Optimal Stochastic Planning of DERs in a Game Theory Framework Considering Demand Response and Pollution Issues

  • Pouya SalyaniEmail author
  • Mehdi Abapour
  • Kazem Zare
  • Tohid Babri


Equipping the distribution network with distributed energy resources (DERs) provides a situation that can facilitate the energy delivery to the customers and cut a portion of the requirement to the energy purchased from upstream network. Furthermore, they have an essential effect on pollution reduction. Optimal DER planning under demand response programs (DRPs) can result in a cost-effective siting and sizing of these resources in the network. However, customers who participated in DRP follow their own motivation to increase their payoff. This issue leads to conflict between the planning decision of DisCo and consumption decision of customers. Therefore, by consideration of network uncertainties and modeling the problem in a Stackelberg framework, this paper introduces a new concept in probabilistic planning of distribution network. In addition, the planning in this paper has the concern of pollution and is in the perspective of CO2 emission reduction.


DER Distribution network planning Demand response Stackelberg CO2 emission 

List of Symbols


Set of buses


Set of scenarios


Planning horizon (year)


Number of hours in a day

\( {\varsigma}_i^{Dr} \)

Binary parameter that is 1 if ith customer is participated in DRP

\( {\varsigma}_i^{Du} \)

Binary parameter that is 1 if ith customer is not interested in DRP

\( {P}_{i,t,h,\omega}^{Dr} \)

Demand of ith DR customer in year t, hour h, and scenario ω

\( {P}_{i,t,h,\omega}^{Du} \)

Demand of ith DU customer in year t, hour h, and scenario ω


Capital cost of CHP ($/MW)


Maintenance cost of CHP ($/MWh)


Fuel cost of CHP ($/MWh)


Capital cost of WT ($/MW)


Maintenance cost of WT ($/MWh)


Capital cost of PV ($/MW)


Maintenance cost of PV ($/MWh)

\( {\xi}_i^{CHP} \)

Binary decision variable that is 1 if a CHP is installed in bus i

\( {\xi}_i^{WT} \)

Binary decision variable that is 1 if a WT is installed in bus i

\( {\xi}_i^{PV} \)

Binary decision variable that is 1 if a PV is installed in bus i

\( {P}_i^{CHP} \)

Rated power of CHP in bus i (MW)

\( {P}_{r,i}^{WT} \)

Rated power of WT in bus i (MW)

\( {P}_{r,i}^{PV} \)

Rated power of PV in bus i (MW)

\( {P}_{i,t,h,\omega}^{WT} \)

Power of WT in bus i, year t, hour h, and scenario ω (MW)

\( {P}_{i,t,h,\omega}^{PV} \)

Power of PV in bus i, year t, hour h, and scenario ω (MW)

\( {P}_{t,h,\omega}^{\mathrm{G}} \)

Purchased power from upstream network in year t, hour h, and scenario ω (MW)


Penalty of CO2 emission by conventional plants in the main grid ($/kWh)


Penalty of CO2 emission by CHP ($/kWh)

Vi, t, h, ω

Voltage of bus i in year t, hour h, and scenario ω (pu)

δi, t, h, ω

Voltage angle of bus i in year t, hour h, and scenario ω (rad)

\( {\lambda}_{i,t,h,\omega}^{Dr} \)

Energy selling price in year y, hour t, and scenarioω for ith DR customer ($/MWh)

\( {\lambda}_h^0 \)

Selling energy price to the entire customers in hour h

\( {\rho}_h^g \)

Energy price bought from upstream network in hour h

\( {E}_{i,t}^{Min} \)

Minimum energy consumption of ith DR customer in year t

\( {E}_{i,t}^{\mathrm{Max}} \)

Maximum energy consumption of ith DR customer in year t


Probability of scenario ω


Present worth factor in year t

inf _ r

Inflation rate

int _ r

Interest rate


Impedance between bus i and j


Total number of days in a year


Cut-in speed (m/s)


Rated speed (m/s)


Cut-out speed (m/s)


Maximum solar irradiation (m/s)


