Optimal storage and transmission investments in a bilevel electricity market model

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.

[1]  P. Denholm,et al.  Estimating the value of electricity storage in PJM: Arbitrage and some welfare effects , 2009 .

[2]  Yves Smeers,et al.  Alternative Models of Restructured Electricity Systems, Part 1: No Market Power , 2001, Oper. Res..

[3]  Tobias Achterberg,et al.  SCIP: solving constraint integer programs , 2009, Math. Program. Comput..

[4]  Bert Willems,et al.  The effect of counter-trading on competition in electricity markets , 2011 .

[5]  Masahiro Inuiguchi,et al.  Global optimality test for maximin solution of bilevel linear programming with ambiguous lower-level objective function , 2017, Ann. Oper. Res..

[6]  Martin Weibelzahl,et al.  Nodal, zonal, or uniform electricity pricing: how to deal with network congestion , 2017 .

[7]  José Fortuny-Amat,et al.  A Representation and Economic Interpretation of a Two-Level Programming Problem , 1981 .

[8]  Yves Smeers,et al.  Inefficiencies in European Congestion Management Proposals , 2004 .

[9]  Yang Gu,et al.  Market-based transmission expansion planning under uncertainty , 2010, North American Power Symposium 2010.

[10]  S. Oren,et al.  Proactive planning and valuation of transmission investments in restructured electricity markets , 2006 .

[11]  Enzo Sauma,et al.  Basic theoretical foundations and insights on bilevel models and their applications to power systems , 2017, Ann. Oper. Res..

[12]  S. Binato,et al.  Large scale transmission network planning using optimization and heuristic techniques , 1995 .

[13]  Main grid development planning in a deregulated market regime , 2000, 2000 IEEE Power Engineering Society Winter Meeting. Conference Proceedings (Cat. No.00CH37077).

[14]  Hamidreza Zareipour,et al.  A Transmission Planning Framework Considering Future Generation Expansions in Electricity Markets , 2010, IEEE Transactions on Power Systems.

[15]  MANOEL CAMPÊLO,et al.  A Simplex Approach for Finding Local Solutions of a Linear Bilevel Program by Equilibrium Points , 2005, Ann. Oper. Res..

[16]  Heinrich von Stackelberg Market Structure and Equilibrium , 2010 .

[17]  Antonio J. Conejo,et al.  Transmission network cost allocation based on equivalent bilateral exchanges , 2003 .

[18]  Oleg A. Prokopyev,et al.  A note on linearized reformulations for a class of bilevel linear integer problems , 2019, Ann. Oper. Res..

[19]  Stephan Dempe,et al.  Foundations of Bilevel Programming , 2002 .

[20]  Kurt Jörnsten,et al.  Benefits from coordinating congestion management—The Nordic power market , 2007 .

[21]  Derek W. Bunn,et al.  Evaluating Individual Market Power in Electricity Markets via Agent-Based Simulation , 2003, Ann. Oper. Res..

[22]  M. Bjørndal,et al.  Congestion Management in the Nordic Power Market — Counter Purchases and Zonal Pricing , 2003 .

[23]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[24]  Kit Po Wong,et al.  Flexible Transmission Network Planning Considering Distributed Generation Impacts , 2011, IEEE Transactions on Power Systems.

[25]  Goran Strbac,et al.  Investing in Transmission , 2005 .

[26]  Grisselle Centeno,et al.  Stochastic optimization for power system configuration with renewable energy in remote areas , 2013, Ann. Oper. Res..

[27]  Antonio J. Conejo,et al.  Long-term coordination of transmission and storage to integrate wind power , 2017 .

[28]  Christoph Weber,et al.  Renewable Electric Energy Integration: Quantifying the Value of Design of Markets for International Transmission Capacity , 2011 .

[29]  Stephan Dempe,et al.  Bilevel road pricing: theoretical analysis and optimality conditions , 2012, Ann. Oper. Res..

[30]  Robert G. Jeroslow,et al.  The polynomial hierarchy and a simple model for competitive analysis , 1985, Math. Program..

[31]  Florian Steinke,et al.  Grid vs. storage in a 100% renewable Europe , 2013 .

[32]  Yves Smeers,et al.  The EU regulation on cross-border trade of electricity: A two-stage equilibrium model , 2007, Eur. J. Oper. Res..

[33]  Jaeseok Choi,et al.  Transmission System Expansion Planning Considering Outage Cost , 2007, Second International Conference on Innovative Computing, Informatio and Control (ICICIC 2007).

[34]  A. Conejo,et al.  A Bilevel Approach to Transmission Expansion Planning Within a Market Environment , 2009, IEEE Transactions on Power Systems.

[35]  Cristian Zambrano,et al.  An agent-based simulation approach to congestion management for the Colombian electricity market , 2016, Annals of Operations Research.

