Document Type : Original Research Paper


Department of Electrical Engineering, Faculty of Engineering, Shahid Bahonar University of Kerman, Kerman, Iran


In this paper, the concept of Conjectural Variation (CV) is used to specify optimal generation decision for generation companies (Gencos). The conjecture of Genco is defined as its belief or expectation about the reaction of rivals to change of its output. Using CV method, each Genco has to learn and estimate strategic behaviors of other competitors from available historical market operation data. Therefore, accuracy of generation decision depends on the accuracy of estimating other competitors’ decision within CV context. In this paper, adjusted Lerner index is used to improve the accuracy of estimating CV parameter. In electricity market, the adjusted Lerner index can be directly computed using price, market shares, marginal cost and industry elasticity of demand. It must be noted that due to repeated power market, Gencos need to modify their behavior over time. In response to this need, dynamic learning is considered in case studies which improve results.


[1] F. S. Wen, andA. K. David, "Optimal Bidding Strategies And Modeling of Imperfect Information Among Competitive Generators," IEEE Trans. Power Syst, Vol. 16, pp. 15-21, 2001.
[2] Y Song, Y Ni, F Wen, ZHouand F. F. Wu, " Conjectural Variation Based Bidding Strategy in Spot Markets: Fundamentals and Comparison with Classical Game Theoretical Bidding Strategies," E Electric Power Syst Res, Vol. 67, pp.45-51, 2003. [3] A. K. David, andF. S. Wen, " Strategic Bidding in Competitive Electricity Markets: A Literature Survey," Power EngngSoc Summer Meet, Vol.4, pp.2168-2173, 2000.
[4] R. W. Ferrero, J. F. Rivera, and S. M. Shahidehpour, "Application of Games with Incomplete Information for Pricing Electricity In Deregulated Power Pools," IEEE Trans on Power System, Vol.13, pp.184–189, 1998.
[5] B. R.Szkuta, L. A.Sanabria, and T.S.Dillon, "Electricity Price Short-Term Forecasting Using Artificial Neural Networks," IEEE Trans Power Syst, Vol.14, pp.851-857, 1999.
[6] Y. Y. Hong, S. W. Weng, and M. T. Weng, " "Bidding Strategy Based on Artificial Intelligence for a Competitive Electric Market," IEE Proc Gener Transm Distrib, Vol.148, pp.150-164, 2001.
[7] F. J. Nogales, J Contreras, and A. J. Conejo, "Forecasting NextDay Electricity Prices by Time Series Models". IEEE Trans Power Syst, Vol.16, pp. 342-348, 2002.
[8] C. J. Day, B. F. Hobbs, and J Pang, " Oligopolistic Competition in Power Networks: a Conjectured Supply Function Approach, "IEEE Trans Power Syst, Vol. 17, pp. 597–607, 2002.
[9] I Taheri, M Rashidinejad, A Badri, and A Rahimi-Kian, "Analytical Approach in Computing Nash Equilibrium for Oligopolistic Competition of Transmission-Constrained GENCOs," IEEE Systems Journal, Issue. 99, pp. 1–11, 2014.
[10] A Garcia-Alcalde, M Ventosa, M Rivier, and A Romos, "Fitting electricity market models: a conjectural variations approach,"Power SystComputConf 2002.
[11] T Lindh, " the Inconsistency of Consistent Conjectures: Coming Back to Cournot,"Journal of Economic Behavior & Organization, Vol. 18, pp. 69–90, 1992.
[12] ZhQiu, N Gui, and G Deconinck, "Analysis of equilibriumoriented bidding strategies with inaccurate electricity market models,"Energy Conversion and Management, Vol. 46, pp. 306–314, 2013.
[13] Y Song, Y Ni, F Wen, ZHou, and FF Wu, "Conjectural Variation Based Learning Model of Strategic Bidding in Spot Market,"Energy Conversion and Management, Vol. 26, pp. 797–804,2004.
[14] J Lagarto, J Sousa, and T. T LIE, "Measuring Market Power in the Spanish Electricity Market Using a Conjectural Variation Approach ". in the 3th international conference ‘the European electricity market.EEM-06’ challenge of uniϐication, 2006
[15] *Conjectural Variations and Competition Policy: Theory and Empirical Techniques. A Report for the OFT by RBB Economics, October 2011*
[16] M. B Naghibi-Sistani, M. R Akbarzadeh-Tootoonchi, M. H JavidiDashte Bayaz, and H. Rajabi-Mashhadi, “Application of QLearning with Temperature Variation for Bidding Strategies in Market Based Power Systems,” Energy Conversion and Management, Vol. 47, pp. 1529–1538, 2006.


Journal of Electrical and Computer Engineering Innovations (JECEI) welcomes letters to the editor for the post-publication discussions and corrections which allows debate post publication on its site, through the Letters to Editor. Letters pertaining to manuscript published in JECEI should be sent to the editorial office of JECEI within three months of either online publication or before printed publication, except for critiques of original research. Following points are to be considering before sending the letters (comments) to the editor.

[1] Letters that include statements of statistics, facts, research, or theories should include appropriate references, although more than three are discouraged.

[2] Letters that are personal attacks on an author rather than thoughtful criticism of the author’s ideas will not be considered for publication.

[3] Letters can be no more than 300 words in length.

[4] Letter writers should include a statement at the beginning of the letter stating that it is being submitted either for publication or not.

[5] Anonymous letters will not be considered.

[6] Letter writers must include their city and state of residence or work.

[7] Letters will be edited for clarity and length.