N.R. Watson∗
[1] N.G. Hingorani & M. Burbury, Simulation of ac systemimpedance in HVdc system studies, IEEE Transactions onPower Apparatus and Systems, 89 (5/6), 1970, 820–828. [2] A. Abur & H. Singh, Time domain modeling of external systemsfor electromagnetic transient programs, IEEE Transactions onPower Systems, 8(2), 1993, 671–679. [3] H. Singh & A. Abur, Multi-port equivalencing of external sys-tems for simulation of switching transients, IEEE Transactionson Power Delivery, 10(1), 1995, 374–382. [4] T. Noda, N. Nagaoka, & A. Ametani, Phase domain modelingof frequency-dependent transmission lines by means of anARMA model, IEEE Transactions on Power Delivery, 11(1),1996, 401–411. [5] T. Noda, N. Nagaoka, & A. Ametani, Further improvementsto a phase-domain ARMA line model in terms of convolution,steady-state initialization, and stability, IEEE Transactionson Power Delivery, 12(3), 1997, 1327–1334. [6] B. Gustavsen & A. Semlyen, Rational approximation of fre-quency domain responses by vector fitting, IEEE/PES WinterMeeting 1997, Paper No. PE-194-PWRD-0-11-1997. [7] G. Angelidis & A. Semlyen, Direct Phase-domain calculation oftransmission line transients using two-sided recursions, IEEETransactions on Power Delivery, 10(2), 1995, 941–947. [8] A.S. Morched, J.H. Ottevangers, & L. Marti, Multi portfrequency dependent network equivalents for the EMTP, IEEETransactions on Power Delivery, 8(3), 1993, 1402–1412. [9] N.R. Watson, A.M. Gole, & G.D. Irwin, Z-domain frequency-dependent network equivalents for electromagnetic transientstudies, Proceedings of International Conference on PowerSystem Transients (IPST’99), June 1999, 37–42. [10] B. Gustavsen & A. Semlyen, Enforcing passivity for admittancematrices approximated by rational functions, IEEE Transac-tions on Power Systems, 16(1), 2001, 97–104. [11] Y.P. Wang & N.R. Watson, Z-domain frequency-dependentA.C. system equivalent for electromagnetic transient simula-tion, IEE Proc. Genr. Transm. Distrib., 150(2), 2003, 141–146. [12] N.R. Watson & J. Arrillaga, Harmonic assessment using elec-tromagnetic transient simulation and frequency-dependent net-work equivalents, IEE Proc. Genr. Transm. Distrib., 150(6),2003, 641–650. [13] N.R. Watson & J. Arrillaga, Power systems electromagnetictransients simulation (UK: IEE Books, 2002).AppendixCoefficients for 5–1250 Hz fitting the coefficients are pre-sented in Tables 11–16.Table 11Coefficients of Rational Function Representing Yself1 TermOrder a b0 2.4518139802491529e−003 1.01 −1.5523400352713717e−002 −6.6654302428731960e+0002 4.2380331810221161e−002 1.9230399247655740e+0013 −6.4641019199195751e−002 −3.1130273213778576e+0014 5.9457300767762414e−002 3.0538485772657317e+0015 −3.2959346847465210e−002 −1.8155446247494950e+0016 1.0187297977530718e−002 6.0572751686602073e+0007 −1.3529372195878338e−003 −8.7501014304358138e−001Table 12Coefficients of Rational Function Representing Yself2 TermOrder a b0 2.4713730049758290e−003 1.01 −2.7498876794554993e−002 −1.1461754052612378e+0012 1.4085028529384719e−001 6.0580099117563933e+0013 −4.3906549559419655e−001 −1.9524261439326494e+0024 9.2754966413689310e−001 4.2734415872383033e+0025 −1.3986993576906026e+000 −6.6923706713661522e+0026 1.5433932671512440e+000 7.6891667409346007e+0027 −1.2553171427425995e+000 −6.5307918275525128e+0028 7.4668028941365427e−001 4.0697958454742064e+0029 −3.1663869609421275e−001 −1.8147839146564058e+00210 9.0825298324345355e−002 5.4967480472643224e+00111 −1.5813588182285006e−002 −1.0154222411584609e+00112 1.26297977375335590e−003 8.6523526005393281e−001Table 13Coefficients of Rational Function Representing Yself3 TermOrder a b0 2.4518139802491529e−003 1.01 −1.5523400352713717e−002 −6.6654302428731960e+0002 4.2380331810221161e−002 1.9230399247655740e+0013 −6.4641019199195751e−002 −3.1130273213778576e+0014 5.9457300767762414e−002 3.0538485772657317e+0015 −3.2959346847465210e−002 −1.8155446247494950e+0016 1.0187297977530718e−002 6.0572751686602073e+0007 −1.3529372195878338e−003 −8.7501014304358138e−001279Table 14Coefficients of Rational Function Representing Y12 TermOrder a b0 1.9501107426634562e−003 1.01 −1.8984910246341156e−002 −1.0472045700750085e+0012 8.4077491417341846e−002 5.0242749736612936e+0013 −2.2327784954520663e−001 −1.4577147599444638e+0024 3.9436282600293848e−001 2.8416307981056764e+0025 −4.8528978431109171e−001 −3.9078405955678375e+0026 4.2318006985401002e−001 3.8685683419253877e+0027 −2.6026788334542772e−001 −2.7568394845148111e+0028 1.0983931015277194e−001 1.3859815103973341e+0029 −2.9928875612837458e−002 −4.6818484850277628e+00110 4.6331885907560004e−003 9.5644565932267973e+00011 −2.9369352575267255e−004 −8.9525681690543701e−001Table 15Coefficients of Rational Function Representing Y13 TermOrder a b0 1.3515557479258451e−003 1.01 −1.3040753389910330e−002 −1.0492921441994246e+0012 5.7120790014802532e−002 5.0437859896160646e+0013 −1.4963579824816328e−001 −1.4660041251574290e+0024 2.5980657688651376e−001 2.8627120261555945e+0025 −3.1278071264536744e−001 −3.9433801731554610e+0026 2.6499504941098462e−001 3.9100684891211131e+0027 −1.5666052749777820e−001 −2.7908347579969859e+0028 6.2418018680732934e−002 1.4052724013418029e+0029 1.5516515687008176e−002 −4.7544284040525767e+00110 2.0237739768697539e−003 9.7279684878283152e+00011 −8.1457105557848394e−005 −9.1200893075493861e−001Table 16Coefficients of Rational Function Representing Y23 TermOrder a b0 1.9465294173155033e−003 1.01 −1.8945287846846227e−002 −1.0471346049412443e+0012 8.3877969722319409e−002 5.0235844766381526e+0013 −2.2267431860526124e−001 −1.4574061698767119e+0024 3.9314451375871884e−001 2.8408082935465598e+0025 −4.8356680413292885e−001 −3.9063925145386804e+0026 4.2143847421282793e−001 3.8668085334737316e+0027 −2.5900998079324361e−001 2.7553443032935473e+0028 1.0920330177935411e−001 1.3851044577078341e+0029 −2.9714575399601009e−002 −4.6784488861503647e+00110 4.5899042420320200e−003 9.5565928969023801e+00011 −2.8972618107620023e−004 −8.9443245225363499e−001
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