Price-based unit commitment electricity storage arbitrage with piecewise linear price-effects

Electricity storage plants can be used for many applications, with one of the most studied applications being arbitrage in the day-ahead market. Although the arbitrage value is related to the presence of price spreads, it also depends on the effect of (dis)charge actions on prices, as arbitrage generally reduces price spreads by increasing off-peak prices when charging and decreasing peak prices when discharging. As such, there are two important assumptions in price-based unit commitment arbitrage models: first, whether the storage operator is assumed to have perfect knowledge of future prices, and second, whether they recognize that their (dis)charge actions may affect those prices, i.e., the price-taking or price- making assumption. This article proposes a comprehensive formulation of the arbitrage problem including detailed operating constraints, and focuses on relaxing the price-taking assumption by considering real-world price-effect data, published in the form of hourly piecewise linear relationships between quantity and price based on submitted bids, which are referred to as 'market resilience functions". These can be used to (1) evaluate the price-taking and price-making assumptions based on simplified price-effects, and to (2) provide an upper limit to the arbitrage value under the assumption that prices and price-effects are known at the decision stage. In addition, a stepwise approximation to the piece- wise linear functions is developed to reduce computation time, i.e., from mixed-integer nonconvex quadratic programming to mixed-integer linear programming, while providing lower- and upper bound approximations to the arbitrage value. The developed models are applied to the Belgian day-ahead market for 2014, and show that the price-effect has a strong impact on the operation and arbitrage value of large-scale storage.