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July  2016, 12(3): 833-850. doi: 10.3934/jimo.2016.12.833

## Auction games for coordination of large-scale elastic loads in deregulated electricity markets

 1 School of Automation, Beijing Institute of Technology, 5th South Street, Zhongguancun, Haidian District, Beijing 100081, China, China, China

Received  June 2014 Revised  April 2015 Published  September 2015

Auctions, e.g. market clearing price (MCP) auctions, have been widely adopted in electricity markets, and progressive second price (PSP) auctions are stated possessing promising properties of incentive compatibility and efficiency. In this work, we study the coordination of large-scale elastic loads in deregulated electricity markets under MCP and PSP auctions. To explore the performances of these auctions in the underlying problems, we focus on the key issues of the payment comparison, incentive compatibility and efficiency of Nash equilibrium (NE), and develop the following results: (i) The individual payment under MCP is always higher than that under PSP, and their difference vanishes asymptotically as the system scale increases; (ii) The incentive compatibility holds under PSP, and holds under MCP only with respect to others' efficient bid profile; (iii) The efficient bid profile under PSP is an NE, while that under MCP is an $\varepsilon$-NE which degenerates to an NE asymptotically as the system scale increases. With these analyses, we claim that it is pretty promising to apply both MCP and PSP auctions to the large-scale load coordination problems in deregulated electricity markets.
Citation: Suli Zou, Zhongjing Ma, Xiangdong Liu. Auction games for coordination of large-scale elastic loads in deregulated electricity markets. Journal of Industrial and Management Optimization, 2016, 12 (3) : 833-850. doi: 10.3934/jimo.2016.12.833
##### References:
 [1] H. Aalami, M. P. Moghaddam and G. Yousefi, Modeling and prioritizing demand response programs in power markets, Electric Power Systems Research, 80 (2010), 426-435. doi: 10.1016/j.epsr.2009.10.007. [2] K. Abbink, J. Brandts and P. Pezanis-Christou, Auctions for government securities: A laboratory comparison of uniform, discriminatory and spanish designs, Journal of Economic Behavior & Organization, 61 (2006), 284-303. [3] M. Albadi and E. El-Saadany, A summary of demand response in electricity markets, Electric Power Systems Research, 78 (2008), 1989-1996. doi: 10.1016/j.epsr.2008.04.002. [4] L. Ausubel and P. Cramton, Demand Reduction and Inefficiency in Multi-Unit Auctions, Working papers, University of Maryland, 2002. [5] F. E. Banks, Economics of electricity deregulation and privatization: an introductory survey, Energy, 21 (1996), 249-261. doi: 10.1016/0360-5442(95)00122-0. [6] E. Bompard, Y. Ma, R. Napoli and G. Abrate, The demand elasticity impacts on the strategic bidding behavior of the electricity producers, IEEE Transactions on Power Systems, 22 (2007), 188-197. doi: 10.1109/TPWRS.2006.889134. [7] D. Callaway and I. Hiskens, Achieving controllability of electric loads, Proceedings of the IEEE, 99 (2011), 184-199. doi: 10.1109/JPROC.2010.2081652. [8] S. Cha, T. Reen and N. Hah, Optimal charging strategies of electric vehicles in the UK power market, in 1st Conference on Innovative Smart Grid Technologies, Gaithersburg, Maryland, 2010, 1-8. [9] K. Dietrich, J. M. Latorre, L. Olmos and A. Ramos, Demand response and its sensitivity to participation rates and elasticities, in 8th International Conference on the European Energy Market (EEM), Zagreb, Croatia, 2011, 716-717. doi: 10.1109/EEM.2011.5953103. [10] N. Fabra, N. Von der Fehr and D. Harbord, Modeling electricity auctions, The Electricity Journal, 15 (2002), 72-81. doi: 10.1016/S1040-6190(02)00347-0. [11] T. Genc, Discriminatory versus uniform-price electricity auctions