can effectively improve the frequency stability with minor sensitivity to the levels of distributed power generation, loading levels, and/or type or location of transient events. [ABSTRACT FROM AUTHOR]