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Price-Based Unit Commitment Electricity Storage Arbitrage with Piecewise Linear Price-Effects


  • Tom Brijs
  • Frederik Geth
  • Sauleh Siddiqui
  • Benjamin F. Hobbs
  • Ronnie Belmans


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.

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  • Tom Brijs & Frederik Geth & Sauleh Siddiqui & Benjamin F. Hobbs & Ronnie Belmans, 2016. "Price-Based Unit Commitment Electricity Storage Arbitrage with Piecewise Linear Price-Effects," Discussion Papers of DIW Berlin 1567, DIW Berlin, German Institute for Economic Research.
  • Handle: RePEc:diw:diwwpp:dp1567

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    References listed on IDEAS

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    Cited by:

    1. Tom Brijs & Arne van Stiphout & Sauleh Siddiqui & Ronnie Belmans, 2016. "Evaluating the Role of Electricity Storage by Considering Short-Term Operation in Long-Term Planning," Discussion Papers of DIW Berlin 1624, DIW Berlin, German Institute for Economic Research.
    2. repec:eee:appene:v:195:y:2017:i:c:p:36-51 is not listed on IDEAS

    More about this item


    electricity storage; arbitrage; day-ahead market; price-effect; piecewise linear market resilience functions; price-based unit commitment;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D4 - Microeconomics - - Market Structure, Pricing, and Design
    • L94 - Industrial Organization - - Industry Studies: Transportation and Utilities - - - Electric Utilities
    • Q41 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - Demand and Supply; Prices

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