Power factor of CHP unit connected to bus i


Penalty multiplier for the Lagrangian function related to PCPM


  1. 1.
    R. Hemmati, H. Saboori, P. Siano, Coordinated short-term scheduling and long-term expansion planning in microgrids incorporating renewable energy resources and energy storage systems. J. Energy 134, 699–708 (2017)CrossRefGoogle Scholar
  2. 2.
    S.S. Tanwar, D.K. Khatod, Techno-economic and environmental approach for optimal placement and sizing of renewable DGs in distribution system. J. Energy 127, 52–67 (2017)CrossRefGoogle Scholar
  3. 3.
    M. Kumar, P. Nallagownden, I. Elamvazuthi, Optimal placement and sizing of renewable distributed generations and capacitor banks into radial distribution systems. J. Energy 10(6), 811 (2017)Google Scholar
  4. 4.
    J. Jung, M. Villaran, Optimal planning and design of hybrid renewable energy systems for microgrids. J. Renew. Sust. Energ. Rev. 75, 180–191 (2017)CrossRefGoogle Scholar
  5. 5.
    M.H. Amini, A. Islam, Allocation of electric vehicles’ parking lots in distribution network, (IEEE ISGT, 2014), pp. 1–5Google Scholar
  6. 6.
    M.J. Mirzaei, A. Kazemi, O. Homaee, A probabilistic approach to determine optimal capacity and location of electric vehicles parking lots in distribution networks. J. IEEE Trans. Ind. Inform. 12(5), 1963–1972 (2016)CrossRefGoogle Scholar
  7. 7.
    S. Shojaabadi, S. Abapour, M. Abapour, A. Nahavandi, Optimal planning of plug-in hybrid electric vehicle charging station in distribution network considering demand response programs and uncertainties. J. IET Gener. Transm. Dis 10(13), 3330–3340 (2016)CrossRefGoogle Scholar
  8. 8.
    M.R. Mozafar, M.H. Moradi, M.H. Amini, A simultaneous approach for optimal allocation of renewable energy sources and electric vehicle charging stations in smart grids based on improved GA-PSO algorithm. J. Sustain. Cities Soc. 32, 627–637 (2017)CrossRefGoogle Scholar
  9. 9.
    M.H. Amini, M.P. Moghaddam, O. Karabasoglu, Simultaneous allocation of electric vehicles’ parking lots and distributed renewable resources in smart power distribution networks. J. Sustain. Cities Soc. 28, 332–342 (2017)CrossRefGoogle Scholar
  10. 10.
    Z. Liu, F. Wen, G. Ledwich, Optimal planning of electric-vehicle charging stations in distribution systems. J. IEEE Trans. Power Delivery 28(1), 102–110 (2013)CrossRefGoogle Scholar
  11. 11.
    X. Lin et al., Distribution network planning integrating charging stations of electric vehicle with V2G. Int. J. Elect. Power 63, 507–512 (2014)CrossRefGoogle Scholar
  12. 12.
    F. Wang et al., Multi-objective optimization model of source–load–storage synergetic dispatch for a building energy management system based on tou price demand response. J. IEEE Trans. Indus. Appl. 54(2), 1017–1028 (2018)CrossRefGoogle Scholar
  13. 13.
    A. Asadinejad, K. Tomsovic, Optimal use of incentive and price based demand response to reduce costs and price volatility. J Elect. Power Syst. Res. 144, 215–223 (2017)CrossRefGoogle Scholar
  14. 14.
    A.S.O. Ogunjuyigbe, C.G. Monyei, T.R. Ayodele, Price based demand side management: a persuasive smart energy management system for low/medium income earners. J. Sustain. Cities Soc. 17, 80–94 (2015)CrossRefGoogle Scholar
  15. 15.
    A.H. Sharifi, P. Maghouli, Energy management of smart homes equipped with energy storage systems considering the PAR index based on real-time pricing. J. Sustain. Cities Soc. 45, 579–587 (2019)CrossRefGoogle Scholar
  16. 16.
    K. Saberi, H. Pashaei-Didani, R. Nourollahi, K. Zare, S. Nojavan, Optimal performance of CCHP based microgrid considering environmental issue in the presence of real time demand response. J. Sustain. Cities Soc. 45, 596–606 (2019)CrossRefGoogle Scholar
  17. 17.
