×

zbMATH — the first resource for mathematics

The value of cooperation in interregional transmission planning: a noncooperative equilibrium model approach. (English) Zbl 1441.91049
Summary: Optimization methods for regional transmission planning overlook boundaries between transmission planning entities and do not account for their lack of coordination. The practical result of those boundaries is inefficient plans because one planning region may disregard the costs and benefits that its network changes impose on other regions. We develop a bi-level EPEC (Equilibrium Problem with Equilibrium Constraints) model that represents a game among multiple noncooperative transmission planners in the upper level together with consumers and generators for the entire region in the lower level. We find that the equilibrium transmission plans from such a framework can differ significantly from those from a cooperative framework and have fewer net benefits. Importantly, we find that cooperation among transmission planners leads to increased competition among generators from adjoining regions, which in turn leads to more efficient generator investments. We prove that the system-wide benefit from cooperation among transmission planners is always positive. We then calculate the value of this cooperation for a small test case with two transmission planners, while also identifying the market parties who gain – and those who lose – from this cooperation.
Reviewer: Reviewer (Berlin)

MSC:
91B74 Economic models of real-world systems (e.g., electricity markets, etc.)
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
91A12 Cooperative games
Software:
AIMMS; CPLEX
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Abe, T., Efficiency and the Core in Games with Positive and Negative Externalities, Technical Report (2016)
[2] Appendix (2019). Online appendix. URL:bit.ly/ejor2019kasinahobbs.
[3] Bakirtzis, A. G.; Ziogos, N. P.; Tellidou, A. C.; Bakirtzis, G., Electricity producer offering strategies in day-ahead energy market with step-wise offers, IEEE Transactions on Power Systems, 22, 4, 1804-1818 (2007)
[4] Belotti, P., Disjunctive cuts for nonconvex MINLP, Mixed integer nonlinear programming, 117-144 (2012), Springer · Zbl 1242.90118
[5] Bertsch, J.; Hagspiel, S.; Just, L., Congestion management in power systems, Journal of Regulatory Economics, 50, 3, 290-327 (2016)
[6] Bilbao, J. M.; Lebrón, E.; Jiménez, N., The core of games on convex geometries, European Journal of Operational Research, 119, 2, 365-372 (1999) · Zbl 0983.91009
[7] Bisschop, J.; Entriken, R., AIMMS: The modeling system (1993), Paragon Decision Technology
[8] Bliek1ú, C.; Bonami, P.; Lodi, A., Solving mixed-integer quadratic programming problems with IBM-CPLEX: a progress report, Proceedings of the twenty-sixth RAMP symposium, 16-17 (2014)
[9] Boţ, R.; Kassay, G.; Wanka, G., Strong duality for generalized convex optimization problems, Journal of Optimization Theory and Applications, 127, 1, 45-70 (2005) · Zbl 1158.90420
[10] Buijs, P.; Belmans, R., Transmission investments in a multilateral context, IEEE Transactions on Power Systems, 27, 1, 475-483 (2012)
[11] Buijs, P.; Meeus, L.; Belmans, R., Modelling bilevel games in transmission investment planning, Proceedings of the IAEE international conference (2012)
[12] CAISO (2018). 2019 Local Capacity Technical Analysis: Final Report and Study Results. Technical report.
[13] Chander, P.; Tulkens, H., The core of an economy with multilateral environmental externalities, Public goods, environmental externalities and fiscal competition, 153-175 (2006), Springer
[14] Chen, B.; Wang, L., Robust transmission planning under uncertain generation investment and retirement, IEEE Transactions on Power Systems, 31, 6, 5144-5152 (2016)
[15] Chen, Y.; Hobbs, B. F.; Leyffer, S.; Munson, T. S., Leader-follower equilibria for electric power and NO_x allowances markets, Computational Management Science, 3, 4, 307-330 (2006) · Zbl 1273.91207
[16] Contreras, J.; Wu, F., Coalition formation in transmission expansion planning, IEEE Transactions on Power Systems, 14, 3, 1144-1152 (1999)
[17] D’Ambrosio, C.; Lodi, A., Mixed integer nonlinear programming tools: an updated practical overview, Annals of Operations Research, 204, 1, 301-320 (2013) · Zbl 1269.90067
[18] De Jonghe, C.; Hobbs, B. F.; Belmans, R., Optimal generation mix with short-term demand response and wind penetration, IEEE Transactions on Power Systems, 27, 2, 830-839 (2012)
[19] Ehrenmann, A., Equilibrium problems with equilibrium constraints and their application to electricity markets (2004), Citeseer, Ph.D. thesis.
