Profitability of energy arbitrage net profit for grid-scale battery energy storage considering dynamic efficiency and degradation using a linear, mixed-integer linear, and mixed-integer non-linear optimization approach

Grid-scale energy storage is becoming an essential element to effectively support the rapid increased use of renewable energy sources in the power network. The present work proposes a long-term techno-economic profitability analysis considering the net profit stream of a grid-level battery energy storage system (BESS) performing energy arbitrage as a grid service. The net profit is a cost function that includes the revenue derived by arbitrage, the import cost and the degradation cost induced by battery capacity fade. Three optimization techniques with a computationally efficient optimization logic are developed. The scenario with no-degradation is formulated as a linear programming (LP) problem, while the scenarios with and without degradation are formulated as mixed-integer linear programming (MILP), and as mixed-integer non-linear programming (MINLP) problems. The non-linearity is introduced by implementing a BESS dynamic charge/discharge efficiency that is a function of the BESS power rate. Based on the obtained BESS optimal scheduling, a long-term profitability analysis is developed during the whole BESS lifetime. In the proposed case study, historical electricity market prices from the CAISO electricity market in the United States, California, are used as input. We found that, even without degradation, the break-even investment cost that makes the BESS profitable with a power to-energy-ratio of 1 MW/2MWh is 210 $/kWh. By implementing a cycle-counting degradation model, we observed a remarkable battery degradation on BESS profitability corresponding to a yearly net profit reduction in the 13-24 % range. From a long-term application perspective, the BESS calendar lifetime could be extended by reducing the battery cycling. Such cycling reduction is obtained by adding a penalty cost in the objective function of the energy arbitrage optimization problem.