Risk-Based Purchasing Energy for Electricity Consumers by Retailer Using Information Gap Decision Theory Considering Demand Response Exchange

  • Ramin NourollahiEmail author
  • Sayyad Nojavan
  • Kazem Zare


Electricity retailer using demand response (DR) programs can reduce their cost in procuring consumers energy. In this chapter, several new demand response schemes are proposed to reduce retailer cost. These new schemes include pool-order DR, forward DR, and reward-base DR. Information gap decision theory (IGDT) technique is proposed to handle the pool market price uncertainty. Furthermore, optimal bidding strategy of electricity retailer is obtained using IGDT technique based on opportunity and robustness functions. Optimal bidding strategy provides stepwise power price in the power price uncertainty condition for submiting to day-ahead market in order to purchase power from pool market. The proposed model based on IGDT technique can be solved using standard Branch and Bound (SBB) solver under GAMS software.


Forward, pool-order, and reward-base DR programs Information gap decision theory (IGDT) Optimal bidding strategy of electricity retailer 




Minimum expected cost of retailer


Critical cost for opportunity function


Critical cost for robustness function


Time period

\( {f}_{po}^{\mathrm{pen}}(t) \)

Penalty of not running pool-order DR in time period t

\( {P}_{f,b}^{\mathrm{DR},\operatorname{MAX}}(t) \)

Highest demand in block b of forward DR f in time period t

\( {P}_{f,b}^{\mathrm{MAX}}(t) \)

Highest demand in block b of forward contract in time period t

\( {\overline{P}}_j^{\mathrm{DR}}(t) \)

Demand in jth step of reward-base DR in time period t

\( {P}_{po}^{\mathrm{MAX}}(t) \)

Highest demand in pool-order DR in time period t


Value of purchased power by retailer in period t

\( {\overline{R}}_j^{\mathrm{DR}}(t) \)

Highest value in jth step of reward-base DR in time period t


Price of pool-order DR in period t

\( {\lambda}_{f,b}^{\mathrm{DR}}(t) \)

Price of block b of forward DR f option in time period t

\( {\lambda}_{f,b}^{\mathrm{F}}(t) \)

Price of the block b of forward contract f in time period t

\( {\tilde{\lambda}}^{\mathrm{p}}(t) \)

Forecasted pool market price


Percentage increase in cost for retailer


Percentage decrease in cost for retailer



Number of blocks in forward DR


Number of forward contracts


Number of blocks in forward contracts


Number of contract in forward DR


Number of steps in reward-base DR


Number of pool-order options



Total cost of forward contracts


Total cost of forward DR program


Total cost of pool-order options


Total cost of power procurement from pool market


Total cost of reward-base DR


Purchased power from reward-base DR in time period t


Purchased power from the pool market in time period t


Purchased power from pool-order in time period t

\( {P}_{f,b}^{\mathrm{DR}}(t) \)

Purchased power from block b of forward DR f in time period t

\( {P}_{f,b}^{\mathrm{F}}(t) \)

Purchased power from block b of forward contract f in time periodt


Value of reward in time period t

\( {R}_j^{\mathrm{DR}}(t) \)

Value of reward of step j in time period t

vDR, j(t)

Binary variable that shows which step is executed in time period t


Binary variable which is 1 if pool-order is run in time period t


Actual pool market price


C(p, λ)

Procurement cost function of retailer

\( \hat{\alpha}\left({C}_{\mathrm{r}}\right) \)

Robustness function

\( \hat{\beta}\left({C}_{\mathrm{o}}\right) \)