[20] EIPC (2010). EIPC modeling results: Futures & sensitivities. http://www.eipconline.com/modeling-results.html.
[21] ERCOT (2014). ERCOT system planning: 2014 regional transmission plan report. http://www.ercot.com/news/presentations/.
[22] FERC (2016). Order no. 1000 - transmission planning and cost allocation. https://www.ferc.gov/industries/electric/indus-act/trans-plan.asp.
[23] Gabriel, S. A.; Conejo, A. J.; Fuller, J. D.; Hobbs, B. F.; Ruiz, C., Complementarity modeling in energy markets, 180 (2012), Springer Science & Business Media
[24] Gately, D., Sharing the gains from regional cooperation: A game theoretic application to planning investment in electric power, International Economic Review, 15, 1, 195-208 (1974) · Zbl 0276.90085
[25] Gu, Y.; McCalley, J. D.; Ni, M., Coordinating large-scale wind integration and transmission planning, IEEE Transaction on Sustainable Energy, 3, 4, 652-659 (2012)
[26] Gu, Y.; Xie, L.; Rollow, B.; Hesselbaek, B., Congestion-induced wind curtailment: Sensitivity analysis and case studies, Proceedings of the North American power symposium (naps), 2011, 1-7 (2011), IEEE
[27] Guajardo, M.; Jörnsten, K.; Rönnqvist, M., Constructive and blocking power in collaborative transportation, OR spectrum, 38, 1, 25-50 (2016) · Zbl 1336.90016
[28] Hafalir, I. E., Efficiency in coalition games with externalities, Games and Economic Behavior, 61, 2, 242-258 (2007) · Zbl 1271.91017
[29] Han, D.; Zhang, H.; Qian, G.; Xu, L., An improved two-step method for solving generalized Nash equilibrium problems, European Journal of Operational Research, 216, 3, 613-623 (2012) · Zbl 1252.90081
[30] Harker, P. T., Generalized nash games and quasi-variational inequalities, European journal of Operational research, 54, 1, 81-94 (1991) · Zbl 0754.90070
[31] Ho, J. L.; Hobbs, B. F.; Donohoo-Vallett, P.; Xu, Q.; Kasina, S.; Park, S.; Ouyang, Y., Planning transmission for uncertainty: Applications and lessons for the western interconnection, Proceedings of the western electricity coordinating council (2016)
[32] Hobbs, B.; Metzler, C.; Pang, J.-S., Strategic gaming analysis for electric power systems: an MPEC approach, IEEE Transactions on Power Systems, 15, 2, 638-645 (2000)
[33] Holt, C. A.; Shobe, W.; Burtraw, D.; Palmer, K. L.; Goeree, J. K., Auction design for selling CO2 emission allowances under the regional greenhouse gas initiative, Technical Report (2007)
[34] Hu, X.; Ralph, D., Using EPECS to model bilevel games in restructured electricity markets with locational prices, Operations research, 55, 5, 809-827 (2007) · Zbl 1167.91357
[35] Hunting, M., Solving convex MINLP problems with AIMMS, An AIMMS white paper (2012)
[36] Huppmann, D.; Egerer, J., National-strategic investment in European power transmission capacity, European Journal of Operational Research, 247, 1, 191-203 (2015) · Zbl 1346.91181
[37] Jackson, M. O.; Wilkie, S., Endogenous games and mechanisms: Side payments among players, The Review of Economic Studies, 72, 2, 543-566 (2005) · Zbl 1121.91013
