Modeling of FACTS Devices Based on SPWM VSCs - CIEP

More documents

Recommendations

Info

Fig. 21.Transient solution comparison for the UPFC.Fig. 19. Steady-state solution comparison for the SSSC.Fig. 22. Steady-state solution comparison for the UPFC.Fig. 20. Harmonic content comparisons. (a) Harmonic content in the dcvoltage. (b) Magnitude <strong>of</strong> selected harmonics in phase A <strong>of</strong> the terminalvoltage. (c) Magnitude <strong>of</strong> selected harmonics in the phase A <strong>of</strong> the seriescurrent.Simulink PSCAD/EMTDC, and the two proposed models. Anintegration step <strong>of</strong> 0.1 s has been used in Simulink, 100 sfor the Fourier approach method, 30 s for the hyperbolictangent model, and 0.1 s in PSCAD/EMTDC. Observe thatthe proposed models closely agree with the solution obtainedwith Simulink and PSCAD/EMTDC.A comparison between the periodic steady-state solutionsis shown in Fig. 19; the capacitor voltage is shown inFig. 19(a), the terminal voltage at node 1 in Fig. 19(b),and the phase A <strong>of</strong> the series current in Fig. 19(c), respectively.Observe that all solutions are again in very closeagreement.Fig. 20(a) shows the harmonic content for , in Fig. 20(b)for , and in Fig. 20(c) for . It can be seen that the proposedmodels are in very good agreement with the solution obtainedwith Simulink and PSCAD/EMTDC.3) Unified Power Flow Controller (UPFC): The UPFC includesthe shunt control described in [15], and the series controlproposed in [16]. The initial condition is zero, except for thedc capacitor voltage, which is 2 p.u. The series controller regulatesthe real ( p.u.) and reactive ( p.u.)power flows by adjusting the injected series voltage. The shuntconverter regulates the dc-side capacitor voltage ( p.u.)and the sending end voltage ( p.u.). The modulationindex is . The maximum harmonic order in the Fourierapproach is 69 (4140 Hz).Fig. 21 shows the transient solution comparison for the capacitorvoltage <strong>of</strong> the UPFC operating in open-loop control.For this operating mode, the initial condition has been assumedzero. This solution has been computed using Simulink, PSCAD/EMTDC and the two proposed models. An integration step <strong>of</strong>0.1 s has been used in Simulink and PSCAD/EMTDC, 80 sfor the Fourier approach method, and 30 s for the hyperbolictangent model.A comparison between the periodic steady-state solution obtainedwith Simulink, the Fourier model, the hyperbolic tangentmodel, and PSCAD/EMTDC is shown in Fig. 22. Fig. 22(a)shows the capacitor voltage , Fig. 22(b) shows the voltage<strong>of</strong> phase A in bus 1, and Fig. 22(c) shows the series current<strong>of</strong> phase A . The slight difference between the solutionobtained with PSCAD/EMTDC and the other solutions is becausethe UPFC implemented in PSCAD/EMTDC is operatingin open-loop control, meanwhile, the other solutions are operatingin closed-loop control; however, all the solutions are ingood agreement.
ACKNOWLEDGMENTThe authors thank the Universidad Michoacana de SanNicolás de Hidalgo (UMSNH) through the División de Estudiosde Posgrado, Facultad de Ingeniería Eléctrica, for thefacilities that were granted to carry out this investigation. Theauthors would also like to thank Pr<strong>of</strong>. Dr. E. Barcenas fromthe Instituto Tecnológico Superior de Irapuato (ITESI) for hisvaluable suggestions and comments.REFERENCESFig. 23. Harmonic content comparisons. (a) Harmonic content in the dcvoltage. (b) Magnitude <strong>of</strong> selected harmonics in phase A <strong>of</strong> the terminalvoltage. (c) Magnitude <strong>of</strong> selected harmonics in the phase A <strong>of</strong> the seriescurrent.A validation <strong>of</strong> the proposed models is further illustrated inFig. 23, which shows the harmonic spectrum for the capacitorvoltage in Fig. 23(a), the voltage <strong>of</strong> phase A at node 1 inFig. 23(b), and the phase A <strong>of</strong> the series current in Fig. 23(c),respectively; all the solutions are in excellent agreement.V. CONCLUSIONTwo efficient VSC models based on Fourier series approachand hyperbolic tangent have been proposed for the six-pulseconverter. The proposed models have been used for the computation<strong>of</strong> the solution <strong>of</strong> <strong>FACTS</strong> devices connected to a powernetwork.It has been shown that the proposed models can be used tocompute both the transient and the periodic steady-state solution<strong>of</strong> a power network containing VSC-based <strong>FACTS</strong>.The response given by the proposed methods has been successfullyvalidated against the solution obtained with the widelyaccepted digital simulators Simulink and PSCAD/EMTDC, respectively,in all the cases the obtained results were in excellentagreement. In addition, it has been shown through simulationsthat the proposed models allow significant larger integrationsteps, as compared with the ideal switch model approach,e.g., for the conducted studies, more than 800 times the integrationstep needed by Simulink and PSCAD/EMTDC when theFourier approach was used, and at least 300 times when the hyperbolictangent method was applied.The proposed VSCs models have been only implemented in anetwork including <strong>FACTS</strong> devices; however, these models canbe used in any power-electronic device based on SPWM sixpulse converters, or even for multilevel converters based on arrangement<strong>of</strong> six-pulse converters.