with supply function equilibrium, Journal of optimization theory and applications, 140 (2009), 9-31. doi: 10.1007/s10957-008-9437-8. [12] V. Gountis and A. Bakirtzis, Bidding strategies for electricity producers in a competitive electricity marketplace, IEEE Transactions on Power Systems, 19 (2004), 356-365. doi: 10.1109/TPWRS.2003.821474. [13] R. Jain and J. Walrand, An efficient Nash-implementation mechanism for network resource allocation, Automatica, 46 (2010), 1276-1283. doi: 10.1016/j.automatica.2010.05.013. [14] P. Jia and P. Caines, Analysis of quantized double auctions with application to competitive electricity markets, INFOR: Information Systems and Operational Research, 48 (2010), 239-250. doi: 10.3138/infor.48.4.239. [15] D. S. Kirschen, Demand-side view of electricity markets, IEEE Transactions on Power Systems, 18 (2003), 520-527. doi: 10.1109/TPWRS.2003.810692. [16] V. Krishna, Auction Theory, Academic Press, 2009. [17] A. Lazar and N. Semret, Design and analysis of the progressive second price auction for network bandwidth sharing, Telecommunication Systems, 13, (1999). [18] G. Li and J. Shi, Agent-based modeling for trading wind power with uncertainty in the day-ahead wholesale electricity markets of single-sided auctions, Applied Energy, 99 (2012), 13-22. doi: 10.1016/j.apenergy.2012.04.022. [19] Z. Ma, D. Callaway and I. Hiskens, Decentralized charging control of large populations of plug-in electric vehicles, IEEE Transactions on Control Systems Technology, 21 (2013), 67-78. [20] P. Maillé and B. Tuffin, The progressive second price mechanism in a stochastic environment, Netnomics, 5 (2003), 119-147. [21] O. Marce, H.-H. Tran and B. Tuffin, Double-sided auctions applied to vertical handover for mobility management in wireless networks, Journal of Network and Systems Management, 22 (2014), 658-681. doi: 10.1007/s10922-013-9269-1. [22] S. Nielsen, P. Sorknæs and P. A. Østergaard, Electricity market auction settings in a future danish electricity system with a high penetration of renewable energy sources: A comparison of marginal pricing and pay-as-bid, Energy, 36 (2011), 4434-4444. doi: 10.1016/j.energy.2011.03.079. [23] S. Sethi, H. Yan, J. Yan and H. Zhang, An analysis of staged purchases in deregulated time-sequential electricity markets, Journal of Industrial and Management Optimization, 1 (2005), 443-463. doi: 10.3934/jimo.2005.1.443. [24] A. Singh, Smart grid dynamic pricing, International Journal of Engineering Research and Applications (IJERA), 2 (2012), 705-742. [25] Y. R. Sood, N. P. Padhy and H. Gupta, Wheeling of power under deregulated environment of power system - a bibliographical survey, IEEE Transactions on Power Systems, 17 (2002), 870-878. doi: 10.1109/TPWRS.2002.800967. [26] K. Vitae and L. Lave, Demand response and electricity market efficiency, The Electricity Journal, 20 (2007), 69-85. [27] F. Wen and A. K. David, Optimal bidding strategies and modeling of imperfect information among competitive generators, IEEE Transactions on Power Systems, 16 (2001), 15-21. [28] J. H. Williams and F. Kahrl, Electricity reform and sustainable development in China, Environmental Research Letters, 3 (2008), 044009. doi: 10.1088/1748-9326/3/4/044009. [29] Z. Xu, W. Xu, W. Shao and Z. Zeng, Real-time pricing control on generation-side: Optimal demand-tracking model and information fusion estimation solver, IEEE Transactions on Power Systems, 29 (2014), 1522-1535. doi: 10.1109/TPWRS.2013.2296809. [30] X. Zhao and C. Ma, Deregulation, vertical unbundling and the performance of China's large coal-fired power plants, Energy Economics, 40 (2013), 474-483. doi: 10.1016/j.eneco.2013.08.003. [31] S. Zou, Z. Ma and X. Liu, Auction-based distributed efficient economic operations of microgrid systems, International Journal of Control, 87 (2014), 2446-2462. doi: 10.1080/00207179.2014.926395.

