IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 23, NO. 1, JANUARY 2008

Thyristor-Controlled Reactors Nonlinear and Linear Dynamic Analytical Models J. E. R. Alves, Jr., Senior Member, IEEE, Luiz A. S. Pilotto, Senior Member, IEEE, and Edson Hirokazu Watanabe, Senior Member, IEEE

Abstract—This work presents the development of analytical models for thyristor-controlled reactors (TCRs). A nonlinear model for the TCR was developed based on the use of Generalized Switching Functions and from this model, a detailed linear model was derived. The linear model allows for the analysis and precise understanding of the behavior of the TCR under small disturbances both in the time and frequency domains, for frequency ranges up to some tens of hertz. This model clearly shows that the TCR dynamics are operating point dependent. System parameter variations are also correctly considered in the model. With the proposed model, it is possible to design static var compensators (SVC) controllers in an integrated form, avoiding risks of instabilities and guaranteeing a good overall dynamic performance for the system. Validation of the models was done by comparing simulated results obtained with the proposed model with those obtained with a traditional electromagnetic transients program (EMTP). Index Terms—Generalized switching functions, reactive power control, static var compensators, SVC analytical models.

TABLE I USUAL VALUES FOR T AND T

I. INTRODUCTION HE ﬁrst generation of FACTS devices was based on thyristors used in combination with reactive components. There is a large number of static var compensators (SVCs) and some few thyristor-controlled series compensation (TCSC) devices currently in operation. A second generation of FACTS devices is based on forced commutated voltage source converters (VSCs). The static synchronous compensator (STATCOM) is a good example of the application of this technology [1] and compared to an SVC, a STATCOM is said to present superior performance [2]. In spite of this, SVC devices based on the use of thyristor-controlled reactors (TCRs) have a proven technology, still lower costs and a performance that is appropriate for most of the applications. For sure, this technology will remain extremely competitive for many years to come. Therefore, the authors believe that modeling these devices is an important task, to guarantee the appropriate design of power system controllers. FACTS equipment are extremely fast power electronic devices [2]. Therefore, their controller design must be coordinated with other equipment with fast dynamic response operating at Manuscript received August 2, 2005; revised July 18, 2007. Paper no. TPWRD-00454-2005. J. E. R. Alves Jr. is with CEPEL—Centro de Pesquisas de Energia Elètrica, CEP:21.941-911, Rio de Janeiro, Brazil (e-mail: alves@cepel.br). L. A. S. Pilotto is with Accenture, CEP: 20.031-170, Rio de Janeiro, Brazil (e-mail: luiz.a.pilotto@accenture.com). E. H. Watanabe is with COPPE—Federal University of Rio de Janeiro, CEP:21.941-972, Rio de Janeiro, Brazil (e-mail: watanabe@coe.ufrj.br). Digital Object Identiﬁer 10.1109/TPWRD.2007.911131

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the same electrical area in order to avoid undesirable control interactions. These devices may interact not only on the electromechanical range of operation, but they may also experience higher frequency interactions. Important interactions between SVCs and other power system components are described in the literature [3]–[6]. Transient stability and conventional eigenvalue programs available nowadays represent the ac network by algebraic equations. Therefore, both transient stability simulations and eigenvalue analysis that make use of conventional models can not predict the high-frequency self-modes of oscillation of the several FACTS devices embedded in a large power system network. Consequently, the investigation of higher frequency controller interactions among the several FACTS devices must be carried out using...