Transient stability improvement by nonlinear controllers based on tracking Juan M. Ramirez a,⇑ , Felipe Valencia Arroyave b , Rosa Elvira Correa Gutierrez b a Centro de Investigacion y Estudios Avanzados, Guadalajara, Mexico. Av. Cientifica 1145. Col. El Bajio. Zapopan, Jal. 45015, Mexico b Universidad Nacional de Colombia, Sede Medellin. Facultad de Minas, Escuela de Mecatronica, Colombia article info Article history: Received 30 September 2009 Received in revised form 21 June 2010 Accepted 13 August 2010 Keywords: Electromechanical oscillations Nonlinear controller Power system control Power system stability abstract This paper deals with the control problem in multi-machine electric power systems, which represent complex great scale nonlinear systems. Thus, the controller design is a challenging problem. These sys- tems are subjected to different perturbations, such as short circuits, connection and/or disconnection of loads, lines, or generators. Then, the utilization of controllers which guarantee good performance under those perturbations is required in order to provide electrical energy to the loads with admissible stability margins. The proposed controllers are based on a systematic strategy, which calculate nonlinear control- lers for generating units in a power plant, both for voltage and velocity regulation. The formulation allows designing controllers in a multi-machine power system without intricate calculations. Results on a power system of the open research indicate the proposition’s suitability. The problem is formulated as a tracking problem. The designed controllers may be implemented in any electric power system. Ó 2010 Elsevier Ltd. All rights reserved. 1. Introduction Electric power systems (EPS) exhibit two major problems: (a) loss of synchronism or angle instability, and (b) terminal voltage instability or collapse due to over loading in transmission lines, reactive constraints, and faults. The generators’ controllers must keep the terminal voltage and frequency close to the reference va- lue and provide sufficient damping to the power oscillations at all admissible operating points. For economical reasons, EPS are becoming more complex due to the increment in load demand. These changes have produced big uncertainties and have pushed the networks closer to their opera- tional limits. Then, EPS will require the application of advanced control technologies. Proper design of these control systems is imperative to guarantee robustness over wide operating condi- tions. Likewise, EPS are affected by diverse perturbations and it must remain stable and maintain the reference terminal voltage under all such perturbations. EPS models are complex large-scale nonlinear systems, sub- jected to variations as a result of changes in system’s loading and configurations. Thus, the controller design for these systems is a challenging problem. Nowadays, attention of researchers has been focused on the de- sign of modern nonlinear controllers for EPS that allow reduce the effect of internal and/or external perturbations. The main features that those controllers must satisfy are described in the following: i. Nonlinear model and controllers. The mathematical models are not linearized. This means that results are not limited to an equilibrium point’s neighborhood. ii. Robustness. The designed controller must guarantee good performance in steady state and in presence of perturba- tions such as parametric variations or faults. iii. Tracking. The controllers are able to track the terminal reference voltage. iv. Bounded control signals. All the non-linearities are consid- ered within the controllers’ design, including limits for the control input. v. Fast dynamics. Fast and non-modelled dynamics may be analyzed to reduce their negative effects. In order to improve the EPS stability, several control techniques have been applied. As a summary, the some of the main strategies are outlined as follows: (a) Adaptive control. The control objective is the controller parameters’ modification while the system conditions are varying. Adaptive control has been utilized to design con- ventional controllers in [1–3]. In [4,5], the adaptive control technique is combined with feedback linearization in an infi- nite machine bus system. (b) Feedback linearization. In this case, the nonlinear models are linearized by a feedback loop in such a way that linear techniques can be utilized. The basics of this methodology can be found in [6], while the applications to infinite machine bus systems are described in [7,8]. In [9,41] feedback lin- earization is applied to multi-machine EPS. Nevertheless, this technique does not offer robustness. Combination of 0142-0615/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijepes.2010.08.028 ⇑ Corresponding author. Tel.: +52 33 3777 3600. E-mail addresses: jramirez@gdl.cinvestav.mx (J.M. Ramirez), fvalenc@unalmed. edu.co (Felipe Valencia Arroyave), recorrea@unalmed.edu.co (R.E. Correa Gutierrez). Electrical Power and Energy Systems 33 (2011) 315–321 Contents lists available at ScienceDirect Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes