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2021 | OriginalPaper | Buchkapitel

7. Transmission Expansion Planning Outside the Box: A Bilevel Approach

verfasst von : Sonja Wogrin, Salvador Pineda, Diego A. Tejada-Arango, Isaac C. Gonzalez-Romero

Erschienen in: Transmission Expansion Planning: The Network Challenges of the Energy Transition

Verlag: Springer International Publishing

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Abstract

Ever since the beginning of the liberalization process of the energy sector and the arrival of electricity markets, decision-making has gone away from centralized planners and has become the responsibility of many different entities such as market operators, private generation companies, transmission system operators, and many more. The interaction and sequence in which these entities make decisions in liberalized market frameworks have led to a renaissance of Stackelberg-type games referred to as bilevel problems, which capture the natural hierarchy in many decision-making processes in power systems. This chapter aims at demonstrating the important insights that such models can provide with respect to transmission expansion planning. Finally, a numerical example is included for illustrative purposes.

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If we convert the maximization into a minimization problem by multiplying the objective function with minus one, then (7.6) is a convex problem, which is what we need to derive meaningful KKT conditions. However, currently the problem is a maximization problem, so actually what we have is a concave objective function with convex constraints. In conclusion, (7.6) satisfies all the requirements for the KKT conditions to be sufficient.

Taking the first derivative of the objective function (7.6a) with respect to \(\overline {p}_g\) is linear an hence both convex and concave, and taking it with respect to p _gt yields: λ _tn − Φ_gp _gt − C _g. Then, the second derivative is − 2 Φ_g, which is smaller or equal to zero for each value of Φ_g ∈ [0, 1∕α], which yields concavity (convexity) of the maximization (minimization) objective function.

Again, since we are maximizing the objective function is actually concave. But multiplying the objective function with minus one makes it convex. Actually, (7.10) is a linear problem, and therefore the resulting KKT conditions are sufficient. Note that the SO is also considered a price taker.

This is not always the case. For example, if we considered a different objective function that maximized social welfare, the arising objective function would not be linear.

J. F. Bard, Practical Bilevel Optimization: Algorithms and Applications (Springer, 1998)

L. Baringo, A. Baringo, A stochastic adaptive robust optimization approach for the generation and transmission expansion planning. IEEE Trans. Power Syst. 33(1), 792–802 (2018)CrossRef

L. Baringo, A.J. Conejo, Transmission and wind power investment. IEEE Trans. Power Syst. 27(2), 885–893 (2012)CrossRef

C.A. Berry, B.F. Hobbs, W.A. Meroney, R.P. O’Neill, W.R. Stewart, Understanding how market power can arise in network competition: a game theoretic approach. Util. Policy 8(3), 139–158 (1999)CrossRef

H.I. Calvete, C. Galé, P.M. Mateo, A new approach for solving linear bilevel problems using genetic algorithms. Eur. J. Oper. Res. 188(1), 14–28 (2008)MathSciNetMATHCrossRef

A. Caprara, M. Carvalho, A. Lodi, G.J. Woeginger, A complexity and approximability study of the bilevel knapsack problem, in Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). LNCS, vol. 7801 (Springer, Berlin/Heidelberg, 2013), pp. 98–109

A. Caprara, M. Carvalho, A. Lodi, G.J. Woeginger, Bilevel Knapsack with interdiction constraints. INFORMS J. Comput. 28(2), 319–333 (2016)MathSciNetMATHCrossRef

J.B. Cardell, C.C. Hitt, W.W. Hogan, Market power and strategic interaction in electricity networks. Resour. Energy Econ. 19, 109–137 (1997)CrossRef

E. Centeno, S. Wogrin, A. López-Pena, M. Vázquez, Analysis of investments in generation capacity: a bilevel approach. IET Gener. Transm. Distrib. 5(8), 842 (2011)

10.

Federal Energy Regulatory Commission et al. Order no. 1000 – transmission planning and cost allocation (2012)

11.

S. Dempe, Annotated bibliography on bilevel programming and mathematical programs with equilibrium constraints. Optimization 52(3), 333–359 (2003)MathSciNetMATHCrossRef

12.

Y. Dvorkin, R. Fernández-Blanco, Y. Wang, B. Xu, D.S. Kirschen, H. Pandžić, J.P. Watson, C.A. Silva-Monroy, Co-planning of investments in transmission and merchant energy storage. IEEE Trans. Power Syst. 33(1), 245–256 (2018)CrossRef

13.

J. Fortuny-Amat, B. McCarl, A representation and economic interpretation of a two-level programming problem. J. Oper. Res. Soc. 32(9), 783–792 (1981)MathSciNetMATHCrossRef

14.

S.A. Gabriel, A.J. Conejo, J.D. Fuller, B.F. Hobbs, C. Ruiz, Complementarity Modeling in Energy Markets, vol. 180 (Springer Science & Business Media, 2012). Berlin, Germany

15.

L.P. Garces, A.J. Conejo, R. Garcia-Bertrand, R. Romero, A bilevel approach to transmission expansion planning within a market environment. IEEE Trans. Power Syst. 24(3), 1513–1522 (2009)CrossRef

16.

I.C. Gonzalez-Romero, S. Wogrin, T. Gomez, A review on generation and transmission expansion co-planning under a market environment (Accepted). IET GTD (2019)

17.

I.C. Gonzalez-Romero, S. Wogrin, T. Gomez, Proactive transmission expansion planning with storage considerations. Energy Strateg. Rev. 24, 154–165 (2019)CrossRef

18.

B.F. Hobbs, C.B. Metzler, J.-S. Pang, Calculating equilibria in imperfectly competitive power markets: An MPEC approach. IEEE Trans. Power Syst. 15, 638–645 (2000)CrossRef

19.

D. Huppmann, S. Siddiqui, An exact solution method for binary equilibrium problems with compensation and the power market uplift problem. Eur. J. Oper. Res. 266(2), 622–638 (2018)MathSciNetMATHCrossRef

20.

M. Jenabi, S.M.T. Fatemi Ghomi, Y. Smeers, Bi-level game approaches for coordination of generation and transmission expansion planning within a market environment. IEEE Trans. Power Syst. 28(3), 2639–2650 (2013)CrossRef

21.

S. Jin, S.M. Ryan, Capacity expansion in the integrated supply network for an electricity market. IEEE Trans. Power Syst. 26(4), 2275–2284 (2011)CrossRef

22.

S. Jin, S.M. Ryan, A tri-level model of centralized transmission and decentralized generation expansion planning for an electricity market – part I. IEEE Trans. Power Syst. 29(1), 132–141 (2014)CrossRef

23.

V. Krebs, L. Schewe, M. Schmidt, Uniqueness and multiplicity of market equilibria on dc power flow networks. Eur. J. Oper. Res. 271(1), 165–178 (2018)MathSciNetMATHCrossRef

24.

H. Le Cadre, I. Mezghani, A. Papavasiliou, A game-theoretic analysis of transmission-distribution system operator coordination. Eur. J. Oper. Res. 274(1), 317–339 (2019)MathSciNetMATHCrossRef

25.

H. Li, L. Fang, An evolutionary algorithm for solving bilevel programming problems using duality conditions. Math. Prob. Eng. 2012, 1–14 (2012)MathSciNet

26.

Z.-Q. Luo, J.-S. Pang, D. Ralph, Mathematical Programs with Equilibrium Constraints (Cambridge University Press, Cambridge, 1996)MATHCrossRef

27.

L. Maurovich-Horvat, T.K. Boomsma, A.S. Siddiqui, Transmission and wind investment in a deregulated electricity industry. IEEE Trans. Power Syst. 30(3), 1633–1643 (2015)CrossRef

28.

