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Advanced SVC models for newton-raphson load flow and ... - ITCJ

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116 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL 15. NO. I. PEBRUARY 2000<br />

by the variable susceptance representation. As expected, both<br />

representations have a minimum impact on network losses, but<br />

at the point of <strong>SVC</strong> connection differences can be observed in<br />

the voltage profile <strong>and</strong> in the reactive power contributed by both<br />

<strong>models</strong>.<br />

As discussed in Section 111, the compound generator-constunt<br />

susceptance representation provides an accurate <strong>load</strong> <strong>flow</strong><br />

represetitation of <strong>SVC</strong>'s <strong>for</strong> the complete range of operation.<br />

However, inefficiencies may be observed owing to the need to<br />

reorder <strong>and</strong> to redimension the linearized systems of equations.<br />

In the OPF <strong>for</strong>mulation, further complications may arise with<br />

this compound representation. The multiplier method, which<br />

has shown to be very effective in en<strong>for</strong>cing variables outside<br />

limits, may have difficulties in checking whether or not a <strong>SVC</strong><br />

is operating within limits when represented as a constant susceptancc.<br />

VIII. CONCLUSIONS<br />

Comprehensive <strong>SVC</strong> <strong>models</strong> suitable <strong>for</strong> conventional<br />

<strong>and</strong> optimal power <strong>flow</strong> analysis have been presented in<br />

this paper, namely <strong>SVC</strong> total suscepiance model <strong>and</strong> <strong>SVC</strong><br />

firing angle model. In contrast to <strong>SVC</strong> <strong>models</strong> reported in<br />

the open literature, the proposed <strong>models</strong> do not make use<br />

of the genera<strong>for</strong> concept normally employed <strong>for</strong> the <strong>SVC</strong><br />

representation. Instead, they use the variable shunt susceptance<br />

concept. Arguably, this has the advantage of representing actual<br />

<strong>SVC</strong> operation more realistically. Moreover, since <strong>SVC</strong> shunt<br />

susceptance <strong>models</strong> only make use of one node to represent<br />

<strong>SVC</strong>'s operating inside <strong>and</strong> outside ranges then Newton based<br />

power <strong>flow</strong> solutions become more efficient, compared to cases<br />

when genera<strong>for</strong> based <strong>models</strong> of <strong>SVC</strong>'s are used in Newton<br />

algorithms. An <strong>SVC</strong> model which uses the thyristor firing angle<br />

as the state variable has shown to provide fuller in<strong>for</strong>mation<br />

that existing <strong>SVC</strong> <strong>models</strong>. The firing angle required to achieve<br />

a specified level of compensation becomes readily available<br />

from the power <strong>flow</strong> solution, as well as the fundamental<br />

frequency, internal <strong>SVC</strong> resonant points. A Newton-Raphson<br />

<strong>load</strong> <strong>flow</strong> <strong>and</strong> a Newton's OPF algorithms have been upgraded<br />

to incorporate the new <strong>SVC</strong> <strong>models</strong>. A real-life, bulk transmission<br />

system has been used as the test case. Conventional <strong>and</strong><br />

optimal solutions were obtained in less than 6 iterations.<br />

ACKNOWLEDGMENT<br />

H. Ambriz-PBrez would like to thank Comisi6n Federal de<br />

Electricidad, MBxico <strong>for</strong> granting him study leave to carry out<br />

Ph.D. studies at the University of Glasgow, Scotl<strong>and</strong>, UK.<br />

- .<br />

REFERHNCES<br />

111 CIGRB. workine ~ rouo 38-01, Task F~~~~ N ~ 2 . un <strong>SVC</strong>. -stittic VAR<br />

comnensutors.". I. A. Enrimez. EL. 1986.<br />

sciencc, 1982.<br />

141 IEEE Special Stability Controls Working Glaup, Working Group 38-01,<br />

Task Force No. 2 an <strong>SVC</strong>, "Static VAR compensator <strong>models</strong> <strong>for</strong> power<br />