[36]  F. Schweppe,et al.  Optimal Pricing in Electrical Networks over Space and Time , 1984 .

[37]  Alexander Martin,et al.  Transmission and generation investment in electricity markets: The effects of market splitting and network fee regimes , 2016, Eur. J. Oper. Res..

[38]  K. Jörnsten,et al.  Zonal Pricing in a Deregulated Electricity Market , 2001 .

[39]  F. D. Galiana,et al.  Modeling Competition in Transmission Expansion , 2002, IEEE Power Engineering Review.

[40]  Yves Smeers,et al.  Market failures of Market Coupling and counter-trading in Europe: An illustrative model based discussion , 2013 .

[41]  Stephen C. Peck,et al.  Reliability Management in Competitive Electricity Markets , 1998 .

[42]  Daniel Ralph,et al.  Using EPECs to Model Bilevel Games in Restructured Electricity Markets with Locational Prices , 2007, Oper. Res..

[43]  Haozhong Cheng,et al.  A Bi-Level Programming Model for Multistage Transmission Network Expansion Planning in Competitive Electricity Market , 2009, 2009 Asia-Pacific Power and Energy Engineering Conference.

[44]  Eitaro Aiyoshi,et al.  Double penalty method for bilevel optimization problems , 1992, Ann. Oper. Res..

[45]  Martin Weibelzahl,et al.  On the effects of storage facilities on optimal zonal pricing in electricity markets , 2018 .

[46]  Fushuan Wen,et al.  Transmission planning and investment under competitive electricity market environment , 2001, 2001 Power Engineering Society Summer Meeting. Conference Proceedings (Cat. No.01CH37262).

[47]  J. Contreras,et al.  Transmission Expansion Planning in Electricity Markets , 2008, IEEE Transactions on Power Systems.

[48]  Antonio J. Conejo,et al.  Transmission expansion planning: a mixed-integer LP approach , 2003 .

[49]  Paul Denholm,et al.  A Dynamic Programming Approach to Estimate the Capacity Value of Energy Storage , 2014, IEEE Transactions on Power Systems.

[50]  Eric Hirst,et al.  Key Transmission Planning Issues , 2001 .

[51]  Alexander Martin,et al.  On the long run effects of market splitting: Why more price zones might decrease welfare , 2016 .

[52]  Jörg Rambau Rapid Mathematical Programming for Cooperative Truck Networks , 2017, OR.

[53]  Y. Smeers,et al.  Bi-Level Game Approaches for Coordination of Generation and Transmission Expansion Planning Within a Market Environment , 2013, IEEE Transactions on Power Systems.

[54]  A. J. Conejo,et al.  Transmission and Wind Power Investment , 2012, IEEE Transactions on Power Systems.

[55]  R. Sioshansi When energy storage reduces social welfare , 2014 .

[56]  Henrik Madsen,et al.  A bilevel model for electricity retailers' participation in a demand response market environment , 2013 .

[57]  Jonas Egerer,et al.  National-Strategic Investment in European Power Transmission Capacity , 2014 .

[58]  Ruben Romero,et al.  Transmission system expansion planning by an extended genetic algorithm , 1998 .

[59]  S. Dempe Annotated Bibliography on Bilevel Programming and Mathematical Programs with Equilibrium Constraints , 2003 .

[60]  Patrice Marcotte,et al.  An overview of bilevel optimization , 2007, Ann. Oper. Res..

[61]  Jean-Michel Glachant,et al.  Nordic congestion's arrangement as a model for Europe? Physical constraints vs. economic incentives , 2005 .

[63]  J. Glachant,et al.  The Diversity of Design of TSOs , 2008 .

[64]  Alexandre Proutière,et al.  Impact of storage on the efficiency and prices in real-time electricity markets , 2013, e-Energy '13.

[65]  Stephen C. Peck,et al.  A market mechanism for electric power transmission , 1996 .

[66]  C. Weber,et al.  Impacts of Res-Generation and Demand Pattern on Net Transfer Capatity: Implications for Effectiveness of Market Splitting in Germany , 2015 .

[67]  M. Arellano,et al.  Spatial peak-load pricing , 2007 .

[68]  O. Mangasarian A simple characterization of solution sets of convex programs , 1988 .

[69]  W. Hogan Contract networks for electric power transmission , 1992 .

[70]  R. Sioshansi Welfare Impacts of Electricity Storage and the Implications of Ownership Structure , 2010 .

[71]  Fushuan Wen,et al.  Transmission investment and expansion planning in a restructured electricity market , 2006 .

[72]  Daniel Huppmann,et al.  National-Strategic Investment in European Power Transmission Capacity , 2014, Eur. J. Oper. Res..