A Comprehensive Methodology for Battery Energy Storage System Representation with Frequency Regulation in Power Flow Studies

Abstract This paper presents a full Newton-based methodology for incorporating battery energy storage systems (BESS) into power flow analysis with explicit modeling of primary frequency regulation. The main contribution is the integration of frequency-dependent BESS behavior into the conventional power flow formulation, enabling the representation of active power adjustments in response to frequency deviations within a steady-state framework. Two operating modes are addressed: isolated (off-grid) operation and grid-connected (on-grid) operation in conjunction with conventional synchronous generators. The proposed formulation is embedded directly into the full Newton power flow algorithm, preserving its numerical characteristics while extending its capability to capture frequency regulation effects. The methodology is validated using two representative test systems: a 6-bus system for the off-grid scenario and the New England test system for the on-grid scenario. The results demonstrate the robustness and accuracy of the proposed approach and confirm its effectiveness in representing frequency-dependent behavior and the contribution of BESS units to primary frequency regulation under different operating conditions.