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March  2020, 16(2): 777-793. doi: 10.3934/jimo.2018178

A real-time pricing scheme considering load uncertainty and price competition in smart grid market

1. 

School of Business, Qingdao University, Qingdao 266071, China

2. 

School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China

3. 

School of Management, University of Shanghai for Science and Technology, Shanghai 200093, China

Received  October 2017 Revised  July 2018 Published  March 2020 Early access  December 2018

As a powerful tool of Demand Response (DR) techniques in smart grid market, Real-time Pricing (RTP) may optimize the electricity consumption pattern of users and improve the efficiency of electricity market. In this paper, a multi-leader-follower Stackelberg Game (SG) based on RTP is established to model the strategic interaction behavior between multiple electricity retailers and multiple users while simultaneously considering the power load uncertainty of users and the price competition among electricity retailers. In the game model, electricity retailers aim to seek their revenue maximization while the optimal power consumption competition among the users is taken into account. Lagrange multiplier method is utilized to solve the Nash Equilibriums (NE) of two non-cooperative games, and the closed-form optimal solution is obtained, then the Stackelberg Equilibrium (SE) consisting of the optimal real-time prices of electricity retailers and the power consumption of users is given. Finally, the numerical analysis results verify that the proposed scheme can reduce the real-time electricity price and increase the users' satisfaction under feasible constraint, which shows the effectiveness and better performance of proposed RTP scheme.

Citation: Yeming Dai, Yan Gao, Hongwei Gao, Hongbo Zhu, Lu Li. A real-time pricing scheme considering load uncertainty and price competition in smart grid market. Journal of Industrial and Management Optimization, 2020, 16 (2) : 777-793. doi: 10.3934/jimo.2018178
References:
[1]

K. Alshehri, J. Liu, X. Chen and T. Basar, A Stackelberg game for multi-period demand response management in the smart grid, in IEEE Conference on Decision and Control, IEEE, (2015), 5889-5894. doi: 10.1109/CDC.2015.7403145.

[2]

A. Anees and Y. P. Chen, True real time pricing and combined power scheduling of electric appliances in residential energy management system, Applied Energy, 165 (2016), 592-600.  doi: 10.1016/j.apenergy.2015.12.103.

[3]

D. AusselR. Correa and M. Marechal, Electricity spot market with transmission losses, Management Optimization, 9 (2013), 275-290.  doi: 10.3934/jimo.2013.9.275.

[4]

R. Bo R and F. Li, Probabilistic LMP Forecasting considering load uncertainty, IEEE Transactions on Power Systems, 24 (2009), 1279-1289.  doi: 10.1109/TPWRS.2009.2023268.

[5] S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, Cambridge, 2004.  doi: 10.1109/TAC.2006.884922.
[6]

M. CarvalhoJ. P. Pedroso and J. Saraiva, Electricity day-ahead markets: Computation of Nash equilibria, Management Optimization, 11 (2015), 985-998.  doi: 10.3934/jimo.2015.11.985.

[7]

J. Chen, B. Yang and X. Guan, Optimal demand response scheduling with Stackelberg game approach under load uncertainty for smart grid, in 2012 IEEE Third International Conference on Smart Grid Communications, IEEE, (2012), 546-551. doi: 10.1109/SmartGridComm.2012.6486042.

[8]

Commonwealth Edison Company, Real-Time Prices. [Online]. Available: https://rrtp.comed.com/live-prices/.

[9]

T. Cortes-ArcosJ. L. Bernal-AgustinR. Dufo-LopezJ. M. Lujano-Rojas and J. Contreras, Multi-objective demand response to real-time prices (RTP) using a task scheduling methodology, Energy, 138 (2017), 19-31.  doi: 10.1016/j.energy.2017.07.056.

[10]

Y. Dai and Y. Gao, Real-time pricing strategy with multi-retailers based on demand-side management for the smart grid, Proceedings of the Chinese Society for Electrical Engineering, 34 (2014), 4244-4249.  doi: 10.13334/j.0258-8013.pcsee.2014.25.006.

