Precision Modeling and Optimization of BESS Reserve Capacity for Provision of Cross-Timescale Frequency Regulation Services

Battery energy storage system (BESS) is an effective means to address the decline of inertia and frequency regulation (FR) capabilities in power systems. However, inertia, primary, and secondary frequency regulation operate on different time scales and exhibit complex coupling relationships, making it difficult for existing scheduling methods to achieve precise deployment of BESS FR reserves. To tackle this issue, this study analyzes the power-frequency dynamics of BESS in providing inertia, primary, and secondary frequency regulation, highlighting the time-division multiplexing characteristic of cross-time-scale FR reserves to avoid redundant deployment. Differential equation (DE) constraints are constructed to describe this dynamic process, enabling precise assessment of the cross-time-scale FR reserve requirements of BESS. Furthermore, a piecewise Bernstein polynomial spline approximation and a solution space transformation method are applied to convert the DE constraints into finite-dimensional algebraic space constraints for efficient model solving. Finally, case studies are conducted to validate the accuracy and effectiveness of the proposed method.