In this paper, a user-side battery energy storage system is modeled, using a linear programming approach to solve the problem of minimum cost and optimal operation strategy. In the accurate modeling of the battery energy storage system, segmented curves are used to subtly describe the charging performance of the battery at different charging levels. Additionally, the Rainflow algorithm is used to calculate the lifetime loss incurred during the charging and discharging of the chemical battery in the energy storage system. By using Benders Decomposition method, the lifetime loss cost of the energy storage system would be further incorporated into the overall energy arbitrage optimization process, in which the cyclic features of the energy arbitrage in electricity market with battery lifetime loss calculation is constructed. Finally, the performance of such an optimal user-side energy arbitrage strategy is analyzed through various simulations, meanwhile showcasing the advantages through comparison study.