Power System Frequency Response Enhancement Using Optimal Placement and Sizing of Battery Energy Storage Systems

The increasing penetration of converter-interfaced renewable energy sources has led to reduced system inertia and increased frequency stability challenges in modern power systems. Battery energy storage systems (BESSs) provide fast active power support. However, their effectiveness depends on the installation location, power rating, and network characteristics. This paper proposes a power-flow-informed, sensitivity-based method for the optimal placement and sizing of distributed BESSs to improve the frequency nadir and rate of change of frequency (RoCoF). The method integrates marginal frequency sensitivity obtained from time-domain simulations with network coupling information derived from power-flow analysis within a constrained optimization framework solved using particle swarm optimization. The network coupling weight, derived from voltage sensitivity, represents the steady-state electrical connectivity and active power redistribution capability, rather than transient frequency dynamics. It is used in combination with frequency sensitivity to improve the discrimination of candidate buses. The method is evaluated on the IEEE 39-bus system under multiple generator outage contingencies. For the most severe contingency (G01), the baseline system exhibits a frequency nadir of 55.9230 Hz and an RoCoF of 0.2404 Hz/s. With the proposed method, the frequency nadir improves to 58.6561 Hz, corresponding to an increase of 2.7330 Hz (4.88%), while the RoCoF is reduced to 0.1224 Hz/s (49.17% reduction). The optimal solution distributes a total BESS capacity of 298 MW across multiple buses, with the largest allocation of 46 MW at Bus 36. Across additional contingencies, the proposed method consistently achieves higher frequency nadirs and lower RoCoFs compared with both the baseline system and benchmark placement methods. The results demonstrate that combining dynamic frequency sensitivity with power-flow-based network coupling provides a physically consistent and computationally efficient strategy for distributed BESS allocation in low-inertia power systems.