A Stochastic Bilevel Scheduling Model for the Determination of the Load Shifting and Curtailment in Demand Response Programs

  • Rad, Ali Shayegan (MAPNA Electric and Control, Engineering & Manufacturing Co. (MECO), Mapna Group.) ;
  • Zangeneh, Ali (Electrical Engineering Department, Shahid Rajaee Teacher Training University)
  • Received : 2016.11.18
  • Accepted : 2018.01.19
  • Published : 2018.05.01


Demand response (DR) programs give opportunity to consumers to manage their electricity bills. Besides, distribution system operator (DSO) is interested in using DR programs to obtain technical and economic benefits for distribution network. Since small consumers have difficulties to individually take part in the electricity market, an entity named demand response provider (DRP) has been recently defined to aggregate the DR of small consumers. However, implementing DR programs face challenges to fairly allocate benefits and payments between DRP and DSO. This paper presents a procedure for modeling the interaction between DRP and DSO based on a bilevel programming model. Both DSO and DRP behave from their own viewpoint with different objective functions. On the one hand, DRP bids the potential of DR programs, which are load shifting and load curtailment, to maximize its expected profit and on the other hand, DSO purchases electric power from either the electricity market or DRP to supply its consumers by minimizing its overall cost. In the proposed bilevel programming approach, the upper level problem represents the DRP decisions, while the lower level problem represents the DSO behavior. The obtained bilevel programming problem (BPP) is converted into a single level optimizing problem using its Karush-Kuhn-Tucker (KKT) optimality conditions. Furthermore, point estimate method (PEM) is employed to model the uncertainties of the power demands and the electricity market prices. The efficiency of the presented model is verified through the case studies and analysis of the obtained results.


  1. Boisvert R. N, Cappers P. A., and Neenan B, "The benefits of consumer participation in wholesale electricity markets," Electr. J., vol. 15, no. 3, pp. 41-51, Apr. 2002.
  2. M. Rastegar, M. Fotuhi-Firuzabad and J. Choi, "Investigating the Impacts of Different Price-Based Demand Response Programs on Home Load Management," J Electr Eng Technol, vol. 9, no. 3, 1125-1131, 2014.
  3. J.-R. Won and K.-B. Song, "An Analysis on Power Demand Reduction Effects of Demand Response Systems in the Smart Grid Environment in Korea," J Electr Eng Technol, Vol. 8, No. 6: 1296-1304, 2013.
  4. Kirschen D. S, "Demand-side view of electricity markets," IEEE Trans. Power Syst., vol. 18, no. 2, pp. 520-527, May 2003.
  5. Gkatzikis L, Koutsopoulos I, Salonidis T, "The Role of Aggregators in Smart Grid Demand Response Markets," IEEE Journal on Selected Areas in Communications, vol. 31, no. 7, July 2013.
  6. Zakariazadeh A, Jadid S, Siano P, "Economic-environmental energy and reserve scheduling of smart distribution system: A multiobjective mathematical programming approach," Energy Conversion and Management, vol. 78, pp. 151-64, 2014.
  7. Alipour M, Zare K, Mohammadi-Ivatloo B, "Optimal risk-constrained participation of industrial cogeneration systems in the day-ahead energy markets," Renew Sustain Energy Rev 2016; 60, pp. 421-32.
  8. Dempe S, Foundations of Bilevel Programming. Dordrecht The Netherlands: Kluwer, 2002.
  9. Carrion M, Arroyo J. M, A. Conejo J, "A Bilevel Stochastic Programming Approach for Retailer Futures Market Trading," IEEE Trans, Power Syst., vol. 24, no. 3, pp. 1446-1456, 2009.
  10. Zugno M, Morales J.M, Pinson P, Madsen H, "A bilevel model for electricity retailers' participation in a demand response market environment," Energy Econ 36 (2013) pp. 182-197.
  11. Saebi J, Javidi M. H, Nguyen D. T, "Integrating demand response market into energy/reserve market: A bilevel approach," IEEE, pp. 5-14, 2014.
  12. Mahmoudi N, Saha T.K, Eghbal M, "Modelling demand response aggregator behavior in wind power offering strategies," Applied Energy 133(2014), pp. 347-355.
  13. El-Khattan W, Bhattacharya K, Hegazy Y, Salama M. M. A, "Optimal investment planning for distributed generation in a competitive electricity market," IEEE Trans. Power Syst., vol. 20, no. 4, pp. 1718-1727, 2005.
  14. Lopez-Lezama J. M, Padilha-Feltrin A, Contreras J, Munoz J. I, "Optimal contract pricing of distributed generation in distribution networks," IEEE Trans. Power Syst., vol. 26, no. 1, pp. 128-136, 2011.
  15. Mohseni Bonab SM, Rabiee A, Mohammadi-Ivatloo B, Jalilzadeh S, Nojavan S, "A two-point estimate method for uncertainty modeling in multi-objective optimal reactive power dispatch problem," Electrical Power and Energy Systems, vol. 75, no. 1, pp. 194-204, 2016.
  16. Morales J. M, Perez-Ruiz J, "Point estimate schemes to solve the probabilistic power flow," IEEE Trans Power Syst., 22 (2007) pp. 1594-1601.
  17. European energy exchange: hourly contracts. [accessed 12.05.12].
  18. The GAMS Software Website [online], Available from: