Optimal storage and transmission investments in a bilevel electricity market model

  • Martin WeibelzahlEmail author
  • Alexandra Märtz
S.I. : Game theory and optimization


This paper analyzes the interplay of transmission and storage investments in a multistage game that we translate into a bilevel market model. In particular, on the first level we assume that a transmission system operator chooses optimal line investments and a corresponding optimal network fee. On the second level we model competitive firms that trade energy on a zonal market with limited transmission capacities and decide on their optimal storage facility investments. To the best of our knowledge, we are the first to analyze interdependent transmission and storage facility investments in a zonal market environment that accounts for the described hierarchical decision structure. As a first best benchmark, we also present an integrated, single-level problem that may be interpreted as a long-run nodal pricing model. Our numerical results show that adequate storage facility investments of firms may in general have the potential to reduce the amount of line investments of the transmission system operator. However, our bilevel zonal pricing model may yield inefficient investments in storages, which may be accompanied by suboptimal network facility extensions as compared to the nodal pricing benchmark. In this context, the chosen zonal configuration of the network will highly influence the equilibrium investment outcomes including the size and location of the newly invested facilities. As zonal pricing is used for instance in Australia or Europe, our models may be seen as valuable tools for evaluating different regulatory policy options in the context of long-run investments in storage and network facilities.


Bilevel problem Multistage game Congestion management Zonal pricing Storage facilities Long-run investments Decision support 



We thank Claudia Ehrig, Arie M.C.A. Koster, Katja Kutzer, Paul Schott and Nils Spiekermann for their valuable comments and discussions. In addition, we highly acknowledge the good cooperation with Veronika Grimm, Alexander Martin, Martin Schmidt, Christian Sölch, and Gregor Zöttl at the Friedrich-Alexander-University Erlangen-Nuremberg in the past years.


