A backstepping-like nonlinear controller design for power systems with SMES


  • Adirak Kanchanaharuthai Department of Electrical Engineering, College of Engineering, Rangsit University, Patumthani 12000, Thailand
  • Arsit Boonyaprapasorn Department of Mechanical Engineering, Chulchomklao Royal Military Academy, Nakhon-Nayok 26001, Thailand


backstepping-like control, nonlinear control, nonlinear system, SMES, transient stability


The design of a backstepping-like control method applying on an electrical system is a main focus of this work.  The proposed method is able to improve dynamic responses of the power system with SMES in terms of transient stability and performance.  The power system considered in this work is contained with the following elements: (i) generator excitation, and (ii) super-conducting magnetic energy system (SMES).  In order to gain the desired stability under the effect of the large or small disturbances, the backstepping-like control is synthesized to stabilize the power system.  Considering the design procedure of the backstepping-like control method, it is clear that the developed design of the method is simpler than that of an advanced control method such as an immersion and invariance (I&I) control method.  However, the method can provide the acceptable effectiveness for the control system.  Illustration for the performance of the designed backstepping-like controller can be shown via the simulation.  The controller is employed for stabilizing a single-machine infinite bus (SMIB) power system with SMES. It is clear that the presented controller can provide the desired characteristics including transient stability and the post-fault dynamic performance of the terminal voltage.  Moreover, compared with I&I and the classical backstepping methods, using the backstepping-like method can achieve the desired performance of the considered power system with a simpler design procedure.


Ali, M. H. (2012). Wind energy systems: Solutions for power quality and stabilization. Boca Raton, FL, USA: CRC Press.

Ali A. H., Wu. B., & Dougal, R. A. (2010). An overview of SMES applications in power and energy systems. IEEE Transactions on Sustainable Energy. 1(1), 38-47. DOI: 10.1109/TSTE.2010.2044901

Astolfi, A., Karagiannis, D., & Oreta, R. (2008). Nonlinear and adaptive control design and applications. London, UK: Springer-Verlag.

Astolfi, A., & Oreta, R. (2003). Immersion and invariance: a new tool for stabilization and adaptive control of nonlinear systems. IEEE Transactions on Automatic Control, 48(4), 590-606. DOI: 10.1109/TAC.2003.809820

Kanchanaharuthai, A. (2014a). Immersion and invariance-based nonlinear dual-excitation and steam-valving control of synchronous generators. International Transactions on Electrical Energy Systems, 24(12), 1671-1687. DOI: 10.1002/etep.1796

Kanchanaharuthai, A. (2014b). Immersion and invariance-based non-linear coordinated control for generator excitation and static synchronous compensator for power systems. Electric Power Components and Systems, 42(10), 1004-1015. DOI:10.1080/15325008.2014.913734

Kanchanaharuthai, A. (2014c). Immersion and invariance-based coordinated generator excitation and SVC control for power systems. Mathematical Problems in Engineering, 2014, Article ID 720570, 1-11. http://dx.doi.org/10.1155/2014/720570

Kanchanaharuthai, A., Chankong, V., & Loparo, K. A. (2015). Nonlinear generator excitation and superconducting magnetic energy storage control for transient stability enhancement via immersion and invariance. Transactions of the Institute of Measurement and Control, 37(10), 1217-1231. DOI: 10.1177/0142331214560048

Kanchanaharuthai, A., & Boonyaprapasorn , A. (2016). A backstepping-like approach to coordinated excitation and STATCOM control for power systems. International Review of Automatic Control, 9(2), 64-71. DOI: 10.15866/ireaco.v9i2.8405

Kanchanaharuthai, A. (2016a). Nonlinear adaptive immersion and invariance control for power systems with SMES. International Jounal of Innovative Computing, Information and Control, 12(4), 1129-1140.

Kanchanaharuthai, A. (2016b). Nonlinear adaptive controller design for power systems with STATCOM via immersion and invariance. ECTI Transactions on Electrical Engineering, Electronics, and Communications, 14(2), 35-46.

Kim, S.-K., Song, H., & Yoon, T.-W. (2015), Damping improvement and terminal voltage regulation for a synchronous machine using an energy storage device. International Journal of Electronics. 102(4), 582-598. DOI: 10.1080/00207217.2014.913318

Krstic, M., Kanellakopoulos, I., & Kokotovic, P. (1995). Nonlinear and adaptive control design. New York, USA: John Willey & Son.

Li, S., & Wang, Y. (2007). Robust adaptive control of synchronous generators with SMES unit via Hamiltonian function method. International Journal Systems Science, 38(3), 187-196. DOI: 10.1080/00207720601110566

Liu, F., Mei, S., Xia, D., Ma, D., Jiang, X., & Lu, Q. (2004). Experimental evaluation of nonlinear robust control for SMES to improve the transient stability of power systems. IEEE Transactions on Energy Conversion, 19(4), 774-782. DOI: 10.1109/TEC.2004.827703

Lu, C.-F., Liu, C.-C., & Wu, C.-J. (1995). Dynamic modelling of battery energy storage system and application to power system stability. IEE Proceedings – Generation, Transmission and Distribution, 142(4), 429-435. DOI: 10.1049/ip-gtd:19951858

Lu, Q., Sun, Y., & Wei, S. (2001). Nonlinear control systems and power system dynamics. Boston, USA: Kluwer Academic Publishers.

Luo, R. (2015). The robust adaptive control of chaotic systems with unknown parameters and external disturbance via a scalar input. International Journal of Adaptive Control and Signal Processing, 29, 1296-1307. DOI: 10.1002/acs.2540

Manjarekar, N. S., & Banavar, R. N. (2012). Nonlinear control synthesis for electrical power systems using controllable series capacitors. London, UK: Springer-Verlag.

Ribeiro, P., Johnson, B., Crow, M.L., Arsoy, A., & Liu, Y. (2000). Energy storage systems for advanced power applications. Proceedings of the IEEE, 89(12), 1744-1756. DOI: 10.1109/5.975900

Tan, Y.-L., & Wang, Y. (1998). Augmentation of transient stability using a superconducting coil and adaptive nonlinear control. IEEE Transactions on Power Systems, 13(2), 361-366. DOI: 10.1109/59.667352

Tan, Y.-L. & Wang, Y. (2004). A robust nonlinear excitation and SMES controller for transient stability. International Journal of Electrical Power Energy Systems, 26(5), 325-332. DOI: 10.1016/j.ijepes.2003.10.017

Wan, Y., & Zhao, J. (2013). Extened backstepping method for single-machine infinite-bus power systems with SMES. IEEE Transactions on Control Systems Technology, 21(3), 915-923. DOI: 10.1109/TCST.2012.2190291

Wang, Y., Feng, G., Cheng, D., & Liu, Y. (2006). Adaptive L2 disturbance attenuation control of multi-machine power systems with SMES units. Automatica, 42(7), 1121-1132. DOI:10.1016/j.automatica.2006.03.014

Wang, Y., Hill, J. H., Middleton, R. H., & Gao, L. (1993). Transient stability enhancement and voltage regulation of power systems. IEEE Transactions on Power Systems, 8(2), 620-627. DOI: 10.1109/59.260819




How to Cite

Adirak Kanchanaharuthai, & Arsit Boonyaprapasorn. (2023). A backstepping-like nonlinear controller design for power systems with SMES. Journal of Current Science and Technology, 7(1), 1–10. Retrieved from https://ph04.tci-thaijo.org/index.php/JCST/article/view/519



Research Article