Design Low Order Robust Controller for the Generator’s Rotor Angle Stabilization PSS System

Vu Ngoc Kien, Nguyen Hien Trung, Nguyen Hong Quang


The electrical system's problem stabilizes the electrical system with three primary parameters: rotor angle stability, frequency stability, and voltage stability. This paper focuses on the problem of designing a low-order stable optimal controller for the generator rotor angle (load angle) stabilization system with minor disturbances. These minor disturbances are caused by lack of damping torque, change in load, or change in a generator during operation. Using the RHoptimal robust design method for the Power System Stabilizer (PSS) to stabilize the generator’s load angle will help the PSS system work sustainably under disturbance. However, this technique's disadvantage is that the controller often has a high order, causing many difficulties in practical application. To overcome this disadvantage, we propose to reduce the order of the higher-order optimal robust controller. There are two solutions to reduce order for high-order optimal robust controller: optimal order reduction according to the given controller structure and order reduction according to model order reduction algorithms. This study selects the order reduction of the controller according to the model order reduction algorithms. In order to choose the most suitable low-order optimal robust controller that can replace the high-order optimal robust controller, we have compared and evaluated the order-reducing controllers according to many model order reduction algorithms. Using robust low-order controllers to control the generator’s rotor angle completely meets the stabilization requirements. The research results of the paper show the correctness of the controller order reduction solution according to the model order reduction algorithms and open the possibility of application in practice.


Doi: 10.28991/esj-2021-01299

Full Text: PDF


Electrical System Stabilization; Generator’s Rotor Angle; Power System Stabilizer; RH∞ Robust Optimal Controllers; Order Reduction Algorithm.


Basler, M.J., and R.C. Schaefer. “Understanding Power System Stability.” 58th Annual Conference for Protective Relay Engineers, (2005). doi:10.1109/cpre.2005.1430421.

Shankar, R., and P. Kundur. "Power system stability and control II." New York, McGraw-Hill Books (1994): 581.

P. Kundur, J. Paserba and et al., “Definition and Classification of Power System Stability IEEE/CIGRE Joint Task Force on Stability Terms and Definitions.” IEEE Transactions on Power Systems 19, no. 3 (August 2004): 1387–1401. doi:10.1109/tpwrs.2004.825981.

Snyder, A.F., N. Hadjsaid, D. Georges, L. Mili, A.G. Phadke, O. Faucon, and S. Vitet. “Inter-Area Oscillation Damping with Power System Stabilizers and Synchronized Phasor Measurements.” POWERCON ’98. International Conference on Power System Technology. Proceedings (Cat. No.98EX151) (1998). doi:10.1109/icpst.1998.729193.

Prasertwong, K., N. Mithulananthan, and D. Thakur. “Understanding Low-Frequency Oscillation in Power Systems.” The International Journal of Electrical Engineering & Education 47, no. 3 (July 2010): 248–262. doi:10.7227/ijeee.47.3.2.

Rogers, Graham. “Power System Oscillations” Kluwer, Norwell, MA (2000). doi:10.1007/978-1-4615-4561-3.

Chen, S. “H∞ Optimisation-Based Power System Stabiliser Design.” IEE Proceedings - Generation, Transmission and Distribution 142, no. 2 (1995): 179-184. doi:10.1049/ip-gtd:19951711..

Jayapal, R., and J. K. Mendiratta. "Design & Simulation of Robust H∞ Control Based Power System Stabilizer for SMIB models." International Journal of Computer Science and Network Security 9, no. 11 (2009): 135-149.

J. C. Doyle, K. Glover, P. P. Khargonekar, B. A. Francis, “State–space solutions to standard H2 and RH∞ control problems,” IEEE Trans. Automat. Contr 34, no. 8, (1989): 831–847.

Hardiansyah, Seizo Furuya, and Juichi Irisawa. “LMI-Based Robust H2 Controller Design for Damping Oscillations in Power Systems.” IEEJ Transactions on Power and Energy 124, no. 1 (2004): 113–120. doi:10.1541/ieejpes.124.113.

Chen, S., and O.P. Malik. “Power System Stabilizer Design Using μ Synthesis.” IEEE Transactions on Energy Conversion 10, no. 1 (March 1995): 175–181. doi:10.1109/60.372584.

