A Multi-objective Transmission Expansion Planning Strategy: A Bilevel Programming Method

Document Type : Research Article


1 Faculty of Electrical Engineering, Urmia University of Technology, Urmia, Iran

2 Department of Electrical Engineering, Pooyesh Institute of Higher Education, Qom, Iran


This paper describes a methodology for transmission expansion planning (TEP) within a deregulated electricity market. Two objective functions including investment cost (IC) and congestion cost (CC) are considered. The proposed model forms a bi-level optimization problem in which upper level problem represents an independent system operator (ISO) making its decisions on investment while in the lower level, the market clearing problem is formulated. ISO tries to minimize the investment cost on new transmission capacity to be installed and to minimize the congestion cost. Minimizing the CC can facilitate the competition between market participants. Locational marginal prices (LMPs) which are necessary to be calculated for the congestion cost are obtained at the lower level. The LMP of buses are dual variables of the corresponding active power balance equation. Lower problem is replaced by its Karush-Kuhn-Tucker (KKT) conditions resulting in a one-level optimization problem which can be efficiently solved by commercial existing solvers. The formulated multi-objective mathematical programming is solved by augmented ε-constraint method which is able to produce the Pareto-optimal solutions. The presented framework is applied to a simple 3-bus power system and also IEEE 24-bus reliability test system (RTS). Results from these illustrative examples are reported and thoroughly discussed. The results show the effectiveness of the presented work.


Main Subjects

[1]A. Andreoni, A. Garcia-Agreda, T. Strada, J. Saraiva, Strategies for power systems expansion planning in a competitive electrical market, Electrical Engineering, 89(5) (2007) 433-441.
[2] A. Orths, A. Schmitt, Z. Styczynski, J. Verstege, Multi-criteria optimization methods for planning and operation of electrical energy systems, Electrical Engineering (Archiv fur Elektrotechnik), 83(5) (2001) 251-258.
[3] T. Akbari, S. Zolfaghari Moghaddam, E. Poorghanaat, F. Azimi, Coordinated planning of generation capacity and transmission network expansion: A game approach with multi‐leader‐follower, International Transactions on Electrical Energy Systems, 27(7) (2017) e2339.
[4] N. Alguacil, A.L. Motto, A.J. Conejo, Transmission expansion planning: A mixed-integer LP approach, IEEE Transactions on Power Systems, 18(3) (2003) 1070-1077.
[5] A. Arabali, M. Ghofrani, M. Etezadi-Amoli, M.S. Fadali, M. Moeini-Aghtaie, A multi-objective transmission expansion planning framework in deregulated power systems with wind generation, IEEE Transactions on Power Systems, 29(6) (2014) 3003-3011.
[6] J.H. Zhao, J. Foster, Z.Y. Dong, K.P. Wong, Flexible transmission network planning considering distributed generation impacts, IEEE Transactions on Power Systems, 26(3) (2011) 1434-1443.
[7] R.A. Jabr, Optimization of AC transmission system planning, IEEE Transactions on Power Systems, 28(3) (2013) 2779-2787.
[8] J.A. Taylor, F.S. Hover, Conic AC transmission system planning, IEEE Transactions on Power Systems, 28(2) (2013) 952-959.
[9] P. Maghouli, S.H. Hosseini, M.O. Buygi, M. Shahidehpour, A scenario-based multi-objective model for multi-stage transmission expansion planning, IEEE Transactions on Power Systems, 26(1) (2011) 470-478.
[10] T. Akbari, A. Rahimikian, A. Kazemi, A multi-stage stochastic transmission expansion planning method, Energy Conversion and Management, 52(8-9) (2011) 2844-2853.
[11] T. Akbari, S. Zolfaghari, A. Kazemi, Multi-stage stochastic transmission expansion planning under load uncertainty using benders decomposition, International Review of Electrical Engineering, 4(5) (2009).
[12] M. Moeini-Aghtaie, A. Abbaspour, M. Fotuhi-Firuzabad, Incorporating large-scale distant wind farms in probabilistic transmission expansion planning—Part I: Theory and algorithm, IEEE Transactions on Power Systems, 27(3) (2012) 1585-1593.
[13] J.C. Villumsen, G. Bronmo, A.B. Philpott, Line capacity expansion and transmission switching in power systems with large-scale wind power, IEEE Transactions on Power Systems, 28(2) (2013) 731-739.
[14] G.A. Orfanos, P.S. Georgilakis, N.D. Hatziargyriou, Transmission expansion planning of systems with increasing wind power integration, IEEE Trans. Power Syst, 28(2) (2013) 1355-1362.
[15] Y. Gu, J.D. McCalley, M. Ni, Coordinating large-scale wind integration and transmission planning, IEEE Transactions on Sustainable Energy, 3(4) (2012) 652-659.
[16] T. Kristiansen, J. Rosellon, Merchant electricity transmission expansion: A European case study, Energy, 35(10) (2010) 4107-4115.
[17] M. Hesamzadeh, N. Hosseinzadeh, P.J. Wolfs, A leader–followers model of transmission augmentation for considering strategic behaviours of generating companies in energy markets, International Journal of Electrical Power & Energy Systems, 32(5) (2010) 358-367.
[18] I. Sharan, R. Balasubramanian, Integrated generation and transmission expansion planning including power and fuel transportation constraints, Energy Policy, 43 (2012) 275-284.
[19] G. Liu, H. Sasaki, N. Yorino, Application of network topology to long range composite expansion planning of generation and transmission lines, Electric Power Systems Research, 57(3) (2001) 157-162.
[20] J.L. Cohon, Multiobjective programming and planning, Courier Corporation, 2004.
[21] L.S. Lasdon, Optimization theory for large systems, Courier Corporation, 2002.
[22] C. Grigg, P. Wong, P. Albrecht, R. Allan, M. Bhavaraju, R. Billinton, Q. Chen, C. Fong, S. Haddad, S. Kuruganty, The IEEE reliability test system-1996. A report prepared by the reliability test system task force of the application of probability methods subcommittee, IEEE Transactions on power systems, 14(3) (1999) 1010-1020.
[23] S. Hajri-Gabouj, A fuzzy genetic multiobjective optimization algorithm for a multilevel generalized assignment problem, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), 33(2) (2003) 214-224.