A holistic day-ahead distributed energy management approach: Equilibrium selection for customers' game

Document Type : Article


Department of Electrical and Computer, Isfahan University of Technology, Isfahan, 84156-83111, Iran.


n this paper, a new holistic distributed day-ahead energy management approach with desired equilibrium selection capability in a smart distribution grid is proposed. The interaction between customers and the distribution company is modeled as a single-leader multiple-follower Stackelberg game. The interaction among customers is modeled as a non-cooperative generalized Nash game because they meet a common constraint. Customers hold the average of the aggregate load in the appropriate domain to reshape it and improve the Load Factor. The strategy of the distribution company is day-ahead energy pricing obtained through maximizing its profit which is formulated as a stochastic conditional value at risk optimization to consider the uncertainty of the price of electricity in the wholesale market. Customers’ strategies are based on hourly consumption of deferrable loads and scheduled charge/discharge rates of energy storage devices in response to price. It is proved that the generalized Nash game has multiple equilibria; hence, the distributed proximal Tikhonov regularization algorithm is proposed here to achieve the desired equilibrium. The simulation results validate the performance of the proposed algorithm with 31.46% increase in the Load Factor besides 45.89 % and 14.23 % reduction in the maximum aggregate demand and aggregate billing cost, respectively.


Main Subjects

1. Palensky, P. and Dietrich, D. "Demand side management: Demand response, intelligent energy systems, and smart loads", IEEE Transactions on Industrial Informatics, 7(3), pp. 381-388 (2011).
2. Molderink, A., Bakker, V., Bosman, M.G.C., Hurink, J.L., and Smit, G.J.M. "Management and control of domestic smart grid technology", IEEE Transactions on Smart Grid, 1(2), pp. 109-119 (2010).
3. Papaefthymiou, G., Hasche, B., and Nabe, C. "Potential of heat Pumps for demand side management and wind power integration in the German electricity market", IEEE Transactions on Sustainable Energy, 3(4), pp. 636-642 (2012).
4. Yang, P., Tang, G., and Nehorai, A. "A game-theoretic approach for optimal time-of-use electricity pricing", IEEE Transactions on Power Systems, 28(2), pp. 884- 892 (2013).
5. Chai, B., Chen, J., Yang, Z., and Zhang, Y. "Demand response management with multiple utility companies: A two-level game approach", IEEE Transactions on Smart Grid, 5(2), pp. 722-731 (2014).
6. Atzeni, I., Ordonez, L.G., Scutari, G., Palomar, D.P., and Fonollosa, J.R. "Demand-side management via distributed energy generation and storage optimization", IEEE Transactions on Smart Grid, 4(2), pp. 866-876 (2013).
7. Jia, L. and Tong, L. "Dynamic pricing and distributed energy management for demand response", IEEE Transactions on Smart Grid, 7(2), pp. 1128- 1136 (2016).
8. Mohsenian-Rad, A.H., Wong, V.W.S., Jatskevich, J., Schober, R., and Leon-Garcia, A. "Autonomous demand-side Management based on game-theoretic energy consumption scheduling for the future smart grid", IEEE Transactions on Smart Grid, 1(3), pp. 320-331 (2010).
9. Chen, H., Li, Y., Louie, R.H.Y., and Vucetic, B. "Autonomous demand side management based on energy consumption scheduling and instantaneous load billing: An aggregative game approach", IEEE Transactions on Smart Grid, 5(4), pp. 1744-1754 (2014).
10. Deng, R., Yang, Z., Chen, J., Asr, N.R., and Chow, M.Y. "Residential energy consumption scheduling: A coupled-constraint game approach", IEEE Transactions on Smart Grid, 5(3), pp. 1340-1350 (2014).
11. Fadlullah, Z. M., Quan, D.M., Kato, N., and Stojmenovic, I. "GTES: An optimized game-theoretic demandside management scheme for smart grid", IEEE Systems Journal, 8(2), pp. 588-597 (2014).
12. Nguyen, H.K., Song, J.B., and Han, Z. "Distributed demand side management with energy storage in smart grid", IEEE Transactions on Parallel and Distributed Systems, 26(12), pp. 3346-3357 (2015).
13. Yaagoubi, N. and Mouftah, H.T. "User-aware game theoretic approach for demand management", IEEE Transactions on Smart Grid, 6(2), pp. 716-725 (2015).
14. Soliman, H.M. and Leon-Garcia, A. "Game-theoretic demand-side management with storage devices for the future Smart Grid", IEEE Transactions on Smart Grid, 5(3), pp. 1475-1485 (2014).
15. Maharjan, S., Zhu, Q., Zhang, Y., Gjessing, S., and Basar, T. "Demand response management in the smart grid in a large population regime", IEEE Transactions on Smart Grid, 7(1), pp. 189-199 (2016).
16. Scutari, G., Palomar, D.P., Facchinei, F., and Pang, J.S. "Monotone games for cognitive radio systems", Distributed Decision-Making and Control, ser. Lecture Notes Contr. Inf. Sci. Series, New York, NY, USA; Springer-Verlag Inc. (2011).
17. Scutari, G., Facchinei, F., Pang, J. Sh., and Palomar, D. "Real and complex monotone communication games", IEEE Trans. on Information Theory, 60(7), pp. 4197-4231 (2014).
18. Boyd, S. and Vandenberghe, L., Convex Optimization, Cambridge University Press (2009).
19. Grant, M. and Boyd, S., CVX: Matlab software for disciplined convex programming, version 2.0 beta.http://cvxr.com/cvx (2013).
20. Paatero, J.V. and Lund, P.D. "A model for generating household electricity load profiles" , Int. J. Energy Res., 30(5), pp. 273- 290 (2006).