Opportunity function


  1. 1.
    S. Nojavan, K. Zare, B. Mohammadi-Ivatloo, Risk-based framework for supplying electricity from renewable generation-owning retailers to price-sensitive customers using information gap decision theory. Int. J. Electr. Power Energy Syst. 93, 156–170 (2017)CrossRefGoogle Scholar
  2. 2.
    M. Marzband, M.H. Fouladfar, M.F. Akorede, G. Lightbody, E. Pouresmaeil, Framework for smart transactive energy in home-microgrids considering coalition formation and demand side management. Sustain. Cities Soc. 40, 136–154 (2018)CrossRefGoogle Scholar
  3. 3.
    S. Nojavan, K. Zare, B. Mohammadi-Ivatloo, Selling price determination by electricity retailer in the smart grid under demand side management in the presence of the electrolyser and fuel cell as hydrogen storage system. Int. J. Hydrogen Energy 42(5), 3294–3308 (2017)CrossRefGoogle Scholar
  4. 4.
    S. Nojavan, M. Mehdinejad, K. Zare, B. Mohammadi-Ivatloo, Energy procurement management for electricity retailer using new hybrid approach based on combined BICA–BPSO. Int. J. Electr. Power Energy Syst. 73, 411–419 (2015)CrossRefGoogle Scholar
  5. 5.
    M. Nazari, A.A. Foroud, Optimal strategy planning for a retailer considering medium and short-term decisions. Int J. Electr Power Energy Syst. 45(1), 107–116 (2013)CrossRefGoogle Scholar
  6. 6.
    S.A. Gabriel, A.J. Conejo, M.A. Plazas, S. Balakrishnan, Optimal price and quantity determination for retail electric power contracts. IEEE Trans. Power Syst. 21(1), 180–187 (2006)CrossRefGoogle Scholar
  7. 7.
    M. Carrion, A.J. Conejo, J.M. Arroyo, Forward contracting and selling price determination for a retailer. IEEE Trans. Power Syst. 22(4), 2105–2114 (2007)CrossRefGoogle Scholar
  8. 8.
    J. Kettunen, A. Salo, D.W. Bunn, Optimization of electricity retailer’s contract portfolio subject to risk preferences. IEEE Trans. Power Syst. 25(1), 117–128 (2010)CrossRefGoogle Scholar
  9. 9.
    A.R. Hatami, H. Seifi, M.K. Sheikh-El-Eslami, Optimal selling price and energy procurement strategies for a retailer in an electricity market. Electr. Power Syst. Res. 79(1), 246–254 (2009)CrossRefGoogle Scholar
  10. 10.
    A. Ahmadi, M. Charwand, J. Aghaei, Risk-constrained optimal strategy for retailer forward contract portfolio. Int. J. Electr. Power Energy Syst. 53, 704–713 (2013)CrossRefGoogle Scholar
  11. 11.
    A. Hatami, H. Seifi, M.K. Sheikh-El-Eslami, A stochastic-based decision-making framework for an electricity retailer: time-of-use pricing and electricity portfolio optimization. IEEE Trans. Power Syst. 26(4), 1808–1816 (2011)CrossRefGoogle Scholar
  12. 12.
    R. Garcia-Bertrand, Sale prices setting tool for retailers. IEEE Trans. Smart Grid 4(4), 2028–2035 (2013)CrossRefGoogle Scholar
  13. 13.
    M. Carrion, J.M. Arroyo, A.J. Conejo, A bilevel stochastic programming approach for retailer futures market trading. IEEE Trans. Power Syst. 24(3), 1446–1456 (2009)CrossRefGoogle Scholar
  14. 14.
    M. Charwand, Z. Moshvash, Midterm decision-making framework for an electricity retailer based on information gap decision theory. Int. J. Electr. Power Energy Syst. 63, 185–195 (2014)CrossRefGoogle Scholar
  15. 15.
    M.H. Albadi, E.F. El-Saadany, A summary of demand response in electricity markets. Electr. Power Syst. Res. 78(11), 1989–1996 (2008)CrossRefGoogle Scholar
  16. 16.
    P. Fazlalipour, M. Ehsan, B. Mohammadi-Ivatloo, Optimal participation of low voltage renewable micro-grids in energy and spinning reserve markets under price uncertainties. Int. J. Electr. Power Energy Syst. 102, 84–96 (2018)CrossRefGoogle Scholar
