Thyristor Control Reactors Nonlinear and Linear Dynamic Analytical Models

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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

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[22] A. V. Oppenheim, A. S. Willsky, and I. T. Young, Signal and Systems. London, U.K.: Prentice-Hall, 1983. [23] L. A. S. Pilotto, A. Bianco, W. F. Long, and A. A. Edris, “Impact of TCSC control methodologies on subsynchronous oscillation,” IEEE Trans. Power Del., vol. 18, no. 1, pp. 243–252, Jan. 2003. J. E. R. Alves, Jr. (M’92–SM’05) was born in Juiz de Fora, Brazil, on November 30, 1963. He received the B.Sc., M.Sc., and D.Sc. degrees in electrical engineering, in 1986, 1991 and 1999, respectively, from the Federal University of Rio de Janeiro. In 1991, he became an Assistant Professor and in 1999 an Adjunct Professor at the Federal Fluminense University, where he teaches electronics and metering. Since 1995, he has been with CEPEL, the Brazilian Electrical Energy Research Center, Rio de Janeiro., where he is currently a Project Manager. His research interests are in the analysis of HVdc transmission systems, FACTS devices, power electronic controllers, distribution systems, and metering. Dr. Alves is currently Chair of IEEE Rio de Janeiro Section 2006-2007. Luiz A. S. Pilotto (M’88–SM’96) was born in Rio de Janeiro, Brazil. He received the P.Eng., M.Sc., and D.Sc. degrees in electrical engineering in 1981, 1983 and 1994, respectively, from the Federal University of Rio de Janeiro, Rio de Janeiro, Brazil. In 1983, he joined CEPEL, the Brazilian Electrical Energy Research Center, Rio de Janeiro, Brazil, serving it in several different technical and executive positions, including R&D Director from 2000 until 2003. From May 2003 until April 2005, he was with Andrade & Canellas, a consultant company in Brazil, as Partner and Business Development Director. Since June 2005, he has been with Accenture Brazil, working as a Business Development Director responsible for projects aimed at the Brazilian Power Sector. His international experience includes work developed at Brown Boveri and ABB in Switzerland and the participation in several projects/initiatives for both EPRI and the NSF in the U.S. His professional interests are in the analysis of HVdc transmission systems, FACTS devices, power electronic controllers, power system dynamics, SCADA/EMS systems, energy market structures, and hydro and thermal plants design and implementation. Dr. Pilotto is associated with the Power Engineering, Control Systems, Power Electronics, and Engineering Management Societies of the IEEE. He also participates in Cigrè. He is the IEEE Region 9 Director 2006-2007 and a Member of the Board of Directors of the IEEE. He has more than 100 papers published in international journals and conference proceedings and has received several awards for excellence in engineering, including the IEEE Award for “Notable Services and Contributions Towards the Advancement of IEEE and the Engineering Professions”. He is listed in Who’s Who in the Leadership of the United States. Edson Hirokazu Watanabe (M’76–SM’02) was born in Rio de Janeiro State, Brazil, on November 7, 1952. He received the B.Sc. degree in electronic engineering and the M.Sc. degree in electrical engineering in 1975 and 1976, respectively, from the Federal University of Rio de Janeiro. He received the D.Eng. degree from the Tokyo Institute of Technology, Tokyo, Japan, in 1981. In 1981, he became an Associate Professor and in 1993 a Professor at COPPE/ Federal University of Rio de Janeiro, where he teaches power electronics. His main fields of interests are converter analysis, modeling and design, active filters, and FACTS technologies. He is also the co-author of the book Instantaneous Power Theory and Applications to Power Conditioners (IEEE/Wiley, 2007). He is a member of the IEE-Japan, The Brazilian Society for Automatic Control, The Brazilian Power Electronics Society, CIGRE, and the Power Engineering, Industry Applications, and Power Electronics Societies of IEEE. In 2005, he was admitted to the National Order of Scientific Merit (Brazil).