Contreras, Javier and Krawczyk, Jacek and Zuccollo, James (2008): Can planners control competitive generators?
Download (177Kb) | Preview
Consider an electricity market populated by competitive agents using thermal generating units. Generation often emits pollution which a planner may wish to constrain through regulation. Furthermore, generators’ ability to transmit energy may be naturally restricted by the grid’s facilities. The existence of both pollution standards and transmission constraints can impose several restrictions upon the joint strategy space of the agents. We propose a dynamic, game-theoretic model capable of analysing coupled constraints equilibria (also known as generalised Nash equilibria). Our equilibria arise as solutions to the planner’s problem of avoiding both network congestion and excessive pollution. The planner can use the coupled constraints’ Lagrange multipliers to compute the charges the players would pay if the constraints were violated. Once the players allow for the charges in their objective functions they will feel compelled to obey the constraints in equilibrium. However, a coupled constraints equilibrium needs to exist and be unique for this modiﬁcation of the players’ objective functions ..[there was a “to” here, incorrect?].. induce the required behaviour. We extend the three-node dc model with transmission line constraints described in  and  to utilise a two-period load duration curve, and impose multi-period pollution constraints. We discuss the economic and environmental implications of the game’s solutions as we vary the planner’s preferences.
|Item Type:||MPRA Paper|
|Original Title:||Can planners control competitive generators?|
|Subjects:||C - Mathematical and Quantitative Methods > C6 - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C63 - Computational Techniques; Simulation Modeling
C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games
|Depositing User:||James Zuccollo|
|Date Deposited:||10. Sep 2008 10:57|
|Last Modified:||13. Feb 2013 18:00|
 K.-C. Chu, M. Jamshidi, and R. Levitan, An approach to on-line power dispatch with ambient air pollution constraints,IEEE Transactions on Automatic Control 22 (1977), no. 3, 385–396.
 J. Contreras, M. Klusch, and J. B. Krawczyk, Numerical solutions to Nash-Cournot equilibria in coupled constraint electricity markets, IEEE Transactions on Power Systems 19 (2004), no. 1, 195–206.
 J. Contreras, J Krawczyk, and J. Zuccollo, Electricity market games with constraints on transmission capacity and emissions,30th Conference of the International Association for Energy Economics, February 2007, Wellington, New Zealand.
, The invisible polluter: Can regulators save consumer surplus?, 13th International Symposium of the International Society of Dynamic Games, June 30 - July 3 2008, Wrocław, Poland.
 A.G. Exposito and A. Abur, Analisis y operacion de sistemas de energia electrica, McGraw-Hill-Interamericana de Espana, 2002.
 P. T. Harker, Generalized Nash games and quasivariational inequalities, European Journal of Operational Research 4 (1991), 81–94.
 A. Haurie, Environmental coordination in dynamic oligopolistic markets, Group Decision and Negotiation 4 (1994), 46–67.
 A. Haurie and J. B. Krawczyk, Optimal charges on river efﬂuent from lumped and distributed sources, Environmental Modelling and Assessment 2 (1997), 177–199.
 A. Haurie and J. B. Krawczyk, An Introduction to Dynamic Games. Internet textbook, URL: http://ecolu-info.unige.ch/˜haurie/fame/textbook.pdf, 2002.
 B.F. Hobbs, Linear complementarity models of Nash-Cournot competition in bilateral and poolco power markets, IEEE Transactions on Power Systems 16 (2001), no. 2, 194–202.
 B.F. Hobbs and J.-S. Pang, Nash-Cournot equilibria in electric power markets with piecewise linear demand functions and joint constraints, Operations Research 55 (2007), no. 1, 113–127.
 J.B. Krawczyk, Coupled constraint Nash equilibria in environmental games, Resource and Energy Economics 27 (2005), 157–181.
 J.B. Krawczyk, Numerical solutions to coupled-constraint (or generalised) Nash equilibrium problems, Computational Management Science (Online Date: November 09, 2006), http://dx.doi.org/10.1007/s10287–006–0033–9.
 J.B. Krawczyk, J. Contreras, and J. Zuccollo, Thermal electricity generator’s competition with coupled constraints, Invited paper presented at the International Conference on Modeling, Computation and Optimization (Indian Statistical Institute, ed.), 9-10 January 2008, Delhi Centre, New Delhi, India.
 J.B. Krawczyk and S. Uryasev, Relaxation algorithms to ﬁnd Nash equilibria with economic applications, Environmental Modelling and Assessment 5 (2000), 63–73.
 J.B. Krawczyk and J. Zuccollo, NIRA-3: A MATLAB package for ﬁnding Nash equilibria in inﬁnite games, Working Paper, School of Economics and Finance, VUW, 2006.
 L. Mathiesen, A Cournot model with coupled constraints, The Norwegian School of Economics and Business Administration, Bergen, July 2007.
 E.A. Nurminski, Progress in nondifferentiable optimization, ch. Subgradient Method for Minimizing Weakly Convex Functions and -Subgradient Methods of Convex Optimisation, pp. 97–123, International Institute for Applied Systems Analysis, Laxenburg, Austria, 1982.
 J.-S. Pang and M. Fukushima, Quasi-variational inequalities, generalized Nash equilibria and multi-leader-follower games, Computational Management Science 1 (2005), 21–56.
 R. Ramanathan, Emission constrained economic dispatch, IEEE Transactions on Power Systems 9 (1994), no. 4, 1994–2000.
 J.B. Rosen, Existence and uniqueness of equilibrium points for concave n-person games, Econometrica 33 (1965), no. 3, 520–534.
 W.D. Stevenson, Elements of power system analysis, McGraw-Hill New York, 1982.
 S. Uryasev and R.Y. Rubinstein, On relaxation algorithms in computation of noncooperative equilibria, IEEE Transactions on Automatic Control 39 (1994), no. 6, 1263–1267.
 C. von Heusingen and A. Kanzow, Optimization reformulations of the generalized Nash equilibrium problem using Nikaido- Isoda-type functions, Preprint 269, University of Wurzburg, Institute of Mathematics, 2006. u
 J.-Y Wei and Y. Y. Smeers, Spatial oligopolistic electricity models with Cournot generators and regulated transmission prices, Operations Research 2 (1999), 102–112.