Energy storage participating as an independent entity in the frequency regulation market can enhance power system economic operation efficiency and frequency regulation performance in power market reform. A bi-level optimization strategy for energy and frequency regulation market operation considering energy storage degradation costs is proposed. First

a piecewise linearization method is employed to treat the depth-of-discharge curve of energy storage

and to establish a degradation cost model. Second

energy storage units incorporating degradation costs are treated as bidding entities in the market

and a bi-level optimization framework for joint energy and frequency regulation markets is developed to co-optimize energy storage revenue and lifespan. Additionally

based on the strong duality theory and the Karush-Kuhn-Tucker (KKT) conditions

the bi-level model is reconstructed into a mixed-integer programming problem for solution. Finally

case studies are conducted to determine the optimal clearing prices for thermal power units and energy storage power stations in the energy and frequency regulation markets

verifying the effectiveness of the proposed model in coordinating energy storage economic revenue and lifespan losses.