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access icon free Electricity market short-term risk management via risk-adjusted probability measures

© The Institution of Engineering and Technology
Received 31/10/2016, Accepted 17/03/2017, Revised 10/03/2017, Published 29/03/2017

This study presents an iterative algorithm for modelling the mean-risk model with the conditional value at risk (CVaR). The algorithm is based on the Lagrangian relaxation decomposition, and its main advantage is that it allows removing the coupling between the scenarios due to the constraints used to model the risk. At each stage of the algorithm, a risk-neutral stochastic optimisation problem is solved with the risk-adjusted probabilities that substitute the original ones. The study presents the application of the proposed iterative CVaR algorithm to two different short-term problems where the decision makers are exposed to a high volatility of electricity spot market prices. In the first problem, a time horizon of 1 week is taken into account and a future physical contract is employed as a hedging mechanism. The second problem includes a very detailed formulation of the unit commitment problem. The numerical application is based on realistic data of the Iberian electricity market, where the algorithm has shown a good performance in terms of accuracy and computational time. In addition, this study provides a criterion for selecting the value of the parameters used to implement the CVaR model.

Inspec keywords: iterative methods; risk management; power generation scheduling; probability; stochastic programming; power markets; power generation dispatch; relaxation theory

Other keywords: Lagrangian relaxation decomposition; numerical application; electricity spot market price; iterative CVaR algorithm; hedging mechanism; unit commitment problem; risk-neutral stochastic optimisation problem; risk-adjusted probability measures; Iberian electricity market; iterative algorithm; mean-risk model; electricity market short-term risk management; conditional value at risk

Subjects: Interpolation and function approximation (numerical analysis); Power system management, operation and economics; Other topics in statistics; Optimisation techniques

References

    1. 1)
      • 7. Künzi-Bay, A., Mayer, J.: ‘Computational aspects of minimizing conditional value-at-risk’, Comput. Manag. Sci., 2006, 3, (1), pp. 3–27.
    2. 2)
      • 13. Abad, C., Iyengar, G.: ‘Portfolio selection with multiple spectral risk constraints’, SIAM J. Finan. Math., 2015, 6, (1), pp. 467–486.
    3. 3)
      • 16. Morales-España, G., Ramos, A., García-González, J.: ‘An MIP formulation for joint market-clearing of energy and reserves based on ramp scheduling’, IEEE Trans. Power Syst., 2014, 29, (1), pp. 476–488.
    4. 4)
      • 25. Asensio, M., Contreras, J.: ‘Stochastic unit commitment in isolated systems with renewable penetration under CVaR assessment’, IEEE Trans. Smart Grid, 2016, 7, (3), pp. 1356–1367.
    5. 5)
      • 2. Artzner, P., Delbaen, F., Eber, J.M., et al: ‘Coherent measures of risk’, Math. Fin., 1999, 9, (3), pp. 203–228.
    6. 6)
      • 1. Birge, J.R., Louveaux, F.: ‘Introduction to stochastic programming’ (Springer Science & Business Media, 1997).
    7. 7)
      • 20. Chatterjee, R.: ‘Practical methods of financial engineering and risk management: tools for modern financial professionals’ (Apress, 2014).
    8. 8)
      • 23. Morales-España, G., Correa-Posada, C.M., Ramos, A.: ‘Tight and compact MIP formulation of configuration-based combined-cycle units’, IEEE Trans. Power Syst., 2016, 31, (2), pp. 1350–1359.
    9. 9)
      • 10. Noyan, N.: ‘Risk-averse two-stage stochastic programming with an application to disaster management’, Comput. Oper. Res., 2012, 39, (3), pp. 541–559.
    10. 10)
      • 14. Cerisola, S., Jovanović, N., García-González, J., et al: ‘Decomposing the mean risk problem: a Lagrangian Relaxation approach and its comparison with the Benders decomposition algorithm’. Working Paper, Institute for Research in Technology, ICAI School of Engineering, Comillas Pontifical University, Madrid, April 2016.
    11. 11)
      • 3. Rockafellar, R., Uryasev, S.: ‘Optimization of conditional value-at-risk’, J. Risk, 2000, 2, (3), pp. 21–41.
    12. 12)
      • 21. Padhy, N.P.: ‘Unit commitment-a bibliographical survey’, IEEE Trans. Power Syst., 2004, 19, (2), pp. 1196–1205.
    13. 13)
      • 5. Pineda, S., Conejo, A.J.: ‘Scenario reduction for risk-averse electricity trading’, IET Gener. Transm. Distrib., 2010, 4, (6), pp. 694–705.
    14. 14)
      • 8. Ahmed, S.: ‘Convexity and decomposition of mean-risk stochastic programs’, Math. Program., 2006, 106, (3), pp. 433–446.
    15. 15)
      • 22. Bavafa, F., Niknam, T., Azizipanah-Abarghooee, R., et al: ‘A new biobjective probabilistic risk-based wind-thermal unit commitment using heuristic techniques’, IEEE Trans. Ind. Inf., 2017, 13, (1), pp. 115–124.
    16. 16)
      • 11. Miller, N., Ruszczyński, A.: ‘Risk-adjusted probability measures in portfolio optimization with coherent measures of risk’, Eur. J. Oper. Res., 2008, 191, (1), pp. 193–206.
    17. 17)
      • 24. Zare, M., Niknam, T., Azizipanah-Abarghooee, R., et al: ‘New stochastic bi-objective optimal cost and chance of operation management approach for smart microgrid’, IEEE Trans. Ind. Inf., 2016, 12, (6), pp. 2031–2040.
    18. 18)
      • 12. Ehrenmann, A., Smeers, Y.: ‘Generation capacity expansion in a risky environment: a stochastic equilibrium analysis’, Oper. Res., 2011, 59, (6), pp. 1332–1346.
    19. 19)
      • 27. ‘Electricity market operator on the Iberian Peninsula’, 2015. http://www.omie.es/inicio, accessed September 2015.
    20. 20)
      • 4. Conejo, A.J., García-Bertrand, R., Carrion, M., et al: ‘Optimal involvement in futures markets of a power producer’, IEEE Trans. Power Syst., 2008, 23, (2), pp. 703–711.
    21. 21)
      • 9. Fábián, C.I.: ‘Handling CVaR objectives and constraints in two-stage stochastic models’, Eur. J. Oper. Res., 2008, 191, (3), pp. 888–911.
    22. 22)
      • 6. García-Bertrand, R., Mínguez, R.: ‘Iterative scenario based reduction technique for stochastic optimisation using conditional value-at-risk’, Optim. Eng., 2014, 15, (2), pp. 355–380.
    23. 23)
      • 26. ‘GAMS Home Page’, 2016. https://www.gams.com/, accessed May 2016.
    24. 24)
      • 17. Benders, J.F.: ‘Partitioning procedures for solving mixed-variables programming problems’, Numer. Math., 1962, 4, (1), pp. 238–252.
    25. 25)
      • 18. Nowak, I.: ‘Relaxation and decomposition methods for mixed integer nonlinear programming’ (Birkhäuser, Boston, MA, 2005).
    26. 26)
      • 19. Dantzig, G.B., Wolfe, P.: ‘Decomposition principle for linear programs’, Oper. Res., 1960, 8, (1), pp. 101–111.
    27. 27)
      • 15. Rockafellar, R., Uryasev, S., Zabarankin, M.: ‘Deviation measures in risk analysis and optimisation’. Technical Report, Research Report 2002–2007, Department of Industrial and Systems Engineering, University of Florida, December 2002.
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