E. Moiseeva, S. Wogrin, M.R. Hesamzadeh, Generation flexibility in ramp rates: strategic behavior and lessons for electricity market design. Eur. J. Oper. Res. 261(2), 755–771 (2017)MathSciNetMATHCrossRef

29.

A. Motamedi, H. Zareipour, M.O. Buygi, W.D. Rosehart, A transmission planning framework considering future generation expansions in electricity markets. IEEE Trans. Power Syst. 25(4), 1987–1995 (2010)CrossRef

30.

Office of Energy Analysis, Annual energy outlook 2019 with projections to 2050. Technical report, U.S. Energy Information Administration (2019)

31.

B. Palmintier, M. Webster, Impact of unit commitment constraints on generation expansion planning with renewables, in 2011 IEEE Power and Energy Society General Meeting (2011), pp. 1–7

32.

H. Pandžić, Y. Dvorkin, M. Carrión, Investments in merchant energy storage: trading-off between energy and reserve markets. Appl. Energy 230, 277–286 (2018)CrossRef

33.

S. Pineda, H. Bylling, J.M. Morales, Efficiently solving linear bilevel programming problems using off-the-shelf optimization software. Optim. Eng. 19(1), 187–211 (2018)MathSciNetMATHCrossRef

34.

S. Pineda, J.M. Morales, Solving linear bilevel problems using big-ms: Not all that glitters is gold. IEEE Trans. Power Syst. 34(3), 2469–2471 (2019)CrossRef

35.

P. Pisciella, M. Bertocchi, M.T. Vespucci, A leader-followers model of power transmission capacity expansion in a market driven environment. Comput. Manag. Sci. 10, 87–118 (2014)MathSciNetMATH

36.

D. Pozo, J. Contreras, E. Sauma, If you build it, he will come: anticipative power transmission planning. Energy Econ. 36, 135–146 (2013)CrossRef

37.

D. Pozo, E. Sauma, J. Contreras, A three-level static MILP model for generation and transmission expansion planning. IEEE Trans. Power Syst. 28(1), 202–210 (2013)CrossRef

38.

D. Pozo, E. Sauma, J. Contreras, When doing nothing may be the best investment action: pessimistic anticipative power transmission planning. Appl. Energy 200, 383–398 (2017)CrossRef

39.

D. Ralph, S.J. Wright, Some properties of regularization and penalization schemes for MPECs. Optim. Methods Softw. 19(5), 527–556 (2004)MathSciNetMATHCrossRef

40.

A. Ramos, M. Ventosa, M. Rivier, Modeling competition in electric energy markets by equilibrium constraints. Util. Policy 7, 233–242 (1999)CrossRef

41.

J.H. Roh, M. Shahidehpour, Y. Fu, Market-based coordination of transmission and generation capacity planning. IEEE Trans. Power Syst. 22(4), 1406–1419 (2007)CrossRef

42.

E.E. Sauma, S.S. Oren, Proactive planning and valuation of transmission investments in restructured electricity markets. J. Regul. Econ. 30(3), 358–387 (2006)CrossRef

43.

E.E. Sauma, S.S. Oren, Economic criteria for planning transmission investment in restructured electricity markets. IEEE Trans. Power Syst. 22(4), 1394–1405 (2007)CrossRef

44.

S. Scholtes, Convergence properties of a regularization scheme for mathematical programs with complementarity constraints. SIAM J. Optim. 11(4), 918–936 (2001)MathSciNetMATHCrossRef

45.

C. Shi, J. Lu, G. Zhang, H. Zhou, An extended branch and bound algorithm for linear bilevel programming. Appl. Math. Comput. 180(2), 529–537 (2006)MathSciNetMATH

46.

S. Siddiqui, S.A. Gabriel, An SOS1-based approach for solving MPECs with a natural gas market application. Netw. Spat. Econ. 13(2), 205–227 (2012)MathSciNetMATHCrossRef

47.