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##### References:
 [1] H. Aalami, M. P. Moghaddam and G. Yousefi, Modeling and prioritizing demand response programs in power markets, Electric Power Systems Research, 80 (2010), 426-435. doi: 10.1016/j.epsr.2009.10.007. [2] K. Abbink, J. Brandts and P. Pezanis-Christou, Auctions for government securities: A laboratory comparison of uniform, discriminatory and spanish designs, Journal of Economic Behavior & Organization, 61 (2006), 284-303. [3] M. Albadi and E. El-Saadany, A summary of demand response in electricity markets, Electric Power Systems Research, 78 (2008), 1989-1996. doi: 10.1016/j.epsr.2008.04.002. [4] L. Ausubel and P. Cramton, Demand Reduction and Inefficiency in Multi-Unit Auctions, Working papers, University of Maryland, 2002. [5] F. E. Banks, Economics of electricity deregulation and privatization: an introductory survey, Energy, 21 (1996), 249-261. doi: 10.1016/0360-5442(95)00122-0. [6] E. Bompard, Y. Ma, R. Napoli and G. Abrate, The demand elasticity impacts on the strategic bidding behavior of the electricity producers, IEEE Transactions on Power Systems, 22 (2007), 188-197. doi: 10.1109/TPWRS.2006.889134. [7] D. Callaway and I. Hiskens, Achieving controllability of electric loads, Proceedings of the IEEE, 99 (2011), 184-199. doi: 10.1109/JPROC.2010.2081652. [8] S. Cha, T. Reen and N. Hah, Optimal charging strategies of electric vehicles in the UK power market, in 1st Conference on Innovative Smart Grid Technologies, Gaithersburg, Maryland, 2010, 1-8. [9] K. Dietrich, J. M. Latorre, L. Olmos and A. Ramos, Demand response and its sensitivity to participation rates and elasticities, in 8th International Conference on the European Energy Market (EEM), Zagreb, Croatia, 2011, 716-717. doi: 10.1109/EEM.2011.5953103. [10] N. Fabra, N. Von der Fehr and D. Harbord, Modeling electricity auctions, The Electricity Journal, 15 (2002), 72-81. doi: 10.1016/S1040-6190(02)00347-0. [11] T. Genc, Discriminatory versus uniform-price electricity auctions with supply function equilibrium, Journal of optimization theory and applications, 140 (2009), 9-31. doi: 10.1007/s10957-008-9437-8. [12] V. Gountis and A. Bakirtzis, Bidding strategies for electricity producers in a competitive electricity marketplace, IEEE Transactions on Power Systems, 19 (2004), 356-365. doi: 10.1109/TPWRS.2003.821474. [13] R. Jain and J. Walrand, An efficient Nash-implementation mechanism for network resource allocation, Automatica, 46 (2010), 1276-1283. doi: 10.1016/j.automatica.2010.05.013. [14] P. Jia and P. Caines, Analysis of quantized double auctions with application to competitive electricity markets, INFOR: Information Systems and Operational Research, 48 (2010), 239-250. doi: 10.3138/infor.48.4.239. [15] D. S. Kirschen, Demand-side view of electricity markets, IEEE Transactions on Power Systems, 18 (2003), 520-527. doi: 10.1109/TPWRS.2003.810692. [16] V. Krishna, Auction Theory, Academic Press, 2009. [17] A. Lazar and N. Semret, Design and analysis of the progressive second price auction for network bandwidth sharing, Telecommunication Systems, 13, (1999). [18] G. Li and J. Shi, Agent-based modeling for trading wind power with uncertainty in the day-ahead wholesale electricity markets of single-sided auctions, Applied Energy, 99 (2012), 13-22. doi: 10.1016/j.apenergy.2012.04.022. [19] Z. Ma, D. Callaway and I. Hiskens, Decentralized charging control of large populations of plug-in electric vehicles, IEEE Transactions on Control Systems Technology, 21 (2013), 67-78. [20] P. Maillé and B. Tuffin, The progressive second price mechanism in a stochastic environment, Netnomics, 5 (2003), 119-147. [21] O. Marce, H.-H. Tran and B. Tuffin, Double-sided auctions applied to vertical handover for mobility management in wireless networks, Journal of Network and Systems Management, 22 (2014), 658-681. doi: 10.1007/s10922-013-9269-1. [22] S. Nielsen, P. Sorknæs and P. A. Østergaard, Electricity market auction settings in a future danish electricity system with a high penetration of renewable energy sources: A comparison of marginal pricing and pay-as-bid, Energy, 36 (2011), 4434-4444. doi: 10.1016/j.energy.2011.03.079. [23] S. Sethi, H. Yan, J. Yan and H. Zhang, An analysis of staged purchases in deregulated time-sequential electricity markets, Journal of Industrial and Management Optimization, 1 (2005), 443-463. doi: 10.3934/jimo.2005.1.443. [24] A. Singh, Smart grid dynamic pricing, International Journal of Engineering Research and Applications (IJERA), 2 (2012), 705-742. [25] Y. R. Sood, N. P. Padhy and H. Gupta, Wheeling of power under deregulated environment of power system - a bibliographical survey, IEEE Transactions on Power Systems, 17 (2002), 870-878. doi: 10.1109/TPWRS.2002.800967. [26] K. Vitae and L. Lave, Demand response and electricity market efficiency, The Electricity Journal, 20 (2007), 69-85. [27] F. Wen and A. K. David, Optimal bidding strategies and modeling of imperfect information among competitive generators, IEEE Transactions on Power Systems, 16 (2001), 15-21. [28] J. H. Williams and F. Kahrl, Electricity reform and sustainable development in China, Environmental Research Letters, 3 (2008), 044009. doi: 10.1088/1748-9326/3/4/044009. [29] Z. Xu, W. Xu, W. Shao and Z. Zeng, Real-time pricing control on generation-side: Optimal demand-tracking model and information fusion estimation solver, IEEE Transactions on Power Systems, 29 (2014), 1522-1535. doi: 10.1109/TPWRS.2013.2296809. [30] X. Zhao and C. Ma, Deregulation, vertical unbundling and the performance of China's large coal-fired power plants, Energy Economics, 40 (2013), 474-483. doi: 10.1016/j.eneco.2013.08.003. [31] S. Zou, Z. Ma and X. Liu, Auction-based distributed efficient economic operations of microgrid systems, International Journal of Control, 87 (2014), 2446-2462. doi: 10.1080/00207179.2014.926395.
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