Computational Management Science

, Volume 11, Issue 1–2, pp 57–86

Capacity expansion and forward contracting in a duopolistic power sector

Original Paper
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Abstract

The surge in demand for electricity in recent years requires that power companies expand generation capacity sufficiently. Yet, at the same time, energy demand is subject to seasonal variations and peak-hour factors that cause it to be extremely volatile and unpredictable, thereby complicating the decision-making process. We investigate how power companies can optimise their capacity-expansion decisions while facing uncertainty and examine how expansion and forward contracts can be used as suitable tools for hedging against risk under market power. The problem is solved through a mixed-complementarity approach. Scenario-specific numerical results are analysed, and conclusions are drawn on how risk aversion, competition, and uncertainty interact in hedging, generation, and expansion decisions of a power company. We find that forward markets not only provide an effective means of risk hedging but also improve market efficiency with higher power output and lower prices. Power producers with higher levels of risk aversion tend to engage less in capacity expansion with the result that together with the option to sell in forward markets, very risk-averse producers generate at a level that hardly varies with scenarios.

Keywords

Stochastic programming Complementarity modelling  Energy markets Risk management Capacity expansion 

Sets

\(\varOmega \)

Scenarios

\(\mathcal I \)

Producers

\(\mathcal N \)

Forward blocks

Indices

\(\omega \)

Scenario index, \(\omega \in \varOmega \)

\(i \)

Producer index, \(i \in \mathcal I \)

\(n \)

Forward block index, \(n \in \mathcal N \)

Decision variables

\(p^S_{i,\omega }\)

Power sold in the spot by producer \(i\) in scenario \(\omega \) (MW)

\(p^F_{i,n}\)

Power sold forward by producer \(i\) in forward block \(n\) (MW)

\(p^G_{i,\omega }\)

Total power generated by producer \(i\) in scenario \(\omega \) (MW)

\(\lambda ^S_\omega \)

Spot price of power in scenario \(\omega \) ($/MW)

\(\Delta _i\)

Amount of capacity expansion done by producer \(i\) (MW)

\(R^S_{i,\omega }\)

Spot revenue earned by producer \(i\) in scenario \(\omega \) ($)

\(\zeta _i\)

Value-at-risk (VaR) of producer \(i\) ($)

\(\eta _{i,\omega }\)

Auxiliary variable that varies with scenario \(\omega \) used to calculate the CVaR of producer \(i\)

Parameters

\(\pi _\omega \)

Probability of scenario \(\omega \)

\(\lambda ^{S0}_\omega \)

Intercept of the inverse spot demand curve in scenario \(\omega \) ($/MW)

\(\gamma \)

Slope of the inverse spot demand curve ($/MW\(^2\))

\(\lambda ^F_n\)

Forward price of power in block \(n\) ($/MW)

\(c^G_{1,i}\)

Linear coefficient of cost function for producer \(i\) ($/MW)

\(c^G_{2,i}\)

Quadratic coefficient of cost function for producer \(i\) ($/MW\(^2\))

\(P^{max}_i\)

Maximum initial generating capacity of producer \(i\) (MW)

\(Q^F_{i,n}\)

Maximum quantity of forward sales by producer \(i\) in block \(n\) (MW)

\(\bar{\Delta }_i\)

Maximum capacity expansion permitted for producer \(i\) (MW)

\(c^E_i\)

Per-unit cost of expansion for producer \(i\) ($/MW)

\(\alpha \)

Confidence level used for calculation of CVaR

\(\beta _i\)

Measure of risk aversion of producer \(i\)

Dual variables

\(\phi _{i,\omega }\)

Dual price for capacity constraint of producer \(i\) in scenario \(\omega \) ($/MW)

\(\rho _i\)

Dual price for expansion constraint of producer \(i\) ($/MW)

\(\theta _{i,\omega }\)

Dual price of the constraint imposed to calculate the CVaR of producer \(i\) in scenario \(\omega \)

\(\delta _{i,n}\)

Dual price of the forward block-quantity constraint for producer \(i\) in block \(n\) ($/MW)