  1. Alguacil, N., Motto, A. L., & Conejo, A. J. (2003). Transmission expansion planning: A mixed-integer LP approach. IEEE Transactions on Power Systems, 18(3), 1070–1077.
  2. Baringo, L., & Conejo, A. J. (2012). Transmission and wind power investment. IEEE Transactions on Power Systems, 27(2), 885–893.
  3. Bjørndal, E., Bjørndal, M., & Cai, H. (2014). Nodal pricing in a coupled electricity market. In 2014 11th international conference on the European energy market (EEM) (pp. 1–6). IEEE.Google Scholar
  4. Bjørndal, M., & Jørnsten, K. (2001). Zonal pricing in a deregulated electricity market. The Energy Journal, 22(1), 51–73.CrossRefGoogle Scholar
  5. Bjørndal, M., & Jørnsten, K. (2007). Benefits from coordinating congestion management: The Nordic power market. Energy Policy, 35(3), 1978–1991.CrossRefGoogle Scholar
  6. Bjørndal, M., Jørnsten, K., & Pignon, V. (2003). Congestion management in the nordic power market: Counter purchasers and zonal pricing. Journal of Network Industries, 4(3), 271–292.Google Scholar
  7. Bohn, R. E., Caramanis, M. C., & Schweppe, F. C. (1984). Optimal pricing in electrical networks over space and time. The RAND Journal of Economics, 15, 360–376.CrossRefGoogle Scholar
  8. Boucher, J., & Smeers, Y. (2001). Alternative models of restructured electricity systems, part 1: No market power. Operations Research, 49(6), 821–838.
  9. Boyd, S., & Vandenberghe, L. (2004). Convex optimization. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  10. Bucksteeg, M., Trepper, K., & Weber, C. (2015). Impacts of RES-generation and demand pattern on net transfer capacity: Implications for effectiveness of market splitting in Germany. Generation Transmission and Distribution (Vol. 9, pp. 1510–1518)Google Scholar
  11. Bunn, D. W., & Oliveira, F. S. (2003). Evaluating individual market power in electricity markets via agent-based simulation. Annals of Operations Research, 121(1), 57–77.CrossRefGoogle Scholar
  12. Campêlo, M., & Scheimberg, S. (2005). A simplex approach for finding local solutions of a linear bilevel program by equilibrium points. Annals of Operations Research, 138(1), 143–157.CrossRefGoogle Scholar
  13. Chao, H.-P., & Peck, S. (1996). A market mechanism for electric power transmission. Journal of Regulatory Economics, 10(1), 25–59.CrossRefGoogle Scholar
  14. Chao, H.-P., & Peck, S. (1998). Reliability management in competitive electricity markets. Journal of Regulatory Economics, 14(2), 189–200.
  15. Colson, B., Marcotte, P., & Savard, G. (2007). An overview of bilevel optimization. Annals of Operations Research, 153(1), 235–256.CrossRefGoogle Scholar
  16. Conejo, A. J., Cheng, Y., Zhang, N., & Kang, C. (2017). Long-term coordination of transmission and storage to integrate wind power. CSEE Journal of Power and Energy Systems, 3(1), 36–43.CrossRefGoogle Scholar
  17. CPLEX. (2013). User’s manual for CPLEX, 12.6 edition. Armonk: IBM Corporation.Google Scholar
  18. David, A., & Wen, F. (2001). Transmission planning and investment under competitive electricity market environment. In Power engineering society summer meeting, 2001 (Vol. 3, pp. 1725–1730). IEEE.Google Scholar
  19. Daxhelet, O., & Smeers, Y. (2007). The EU regulation on cross-border trade of electricity: A two-stage equilibrium model. European Journal of Operational Research, 181(3), 1396–1412.
  20. Dempe, S. (2002). Foundations of bilevel programming. Springer.Google Scholar
  21. Dempe, S. (2003). Annotated bibliography on bilevel programming and mathematical programs with equilibrium constraints. Optimization, 52(3), 333–359.CrossRefGoogle Scholar
  22. Dempe, S., & Zemkoho, A. B. (2012). Bilevel road pricing: Theoretical analysis and optimality conditions. Annals of Operations Research, 196(1), 223–240.CrossRefGoogle Scholar
  23. Dijk, J., & Willems, B. (2011). The effect of counter-trading on competition in electricity markets. Energy Policy, 39(3), 1764–1773.CrossRefGoogle Scholar
  24. Ehrenmann, A., & Smeers, Y. (2005). Inefficiencies in European congestion management proposals. Utilities policy, 13(2), 135–152.
  25. Fan, H., Cheng, H., & Yao, L. (2009). A bi-level programming model for multistage transmission network expansion planning in competitive electricity market. In Power and energy engineering conference, 2009. APPEEC 2009. Asia-Pacific (pp. 1–6). IEEE.Google Scholar
  26. Fortuny-Amat, J., & McCarl, B. (1981). A representation and economic interpretation of a two-level programming problem. Journal of the operational Research Society, 32(9), 783–792.CrossRefGoogle Scholar
  27. Galiana, F. D., Conejo, A. J., & Gil, H. A. (2003). Transmission network cost allocation based on equivalent bilateral exchanges. IEEE Transactions on Power Systems, 18(4), 1425–1431.CrossRefGoogle Scholar
  28. Gallego, R. A., Monticelli, A., & Romero, R. (1998). Transmission system expansion planning by an extended genetic algorithm. IEEE Proceedings-Generation, Transmission and Distribution, 145(3), 329–335.
  29. Garcés, L. P., Conejo, A. J., García-Bertrand, R., & Romero, R. (2009a). A bilevel approach to transmission expansion planning within a market environment. IEEE Transactions on Power Systems, 24(3), 1513–1522.CrossRefGoogle Scholar
  30. Garcés, L. P., Conejo, A. J., García-Bertrand, R., & Romero, R. (2009b). A bilevel approach to transmission expansion planning within a market environment. IEEE Transactions on Power Systems, 24(3), 1513–1522.CrossRefGoogle Scholar
  31. Gast, N., Le Boudec, J.-Y., Proutière, A., & Tomozei, D.-C. (2013). Impact of storage on the efficiency and prices in real-time electricity markets. In Proceedings of the fourth international conference on future energy systems (pp. 15–26). ACM.Google Scholar
  32. German-Transmission-System-Operators. (2017). Grid development plan electricity 2030. Accessed March 2017
  33. Gil, H. A., Da Silva, E. L., & Galiana, F. D. (2002). Modeling competition in transmission expansion. IEEE Transactions on Power Systems, 17(4), 1043–1049.CrossRefGoogle Scholar
  34. Glachant, J.-M., & Pignon, V. (2005). Nordic congestion’s arrangement as a model for europe? Physical constraints vs. economic incentives. Utilities Policy, 13(2), 153–162.CrossRefGoogle Scholar
