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Asymmetric risk and fuel neutrality in electricity capacity markets


In many liberalized electricity markets, power generators can receive payments for maintaining capacity through capacity markets. These payments help stabilize generator revenues, making investment in capacity more attractive for risk-averse investors when other outlets for risk trading are limited. Here we develop a heuristic algorithm to solve large-scale stochastic equilibrium models describing a competitive market with incomplete risk trading. Introduction of a capacity mechanism has an asymmetric effect on the risk profile of different generation technologies, tilting the resource mix towards those with lower fixed costs and higher operating costs. One implication of this result is that current market structures may be ill-suited to financing low-carbon resources, the most scalable of which have high fixed costs and near-zero operating costs. Development of new risk trading mechanisms to replace or complement current capacity obligations could lead to more efficient outcomes.

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Fig. 1: Decline of baseload capacity with increased options trading.

Data availability

The code and data used for numerical tests in this study are available in a public repository (


  1. Bushnell, J., Flagg, M. & Mansur, E. Capacity Markets at a Crossroads Working Paper 278 (Energy Institute at Haas, 2017).

  2. Oren, S. S. Generation adequacy via call options obligations: safe passage to the promised land. Electricity J. 18, 28–42 (2005).

    Article  Google Scholar 

  3. Joskow, P. in The New Energy Paradigm (ed. Helm, D.) Ch. 4 (Oxford Univ. Press, 2007).

  4. Cramton, P. & Stoft, S. The Convergence of Market Designs for Adequate Generating Capacity with Special Attention to the CAISO's Resource Adequacy Problem (MIT Center for Energy and Environmental Policy Research, 2006);

  5. Hogan, W. W. Electricity scarcity pricing through operating reserves. Econ. Energy Environ. Policy 2, 65–86 (2013).

    Article  Google Scholar 

  6. Joskow, P. & Tirole, J. Reliability and competitive electricity markets. RAND J. Econ. 38, 60–84 (2007).

    Article  Google Scholar 

  7. Cramton, P., Ockenfels, A. & Stoft, S. Capacity market fundamentals. Econ. Energy Environ. Policy 2, 27–46 (2013).

    Article  Google Scholar 

  8. Bothwell, C. & Hobbs, B. F. Crediting wind and solar renewables in electricity capacity markets: the effects of alternative definitions upon market efficiency. Energy J. 38(SI), 173–188 (2017).

    Google Scholar 

  9. Ehrenmann, A. & Smeers, Y. Generation capacity expansion in a risky environment: a stochastic equilibrium analysis. Oper. Res. 59, 1332–1346 (2011).

    Article  MathSciNet  Google Scholar 

  10. Vazquez, C., Rivier, M. & Perez-Arriaga, I. J. A market approach to long-term security of supply. IEEE Trans. Power Syst. 17, 349–357 (2002).

    Article  Google Scholar 

  11. Neuhoff, K. & De Vries, L. Insufficient incentives for investment in electricity generations. Util. Policy 12, 253–267 (2004).

    Article  Google Scholar 

  12. Schiro, D. A., Hobbs, B. F. & Pang, J. S. Perfectly competitive capacity expansion games with risk-averse participants. Comput. Optim. Appl. 65, 511–539 (2016).

    Article  MathSciNet  Google Scholar 

  13. Roques, F. A., Nuttall, W. J., Newberry, D. M., de Neufville, R. & Connors, S. Nuclear power: a hedge against uncertain gas and carbon prices? Energy J. 27, 1–24 (2006).

    Article  Google Scholar 

  14. Roques, F. A., Newbery, D. M. & Nuttall, W. J. Fuel mix diversification incentives in liberalized electricity markets: a mean–variance portfolio theory approach. Energy Econ. 30, 1831–1849 (2008).

    Article  Google Scholar 

  15. Gross, R., Blyth, W. & Heptonstall, P. Risks, revenues and investment in electricity generation: why policy needs to look beyond costs. Energy Econ. 32, 796–804 (2010).

    Article  Google Scholar 

  16. Guo, X., Beskos, A. & Siddiqui, A. The natural hedge of a gas-fired power plant. Comput. Manag. Sci. 13, 63–86 (2016).

    Article  MathSciNet  Google Scholar 

  17. Ehrenmann, A. & Smeers, Y. in Stochastic Optimization Methods in Finance and Energy: New Financial Products and Energy Market Strategies (eds. Bertocchi, M., Consigli, G. & Dempster, M. A. H.) 273–310 (Springer, 2011).

  18. Philpott, A., Ferris, M. & Wets, R. Equilibrium, uncertainty and risk in hydrothermal electricity systems. Math. Program. 157, 483–513 (2016).

    Article  MathSciNet  Google Scholar 

  19. Ferris, M. & Philpott, A. Dynamic Risked Equilibrium (2018);

  20. Ralph, D. & Smeers, Y. Risk trading and endogenous probabilities in investment equilibria. SIAM J. Optim. 25, 2589–2611 (2015).

    Article  MathSciNet  Google Scholar 

  21. Newbery, D. Missing money and missing markets: reliability, capacity auctions and interconnectors. Energy Policy 94, 401–410 (2016).

    Article  Google Scholar 

  22. O’Shaughnessy, E., Heeter, J. & Sauer, J. Status and Trends in the US Voluntary Green Power Market (2017 Data) (National Renewable Energy Laboratory, 2018);

  23. Joskow, P. Capacity payments in imperfect electricity markets: need and design. Util. Policy 16, 159–170 (2008).

    Article  Google Scholar 

  24. Cheng, I. H. & Xiong, W. Financialization of commodity markets. Annu. Rev. Financ. Econ. 6, 419–441 (2014).

    Article  Google Scholar 

  25. Hirshleifer, D. Hedging pressure and futures price movements in a general equilibrium model. Econometrica 58, 411–428 (1990).

    Article  MathSciNet  Google Scholar 

  26. Resource Investment in Competitive Markets (PJM Interconnection, 2016);

  27. Pierpont, B. & Nelson, D. Markets for Low Carbon, Low Cost Electricity Systems (Climate Policy Initiative, 2017);

  28. Gimon, E. On Market Designs for a Future with a High Penetration of Variable Renewable Generation (Energy Innovation LLC, 2017);

  29. Macdonald, B. & Du, M. Project Finance Industry Report Card (S&P Global Ratings, 2017);

  30. Butler, L. & Neuhoff, K. Comparison of feed-in tariff, quota and auction mechanisms to support wind power development. Renew. Energy 33, 1854–1867 (2008).

    Article  Google Scholar 

  31. Polzin, F., Egli, F., Steffen, B. & Schmidt, T. S. How do policies mobilize private finance for renewable energy? A systematic review with an investor perspective. Appl. Energy 236, 1249–1268 (2019).

    Article  Google Scholar 

  32. Levin, T. & Botterud, A. Electricity market design for generator revenue sufficiency with increased variable generation. Energy Policy 87, 392–406 (2015).

    Article  Google Scholar 

  33. Frew, B. A. et al. Revenue Sufficiency and Reliability in a Zero Marginal Cost Future (National Renewable Energy Laboratory, 2016);

  34. Milligan, M. et al. Wholesale electricity market design with increasing levels of renewable generation: revenue sufficiency and long-term reliability. Electricity J. 29, 26–38 (2016).

    Article  Google Scholar 

  35. Joskow, P. L. Challenges for wholesale electricity markets with intermittent renewable generation at scale: the US experience. Oxf. Rev. Economic Policy 35, 291–331 (2019).

    Article  Google Scholar 

  36. Artzner, P., Delbaen, F., Eber, J. M. & Heath, D. Coherent measures of risk. Math. Finance 9, 203–228 (1999).

    Article  MathSciNet  Google Scholar 

  37. Rockafellar, R. T. & Uryasev, S. Optimization of conditional value-at-risk. J. Risk 2, 21–41 (2000).

    Article  Google Scholar 

  38. Strengthening Reliability: An Analysis of Capacity Performance (PJM Interconnection, 2018); (2018).

  39. de Maere d’Aertrycke, G., Ehrenmann, A. & Smeers, Y. Investment with incomplete markets for risk: the need for long-term contracts. Energy Policy 105, 571–583 (2017).

    Article  Google Scholar 

  40. Renewable Energy Certificates Annex to the EEI Master Power Purchase and Sale Agreement (Edison Electric Institute, 2010);

  41. D’Aertrycke, G., Ehrenmann, A., Ralph, D. & Smeers, Y. Risk Trading in Capacity Equilibrium Models Cambridge Working Paper Economics: 1757 (University of Cambridge, 2017).

  42. Abada, I., de Maere d’Aertrycke, G. & Smeers, Y. On the multiplicity of solutions in generation capacity investment models with incomplete markets: a risk-averse stochastic equilibrium approach. Math. Program. 165, 5–69 (2017).

    Article  MathSciNet  Google Scholar 

  43. Britz, W., Ferris, M. & Kuhn, A. Modeling water allocating institutions based on multiple optimization problems with equilibrium constraints. Environ. Model. Softw. 46, 196–207 (2013).

    Article  Google Scholar 

  44. Ferris, M. C. & Munson, T. S. Complementarity problems in GAMS and the PATH solver. J. Economic Dyn. Control 24, 165–188 (2000).

    Article  MathSciNet  Google Scholar 

  45. Höschle, H., Le Cadre, H., Smeers, Y., Papavasiliou, A. & Belmans, R. An ADMM-based method for computing risk-averse equilibrium in capacity markets. IEEE Trans. Power Syst. 33, 4819–4830 (2018).

    Article  Google Scholar 

  46. Fourer, R., Gay, D. M. & Kernighan, B. W. in Algorithms and Model Formulations in Mathematical Programming (eds. Wallace, S. W.) 150–151 (Springer, 1989).

  47. IBM ILOG CPLEX optimizer (IBM, 2015).

  48. Schwele, A., Kazempour, J. & Pinson, P. Do unit commitment constraints affect generation expansion planning? A scalable stochastic model. Energy Syst. (2019).

  49. Glowinski, R. & Marroco, A. Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. ESAIM: Math. Model. Num. 9, 41–76 (1975).

    MATH  Google Scholar 

  50. Gabay, D. & Mercier, B. A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers Math. Appl. 2, 17–40 (1976).

    Article  Google Scholar 

  51. Gérard, H., Leclère, V. & Philpott, A. On risk averse competitive equilibrium. Oper. Res. Lett. 46, 19–26 (2018).

    Article  MathSciNet  Google Scholar 

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This research was supported, in part, by Northwestern University’s Center for Optimization and Statistical Learning. The views expressed in this article are not necessarily those of the Federal Energy Regulatory Commission.

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Authors and Affiliations



J.M. planned and performed the analysis. D.P.M. reviewed the manuscript, in particular with reference to the models and algorithm. R.P.O. reviewed the manuscript, in particular with reference to the electricity market design.

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Correspondence to Jacob Mays.

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Supplementary Information

Supplementary notes 1–5, Tables 1 and 2 and refs. 1–8.

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Mays, J., Morton, D.P. & O’Neill, R.P. Asymmetric risk and fuel neutrality in electricity capacity markets. Nat Energy 4, 948–956 (2019).

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