Transmission Expansion Planning with Linearized AC Load Flow by Special Ordered Set Method
Publication: Journal of Energy Engineering
Volume 144, Issue 2
Abstract
This paper presents a model for a transmission expansion planning (TEP) problem in which both active and reactive power as well as voltage magnitude of buses are considered through linearized alternating current (AC) load-flow constraints. The proposed approach uses the special ordered set of Type 2 (SOS2) to obtain the optimal global solution of the approximated linear model of TEP, which is indeed a mixed-integer linear programming (MILP) problem. This linear binary model can be effectively solved by existing off-the-shelf solvers using the branch and bound algorithm. The solution obtained is guaranteed to be globally optimal, whereas most mixed-integer nonlinear programming (MINLP) solvers could not guarantee an obtainable global optimal solution for nonconvex problems. The accuracy level of the solutions for the approximated linearized model can be easily controlled by adjusting specific parameters to suitable values. Results obtained through a simulation study show the effectiveness and applicability of the linear model presented. As numerous simulation studies show, the proposed methodology is reliable and robust.
Get full access to this article
View all available purchase options and get full access to this article.
References
Akbari, T., and Bina, M. T. (2014). “A linearized formulation of AC multi-year transmission expansion planning: A mixed-integer linear programming approach.” Electr. Power Syst. Res., 114, 93–100.
Akbari, T., Rahimi-Kian, A., and Heidarizadeh, M. (2011). “Security-constrained transmission expansion planning: A multi-objective approach.” Proc., 19th Iranian Conf. on Electrical Engineering, IEEE, New York, 1–6.
Akbari, T., and Tavakoli-Bina, M. (2016a). “Approximated MILP model for AC transmission expansion planning: Global solutions versus local solutions.” IET Gener. Transm. Dis., 10(7), 1563–1569.
Akbari, T., and Tavakoli-Bina, M. (2016b). “Linear approximated formulation of AC optimal power flow using binary discretization.” IET Gener. Transm. Dis., 10(5), 1117–1123.
Akbari, T., Tavakoli-Bina, M., and Abedini, A. (2012). “AC-OPF based static transmission expansion planning: A multi-objective approach.” Proc., 20th Iranian Conf. on Electrical Engineering, IEEE, New York, 364–369.
Alizadeh-Mousavi, O., and Zima-Bočkarjova, M. (2016). “Efficient Benders cuts for transmission expansion planning.” Electr. Power Syst. Res., 131, 275–284.
BARON version 16 [Computer software]. The Optimization Firm, Champaign, IL.
Beale, E. M. L. (1963). “Two transportation problems.” Proc., 3rd Int. Conf. on Operational Research, Tavistok Publication, London, 780–788.
Beale, E. M. L., and Tomlin, J. A. (1970). “Special facilities in a general mathematical programming system for non-convex problems using ordered sets of variables.” Proc., 5th Int. Conf. on Operational Research, Tavistok Publication, London, 447–454.
BONMIN version 1.8 [Computer software]. IBM, Armonk, NY.
Camponogara, E., Almeida, K., and Hardt, R. (2015). “Piecewise-linear approximations fora non-linear transmission expansion planning problem.” IET Gener. Transm. Dis., 9(12), 1235–1244.
Capasso, A., Cervone, A., Lamedica, R., and Palagi, L. (2015). “A new deterministic approach for transmission system planning in deregulated electricity markets.” Int. J. Electr. Power, 73, 1070–1078.
CONOPT version 3.1 [Computer software]. ARKI Consulting and Development, Bagsværd, Denmark.
Correa, C. A., Bolanos, R., and Garces, A. (2014). “Enhanced multi-objective algorithm for transmission expansion planning considering N–1 security criterion.” Int. Trans. Electr. Energy Syst., 25(10), 2225–2246.
CPLEX version 12 [Computer software]. IBM, Armonk, NY.
Czyzyk, J., Mesnier, M. P., and Moré, J. J. (1997). “The NEOS server.” Int. J. Comput. Sci. Eng., 5(3), 68–75.
da Silva, A. M. L., Freire, M. R., and Honório, L. M. (2016). “Transmission expansion planning optimization by adaptive multi-operator evolutionary algorithms.” Electr. Power Syst. Res., 133, 173–181.
DICOPT version 24.8 [Computer software]. EDRC, Carnegie Mellon Univ., Pittsburgh.
GAMS version 24.8 [Computer software]. GAMS Corporation, Fairfax, VA.
Gropp, W., and Moré, J. J. (1997). “Optimization environments and the NEOS server. Approximation theory and optimization.” Cambridge University Press, Cambridge, U.K., 167–182.
Hemmati, R., Hooshmand, R., and Khodabakhshian, A. (2016). “Coordinated generation and transmission expansion planning in deregulated electricity market considering wind farms.” Renewable Energy, 85, 620–630.
IEEE Committee. (1996). “The IEEE reliability test system.” IEEE Trans. Power Syst., 14(6), 1010–1020.
Jabr, R. A. (2013). “Optimization of AC transmission system planning.” IEEE Trans. Power Syst., 28(3), 2779–2787.
KNITRO version 10.3 [Computer software]. Artelys Company, Paris.
Macedo, L. H., Montes, C. V., Franco, J. F., Rider, M. J., and Romero, R. (2016). “MILP branch flow model for concurrent AC multistage transmission expansion and reactive power planning with security constraints.” IET Gener. Transm. Dis., 10(12), 3023–3032.
MATPOWER version 6 [Computer software]. Power Systems Engineering Research Center, Tempe, AZ.
Munoz, C., Sauma, E., and Contreras, J. (2012). “Impact of high wind power penetration on transmission network expansion planning.” IET Gener. Transm. Dis., 6(12), 1281–1291.
Qiu, T., Xu, B., Wang, Y., Dvorkin, Y., and Kirschen, D. (2017). “Stochastic multi-stage co-planning of transmission expansion and energy storage.” IEEE Trans. Power Syst., 32(1), 643–651.
SBB version 24.8 [Computer software]. GAMS Corporation, Fairfax, VA.
Seddighi, A. H., and Ahmadi-Javid, A. (2015). “Integrated multiperiod power generation and transmission expansion planning with sustainability aspects in a stochastic environment.” Energy, 86, 9–18.
Taylor, J. A., and Hover, F. S. (2013). “Linear relaxations for transmission system planning.” IEEE Trans. Power Syst., 26(4), 2533–2538.
Torres, S. P., and Castro, C. A. (2014). “Expansion planning for smart transmission grids using AC model and shunt compensation.” IET Gener. Transm. Dis., 8(5), 966–975.
Trodden, P. A., Ahmed-Bukhsh, W., Grothey, A., and Ken, I. (2014). “Optimization-based islanding of power networks using piecewise linear AC power flow.” IEEE Trans. Power Syst., 29(3), 1212–1220.
Williams, H. P. (2013). Model building in mathematical programming, Wiley, New York, 1223.
Zhang, H., Heydt, T., Vittal, V., and Quintero, J. (2013). “An improved network model for transmission expansion planning considering reactive power and network losses.” IEEE Trans. Power Syst., 28(3), 3471–3479.
Information & Authors
Information
Published In
Copyright
©2018 American Society of Civil Engineers.
History
Received: Mar 30, 2017
Accepted: Sep 20, 2017
Published online: Feb 7, 2018
Published in print: Apr 1, 2018
Discussion open until: Jul 7, 2018
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.