Wind energy's role in the global electric grid is set to expand significantly. New York State alone anticipates offshore wind farms (WFs) contributing 9GW by 2035. Integration of energy storage emerges as crucial for this advancement. In this study, we focus on a WF paired with a captive battery energy storage system (BESS). We aim to ascertain the capacity credit for a BESS with specified energy and power ratings. Unlike prior methods rooted in reliability theory, we define a power alignment function, which leads to a straightforward definition of capacity and incremental capacity for the BESS. We develop a solution method based on a linear programming formulation. Our analysis utilizes wind data, collected by NYSERDA off Long Island's coast and load demand data from NYISO. Additionally, we present theoretical insights into BESS sizing and a key time-series property influencing BESS capacity, aiding in simulating wind and demand for estimating BESS energy requirements.

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