Rios, M., N. Hadjsaid, R. Feuillet, and A. Torres. “Power Systems Stability Robustness Evaluation by μ Analysis.” IEEE Transactions on Power Systems 14, no. 2 (May 1999): 648–653. doi:10.1109/59.761893.

Mendiratta, J. K., and R. Jayapal. "H∞ loop shaping based robust power system stabilizer for three machine power system." International Journal of Computer Applications 1 (2010): 106-112.

Skogestad, Sigurd, and Ian Postlethwaite. “Multivariable feedback control: analysis and design.” Vol. 2. , John Wiley and Sons, (2007).

Dehghani, M., and S.K.Y. Nikravesh. “Robust Tuning of PSS Parameters Using the Linear Matrix Inequalities Approach.” 2007 IEEE Lausanne Power Tech (July 2007). doi:10.1109/pct.2007.4538337.

Gahinet, Pascal, and Pierre Apkarian. “A Linear Matrix Inequality Approach to H∞ Control.” International Journal of Robust and Nonlinear Control 4, no. 4 (1994): 421-448. doi:10.1002/rnc.4590040403.

Hung-Chi Tsai, Chia-Chi Chu, and Yung-Shan Chou. “Robust Power System Stabilizer Design for an Industrial Power System in Taiwan Using Linear Matrix Inequality Techniques.” IEEE Power Engineering Society General Meeting, (2004). doi:10.1109/pes.2004.1373179.

Zhang, P., and A.H. Coonick. “Coordinated Synthesis of PSS Parameters in Multi-Machine Power Systems Using the Method of Inequalities Applied to Genetic Algorithms.” IEEE Transactions on Power Systems 15, no. 2 (May 2000): 811–816. doi:10.1109/59.867178.

Peng, Shan, and Qingzi Wang. “Power System Stabilizer Parameters Optimization Using Immune Genetic Algorithm.” IOP Conference Series: Materials Science and Engineering 394 (August 8, 2018): 042091. doi:10.1088/1757-899x/394/4/042091.

Zhang, Y., G.P. Chen, O.P. Malik, and G.S. Hope. “An Artificial Neural Network Based Adaptive Power System Stabilizer.” IEEE Transactions on Energy Conversion 8, no. 1 (March 1993): 71–77. doi:10.1109/60.207408.

Hariri, A., and O.P. Malik. “A Fuzzy Logic Based Power System Stabilizer with Learning Ability.” IEEE Transactions on Energy Conversion 11, no. 4 (1996): 721–727. doi:10.1109/60.556370.

Hosseinzadeh, N., and A. Kalam. “A Direct Adaptive Fuzzy Power System Stabilizer.” IEEE Transactions on Energy Conversion 14, no. 4 (1999): 1564–1571. doi:10.1109/60.815106.

Dasu, Butti, Mangipudi Siva Kumar, and Rayapudi Srinivasa Rao. “Design of Robust Modified Power System Stabilizer for Dynamic Stability Improvement Using Particle Swarm Optimization Technique.” Ain Shams Engineering Journal 10, no. 4 (December 2019): 769–783. doi:10.1016/j.asej.2019.07.002.

Ben Meziane, Khaddouj, and Ismail Boumhidi. “Optimized Type-2 Fuzzy Logic PSS Combined with H∞ Tracking Control for the Multi-Machine Power System.” Advances in Intelligent Systems and Computing (2020): 193-204. doi:10.1007/978-981-15-0947-6_19.

Devarapalli, Ramesh, and Biplab Bhattacharyya. “A Hybrid Modified Grey Wolf Optimization‐sine Cosine Algorithm‐based Power System Stabilizer Parameter Tuning in a Multimachine Power System.” Optimal Control Applications and Methods 41, no. 4 (March 26, 2020): 1143–1159. doi:10.1002/oca.2591.

Dey, Prasenjit, Anulekha Saha, Aniruddha Bhattacharya, and Boonruang Marungsri. “Analysis of the Effects of PSS and Renewable Integration to an Inter-Area Power Network to Improve Small Signal Stability.” Journal of Electrical Engineering & Technology 15, no. 5 (August 3, 2020): 2057–2077. doi:10.1007/s42835-020-00499-2.

