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This paper presents a computation-efficient stochastic dynamic programming algorithm for solving energy storage price arbitrage considering variable charge and discharge efficiencies. We formulate the price arbitrage problem using stochastic dynamic programming and model real-time prices as a Markov process. Then we propose an analytical solution algorithm using a piecewise linear approximation of the value-to-go function. Our solution algorithm achieves extreme computation performance and solves the proposed arbitrage problem for one operating day in less than one second on a personal computer. We demonstrate our approach using historical price data from four price zones in New York Independent System Operator, with case studies comparing the performance of different stochastic models and storage settings. Our results show that the proposed method captures 50&#x0025; to 90&#x0025; of arbitrage profit compared to perfect price forecasts. In particular, our method captures more than 80&#x0025; of arbitrage profit in three out of the four price zones when considering batteries with more than two-hour duration and realistic degradation cost.

Arbitraging Variable Efficiency Energy Storage Using Analytical Stochastic Dynamic Programming