E. Spyrou, J.L. Ho, B.F. Hobbs, R.M. Johnson, J.D. McCalley, What are the benefits of co-optimizing transmission and generation investment? Eastern interconnection case study. IEEE Trans. Power Syst. 32(6), 4265–4277 (2017)CrossRef

48.

S.S. Taheri, J. Kazempour, S. Seyedshenava, Transmission expansion in an oligopoly considering generation investment equilibrium. Energy Econ. 64, 55–62 (2017)CrossRef

49.

D.A. Tejada-Arango, M. Domeshek, S. Wogrin, E. Centeno, Enhanced representative days and system states modeling for energy storage investment analysis. IEEE Trans. Power Syst. 33(6), 6534–6544 (2018)CrossRef

50.

Y. Tohidi, M.R. Hesamzadeh, F. Regairaz, Sequential coordination of transmission expansion planning with strategic generation investments. IEEE Trans. Power Syst. 32(4), 2521–2534 (2017)CrossRef

51.

K. Vaillancourt, Electricity transmission and distribution. Technical report, IEA ETSAP (2014)

52.

H. Von Stackelberg, Marktform und Gleichgewicht (J. Springer, 1934). Berlin, Germany

53.

J.D. Weber, T.J. Overbye, A two-level optimization problem for analysis of market bidding strategies, in IEEE Power Engineering Society Summer Meeting, Edmonton (1999), pp. 682–687

54.

M. Weibelzahl, A. Märtz, Optimal storage and transmission investments in a bilevel electricity market model. Ann. Oper. Res. 287(2), 911–940 (2020)MathSciNetMATHCrossRef

55.

S. Wogrin, E. Centeno, J. Barquín, Generation capacity expansion in liberalized electricity markets: a stochastic MPEC approach. IEEE Trans. Power Syst. 26(4), 2526–2532 (2011)CrossRef

56.

S. Wogrin, E. Centeno, J. Barquin, Generation capacity expansion analysis: open loop approximation of closed loop equilibria. IEEE Trans. Power Syst. 28(3), 3362–3371 (2013)CrossRef

57.

S. Wogrin, D. Galbally, J. Reneses, Optimizing storage operations in medium- and long-term power system models. IEEE Trans. Power Syst. 31(4), 3129–3138 (2016)CrossRef

58.

S. Wogrin, B.F. Hobbs, D. Ralph, E. Centeno, J. Barquín, Open versus closed loop capacity equilibria in electricity markets under perfect and oligopolistic competition. Math. Program. 140(2), 295–322 (2013)MathSciNetMATHCrossRef

59.

J. Yao, I. Adler, S.S. Oren, Modeling and computing two-settlement oligopolistic equilibrium in a congested electricity network. Oper. Res. 56(1), 34–47 (2008)MathSciNetMATHCrossRef

60.

Y. Ye, D. Papadaskalopoulos, J. Kazempour, G. Strbac, Incorporating non-convex operating characteristics into bi-level optimization electricity market models. IEEE Trans. Power Syst. 35(1), 163–176 (2020)CrossRef

61.

M.H. Zare, J.S. Borrero, B. Zeng, O.A. Prokopyev, A note on linearized reformulations for a class of bilevel linear integer problems. Ann. Oper. Res. 272(1–2), 99–117 (2019)MathSciNetMATHCrossRef

Titel: Transmission Expansion Planning Outside the Box: A Bilevel Approach
verfasst von: Sonja Wogrin
Salvador Pineda
Diego A. Tejada-Arango
Isaac C. Gonzalez-Romero
Verlag: Springer International Publishing
Buch: Transmission Expansion Planning: The Network Challenges of the Energy Transition
Print ISBN: 978-3-030-49427-8

Electronic ISBN: 978-3-030-49428-5

Copyright-Jahr: 2021
DOI: https://doi.org/10.1007/978-3-030-49428-5_7