Dey, Prasenjit, Aniruddha Bhattacharya, and Priyanath Das. "Tuned power system stabilizer for enhancing small signal stability of large interconnected power system." Caribbean Journal of Science 53, no. 1 (2019): 843–857.

Nguyen Hien Trung, “Application of RH∞ optimal theory to improve quality of Power system stabilizer.” PhD thesis, Thai Nguyen University of Technology, Thai Nguyen University, (2012).

IEEE Std. "IEEE Recommended Practice for Excitation System Models for Power System Stability studies." IEEE Standard 421.5–2005, IEEE Power Engineering Society by Energy Development and Power Generation Committee (2005).

Youla, D., J. Bongiorno, and H. Jabr. “Modern Wiener--Hopf Design of Optimal Controllers Part I: The Single-Input-Output Case.” IEEE Transactions on Automatic Control 21, no. 1 (February 1976): 3–13. doi:10.1109/tac.1976.1101139.

Ma, Jing, Shangxing Wang, Xiang Gao, Xiangsheng Zhu, Yang Qiu, and Zengping Wang. “Youla Parameterization Robust Control Strategy Considering Power System Uncertainties.” Electric Power Components and Systems 42, no. 11 (July 30, 2014): 1152–1157. doi:10.1080/15325008.2014.921948.

Gu, Da-Wei, Petko H. Petkov, and Mihail M Konstantinov. “Robust Control Design with MATLAB®.” Advanced Textbooks in Control and Signal Processing (2013). doi:10.1007/978-1-4471-4682-7.

Nguyen, Cong Huu, Kien Ngoc Vu, and Hai Trung Do. “Model Reduction Based on Triangle Realization with Pole Retention.” Applied Mathematical Sciences 9 (2015): 2187–2196. doi:10.12988/ams.2015.5290.

Moore, B. “Principal Component Analysis in Linear Systems: Controllability, Observability, and Model Reduction.” IEEE Transactions on Automatic Control 26, no. 1 (February 1981): 17–32. doi:10.1109/tac.1981.1102568.

Safonov, M.G., and R.Y. Chiang. “A Schur Method for Balanced-Truncation Model Reduction.” IEEE Transactions on Automatic Control 34, no. 7 (July 1989): 729–733. doi:10.1109/9.29399.

Glover, Keith. “All Optimal Hankel-Norm Approximations of Linear Multivariable Systems and their L, ∞-Error Bounds†.” International Journal of Control 39, no. 6 (June 1984): 1115-1193. doi:10.1080/00207178408933239.

A. Antoulas, Approximation of Large-Scale Dynamical System, SIAM: Philadelphia, PA, USA, (2005).

Prajapati, Arvind Kumar, and Rajendra Prasad. “Order Reduction in Linear Dynamical Systems by Using Improved Balanced Realization Technique.” Circuits, Systems, and Signal Processing 38, no. 11 (April 5, 2019): 5289–5303. doi:10.1007/s00034-019-01109-x.

Zilouchian, A. “Balanced Structures and Model Reduction of Unstable Systems.” IEEE Proceedings of the SOUTHEASTCON ’91 (1991). doi:10.1109/secon.1991.147956.

Minh, Ha Binh, Chu Binh Minh, and Victor Sreeram. “Balanced Generalized Singular Perturbation Method for Unstable Linear Time Invariant Continuous Systems.” Acta Mathematica Vietnamica 42, no. 4 (June 23, 2017): 615–635. doi:10.1007/s40306-017-0215-2.

Zhou, Kemin, Gregory Salomon, and Eva Wu. "Balanced realization and model reduction for unstable systems." International Journal of Robust and Nonlinear Control: IFAC‐Affiliated Journal 9, no. 3 (1999): 183-198. doi:10.1002/(sici)1099-1239(199903)9:3<183::aid-rnc399>;2-e.

Jonckheere, E., and L. Silverman. “A New Set of Invariants for Linear Systems--Application to Reduced Order Compensator Design.” IEEE Transactions on Automatic Control 28, no. 10 (October 1983): 953–964. doi:10.1109/tac.1983.1103159.

Full Text: PDF

DOI: 10.28991/esj-2021-01299


  • There are currently no refbacks.

Copyright (c) 2021 Hong Quang Nguyen