  35. Grimm, V., Martin, A., Schmidt, M., Weibelzahl, M., & Zöttl, G. (2016a). Transmission and generation investment in electricity markets: The effects of market splitting and network fee regimes. European Journal of Operational Research, 254(2), 493–509.CrossRefGoogle Scholar
  36. Grimm, V., Martin, A., Weibelzahl, M., & Zöttl, G. (2016b). On the long-run effects of market splitting: Why more price zones might decrease welfare. Energy Policy, 94, 453–467.CrossRefGoogle Scholar
  37. Hirst, E., & Kirby, B. (2001). Key transmission planning issues. The Electricity Journal, 14(8), 59–70.CrossRefGoogle Scholar
  38. Hogan, W. (1992). Contract networks for electric power transmission. Journal of Regulatory Economics, 4(3), 211–242.CrossRefGoogle Scholar
  39. Hornnes, K. S., Grande, O. S., & Bakken, B. H. (2000). Main grid development planning in a deregulated market regime. In Power engineering society winter meeting, 2000 (Vol. 2, pp. 845–849). IEEE.Google Scholar
  40. Hu, X., & Ralph, D. (2007). Using EPECs to model bilevel games in restructured electricity markets with locational prices. Operations Research, 55(5), 809–827.
  41. Huppmann, D., & Egerer, J. (2015). National-strategic investment in european power transmission capacity. European Journal of Operational Research, 247(1), 191–203.CrossRefGoogle Scholar
  42. Ishizuka, Y., & Aiyoshi, E. (1992). Double penalty method for bilevel optimization problems. Annals of Operations Research, 34(1), 73–88.CrossRefGoogle Scholar
  43. Jenabi, M., Ghomi, S. M. T. F., & Smeers, Y. (2013). Bi-level game approaches for coordination of generation and transmission expansion planning within a market environment. IEEE Transactions on Power Systems, 28(3), 2639–2650.
  44. Jeroslow, R. G. (1985). The polynomial hierarchy and a simple model for competitive analysis. Mathematical Programming, 32(2), 146–164.
  45. Kirschen, D., & Strbac, G. (2005). Investing in transmission. Fundamentals of Power System Economics (pp. 227–264).Google Scholar
  46. Koch, T. (2005). Rapid mathematical programming. Dissertation for the Doctoral Degree. Berlin: Technische Universitay.Google Scholar
  47. Kuznia, L., Zeng, B., Centeno, G., & Miao, Z. (2013). Stochastic optimization for power system configuration with renewable energy in remote areas. Annals of Operations Research, 210(1), 411–432.CrossRefGoogle Scholar
  48. Mangasarian, O. (1988). A simple characterization of solution sets of convex programs. Operations Research Letters, 7(1), 21–26.CrossRefGoogle Scholar
  49. Neuhoff, K., Barquin, J., Bialek, J. W., Boyd, R., Dent, C. J., Echavarren, F., et al. (2013). Renewable electric energy integration: Quantifying the value of design of markets for international transmission capacity. Energy Economics, 40, 760–772.CrossRefGoogle Scholar
  50. Oggioni, G., & Smeers, Y. (2013). Market failures of market coupling and counter-trading in Europe: An illustrative model based discussion. Energy Economics, 35, 74–87.
  51. Pozo, D., Sauma, E., & Contreras, J. (2017). Basic theoretical foundations and insights on bilevel models and their applications to power systems. Annals of Operations Research, 254(1–2), 303–334.CrossRefGoogle Scholar
  52. Rious, V., Glachant, J.-M., Perez, Y., & Dessante, P. (2008). The diversity of design of tsos. Energy Policy, 36(9), 3323–3332.CrossRefGoogle Scholar
  53. Sariddichainunta, P., & Inuiguchi, M. (2017). Global optimality test for maximin solution of bilevel linear programming with ambiguous lower-level objective function. Annals of Operations Research, 256(2), 285–304.CrossRefGoogle Scholar
  54. Sauma, E. E., & Oren, S. S. (2006). Proactive planning and valuation of transmission investments in restructured electricity markets. Journal of Regulatory Economics, 30(3), 261–290.CrossRefGoogle Scholar
  55. Sioshansi, R. (2010). Welfare impacts of electricity storage and the implications of ownership structure. The Energy Journal, 31(2), 173–198.CrossRefGoogle Scholar
  56. Sioshansi, R. (2014). When energy storage reduces social welfare. Energy Economics, 41, 106–116.CrossRefGoogle Scholar
  57. Sioshansi, R., Denholm, P., Jenkin, T., & Weiss, J. (2009). Estimating the value of electricity storage in PJM: Arbitrage and some welfare effects. Energy Economics, 31(2), 269–277.CrossRefGoogle Scholar
  58. Sioshansi, R., Madaeni, S. H., & Denholm, P. (2014). A dynamic programming approach to estimate the capacity value of energy storage. IEEE Transactions on Power Systems, 29(1), 395–403.CrossRefGoogle Scholar
  59. Steinke, F., Wolfrum, P., & Hoffmann, C. (2013). Grid vs. storage in a 100% renewable europe. Renewable Energy, 50, 826–832.CrossRefGoogle Scholar
  60. Von Stackelberg, H. (2010). Market structure and equilibrium. Springer.Google Scholar
  61. Weibelzahl, M. (2017). Nodal, zonal, or uniform electricity pricing: How to deal with network congestion? Frontiers in Energy, 11(2), 210–232.CrossRefGoogle Scholar
  62. Weibelzahl, M., & Märtz, A. (2017). On the effects of storage facilities on optimal zonal pricing in electricity markets. Energy Policy, 113(2), 778–794.Google Scholar
  63. Zambrano, C., & Olaya, Y. (2017). An agent-based simulation approach to congestion management for the colombian electricity market. Annals of Operations Research, 258(2), 217–236.CrossRefGoogle Scholar
  64. Zare, M. H., Borrero, J. S., Zeng, B., & Prokopyev, O. A. (2017). A note on linearized reformulations for a class of bilevel linear integer problems. Annals of Operations Research, 1–19.Google Scholar
  65. Zugno, M., Morales, J. M., Pinson, P., & Madsen, H. (2013). A bilevel model for electricity retailers’ participation in a demand response market environment. Energy Economics, 36, 182–197.CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.FIM Research CenterBayreuthGermany
  2. 2.University of BayreuthBayreuthGermany
  3. 3.Chair of Energy Economics, Institute for Industrial Production (IIP)Karlsruhe Institute of TechnologyKarlsruheGermany
  4. 4.Discrete OptimizationFriedrich-Alexander-Universität Erlangen-NürnbergErlangenGermany

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