[11]

Y. Dai and Y. Gao, Real-time pricing decision-making in smart grid with multi-type users and multi-type power sources, Systems Engineering-Theory and Practice, 35 (2015), 2315-2323. 

[12]

P. DuanJ. LiY. WangH. Sang and B. Jia, Solving chiller loading optimization problems using an improved teaching-learning-based optimization algorithm, Methods, 39 (2018), 65-77.  doi: 10.1002/oca.2334.

[13]

R. Dufo-Lopez, Optimisation of size and control of grid-connected storage under real time electricity pricing conditions, Applied Energy, 140 (2015), 395-408.  doi: 10.1016/j.apenergy.2014.12.012.

[14]

O. ElmaA. TascikarogluA. T. Ince and U. S. Selamogullari, Implementation of a dynamic energy management system using real time pricing and local renewable energy generation forecasts, Energy, 134 (2017), 206-220.  doi: 10.1016/j.energy.2017.06.011.

[15]

Z. FanP. KulkarniS. GormusC. EfthymiouG. KalogridisM. SooriyabandaraZ. ZhuS. Lambotharan and W. H. Chin, Smart grid communications: Overview of research challenges, solutions, and standardization activities, Tutorials, 15 (2013), 21-38.  doi: 10.1109/SURV.2011.122211.00021.

[16]

H. Farhangi, The path of the smart grid, Energy Magazine, 8 (2010), 18-28.  doi: 10.1109/MPE.2009.934876.

[17]

S. FavuzzaG. GaliotoM. G. IppolitoF. MassaroF. MilazzoG. PecoraroE. Riva Sanseverino and E. Telaretti, Real-time pricing for aggregates energy resources in the Italian energy market, Energy, 87 (2015), 251-258.  doi: 10.1016/j.energy.2015.04.105.

[18]

Y. DaiY. GaoH. Gao and H. Zhu, Real-time pricing scheme based on Stackelberg game in smart grid with multiple power retailers, Neurocomputing, 260 (2017), 149-156.  doi: 10.1016/j.neucom.2017.04.027.

[19]

A. GoudarziA. G. SwansonJ. V. Coller and P. Siano, Smart real-time scheduling of generating units in an electricity market considering environmental aspects and physical constraints of generators, Applied Energy, 189 (2017), 667-696.  doi: 10.1016/j.apenergy.2016.12.068.

[20]

C. LiZ. DingD. ZhaoJ. Yi and G. Zhang, Building energy consumption prediction: An extreme deep learning approach, Energies, 10 (2017), 1525-1525.  doi: 10.3390/en10101525.

[21]

J. LiH. SangY. Han and K. Gao, Efficient multi-objective optimization algorithm for hybrid flow shop scheduling problems with setup energy consumptions, Journal of Cleaner Production, 181 (2018), 584-598.  doi: 10.1016/j.jclepro.2018.02.004.

[22]

C. LiJ. GaoJ. Yi and G. Zhang, Analysis and design of functionally weighted single-input-rule-modules connected fuzzy inference systems, IEEE Transactions on Fuzzy Systems, 26 (2018), 56-71.  doi: 10.1109/TFUZZ.2016.2637369.

[23]

X. LiuZ. Ma and S. Zou, Auction games for coordination of large-scale elastic loads in deregulated electricity markets, Management Optimization, 12 (2016), 833-850.  doi: 10.3934/jimo.2016.12.833.

[24]

S. MaharjanQ. ZhuY. ZhangS. Gjessing and T. Basar, Dependable demand response management in the smart grid: A Stackelberg game approach, IEEE Transactions on Smart Grid, 4 (2013), 120-132.  doi: 10.1109/TSG.2012.2223766.

[25]

A. H. Mohsenian-Rad and A. Leon-Garcia, Optimal residential load control with price prediction in real-time electricity pricing environments, IEEE Transactions on Smart Grid, 1 (2010), 120-133.  doi: 10.1109/TSG.2010.2055903.

