Chance-constrained optimal sizing of BESS with emergency load shedding for frequency stability

The integration of renewable energy sources may result in more severe active power disturbances, and requires more load shedding. The battery energy storage system (BESS) characterized with high flexibility can handle such uncertain disturbances and reduce load shedding amount. This paper proposes a chance-constrained optimal sizing scheme of the BESS to coordinate with the synchronous generator and emergency load shedding (ELS) for frequency stability. First, considering the role of the synchronous generator, BESS, and ELS in frequency stability control, an extended system frequency response model is established to calculate the amount of load shedding, and the required capability of frequency regulation. Then, a multi-objective and chance-constrained mixed integer nonlinear programming (MINLP) model is built for the BESS sizing to minimize investment cost and maximize operation profits, which considers the uncertainties of disturbances. With the utilization of the linear weighted method, max-affine function-based piecewise linearization method and Bernstein approximation, the model is reformulated into a tractable form, which is iteratively solved by the multi-cut Benders decomposition. Case studies were carried out to verify the effectiveness of the proposed scheme, showing superior performance in reducing load shedding amount and improving frequency nadir.