# Competition and Cooperation in a Bidding Model of Electrical Energy Trade

- 204 Downloads
- 3 Citations

## Abstract

A cooperative game-theoretic framework is introduced to study the behavior of cooperating and competing electrical-energy providers in the wholesale market considering price-preference rational consumers. We study the physical and economic aspects of the power transmission system operation focussing on the incentives for group formation. We analyze the interactions of generators in an idealized environment described by a DC load flow model where the network is lossless and is operated by an independent network operator who ensures network stability and fulfillment of consumption needs while taking into account the preferences of consumers over generators. We show that cooperation of generators may be necessary to divert consumers from their previous providers. In the second part of the paper we assume an iterative process in which the generators publish their price offers simultaneously, based on which the consumers preferences are determined. We study the dynamics of the prices and profits as the system evolves in time while each coalition is trying to maximize its expected profit in each step. The model deals with network congestion and *n* − 1 line-contingency reliability as not every generator-consumer matching is allowed to ensure the safe operation of the transmission system. The profit of the generators is determined as the difference between their income and their production cost, which is a quadratic concave function of the production amount. Any non-monopolistic proper subset of the generators may cooperate and harmonize their offered prices to increase their resulting profit. Since we allow the redistribution of profits among cooperating generators, a transferable-utility game-theoretic framework is used. Furthermore, as cooperation affects the outsiders as well, the resulting game is defined in partition function form. The model is able to demonstrate some interesting benefits of cooperation as well as the effect of market regulations and asymmetric information on the resulting profits and total social cost.

