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Revenue Adequate Prices for Chance-Constrained Electricity Markets with Variable Renewable Energy Sources

Author

Listed:
  • Xin Shi
  • Alberto J. Lamadrid L.
  • Luis F. Zuluaga

Abstract

In a commodity market, revenue adequate prices refer to compensations that ensure that a market participant has a non-negative profit. In this article, we study the problem of deriving revenue adequate prices for an electricity market-clearing model with uncertainties resulting from the use of variable renewable energy sources (VRES). To handle the uncertain nature of the problem, we use a chance-constrained optimization (CCO) approach, which has recently become very popular choice when constructing dispatch electricity models with penetration of VRES (or other sources of uncertainty). Then, we show how prices that satisfy revenue adequacy in expectation for the market administrator, and cost recovery in expectation for all conventional and VRES generators, can be obtained from the optimal dual variables associated with the deterministic equivalent of the CCO market-clearing model. These results constitute a novel contribution to the research of research on revenue adequate, equilibrium, and other types of pricing schemes that have been derived in the literature when the market uncertainties are modeled using stochastic or robust optimization approaches. Unlike in the stochastic approach, the CCO market-clearing model studied here produces uncertainty uniform real-time prices that do not depend on the real-time realization of the VRES generation outcomes. To illustrate our results, we consider a case study electricity market, and contrast the market prices obtained using a revenue adequate stochastic approach and the proposed revenue adequate CCO approach.

Suggested Citation

  • Xin Shi & Alberto J. Lamadrid L. & Luis F. Zuluaga, 2021. "Revenue Adequate Prices for Chance-Constrained Electricity Markets with Variable Renewable Energy Sources," Papers 2105.01233, arXiv.org.
  • Handle: RePEc:arx:papers:2105.01233
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    1. Jeremy T. Fox & Patrick Bajari, 2013. "Measuring the Efficiency of an FCC Spectrum Auction," American Economic Journal: Microeconomics, American Economic Association, vol. 5(1), pages 100-146, February.
    2. O'Neill, Richard P. & Sotkiewicz, Paul M. & Hobbs, Benjamin F. & Rothkopf, Michael H. & Stewart, William R., 2005. "Efficient market-clearing prices in markets with nonconvexities," European Journal of Operational Research, Elsevier, vol. 164(1), pages 269-285, July.
    3. Paul Milgrom, 2000. "Putting Auction Theory to Work: The Simultaneous Ascending Auction," Journal of Political Economy, University of Chicago Press, vol. 108(2), pages 245-272, April.
    4. Zakeri, Golbon & Pritchard, Geoff & Bjørndal, Mette & Bjørndal, Endre, 2016. "Pricing wind: A revenue adequate, cost recovering uniform price for electricity markets with intermittent generation," Discussion Papers 2016/15, Norwegian School of Economics, Department of Business and Management Science.
    5. Herbert E. Scarf, 1990. "Mathematical Programming and Economic Theory," Operations Research, INFORMS, vol. 38(3), pages 377-385, June.
    6. Kuang, Xiaolong & Lamadrid, Alberto J. & Zuluaga, Luis F., 2019. "Pricing in non-convex markets with quadratic deliverability costs," Energy Economics, Elsevier, vol. 80(C), pages 123-131.
    7. Geoffrey Pritchard & Golbon Zakeri & Andrew Philpott, 2010. "A Single-Settlement, Energy-Only Electric Power Market for Unpredictable and Intermittent Participants," Operations Research, INFORMS, vol. 58(4-part-2), pages 1210-1219, August.
    8. Victor M. Zavala & Kibaek Kim & Mihai Anitescu & John Birge, 2017. "A Stochastic Electricity Market Clearing Formulation with Consistent Pricing Properties," Operations Research, INFORMS, vol. 65(3), pages 557-576, June.
    9. Bjørndal, Mette & Jörnsten, Kurt, 2008. "Equilibrium prices supported by dual price functions in markets with non-convexities," European Journal of Operational Research, Elsevier, vol. 190(3), pages 768-789, November.
    10. Suvrajeet Sen & Lihua Yu & Talat Genc, 2006. "A Stochastic Programming Approach to Power Portfolio Optimization," Operations Research, INFORMS, vol. 54(1), pages 55-72, February.
    11. Ali Hortaçsu & Steven L. Puller, 2008. "Understanding strategic bidding in multi‐unit auctions: a case study of the Texas electricity spot market," RAND Journal of Economics, RAND Corporation, vol. 39(1), pages 86-114, March.
    12. Javad Khazaei & Golbon Zakeri & Shmuel S. Oren, 2017. "Single and Multisettlement Approaches to Market Clearing Under Demand Uncertainty," Operations Research, INFORMS, vol. 65(5), pages 1147-1164, October.
    13. of England, Bank, 2016. "Markets and operations," Bank of England Quarterly Bulletin, Bank of England, vol. 56(4), pages 212-221.
    14. Joskow, Paul L & Schmalensee, Richard & Bailey, Elizabeth M, 1998. "The Market for Sulfur Dioxide Emissions," American Economic Review, American Economic Association, vol. 88(4), pages 669-685, September.
    15. George Liberopoulos & Panagiotis Andrianesis, 2016. "Critical Review of Pricing Schemes in Markets with Non-Convex Costs," Operations Research, INFORMS, vol. 64(1), pages 17-31, February.
    16. Jikai Zou & Shabbir Ahmed & Xu Andy Sun, 2018. "Partially Adaptive Stochastic Optimization for Electric Power Generation Expansion Planning," INFORMS Journal on Computing, INFORMS, vol. 30(2), pages 388-401, May.
    17. Álvaro Lorca & X. Andy Sun & Eugene Litvinov & Tongxin Zheng, 2016. "Multistage Adaptive Robust Optimization for the Unit Commitment Problem," Operations Research, INFORMS, vol. 64(1), pages 32-51, February.
    18. Bjørndal, Endre & Bjørndal, Mette & Midthun, Kjetil & Zakeri, Golbon, 2016. "Congestion Management in a Stochastic Dispatch Model for Electricity Markets," Discussion Papers 2016/12, Norwegian School of Economics, Department of Business and Management Science.
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