<strong>flow</strong> <strong>and</strong> dynamic per<strong>for</strong>mance simulation," IEEE T,una. on Po'owrr Syrtems,<br />

vol. 9, no. I, pp. 229-240, Feb. 1995.<br />

151 J. 1. Rico, E. Acha, <strong>and</strong> 1: J. H. Miller, 'Harmunic dainain modelling of<br />

three phme thyristor-cuntmlled ceilctors by means of switching vectors<br />

<strong>and</strong> tllscmte COrIVOIUtionS," /BEE Pwl.;. on Power. Delivery, vol. I I, no.<br />

3, pp. 1678-1684, July 1996.<br />

I61 C. R. Fuerte-Esquivel, E. Acha, S. G. Tang, <strong>and</strong> J. I. Rico, "Ellicient ohjcct<br />

orienled power systems saftwarc <strong>for</strong> the antilysis of lsrge~scalc networks<br />

containing FACTS-controlled branches," IBm 7mns. on Power<br />

Sy.~lons, vol. 13, no. 2, pp. 464472, May 1998.<br />

171 E Aboytes <strong>and</strong> G. Arroyo, "Sccurity assessment in the operation of 1011-<br />

gitudinal power systems,"lEEE Trans. on PwrrSystcms, vol. PWRS- I,<br />

no. 2, pp. 225-232, May 1986.<br />

181 D. I. Sun, B. Ashley. B. Rrcewer, A. Hughes, <strong>and</strong> W. E Tinney, "Optimal<br />

power <strong>flow</strong> by Newton approach," IEEE Tmns. on I'owerAppapnmtusnnd<br />

Sysrems, vol. PAS-103, no. IO, pp. 286G2880, Oct. 19x4.<br />

I91 D. 1. Sun, T. I. Hu, G. S. Lin, C. 1. Lin, <strong>and</strong> C. H. Chen, "Expericnces<br />

wilh implementing optimal power <strong>flow</strong> <strong>for</strong> ceactive scheduling in the<br />

Taiwan power system," I Trrms. on Power S),,rremu, vol. 3, no. 3, pp,<br />

1193-1200, Aug. 1988.<br />

I101 D. P. Bettsekas, "Multiplier methods: A wrvcy," in Auroniurlco: PergamonPress,<br />

1976, vol. 12, pp. 133-145.<br />

[I 11 D. G. Luenberger, Intmducfirm to Linear <strong>and</strong> Nonlineur Pmgramming,<br />

2nd e& Addisun-Wesley Publishing Ca., 1984.<br />

It. Aeha was horn in Mexico. He graduated from University of Michoilcdn<br />

in 1979 <strong>and</strong> rcceiverl the Ph.D. degrcc from the University of Canterbury,<br />

Christchurch, New Zeal<strong>and</strong>, in 1988, He was a postdoctoral Fellow at the<br />

University of Toronto, Cantidti <strong>and</strong> the Univcrsity of Durham, Engl<strong>and</strong>. He<br />

is currently n Senior Lecturer ut the University 01 Glasgow, Scotl<strong>and</strong>, wherc<br />

hc lectures <strong>and</strong> conducts mseilrcli on power systems analysis i~nd power<br />

electronics applications. His research interests arc in the aceus of FACTS,<br />

custom power, <strong>and</strong> real-time modeling <strong>and</strong> iinalysis.<br />

C. R. Focrte-Esqaivel was barii in Mexico in 1964. He received the B.Eng. degree<br />

(Hans) from Institute Tecnol6gicn de March, Mexico in 1990, the MSc.<br />

degree 1wm lnstiluto Politecnico Naciunal, Mexico in 1993, <strong>and</strong> thc Ph.D degree<br />

from the University dGlasgaw, Scotl<strong>and</strong>, UK, in lY97. He is currently :NI<br />

Assistant Professor at thc Institute TecnolOgico de March His main research<br />

interests lie oil the dynamic <strong>and</strong> steady-state analysis of FACTS, custom power,<br />

<strong>and</strong> real-time modeling <strong>and</strong> analysis.

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