[38] Jin, S.; Ryan, S., A tri-level model of centralized transmission and decentralized generation expansion planning for an electricity market part II, IEEE Transactions on Power Systems, 29, 1, 142-148 (2014)
[39] Joskow, P. L., Transmission policy in the united states, Utilities Policy, 13, 2, 95-115 (2005)
[40] Kazempour, S. J.; Conejo, A. J.; Ruiz, C., Strategic generation investment using a complementarity approach, IEEE Transactions on Power Systems, 26, 2, 940-948 (2011)
[41] Krishnan, V.; Ho, J.; Hobbs, B. F.; Liu, A. L.; McCalley, J. D.; Shahidehpour, M.; Zheng, Q. P., Co-optimization of electricity transmission and generation resources for planning and policy analysis: Review of concepts and modeling approaches, Energy Systems, 7, 2, 297-332 (2016)
[42] Lam, L. T.; Branstetter, L.; Azevedo, I. M., China’s wind electricity and cost of carbon mitigation are more expensive than anticipated, Environmental Research Letters, 11, 8, 084015 (2016)
[43] Leng, M.; Parlar, M., Allocation of cost savings in a three-level supply chain with demand information sharing: A cooperative-game approach, Operations Research, 57, 1, 200-213 (2009) · Zbl 1181.90015
[44] Leng, M.; Zhu, A., Side-payment contracts in two-person nonzero-sum supply chain games: Review, discussion and applications, European Journal of Operational Research, 196, 2, 600-618 (2009) · Zbl 1163.90556
[45] Li, F.; Bo, R., DCOPF-based LMP simulation: algorithm, comparison with ACOPF, and sensitivity, IEEE Transactions on Power Systems, 22, 4, 1475-1485 (2007)
[46] Lindgreen, A.; Hingley, M.; Lawson, R.; Guthrie, J.; Cameron, A.; Fischer, W. C., Creating value through cooperation: An investigation of farmers’ markets in new zealand, British Food Journal, 110, 1, 11-25 (2008)
[47] Lozano, S.; Moreno, P.; Adenso-Díaz, B.; Algaba, E., Cooperative game theory approach to allocating benefits of horizontal cooperation, European Journal of Operational Research, 229, 2, 444-452 (2013) · Zbl 1317.91003
[48] Luo, Z.-Q.; Pang, J.-S.; Ralph, D., Mathematical programs with equilibrium constraints (1996), Cambridge University Press
[49] Manley, J. (2016). India already has a problem with wasting renewable energy on the grid. https://www.greentechmedia.com/articles/read/how-can-india-avoid-wasting-renewable-energy.
[50] MISO (2014). MISO transmission expansion plan 2014. https://www.misoenergy:org/Library/Repository/Study/MTEP/MTEP14/MTEP14%20Full%20Report:pdf.
[51] Munoz, F.; Hobbs, B.; Ho, J.; Kasina, S., An engineering-economic approach to transmission planning under market and regulatory uncertainties: WECC case study, IEEE Transactions on Power Systems, 29, 1, 307-317 (2014)
[52] Munoz, F. D.; Hobbs, B.; Kasina, S., Efficient proactive transmission planning to accommodate renewables, Proceedings of the IEEE PES general meeting, 1-7 (2012)
[53] O’Malley, C. (2015). 2 of 3 MISO-SPP seams projects likely doomed. https://www.rtoinsider.com/miso-spp-interregional-transmission-17298/.