### Keywords

Networks Power Transmission Game theory Externalities### References

- Arnold T, Schwalbe U (2002) Dynamic coalition formation and the core. J Economic Behav Organ 49(3):363–380. doi: 10.1016/S0167-2681(02)00015-X CrossRefGoogle Scholar
- Bai X, Shahidehpour S, Ramesh V (1997) Transmission analysis by nash game method. IEEE Trans Power Syst 12:1046–1052CrossRefGoogle Scholar
- Bakirtzis AG, Ziogos NP, Tellidou AC, Bakirtzis GA (2007) Electricity producer offering strategies in day-ahead energy market with step-wise offers. IEEE Trans Power Syst 22(4):1804–1818CrossRefGoogle Scholar
- Berndt ER, Wood DO (1975) Technology, prices, and the derived demand for energy. The review of Economics and StatisticsGoogle Scholar
- Bernstein MA, Griffin JM, Infrastructure S (2006) Regional differences in the price-elasticity of demand for energy. National renewable energy laboratoryGoogle Scholar
- Bolle F (1992) Supply function equilibria and the danger of tacit collusion: the case of spot markets for electricity. Energy Econ 14(2):94–102CrossRefGoogle Scholar
- Cardell JB, Hitt CC, Hogan WW (1997) Market power and strategic interaction in electricity networks. Resour Energy Econ 19(1-2):109–137. doi: 10.1016/S0928-7655(97)00006-7 CrossRefGoogle Scholar
- Chen Y, Hobbs B, Leyffer S, Munson TS (2006) Leader-follower equilibria for electric power and NO
_{x}allowances markets. Comput Manag Sci 3:307–330CrossRefGoogle Scholar - Cheng CP, Liu CW, Liu CC (2000) Unit commitment by lagrangian relaxation and genetic algorithms. IEEE Trans Power Syst 15(2):707–714CrossRefGoogle Scholar
- Christie R, Wollenberg B, Wangensteen I (2000) Transmission management in the deregulated environment. IEEE Trans Power Syst 88:170–195Google Scholar
- Conejo AJ, Aguado JA (1998) Multi-area coordinated decentralized dc optimal power flow. IEEE Trans on Power Syst 13(4):1272–1278CrossRefGoogle Scholar
- Contreras J (1997) A cooperative game theory approach to transmission planning in power systems. PhD thesis, University of California, BerkeleyGoogle Scholar
- Contreras J, Wu F (1999) Coalition formation in transmission expansion planning. IEEE Trans Power Syst 14:1144–1152CrossRefGoogle Scholar
- Contreras J, Wu F (2000) A kernel-oriented algorithm for transmission expansion planning. IEEE Trans Power Syst 15:1434–1440CrossRefGoogle Scholar
- Contreras J, Gross G, Arroyo JM, Muñoz JI (2009) An incentive-based mechanism for transmission asset investment. Decis Support Syst 47:22–31. doi: 10.1016/j.dss.2008.12.005. http://dl.acm.org/citation.cfm?id=1519538.1519674 CrossRefGoogle Scholar
- Csercsik D, Kóczy LÁ (2011) Externalities in the games over electrical power transmission networks. Discussion Paper 2011.25, Centre for Economic Studies, Budapest http://econ.core.hu/file/download/mtdp/MTDP1125.pdf
- Currie J, Wilson DI (2012) Opti: Lowering the barrier between open source optimizers and the industrial matlab user. Foundations of Computer-Aided Process Operations, Savannah, Georgia, USA, 8–11Google Scholar
- Ding F, Fuller J (2005) Nodal, uniform, or zonal pricing: distribution of economic surplus. IEEE Trans Power Syst 20(2):875–882. doi: 10.1109/TPWRS.2005.846042 CrossRefGoogle Scholar
- Ehrenmann A (2004) Equilibrium problems with equilibrium constraints and their application to electricity markets. Fitzwilliam College, FitzwilliamGoogle Scholar
- Evans F, Zolezzi J, Rudnick H (2003) Cost assignment model for electrical transmission system expansion: an approach through the kernel theory. IEEE Trans Power Syst 18:625–632CrossRefGoogle Scholar
- Fisher EB, O’Neill RP, Ferris MC (2008) Optimal transmission switching. IEEE Trans Power Syst 23(3):1346–1355CrossRefGoogle Scholar
- Fuller J (2005) Relations among prices at adjacent nodes in an electric transmission network. Networks and Spatial Econ 5(3):279–292. doi: 10.1007/s11067-005-3036-0 CrossRefGoogle Scholar
- Gabriel S, Siddiqui S, Conejo A, Ruiz C (2013) Solving discretely-constrained nashcournot games with an application to power markets. Networks and Spatial Economics 13(3):307–326. doi: 10.1007/s11067-012-9182-2 CrossRefGoogle Scholar
- Gately D (1974) Sharing the gains from regional cooperation: A game theoretic application to planning investment in electric power. Int Econ Rev 15:195–208CrossRefGoogle Scholar
- Gilbert R, Neuhoff K, Newbery D (2004) Allocating transmission to mitigate market power in electricity networks. RAND J Econ 35(4):691–709. http://www.jstor.org/pss/1593768 CrossRefGoogle Scholar
- Habis H, Csercsik D (2014) Cooperation with externalities and uncertainty. Networks and Spatial Economics:1–16. doi: 10.1007/s11067-014-9265-3
- Habis H, Herings PJJ (2011) Transferable utility games with uncertainty. J Econ Theory 146(5):2126–2139. http://ideas.repec.org/a/eee/jetheo/v146y2011i5p2126-2139.html CrossRefGoogle Scholar
- Harrington J, Hobbs BF, Pang JS, Liu A, Roch G (2005) Collusive game solutions via optimization. Math Program 104(2–3):407–435CrossRefGoogle Scholar
- Hedman KW, O’Neill RP, Fisher EB, Oren SS (2008) Optimal transmission switching sensitivity analysis and extensions. IEEE Trans Power Syst 23(3):1469–1479CrossRefGoogle Scholar
- Hedman KW, O’Neill RP, Fisher EB, Oren SS (2009) Optimal transmission switching with contingency analysis. IEEE Trans Power Syst 24(3):1577–1586CrossRefGoogle Scholar
- Hedman KW, Ferris MC, O’Neill RP, Fisher EB, Oren SS (2010) Co-optimization of generation unit commitment and transmission switching with n-1 reliability. IEEE Trans Power Syst 25(2):1052–1063CrossRefGoogle Scholar