  17. 17.
    V. Oboskalov, T. Panikovskaya, Bid strategy under price uncertainty, in Power and Electrical Engineering of Riga Technical University (RTUCON), 2014 55th International Scientific Conference on 2014 Oct 14 (pp. 251–254). IEEEGoogle Scholar
  18. 18.
    F. Ziel, R. Steinert, Probabilistic mid-and long-term electricity price forecasting. Renew. Sustain. Energy Rev. 94, 251–266 (2018)CrossRefGoogle Scholar
  19. 19.
    D.S. Kirschen, G. Strbac, P. Cumperayot, D. de Paiva Mendes, Factoring the elasticity of demand in electricity prices. IEEE Trans. Power Syst. 15(2), 612–617 (2000)CrossRefGoogle Scholar
  20. 20.
    H.A. Aalami, M.P. Moghaddam, G.R. Yousefi, Modeling and prioritizing demand response programs in power markets. Electr. Power Syst. Res. 80(4), 426–435 (2010)CrossRefGoogle Scholar
  21. 21.
    H. Zhong, L. Xie, Q. Xia, Coupon incentive-based demand response: theory and case study. IEEE Trans. Power Syst. 28(2), 1266–1276 (2013)CrossRefGoogle Scholar
  22. 22.
    P.K. Adom, M. Insaidoo, M.K. Minlah, A.M. Abdallah, Does renewable energy concentration increase the variance/uncertainty in electricity prices in Africa? Renew. Energy 107, 81–100 (2017)CrossRefGoogle Scholar
  23. 23.
    V. Fanelli, L. Maddalena, S. Musti, Asian options pricing in the day-ahead electricity market. Sustain. Cities Soc. 27, 196–202 (2016)CrossRefGoogle Scholar
  24. 24.
    A.H. Mohsenian-Rad, V.W. Wong, J. Jatskevich, R. Schober, A. Leon-Garcia, Autonomous demand-side management based on game-theoretic energy consumption scheduling for the future smart grid. IEEE Trans. Smart Grid 1(3), 320–331 (2010)CrossRefGoogle Scholar
  25. 25.
    L. Gelazanskas, K.A. Gamage, Demand side management in smart grid: a review and proposals for future direction. Sustain. Cities Soc. 11, 22–30 (2014)CrossRefGoogle Scholar
  26. 26.
    A. Sheikhi, M. Rayati, A.M. Ranjbar, Demand side management for a residential customer in multi-energy systems. Sustain. Cities Soc. 22, 63–77 (2016)CrossRefGoogle Scholar
  27. 27.
    F.C. Robert, G.S. Sisodia, S. Gopalan, A critical review on the utilization of storage and demand response for the implementation of renewable energy microgrids. Sustain. Cities Soc. 40, 735–745 (2018)CrossRefGoogle Scholar
  28. 28.
    H. Shakouri, A. Kazemi, Multi-objective cost-load optimization for demand side management of a residential area in smart grids. Sustain. Cities Soc. 32, 171–180 (2017)CrossRefGoogle Scholar
  29. 29.
    S. Nojavan, K. Zare, B. Mohammadi-Ivatloo, Optimal stochastic energy management of retailer based on selling price determination under smart grid environment in the presence of demand response program. Appl. Energy 187, 449–464 (2017)CrossRefGoogle Scholar
  30. 30.
    A.J. Conejo, J.M. Morales, L. Baringo, Real-time demand response model. IEEE Trans. Smart Grid 1(3), 236–242 (2010)CrossRefGoogle Scholar
  31. 31.
    E. Celebi, J.D. Fuller, Time-of-use pricing in electricity markets under different market structures. IEEE Trans. Power Syst. 27(3), 1170–1181 (2012)CrossRefGoogle Scholar
  32. 32.
    L. Kreuder, C. Spataru, Assessing demand response with heat pumps for efficient grid operation in smart grids. Sustain. Cities Soc. 19, 136–143 (2015)CrossRefGoogle Scholar
  33. 33.
    F. Sehar, M. Pipattanasomporn, S. Rahman, Integrated automation for optimal demand management in commercial buildings considering occupant comfort. Sustain. Cities Soc. 28, 16–29 (2017)CrossRefGoogle Scholar
  34. 34.
    C. Eid, E. Koliou, M. Valles, J. Reneses, R. Hakvoort, Time-based pricing and electricity demand response: existing barriers and next steps. Utilities Policy 40, 15–25 (2016)CrossRefGoogle Scholar
