Load shifting demand response in energy scheduling based on payment cost minimization auction mechanism

Document Type : Article


1 Department of Electrical Engineering, Kerman Graduate University of Technology, Kerman, Iran

2 Department of Electrical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran


Demand response (DR) is proven to be very efficacious for load mitigation especially in peak time period. On the other hand, DR facilitates both consumers, system operator as well as producers to moderate their payments while reducing system operating costs. Offer cost minimization is currently used as the clearing mechanism associated with locational marginal pricing scheme to determine the consumers’ payments. Such clearing and pricing mechanisms are inconsistent as the system costs is being minimized, while the payments are calculated based upon marginal prices. Payment cost minimization auction as a price-based clearing mechanism is envisaged to be an effective alternative to solve such a crucial issue. This paper shows how to include DR in PCM mechanism to further reduce the consumers’ payment. It facilitates utilizing price responsive consumers for load shifting DR in a PCM auction. The optimization problem is modeled as a mixed-integer nonlinear bi-level programming. Duality theorem, KKT conditions and integer algebra are used to convert such a complicated optimization problem to a single level MILP problem. This problem is then solved by CPLEX in GAMS. The impacts are studied by implementing the proposed formulation to solve the clearing problem in the case studies deriving promising numerical results.


1. U.S. Federal Energy Regulatory Commission Order No. 888, Promoting Wholesale Competition through Open Access Non-Discriminatory Transmission Services by Public Utilities; FERC: Washington, DC, USA (1996). Available online: http://www.ferc.gov/legal/maj-ord-reg/landdocs/ rm95-8-00v.txt.
2. Durvasulu, V. and Hansen, T. "Benefits of a demand response exchange participating in existing bulk-power markets", Energies, special issue on Demand Response in Electricity Markets, 11, pp. 1-3 (2018).
3. Hamian, M., Darvishan, A., Hosseinzadeh, M., et al. "A framework to expedite joint energy-reserve payment cost minimization using a custom-designed method based on mixed integer genetic algorithm", Eng. Appl. of AI, 72, pp. 203-212 (2018).
4. Luh, P.B, Blankson, W.E, Chen, Y., et al. "Payment cost minimization auction for deregulated electricity markets using surrogate optimization", IEEE Trans. Power Syst., 21(2), pp. 568-578 (2006).
5. Fernandez-Blanco, R., Arroyo, J.M., and Alguacil, N. "Network-constrained day-ahead auction for consumer payment minimization", IEEE Trans. Power Syst., 29(2), pp. 526-536 (2014).
6. Bragin, M.A., Han, X., Luh, P.B., et al. "Payment costminimization using Lagrangian relaxation and modified surrogate optimization approach", In Proc. IEEE Power Energy Soc. Gen. Meet., pp. 24-29 (2011).
7. Chang, T.S. "Comments on surrogate gradient algorithm for Lagrangian relaxation", J. Optim. Theory Appl., 137(3), pp. 691-697 (2008).
8. Vazquez, C., Rivier, M., and Perez-Arriaga, I.J. "Production cost minimization versus consumer payment minimization in electricity pools", IEEE Trans. Power Syst., 17(1), pp. 119-127 (2002).
9. Mendes, D.P. "Resource scheduling and pricing in a centralised energy market", In Proc. 14th Power Syst. Comput. Conf., Seville, Spain, pp. 1-7 (2002).
10. Fernandez-Blanco, R., Arroyo, J.M. and Alguacil, N. "A unified bilevel programming framework for pricebased market clearing under marginal pricing", IEEE Trans. Power Syst., 27(1), pp. 517-525 (2012).
11. Nouri, A. and Hosseini, S.H. "Payment minimisation auction with security constraints", IET Gener. Transm. Distrib, pp. 1370-1380 (2017).
12. Nouri, A. and Hosseini, S.H. "Comparison of LMPs' sensitivity under payment cost minimization and offer cost minimization mechanisms", IEEE Systems Journal, 9(4), pp. 1507-1518 (2015).
13. Nouri, A., Hosseini, S.H., and Keane, A. "Stochastic network constrained payment minimization in electricity markets", IET Gener. Transm. Distrib, 13(11), pp. 2268-2279 (2019).
14. Bizhaniaram, B. and Nouri, A. "Stochastic payment cost minimization in energy markets with high penetration of renewables", IEEE International Conference on Environment and Electrical Engineering and IEEE Industrial and Commercial Power Systems Europe (EEEIC/I&CPS Europe), Palermo, pp. 1-4 (2018).
15. Su, C.-L. "Optimal demand-side participation in dayahead electricity markets", Ph.D. Dissertation, University Manchester, Manchester, U.K. (2007).