- Hingorani NG (1993) Flexible ac transmission. IEEE spectrum 30(4):40–45CrossRefGoogle Scholar
- Hingorani NG, Gyugyi L, El-Hawary M (2000) Understanding FACTS: concepts and technology of flexible AC transmission systems, vol 1. IEEE press New YorkGoogle Scholar
- Hobbs B, Kelly K (1992) Using game theory to analyze electric transmission pricing policies in the united states. Eur J Oper Res 56:154–171CrossRefGoogle Scholar
- Johnson SG (2010) The nlopt nonlinear-optimization packageGoogle Scholar
- Kirschen D, Strbac G (2004) Fundamentals of power system economics. Wiley. Ltd, Chichester, UK.Google Scholar
- Kirschen D, Allan R, Strbac G (1997) Contributions of individual generators to loads and flows. IEEE Trans Power Syst 12:52–60CrossRefGoogle Scholar
- Kleindorfer P, Wu DJ, Fernando C (2001) Strategic gaming in electric power markets. Eur J Oper Res 130:156–168CrossRefGoogle Scholar
- Le Digabel S (2011) Algorithm 909: Nomad: Nonlinear optimization with the mads algorithm. ACM Trans Math Softw (TOMS) 37(4):44CrossRefGoogle Scholar
- Leuthold F, Weigt H, von Hirschhausen C (2012) A large-scale spatial optimization model of the european electricity market. Networks and Spatial Economics 12(1):75–107. doi: 10.1007/s11067-010-9148-1 CrossRefGoogle Scholar
- Liu A, Hobbs B (2013) Tacit collusion games in pool-based electricity markets under transmission constraints. Math. Program 140(2):351–379. doi: 10.1007/s10107-013-0693-5 CrossRefGoogle Scholar
- Metzler C, Hobbs B, Pang JS (2003) Nash-Cournot equilibria in power markets on a linearized dc network with arbitrage: Formulations and properties. Networks and Spatial Economics 3(2):123–150. doi: 10.1023/A:1023907818360 CrossRefGoogle Scholar
- Neuhoff K, Barquin J, Boots M, Ehrenmann A, Hobbs B, Rijkers F, Vázquez M (2005) Network-constrained Cournot models of liberalized electricity markets: the devil is in the details. Energy Econ 27:495–525CrossRefGoogle Scholar
- Oggioni G, Smeers Y, Allevi E, Schaible S (2012) A generalized Nash equilibrium model of market coupling in the european power system. Networks and Spatial Economics 12(4):503–560. doi: 10.1007/s11067-011-9166-7 CrossRefGoogle Scholar
- Olsson DM, Nelson LS (1975) The nelder-mead simplex procedure for function minimization. Technometrics 17(1):45–51CrossRefGoogle Scholar
- O’Neill RP, Hedman KW, Krall EA, Papavasiliou A, Oren SS (2010) Economic analysis of the n-1 reliable unit commitment and transmission switching problem using duality concepts. Energy Syst 1(2):165–195CrossRefGoogle Scholar
- Orths A, Schmidtt A, Styczynski Z, Verstege J (2001) Multi-criteria optimization methods for planning and operation of electrical energy systems. Electr Eng 83:251–258CrossRefGoogle Scholar
- Ruiz C, Conejo AJ, Smeers Y (2012) Equilibria in an oligopolistic electricity pool with stepwise offer curves. IEEE Trans Power Syst 27(2):752–761CrossRefGoogle Scholar
- Sauma EE, Oren SS (2007) Economic criteria for planning transmission investment in restructured electricity markets. IEEE Trans Power Syst 22(4):1394–1405CrossRefGoogle Scholar
- Sheble GB, Fahd GN (1994) Unit commitment literature synopsis. IEEE Trans Power Syst 9(1):128–135CrossRefGoogle Scholar
- Singh H, Hao S, Papalexopoulos A (1998) Transmission congestion management in competitive electricity markets. IEEE Trans Power Syst 13(2):672 –680. doi: 10.1109/59.667399 CrossRefGoogle Scholar
- Song YH, Johns AT (1999) Flexible ac transmission systems (FACTS), vol 30. IETGoogle Scholar
- Thrall RM, Lucas WF (1963)
*n*-person games in partition function form. Naval Res Logist Q 10(4):281–298CrossRefGoogle Scholar - De la Torre S, Conejo A, Contreras J (2003) Simulating oligopolistic pool-based electricity markets: A multiperiod approach. IEEE Trans Power Syst 18(4):1547–1555CrossRefGoogle Scholar
- De la Torre S, Contreras J, Conejo AJ (2004) Finding multiperiod nash equilibria in pool-based electricity markets. IEEE Trans Power Syst 19(1):643–651CrossRefGoogle Scholar
- Tseng CL, Oren SS, Cheng CS, Li Ca, Svoboda AJ, Johnson RB (1999) A transmission-constrained unit commitment method in power system scheduling. Decis Support Syst 24(3):297–310CrossRefGoogle Scholar
- Van Cutsem T, Vournas C (1998) Voltage stability of electric power systems. Kluwer Academic PublishersGoogle Scholar
- van Laarhoven P, Aarts E (2008) Springer, Simulated annealing: Theory and applicationsGoogle Scholar
- Vaz AIF, Vicente LN (2007) A particle swarm pattern search method for bound constrained global optimization. J Glob Optim 39(2):197–219CrossRefGoogle Scholar
- Wächter A, Biegler LT (2006) On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math Program 106(1):25–57CrossRefGoogle Scholar
- Wijayatunga P (2003) Optimal transmission pricing with generation uncertainty and transmission losses. IEEE Trans Power Syst 150:73–77Google Scholar
- Wood AJ, Wollenberg BF (2012) Power generation, operation, and control. WileyGoogle Scholar
- Wu F, Varaiya P, Spiller P, Oren S (1996) Folk theorems on transmission access: Proofs and counterexamples. J Regul Econ 10(1):5–23. doi: 10.1007/BF00133356 CrossRefGoogle Scholar
- Yao J, Oren SS, Adler I (2004) Computing cournot equilibria in two settlement electricity markets with transmission constraint. In: Proceedings of the 37th Annual Hawaii International Conference on System Sciences, 2004, p. 9. IEEEGoogle Scholar
- Zhuang F, Galiana F (1990) Unit commitment by simulated annealing. IEEE Trans Power Syst 5(1):311–318CrossRefGoogle Scholar