[54] Özdemir, Ö.; Munoz, F. D.; Ho, J. L.; Hobbs, B. F., Economic analysis of transmission expansion planning with price-responsive demand and quadratic losses by successive LP, IEEE Transactions on Power Systems, 31, 2, 1096-1107 (2016)
[55] Pineau, P.-O.; Murto, P., An oligopolistic investment model of the finnish electricity market, Annals of Operations Research, 121, 1-4, 123-148 (2003) · Zbl 1037.91530
[56] Pozo, D.; Contreras, J., Finding multiple Nash equilibria in pool-based markets: A stochastic EPEC approach, IEEE Transactions on Power Systems, 26, 3, 1744-1752 (2011)
[57] Pozo, D.; Sauma, E. E.; Contreras, J., A three-level static MILP model for generation and transmission expansion planning, IEEE Transactions on Power Systems, 28, 1, 202-210 (2013)
[58] Pulido, M. A.; Sánchez-Soriano, J., On the core, the weber set and convexity in games with a priori unions, European Journal of Operational Research, 193, 2, 468-475 (2009) · Zbl 1152.91010
[59] Quesada, I.; Grossmann, I. E., An LP/NLP based branch and bound algorithm for convex MINLP optimization problems, Computers & chemical engineering, 16, 10-11, 937-947 (1992)
[60] Ralph, D.; Smeers, Y., EPECs as models for electricity markets, Proceedings of the power systems conference and exposition, 2006. PSCE’06. 2006 IEEE PES, 74-80 (2006), IEEE
[61] Rivera-Linares, C. (2015). FERC approves order conditionally accepting compliance filings by ISO-NE, NYISO, PJM involving Order 1000 interregional requirements. http://www.transmissionhub.com/articles/2015/05/ferc-approves-order-conditionally-accepting-compliance-filings-by-iso-ne-nyiso-pjm-involving-order-1000-interregional-requirements.html.
[62] Ruiz, C.; Conejo, A. J.; Smeers, Y., Equilibria in an oligopolistic electricity pool with stepwise offer curves, IEEE Transactions on Power Systems, 27, 2, 752-761 (2012)
[63] Sauma, E. E.; Oren, S. S., Proactive planning and valuation of transmission investments in restructured electricity markets, Journal of Regulatory Economics, 30, 3, 261-290 (2006)
[64] Shapley, L. S., Cores of convex games, International journal of game theory, 1, 1, 11-26 (1971) · Zbl 0222.90054
[65] Stoft, S., Problems of transmission investment in a deregulated power market, Competitive electricity markets and sustainability, 87-130 (2006), Edward Elgar
[66] Tohidi, Y.; Hesamzadeh, M. R.; Regairaz, F., Modified benders decomposition for solving transmission investment game with risk measure, IEEE Transactions on Power Systems, 33, 2, 1936-1947 (2017)
[67] Tohidi, Y.; Hesamzadeh, M. R., Multi-regional transmission planning as a non-cooperative decision-making, IEEE Trans. Pow. Sys., 29 (2014)
[68] Von Neumann, J.; Morgenstern, O., Theory of games and economic behavior (2007), Princeton university press
[69] Von Stackelberg, H., Market structure and equilibrium (2010), Springer Science & Business Media
[70] Wang, Q.; Parlar, M., A three-person game theory model arising in stochastic inventory control theory, European Journal of Operational Research, 76, 1, 83-97 (1994) · Zbl 0820.90037
[71] WECC (2013). 2013 Interconnection-wide plan summary. https://www.wecc.biz/Reliability/2013Plan_PlanSummary.pdf.
[72] van der Weijde, A. H.; Hobbs, B. F., The economics of planning electricity transmission to accommodate renewables: Using two-stage optimisation to evaluate flexibility and the cost of disregarding uncertainty, Energy Economics, 34, 6, 2089-2101 (2012)
[73] Weisstein, E. W., Wolfram Research, Inc. (2002)
[74] Whittington, D.; Wu, X.; Sadoff, C., Water resources management in the Nile basin: the economic value of cooperation, Water policy, 7, 3, 227-252 (2005)
[75] Wogrin, S.; Centeno, E.; Barquín, J., Generation capacity expansion in liberalized electricity markets: a stochastic MPEC approach, IEEE Transactions on Power Systems, 26, 4, 2526-2532 (2011)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.