References

  1. Allaz B (1992) Oligopoly, uncertainty and strategic forward transactions. Int J Ind Org 10(2):297–308CrossRefGoogle Scholar
  2. Allaz B, Vila J-L (1993) Cournot competition, forward markets and efficiency. J Econ Theory 59(1):1–16CrossRefGoogle Scholar
  3. Baringo L, Conejo AJ (2011) Wind power investment within a market environment. Appl Energy 88(9):3239–3247CrossRefGoogle Scholar
  4. Conejo AJ, García-Bertrand R, Carrión M, Caballero Á, de Andres A (2008) Optimal involvement in futures markets of a power producer. IEEE Trans Power Syst 23(3):703–711CrossRefGoogle Scholar
  5. Conejo AJ, Carrión M, Morales JM (2010) Decision making under uncertainty in electricity markets. Springer, BerlinCrossRefGoogle Scholar
  6. Ehrenmann A, Smeers Y (2011) Generation capacity expansion in a risky environment: a stochastic equilibrium analysis. Oper Res 59(6):1332–1346CrossRefGoogle Scholar
  7. Eldor R, Zilcha I (1990) Oligopoly, uncertain demand, and forward markets. J Econ Bus 42(1):17–26CrossRefGoogle Scholar
  8. Gabriel SA, Conejo AJ, Fuller JD, Hobbs BF, Ruiz C (2012) Complementarity modeling in energy markets. Springer, BerlinGoogle Scholar
  9. Gabriel SA, Kiet S, Zhuang J (2005) A mixed complementarity-based equilibrium model of natural gas markets. Oper Res 53(5):799–818CrossRefGoogle Scholar
  10. Gabriel SA, Zhuang J, Kiet S (2005) A large-scale linear complementarity model of the North American natural gas market. Energy Econ 27(4):639–665CrossRefGoogle Scholar
  11. Green R (1999) The electricity contract market in England and Wales. J Ind Econ 47(1):107–124CrossRefGoogle Scholar
  12. Green R, Newbery D (1992) Competition in the British electricity spot market. J Polit Econ 100(5):929–953CrossRefGoogle Scholar
  13. Hobbs BF (2001) Linear complementarity models of Nash–Cournot competition in bilateral and POOLCO power markets. IEEE Trans Power Syst 16(2):194–202CrossRefGoogle Scholar
  14. Kazempour SJ, Conejo AJ, Ruiz C (2012) Strategic generation investment considering futures and spot markets. IEEE Trans Power Syst 27(3):1467–1476CrossRefGoogle Scholar
  15. Klemperer PD, Meyer MM (1989) Supply function equilibria in oligopoly under uncertainty. Econometrica 57(6):1243–1277CrossRefGoogle Scholar
  16. Murphy F, Smeers Y (2005) Generation capacity expansion in imperfectly competitive restructured electricity markets. Oper Res 53(4):646–661CrossRefGoogle Scholar
  17. Pineda S, Conejo AJ, Carrión M (2010) Insuring unit failures in electricity markets. Energy Econ 32(6):1268–1276CrossRefGoogle Scholar
  18. Rockafellar RT, Uryasev S (2002) Conditional value-at-risk for general loss distributions. J Bank Financ 26(7):1443–1471CrossRefGoogle Scholar
  19. Ruiz C, Conejo AJ (2009) Pool strategy of a producer with endogenous formation of locational marginal prices. IEEE Trans Power Syst 24(4):1855–1866CrossRefGoogle Scholar
  20. Ventosa M, Denis R, Redondo C (2002) Expansion planning in electricity markets. Two different approaches. In: Proceedings of the 14th Power Systems Computation Conference, session 43–4, pp 1–8. ISBN: 84-89673-25-X, Seville (24–28 June 2002)Google Scholar
  21. Wogrin S, Barquín J, Centeno E (2013) Capacity expansion equilibria in liberalized electricity markets: an EPEC approach. IEEE Trans Power Syst (forthcoming)Google Scholar
  22. Wolak F (2000) An empirical analysis of the impact of hedge contracts on bidding behavior in a competitive electricity market. Int Econ J 14(2):1–39Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Statistical ScienceUniversity College London LondonUK
  2. 2.Department of Computer and Systems SciencesStockholm University StockholmSweden

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