  35. 35.
    P. Guo, V.O. Li, J.C. Lam, Smart demand response in China: challenges and drivers. Energy Policy 107, 1–10 (2017)CrossRefGoogle Scholar
  36. 36.
    D.T. Nguyen, M. Negnevitsky, M. De Groot, Pool-based demand response exchange—concept and modeling. IEEE Trans. Power Syst. 26(3), 1677–1685 (2011)CrossRefGoogle Scholar
  37. 37.
    D.T. Nguyen, M. Negnevitsky, M. de Groot, Walrasian market clearing for demand response exchange. IEEE Trans. Power Syst. 27(1), 535–544 (2012)CrossRefGoogle Scholar
  38. 38.
    O. Sezgen, C.A. Goldman, P. Krishnarao, Option value of electricity demand response. Energy 32(2), 108–119 (2007)CrossRefGoogle Scholar
  39. 39.
    J.Y. Joo, S.H. Ahn, Y.T. Yoon, J.W. Choi, Option valuation applied to implementing demand response via critical peak pricing, in Power Engineering Society General Meeting, 2007. IEEE 2007 Jun 24 (pp. 1–7). IEEEGoogle Scholar
  40. 40.
    R. Tyagi, J.W. Black, J. Petersen, Optimal scheduling of demand response events using options valuation methods, in Power and Energy Society General Meeting, 2011 IEEE 2011 Jul 24 (pp. 1–5). IEEEGoogle Scholar
  41. 41.
    S.C. Oh, J.B. D’Arcy, J.F. Arinez, S.R. Biller, A.J. Hildreth, Assessment of energy demand response options in smart grid utilizing the stochastic programming approach, in Power and Energy Society General Meeting, 2011 IEEE 2011 Jul 24 (pp. 1–5). IEEEGoogle Scholar
  42. 42.
    S. Pal, S. Thakur, R. Kumar, B.K. Panigrahi, A strategical game theoretic based demand response model for residential consumers in a fair environment. Int. J. Electr. Power Energy Syst. 97, 201–210 (2018)CrossRefGoogle Scholar
  43. 43.
    M. Jin, W. Feng, C. Marnay, C. Spanos, Microgrid to enable optimal distributed energy retail and end-user demand response. Appl. Energy 210, 1321–1335 (2018)CrossRefGoogle Scholar
  44. 44.
    A.R. Hatami, H. Seifi, M.K. Sheikh-El-Eslami, Hedging risks with interruptible load programs for a load serving entity. Decis. Support Syst. 48(1), 150–157 (2009)CrossRefGoogle Scholar
  45. 45.
    R. Baldick, S. Kolos, S. Tompaidis, Interruptible electricity contracts from an electricity retailer’s point of view: valuation and optimal interruption. Oper. Res. 54(4), 627–642 (2006)zbMATHCrossRefGoogle Scholar
  46. 46.
    M. Carrion, A.B. Philpott, A.J. Conejo, J.M. Arroyo, A stochastic programming approach to electric energy procurement for large consumers. IEEE Trans. Power Syst. 22(2), 744–754 (2007)CrossRefGoogle Scholar
  47. 47.
    A.A. Algarni, K. Bhattacharya, A generic operations framework for discos in retail electricity markets. IEEE Trans. Power Syst. 24(1), 356–367 (2009)CrossRefGoogle Scholar
  48. 48.
    H. Li, Y. Li, Z. Li, A multiperiod energy acquisition model for a distribution company with distributed generation and interruptible load. IEEE Trans. Power Syst. 22(2), 588–596 (2007)CrossRefGoogle Scholar
  49. 49.
    I. Horowitz, C.K. Woo, Designing pareto-superior demand-response rate options. Energy 31(6), 1040–1051 (2006)CrossRefGoogle Scholar
  50. 50.
    S. Nojavan, B. Mohammadi-Ivatloo, K. Zare, Robust optimization based price-taker retailer bidding strategy under pool market price uncertainty. Int. J. Electr. Power Energy Syst. 73, 955–963 (2015)CrossRefGoogle Scholar
  51. 51.
    S. Nojavan, B. Mohammadi-Ivatloo, K. Zare, Optimal bidding strategy of electricity retailers using robust optimisation approach considering time-of-use rate demand response programs under market price uncertainties. IET Gener. Transm. Dis. 9(4), 328–338 (2015)CrossRefGoogle Scholar