[1] N. G. Hingorani and L. Gyugyi, Understanding <strong>FACTS</strong>. Piscataway,NJ: IEEE Press, 2000.[2] E. Uzunovic, C. A. Cañizares, and J. Reeve, “Fundamental frequencymodel <strong>of</strong> unified power flow controller,” in Proc. North AmericanPower Symp., Cleveland, OH, Oct. 1998, pp. 294–299.[3] A. Nahavi-Niaki and M. R. Iravani, “Steady-state and dynamic models<strong>of</strong> unified power flow controller for power system studies,” IEEE Trans.Power Syst., vol. 11, no. 4, pp. 1937–1943, Nov. 1996.[4] M. Tavakoli Bina and D. C. Hamill, “Average circuit model for anglecontrolledSTATCOM,” Proc. Inst. Elect. Eng. Power Appl., vol. 152,no. 3, pp. 653–659, May 2005.[5] E. Uzunovic, C. Cañizares, and J. Reeve, “Fundamental frequencymodel <strong>of</strong> static synchronous compensator,” in Proc. North AmericanPower Symp., Laramie, WY, Oct. 1997, pp. 49–54.[6] C. A. Cañizares, “Power flow and transient stability models <strong>of</strong> <strong>FACTS</strong>controllers for voltage and angle stability studies,” in Proc. IEEE PowerEng. Soc. Winter Meeting, Singapore, Jan. 2000.[7] J. Vlach, J. M. Wojciechowski, and A. Opal, “Analysis <strong>of</strong> nonlinear networkswith inconsistent initial conditions,” IEEE Trans. Circuits Syst.,vol. 42, no. 4, pp. 195–200, Apr. 1995.[8] EMTDC User’s Guide 2003, HVDC Res. Ctr..[9] I. A. Hiskens and M. A. Pai, “Trajectory sensitivity analysis <strong>of</strong> hybridsystems,” IEEE Trans. Circuits Syst. I, vol. 47, no. 2, pt. I, pp. 204–220,Feb. 2000.[10] P. W. Lehn, “Exact modeling <strong>of</strong> the voltage source converter,” IEEETrans. Power Del., vol. 17, no. 1, pp. 217–222, Jan. 2002.[11] K. L. Lian and P. W. Lehn, “Steady-state solution <strong>of</strong> a voltage-sourceconverter with full closed-loop control,” IEEE Trans. Circuits Syst., vol.21, no. 4, pp. 2071–2081, Oct. 2006.[12] P. Zuniga-Haro and J. Ramirez, “Multi-pulse switching functions modeling<strong>of</strong> flexible AC transmission systems devices,” Elect. Power ComponentsSyst., vol. 37, no. 1, pp. 20–42, Jan. 2009.[13] C. E. Shannon, “Communication in presence <strong>of</strong> noise,” Reprint asClassic Paper in: Proc. IEEE, vol. 86, no. 2, pp. 447–457, Feb. 1998.[14] Power System Blockset User’s Guide 2001, TEQSIM Int. Inc..[15] B. Mahyavanshi and G. Radman, “A study <strong>of</strong> interaction betweendynamic load and STATCOM,” presented at the Southeastern Symp.System Theory, Cookeville, TN, Mar. 5–7, 2006.[16] H. Fujita, Y. Watanabe, and H. Akagi, “Transient analysis <strong>of</strong> a unifiedpower flow controller and its applications to design <strong>of</strong> the DC link capacitor,”IEEE Trans. Power Electron., vol. 16, no. 5, pp. 735–740, Sep.2001.Juan Segundo-Ramírez received the B.S. degree in electromechanical engineeringfrom the Instituto Tecnológico de Lázaro Cárdenas, Lázaro Cárdenas,Mexico, in 2001, the M.Sc. degree from the CINVESTAV Guadalajara,Guadalajara, Mexico, in 2004, and is currently pursuing the Ph.D. degreeat the División de Estudios de Posgrado, Facultad de Ingeniería Eléctrica,Universidad Michoacana de San Nicolás de Hidalgo (UMSNH), Morelia,México.His area <strong>of</strong> research is the dynamic and steady-state analysis <strong>of</strong> powersystems.Aurelio Medina (SM’02) received the Ph.D. degree from the University <strong>of</strong>Canterbury, Christchurch, New Zealand, in 1992.He was a Postdoctoral Fellow at the University <strong>of</strong> Canterbury, New Zealand,for one year and at the University <strong>of</strong> Toronto, Toronto, ON, Canada, for twoyears. He is currently a staff member with the Facultad de Ingeniería Eléctrica,Universidad Michoacana de San Nicolás de Hidalgo (UMSNH), Morelia,México, where he is the Head <strong>of</strong> the Division for postgraduate studies. His researchinterests are in the dynamic and steady-state analysis <strong>of</strong> power systems.
Page 3 and 4: Fig. 3. Single-phase equivalent cir

Modeling of FACTS Devices Based on SPWM VSCs - CIEP

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?