[26] R. B. Myerson, Game Theory: Analysis of Conflict, Harvard University Press, 1991. 
[27]

N. Nezamoddini and Y. Wang, Real-time electricity pricing for industrial customers: Survey and case studies in the United States, Applied Energy, 195 (2017), 1023-1037.  doi: 10.1016/j.apenergy.2017.03.102.

[28]

N. Nikmehr NS. Najafi-Ravadanegh and A. Khodaei, Probabilistic optimal scheduling of networked microgrids considering time-based demand response programs under uncertainty, Applied Energy, 198 (2017), 267-279.  doi: 10.1016/j.apenergy.2017.04.071.

[29]

L. QianY. A. ZhangJ. Huang and Y. Wu, Demand response management via real-time electricity price control in smart grids, IEEE Journal on Selected Areas in Communications, 31 (2013), 1268-1280.  doi: 10.1109/JSAC.2013.130710.

[30]

P. SamadiH. Mohsenian-RadV. W. S. Wong and R. Schober, Tackling the load uncertainty challenges for energy consumption scheduling in smart grid, IEEE Transactions on Smart Grid, 4 (2013), 1007-1016.  doi: 10.1109/TSG.2012.2234769.

[31]

P. Samadi, A. H. Mohsenian-Rad, R. Schober, V. W. S. Wang and J. Jatskevich, Optimal real-time pricing algorithm based on utilitymaximization for smart grid, in First IEEE International Conference on Smart Grid Communications, IEEE, (2010), 415-420. doi: 10.1109/SMARTGRID.2010.5622077.

[32]

P. Tarasak, Optimal real-time pricing under load uncertainty based on utility maximization for smart grid, in IEEE Conference on Smart Grid Communications, IEEE, (2011), 321-326. doi: 10.1109/SmartGridComm.2011.6102341.

[33]

J. WangH. ZhongX. LaiQ. XiaC. Shu and C. Kang, Distributed real-time demand response based on Lagrangian multiplier optimal selection approach, Applied Energy, 190 (2017), 949-959.  doi: 10.1016/j.apenergy.2016.12.147.

[34]

M. Yu and S. H. Hong, A real-time demand-response algorithm for smart grids: A Stackelberg game approach, IEEE Transactions on Smart Grid, 7 (2016), 879-888.  doi: 10.1109/TSG.2015.2413813.

[35]

M. Yu and S. H. Hong, Supply-demand balancing for power management in smart grid: A Stackelberg game approach, Applied Energy, 164 (2016), 702-710.  doi: 10.1016/j.apenergy.2015.12.039.

show all references

References:
[1]

K. Alshehri, J. Liu, X. Chen and T. Basar, A Stackelberg game for multi-period demand response management in the smart grid, in IEEE Conference on Decision and Control, IEEE, (2015), 5889-5894. doi: 10.1109/CDC.2015.7403145.

[2]

A. Anees and Y. P. Chen, True real time pricing and combined power scheduling of electric appliances in residential energy management system, Applied Energy, 165 (2016), 592-600.  doi: 10.1016/j.apenergy.2015.12.103.

[3]

D. AusselR. Correa and M. Marechal, Electricity spot market with transmission losses, Management Optimization, 9 (2013), 275-290.  doi: 10.3934/jimo.2013.9.275.

[4]

R. Bo R and F. Li, Probabilistic LMP Forecasting considering load uncertainty, IEEE Transactions on Power Systems, 24 (2009), 1279-1289.  doi: 10.1109/TPWRS.2009.2023268.

[5] S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, Cambridge, 2004.  doi: 10.1109/TAC.2006.884922.
[6]

M. CarvalhoJ. P. Pedroso and J. Saraiva, Electricity day-ahead markets: Computation of Nash equilibria, Management Optimization, 11 (2015), 985-998.  doi: 10.3934/jimo.2015.11.985.

[7]

J. Chen, B. Yang and X. Guan, Optimal demand response scheduling with Stackelberg game approach under load uncertainty for smart grid, in 2012 IEEE Third International Conference on Smart Grid Communications, IEEE, (2012), 546-551. doi: 10.1109/SmartGridComm.2012.6486042.

[8]

Commonwealth Edison Company, Real-Time Prices. [Online]. Available: https://rrtp.comed.com/live-prices/.

[9]

T. Cortes-ArcosJ. L. Bernal-AgustinR. Dufo-LopezJ. M. Lujano-Rojas and J. Contreras, Multi-objective demand response to real-time prices (RTP) using a task scheduling methodology, Energy, 138 (2017), 19-31.  doi: 10.1016/j.energy.2017.07.056.

[10]

Y. Dai and Y. Gao, Real-time pricing strategy with multi-retailers based on demand-side management for the smart grid, Proceedings of the Chinese Society for Electrical Engineering, 34 (2014), 4244-4249.  doi: 10.13334/j.0258-8013.pcsee.2014.25.006.

[11]

Y. Dai and Y. Gao, Real-time pricing decision-making in smart grid with multi-type users and multi-type power sources, Systems Engineering-Theory and Practice, 35 (2015), 2315-2323. 

[12]

P. DuanJ. LiY. WangH. Sang and B. Jia, Solving chiller loading optimization problems using an improved teaching-learning-based optimization algorithm, Methods, 39 (2018), 65-77.  doi: 10.1002/oca.2334.

[13]

R. Dufo-Lopez, Optimisation of size and control of grid-connected storage under real time electricity pricing conditions, Applied Energy, 140 (2015), 395-408.  doi: 10.1016/j.apenergy.2014.12.012.

[14]

O. ElmaA. TascikarogluA. T. Ince and U. S. Selamogullari, Implementation of a dynamic energy management system using real time pricing and local renewable energy generation forecasts, Energy, 134 (2017), 206-220.  doi: 10.1016/j.energy.2017.06.011.

[15]

Z. FanP. KulkarniS. GormusC. EfthymiouG. KalogridisM. SooriyabandaraZ. ZhuS. Lambotharan and W. H. Chin, Smart grid communications: Overview of research challenges, solutions, and standardization activities, Tutorials, 15 (2013), 21-38.  doi: 10.1109/SURV.2011.122211.00021.

[16]

H. Farhangi, The path of the smart grid, Energy Magazine, 8 (2010), 18-28.  doi: 10.1109/MPE.2009.934876.

[17]

S. FavuzzaG. GaliotoM. G. IppolitoF. MassaroF. MilazzoG. PecoraroE. Riva Sanseverino and E. Telaretti, Real-time pricing for aggregates energy resources in the Italian energy market, Energy, 87 (2015), 251-258.  doi: 10.1016/j.energy.2015.04.105.

[18]

Y. DaiY. GaoH. Gao and H. Zhu, Real-time pricing scheme based on Stackelberg game in smart grid with multiple power retailers, Neurocomputing, 260 (2017), 149-156.  doi: 10.1016/j.neucom.2017.04.027.

[19]

A. GoudarziA. G. SwansonJ. V. Coller and P. Siano, Smart real-time scheduling of generating units in an electricity market considering environmental aspects and physical constraints of generators, Applied Energy, 189 (2017), 667-696.  doi: 10.1016/j.apenergy.2016.12.068.

[20]

C. LiZ. DingD. ZhaoJ. Yi and G. Zhang, Building energy consumption prediction: An extreme deep learning approach, Energies, 10 (2017), 1525-1525.  doi: 10.3390/en10101525.

[21]

J. LiH. SangY. Han and K. Gao, Efficient multi-objective optimization algorithm for hybrid flow shop scheduling problems with setup energy consumptions, Journal of Cleaner Production, 181 (2018), 584-598.  doi: 10.1016/j.jclepro.2018.02.004.

[22]

C. LiJ. GaoJ. Yi and G. Zhang, Analysis and design of functionally weighted single-input-rule-modules connected fuzzy inference systems, IEEE Transactions on Fuzzy Systems, 26 (2018), 56-71.  doi: 10.1109/TFUZZ.2016.2637369.

[23]

X. LiuZ. Ma and S. Zou, Auction games for coordination of large-scale elastic loads in deregulated electricity markets, Management Optimization, 12 (2016), 833-850.  doi: 10.3934/jimo.2016.12.833.

[24]

S. MaharjanQ. ZhuY. ZhangS. Gjessing and T. Basar, Dependable demand response management in the smart grid: A Stackelberg game approach, IEEE Transactions on Smart Grid, 4 (2013), 120-132.  doi: 10.1109/TSG.2012.2223766.

[25]

A. H. Mohsenian-Rad and A. Leon-Garcia, Optimal residential load control with price prediction in real-time electricity pricing environments, IEEE Transactions on Smart Grid, 1 (2010), 120-133.  doi: 10.1109/TSG.2010.2055903.

[26] R. B. Myerson, Game Theory: Analysis of Conflict, Harvard University Press, 1991. 
[27]

N. Nezamoddini and Y. Wang, Real-time electricity pricing for industrial customers: Survey and case studies in the United States, Applied Energy, 195 (2017), 1023-1037.  doi: 10.1016/j.apenergy.2017.03.102.

[28]

N. Nikmehr NS. Najafi-Ravadanegh and A. Khodaei, Probabilistic optimal scheduling of networked microgrids considering time-based demand response programs under uncertainty, Applied Energy, 198 (2017), 267-279.  doi: 10.1016/j.apenergy.2017.04.071.

[29]

L. QianY. A. ZhangJ. Huang and Y. Wu, Demand response management via real-time electricity price control in smart grids, IEEE Journal on Selected Areas in Communications, 31 (2013), 1268-1280.  doi: 10.1109/JSAC.2013.130710.

[30]

P. SamadiH. Mohsenian-RadV. W. S. Wong and R. Schober, Tackling the load uncertainty challenges for energy consumption scheduling in smart grid, IEEE Transactions on Smart Grid, 4 (2013), 1007-1016.  doi: 10.1109/TSG.2012.2234769.

[31]

P. Samadi, A. H. Mohsenian-Rad, R. Schober, V. W. S. Wang and J. Jatskevich, Optimal real-time pricing algorithm based on utilitymaximization for smart grid, in First IEEE International Conference on Smart Grid Communications, IEEE, (2010), 415-420. doi: 10.1109/SMARTGRID.2010.5622077.

[32]

P. Tarasak, Optimal real-time pricing under load uncertainty based on utility maximization for smart grid, in IEEE Conference on Smart Grid Communications, IEEE, (2011), 321-326. doi: 10.1109/SmartGridComm.2011.6102341.

[33]

J. WangH. ZhongX. LaiQ. XiaC. Shu and C. Kang, Distributed real-time demand response based on Lagrangian multiplier optimal selection approach, Applied Energy, 190 (2017), 949-959.  doi: 10.1016/j.apenergy.2016.12.147.

[34]

M. Yu and S. H. Hong, A real-time demand-response algorithm for smart grids: A Stackelberg game approach, IEEE Transactions on Smart Grid, 7 (2016), 879-888.  doi: 10.1109/TSG.2015.2413813.

[35]

M. Yu and S. H. Hong, Supply-demand balancing for power management in smart grid: A Stackelberg game approach, Applied Energy, 164 (2016), 702-710.  doi: 10.1016/j.apenergy.2015.12.039.

Figure 1.  RTP data from ComEd
Figure 2.  Optimal real-time pricing of retailers
Figure 3.  Optimal real-time pricing of retailers when $ \sigma = 0.1,0.2,0.3 $
Figure 4.  Expected revenue of electricity retailers
Figure 5.  Aggregate power load of user 1 and user 2
Figure 6.  Expected power payoff of user 1 and user 2
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