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Profit maximization algorithms for utility companies in an oligopolistic energy market with dynamic prices and intelligent users

1 Department of Electrical Engineering, University of Southern California, Los Angeles, CA, 90089, USA
2 Department of Electrical Engineering and Computer Science, Syracuse University, Syracuse, NY, 13244, USA

Topical Section: Smart Grids and Networks

Dynamic energy pricing provides a promising solution for the utility companies to incentivize energy users to perform demand side management in order to minimize their electric bills. Moreover, the emerging decentralized smart grid, which is a likely infrastructure scenario for future electrical power networks, allows energy consumers to select their energy provider from among multiple utility companies in any billing period. This paper thus starts by considering an oligopolistic energy market with multiple non-cooperative (competitive) utility companies, and addresses the problem of determining dynamic energy prices for every utility company in this market based on a modified Bertrand Competition Model of user behaviors. Two methods of dynamic energy pricing are proposed for a utility company to maximize its total profit. The first method finds the greatest lower bound on the total profit that can be achieved by the utility company, whereas the second method finds the best response of a utility company to dynamic pricing policies that the other companies have adopted in previous billing periods. To exploit the advantages of each method while compensating their shortcomings, an adaptive dynamic pricing policy is proposed based on a machine learning technique, which finds a good balance between invocations of the two aforesaid methods. Experimental results show that the adaptive policy results in consistently high profit for the utility company no matter what policies are employed by the other companies.
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1. Cui T, Wang Y, Goudarzi H, et al. (2012) Profit maximization for utility companies in an oligopolistic energy market with dynamic prices. Online conference on Green Communications, IEEE.

2. The US Department of Energy (2008) The Smart Grid: An Introduction. How a smarter grid works as an enabling engine.

3. Caron S, Kesidis G, Incentive-based Energy Consumption Scheduling Algorithms for the Smart Grid. Smart Grid Communications, 2010 First IEEE international conference on: 391-396.

4. Chen L, Low S, Doyle J (2010) Two market models for demand response in power networks, Smart Grid Communications, 2010 First IEEE international conference on: 397-402.

5. Samad T, Technology Developments and R&D Challenges for Smart Grid Applications in Homes, Buildings, and Industry, Presentation slides available online.

6. Hatami S, Pedram M (2010) Minimizing the Electricity Bill of Cooperative Users under a QuasiDynamic Energy Pricing Model, Smart Grid Communications, 2010 First IEEE international conference on: 421-426.

7. Goudarzi H, Hatami S, Pedram M (2011) Demand-side load scheduling incentivized by dynamic energy prices, Smart Grid Communications, 2011 First IEEE international conference on: 351-356.

8. Samadi P, Mohsenian-Rad H, Schober R, et al. (2010) Optimal real-time pricing algorithm based on utility maximization for smart grid, Smart Grid Communications, 2010 First IEEE international conference on.

9. Kishore S, Snyder LV (2010) Control Mechanisms for Residential Electricity Demand in SmartGrids. Smart Grid Communications, 2010 First IEEE international conference on: 443-448.

10. O’Neill D, Levorato M, Goldsmith A, et al. (2010) Residential demand response using reinforcement learning. Smart Grid Communications, 2010 First IEEE international conference on: 409-414.

11. Cui T, Goudarzi H, Hatami S, et al. (2012) Concurrent optimization of consumer’s electrical energy bill and producer’s power generation cost under a dynamic pricing model. Proc. of the 3rd IEEE PES Innovative Smart Grid Technologies (ISGT) Conf., 2012.

12. Gregory MN, Principle of Economics, Dryden Press, 1997.

13. Valenzuela J, Mazumdar M (2004) The electricity price duration curve under Bertrand and Cournot models. Probabilistic methods applied to power systems, 2004 International Conference on: 38-43.

14. Narahari Y, Garg D, Narayanam R, et al., Game Theoretic Problems in Network Economics and Mechanism Design Solutions, Advanced Information and Knowledge Process, Springer, 2009.

15. Kirpatrick S, Gerlatt CD, Vecchi MP, Optimization by simulated annealing, Science, 1983.

16. Saad W, Zhu H, Poor HV, et al. (2012) Game-Theoretic Methods for the Smart Grid: An Overview of Microgrid Systems, Demand-Side Management, and Smart Grid Communications, IEEE Signal Processing Magazine 29: 86-105.

17. Hu R, Wang Z, Weighing the Risk and Gains for Enterprise Raising Funds. Forecasting, 2001.

18. Christopher MB, Pattern recognition and machine learning (information science and statistics), Springer, 2007.

19. Freund Y, Schapire RE (1997) A decision-theoretic generalization of on-line learning and an application to boosting. J Comput Syst Sci 55: 119-139.    

20. Dhiman G, Simunic T (2006) Dynamic power management using machine learning. ComputerAided Design, 2006. ICCAD ’06. IEEE/ACM International Conference on: 747-754.

Copyright Info: © 2016, Tiansong Cui, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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