  52. 52.
    A.K. David, Competitive bidding in electricity supply, in IEE Proceedings C (Generation, Transmission and Distribution) 1993 Sep 1 (Vol. 140, No. 5, pp. 421–426). IET Digital LibraryGoogle Scholar
  53. 53.
    F. Wen, A.K. David, Optimal bidding strategies and modeling of imperfect information among competitive generators. IEEE Trans. Power Syst. 16(1), 15–21 (2001)CrossRefGoogle Scholar
  54. 54.
    J.V. Kumar, D.V. Kumar, Optimal bidding strategy in an open electricity market using genetic algorithm. Int. J. Adv. Soft Comput. Appl. 3(1), 55–67 (2011)Google Scholar
  55. 55.
    S.N. Singh, I. Erlich, Strategies for wind power trading in competitive electricity markets. IEEE Trans. Energy Convers. 23(1), 249–256 (2008)CrossRefGoogle Scholar
  56. 56.
    T. Joshi, G. Uberoi, Graphical scheme for determination of market clearing price using quadratic bid functions. Int. J. Adv. Eng. Technol. 1(2), 144 (2011)Google Scholar
  57. 57.
    L. Ma, W. Fushuan, A.K. David, A preliminary study on strategic bidding in electricity markets with step-wise bidding protocol, in Transmission and Distribution Conference and Exhibition 2002: Asia Pacific. IEEE/PES 2002 Oct 6 (Vol. 3, pp. 1960–1965). IEEEGoogle Scholar
  58. 58.
    N. Mahmoudi, M. Eghbal, T.K. Saha, Employing demand response in energy procurement plans of electricity retailers. Int. J. Electr. Power Energy Syst. 63, 455–460 (2014)CrossRefGoogle Scholar
  59. 59.
    J.C. Hull, S. Basu, Options, Futures, and Other Derivatives (Pearson Education India, Noida, 2016)Google Scholar
  60. 60.
    D.S. Kirschen, G. Strbac, Fundamentals of Power System Economics (Wiley, New York, 2004), p. 22CrossRefGoogle Scholar
  61. 61.
    N. Mahmoudi, T.K. Saha, M. Eghbal, Developing a scenario-based demand response for short-term decisions of electricity retailers, in Power and Energy Society General Meeting (PES), 2013 IEEE 2013 Jul 21 (pp. 1–5). IEEEGoogle Scholar
  62. 62.
    Y. Chen, J. Li, Comparison of security constrained economic dispatch formulations to incorporate reliability standards on demand response resources into Midwest ISO co-optimized energy and ancillary service market. Electr. Power Syst. Res. 81(9), 1786–1795 (2011)CrossRefGoogle Scholar
  63. 63.
    C.L. Su, D. Kirschen, Quantifying the effect of demand response on electricity markets. IEEE Trans. Power Syst. 24(3), 1199–1207 (2009)CrossRefGoogle Scholar
  64. 64.
    Y. Ben-Haim, Information Gap Decision Theory, Designs Under Severe Uncertainty (Academic, San Diego, 2001)zbMATHGoogle Scholar
  65. 65.
    K. Bhattacharya, Competitive framework for procurement of interruptible load services. IEEE Trans. Power Syst. 18(2), 889–897 (2003)CrossRefGoogle Scholar
  66. 66.
    T.F. Lee, M.Y. Cho, Y.C. Hsiao, P.J. Chao, F.M. Fang, Optimization and implementation of a load control scheduler using relaxed dynamic programming for large air conditioner loads. IEEE Trans. Power Syst. 23(2), 691–702 (2008)CrossRefGoogle Scholar
  67. 67.
    AEMO price & demand Data [Online],
  68. 68.
    AER, State of the Energy Market, Melbourn, Australia (2011)Google Scholar
  69. 69.
    Power of choice-giving consumers options in the way they use electricity, Direction Paper, March, 2012Google Scholar
  70. 70.
    The GAMS Software Website; 2016 [Online], <>

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Faculty of Electrical and Computer EngineeringUniversity of TabrizTabrizIran
  2. 2.Department of Electrical EngineeringUniversity of BonabBonabIran

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