    M.H. Imani, P. Niknejad, M.R. Barzegaran, The impact of customers’ participation level and various incentive values on implementing emergency demand response program in microgrid operation. Int. J. Elect. Power 96, 114–125 (2018)CrossRefGoogle Scholar
  18. 18.
    Q. Yang, X. Fang, Demand response under real-time pricing for domestic households with renewable DGs and storage. J. IET Gener. Transm. Dis. 11(8), 1910–1918 (2017)Google Scholar
  19. 19.
    A. Asadinejad, A. Rahimpour, K. Tomsovic, H. Qi, C.-f. Chen, Evaluation of residential customer elasticity for incentive based demand response programs. J. Elect. Power Syst. Res. 158, 26–36 (2018)CrossRefGoogle Scholar
  20. 20.
    E. Nekouei, T. Alpcan, D. Chattopadhyay, Game-theoretic frameworks for demand response in electricity markets. J. IEEE Trans. Smart Grid 6(2), 748–758 (2015)CrossRefGoogle Scholar
  21. 21.
    M. Yu, S.H. Hong, A real-time demand-response algorithm for smart grids: a stackelberg game approach. J. IEEE Trans. Smart Grid 7(2), 879–888 (2016)Google Scholar
  22. 22.
    P. Samadi, A.H.M. Rad, R. Schober, V.W.S. Wong, Advanced demand side management for the future smart grid using mechanism design. J. IEEE Trans. Smart Grid 3(3), 1170–1180 (2012)CrossRefGoogle Scholar
  23. 23.
    S. Fan, Q. Ai, L. Piao, Bargaining-based cooperative energy trading for distribution company and demand response. J. Appl. Energy 226, 469–482 (2018)CrossRefGoogle Scholar
  24. 24.
    A. Ghasemi, S.S. Mortazavi, E. Mashhour, Hourly demand response and battery energy storage for imbalance reduction of smart distribution company embedded with electric vehicles and wind farms. J. Renew. Energy 85, 124–136 (2016)CrossRefGoogle Scholar
  25. 25.
    S.-G. Yoon, Y.-J. Choi, J.-K. Park, S. Bahk, Stackelberg-game-based demand response for at-home electric vehicle charging. J. IEEE Trans. Vehicular Technol. 65(6), 4172–4184 (2016)CrossRefGoogle Scholar
  26. 26.
    Q. Zeng, B. Zhang, J. Fang, Z. Chen, A bi-level programming for multistage co-expansion planning of the integrated gas and electricity system. J. Appl. Energy 200, 192–203 (2017)CrossRefGoogle Scholar
  27. 27.
    G.E. Constante-Flores, M.S. Illindala, Data-driven probabilistic power flow analysis for a distribution system with renewable energy sources using Monte Carlo simulation. IEEE Trans. Ind. Appl. 55(1), 174–181 (2019)CrossRefGoogle Scholar
  28. 28.
    P. Salyani, J. Salehi, F.S. Gazijahani, Chance constrained simultaneous optimization of substations, feeders, renewable and non-renewable distributed generations in distribution network. Elect. Power Syst. Res. 158, 56–69 (2018)CrossRefGoogle Scholar
  29. 29.
    W. Shi, X. Xie, C.-C. Chu, R. Gadh, Distributed optimal energy management in microgrids. J. IEEE Trans. Smart Grid 6(3), 1137–1146 (2015)CrossRefGoogle Scholar
  30. 30.
    S. Bahrami, V.W.S. Wong, J. Huang, Data center demand response in deregulated electricity markets. IEEE Trans. on Smart Grid 10(3), 2820–2832 (2019)CrossRefGoogle Scholar
  31. 31.
    A. Ameli, S. Bahrami, F. Khazaeli, M.R. Haghifam, A multiobjective particle swarm optimization for sizing and placement of DGs from DG owner’s and distribution company’s viewpoints. IEEE Trans. Power Delivery 29(4), 1831–1840 (2014)CrossRefGoogle Scholar
  32. 32.
    L. Ju, Z. Tan, J. Yuan, Q. Tan, H. Li, F. Dong, A bi-level stochastic scheduling optimization model for a virtual power plant connected to a wind–photovoltaic–energy storage system considering the uncertainty and demand response. Appl. Energy 171, 184–199 (2016)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Pouya Salyani
    • 1
    Email author
  • Mehdi Abapour
    • 1
  • Kazem Zare
    • 1
  • Tohid Babri
    • 1
  1. 1.Faculty of Electrical and Computer EngineeringUniversity of TabrizTabrizIran

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