16. Aalami, H.A., Moghaddam, M.P., and Yousefi, G.R. "Demand response modeling considering interruptible/ curtailable loads and capacity market programs", Appl. Energy, 87(1), pp. 243-250 (2010).
17. Nikzad, M., Mozafari, B., Bashirvand, M., et al. "Designing time-of-use program based on stochastic security constrained unit commitment considering reliability index", Energy, 41(1), p. 541 (2012).
18. Esmaili, M., Amjady, N., and Shayanfar, H.A. "Stochastic congestion management in power markets using efficient scenario approaches", Energy Convers. Manag., 51(11), pp. 2285-2293 (2010).
19. Rahmani-Andebili, M., Abdollahi A., and Moghaddam M.P. "An investigation of implementing emergency demand response programs (EDRP) in unit commitment problem", In Proc. IEEE PES Gen. Meeting, San Diego, CA, USA, pp. 1-7 (2011).
20. Zarei, E., Hemmatpour, M.H., and Mohammadian, M. "The effects of demand response on securityconstrained unit commitment", Scientia Iranica, Trans. D., 26(3), pp. 1627-1636 (2019).DOI: 10.24200/sci.2017.4536.
21. Ghahary, K., Abdollahi, A., Rashidinejad, M., et al. "Optimal reserve market clearing considering uncertain demand response using information gap decision theory", Int J Electr Power Energy Syst, 101, pp. 213- 22 (2018).
22. Parvania, M. and Fotuhi-Firuzabad, M. "Demand response scheduling by stochastic SCUC", IEEE Trans. Smart Grid, 1(1) pp. 89-98 (2010).
23. Abdollahi, A., Pour-Moallem, N., and Abdollahi, A. "Dynamic negawatt demand response resource modeling and prioritizing in power markets", Scientia Iranica, Trans. D., 27(3), pp. 1361-1372 (2020).DOI: 10.24200/sci.2017.4406.
24. Kirschen, D. and Su, C.L. "Quantifying the effect of demand response on electricity markets", IEEE Transactions on Power Systems, 24(3), pp. 1199-1207 (2009).
25. Hao, S. and Zhuang, F. "New models for integrated short-term forward electricity markets", IEEE Trans. Power Syst., 18(2), pp. 478-485 (2003).
26. Chen, Y, Luh, P.B., Yan. J.H., et al. "Payment minimization auction with demand bids and partial compensation of startup costs for deregulated electricity markets", Presented at the IEEE PES Gen. Meeting, San Francisco, CA, USA (2005).
27. Luh, P.B., Chen, Y., Blankson, W.E., et al. "Payment cost minimization with demand bids and partial capacity cost compensations for day-ahead electricity auctions", In Economic Market Design and Planning for Electric Power Systems, J. Momoh and L. Mili, Eds., Hoboken, NJ, USA: Wiley, pp. 71-85 (2010).
28. Fernandez-Blanco, R., Arroyo, J.M., Alguacil, N., et al. "Incorporating price-responsive demand in energy scheduling based  on consumer payment minimization", IEEE Trans. Smart Grid, 7(2), pp. 817-826 (2016)
29. Bard, J.F., Practical Bilevel Optimization: Algorithms and Applications, Norwell, MA, USA: Kluwer (1998).
30. Arroyo, J.M. "Bilevel programming applied to power system vulnerability analysis under multiple contingencies", IET Gener. Transmiss Distrib., 4(2), pp. 178-190 (2010).
31. Nemhauser, G.L. and Wolsey, L.A., Integer and Combinatorial Optimization, Hoboken, NJ, USA: Wiley (1999).
32. Zhao, F., Luh, P.B., Yan, J.H., et al. "Payment cost minimization auction for deregulated electricity markets with transmission capacity constraints", IEEE Trans. Power Syst., 23(2), pp. 532-544 (2008).
33. Fernandez-Blanco, R., Arroyo, J.M., and Alguacil, N. "Network constrained day-ahead auction for consumer payment minimization", IEEE Trans. Power Syst., 29(2) , pp. 526-536 (2014).
34. Arroyo, J.M. "Bilevel programming applied to power system vulnerability analysis under multiple contingencies", IET Gener. Transmiss Distrib., 4(2), pp. 178-190 (2010).
35. Floudas, C.A., Nonlinear and Mixed-integer Optimization: Fundamentals and Applications, New York, NY, USA: Oxford University Press (1995).
36. Pereira, M.V., Granville, S., Fampa, M.H.C., et al. "Strategic bidding under uncertainty: A binary expansion approach", IEEE Trans. Power Syst., 20(1), pp. 180-188 (2005).
37. Horn, R.A. and Johnson, C.R., Matrix Analysis, 2nd Ed., NY, USA: Cambridge University Press (2012).
38. Grigg, C. "IEEE reliability test system", IEEE Trans. Power App. Syst., PAS-98(6), pp. 2047-2054 (1979).
39. The IBM ILOG CPLEX Website. Available: http://www-01.ibm.com/software/commerce/ optimization/cplex-optimizer.
40. The GAMS Development Corporation Website [Online]. Available: http://www.gams.com (2019).
41. Power Systems Test Case Archive, Dept. Elect. Eng., University Washington, Seattle, WA, USA, (2015). [Online]. Available: http://www.ee.washington.edu/research/pstca.
42. IEEE 118-Bus System (2015) [Online]. Available: http://motor.ece.iit.edu/data/Data 118 Bus.pdf.
Volume 29, Issue 5
Transactions on Computer Science & Engineering and Electrical Engineering (D)
September and October 2022
Pages 2450-2464