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TextState> TextStyle=@ ArialSerial_ParPropDefaultVNormal=@Arial@V Heading 1=@ Arial@V Heading 2=@ Arial@V Heading 3 =@ Arial@V Paragraph =@ Arial@VList =@ Arial@VIndent =@Times New Roman@V Title =@Times New Roman@V Subtitle font_style_listN font_styleO  VariablesTimes New Roman@O  ConstantsTimes New Roman@O TextArial@O Greek VariablesSymbol@O User 1Arial@O User 2 Courier New@O User 3System@O User 4Script@O User 5Roman@O User 6Modern@O User 7Times New Roman@O SymbolsSymbol@O Current Selection FontArial@O Undefined Font@O HeaderArial@O FooterArial@O Rotated Math FontTimes New Romant TextRegion* docRegionFshpBoxT== CharacterMap-RangeMap:@Two Source - One line Power System for Fault Analysis File Name: 2Lin2Src.mcd Richard W. Wall October 14, 1999 (Rev. 2/25/2005) ChrPropMap666 RangeElem;6 ChrPropData7 RangeData<hArial;L7nArial ParPropMap8##_;# ParPropData9@V;_9@VEmbedMap0;LinkMap.;LinkData/@NormalArial *@TPP-BuThis program computes the directional torque equations for relays Rs and Rr with various faults located at F1,F2, and F3. No zero sequence current can flow from source Es since Zs has high zero sequence impedance. Impedance Zt simulates a Delta-Grounded wye transformer so a current polarizing signal can be obtained for relay S. Reverse faults are generated by adding impedance between nodes V1 and V2 and placing the fault impedance matrix, Zf3. Faults at Zf2 can appear forward or reverse depending on the algorithm and the location of the fault as set by the value of m2. 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Symmetrical Component Conversions6&);&*7(}8&+;&,9@V0-;.&.;&//@NormalArial 0*@TX++OX8 y$$-@Ia = 120 degree phase shift operator a2 = 240 degree phase shift operator6*&I1;&2703;470@ Arial15;67037;8705738I9;I:9@V0;;.I<;I=/@NormalArial >*@T83C8@ y\\-h = scale vector68?;@@9@V0@A;.@B;@C/@NormalArial @DeqRegionA@T*BP@ @Etree ? p@F? @E@G?d@Fa@H?@F@I?@@H@J?d@Icos@K?p@I@L?@K@M?t@L2@N?@L@O?d@N\p@P?@N3@Q?5@H@R?@@Q@S?d@Rsin@T?p@R@U?@T@V?t@U2@W?@U@X?d@W\p@Y?@W3@Z?@Q1i@[@A@TT'e`@\? p@]? @\@^?d@]h@_?@]3@`*@Tcwp y -4Phase to Symmetrical Component transformation matrix6484@a;4@b9@V0@c;.4@d;4@e/@NormalArial @f@A@TN-x @g? p@h? @g@i?d@hAsys@j?@h@k?p@@j@l?@k@m?t@l1@n?@lh@o?p@j@p?0@o@q?0A@p@r?0A@q@s?0A@r@t?0A@s@u?0A@t@v?0A@u@w?0A@v@x?0A@w@y?@@x@z?@xa@{?@w@|?d@{a@}?@{2@~?@v1@?@u@?d@a@?@2@?@ta@?@s1@?@r1@?@q1@?@p1@@A@T/ @? p@? @@?@@@?d@ ZsZm_Z012@?p@@? @@?d@Zs@?@Zm@?@@?@@@?@@@?d@Zabc@?p@@?0@@?0A@@?0A@@?0A@@?0A@@?0A@@?0A@@?0A@@?0A@@?@@@?@Zs@?@Zm@?@Zm@?@Zm@?@Zs@?@Zm@?@Zm@?@Zm@?@Zs@?@@?d@Z012@?@@?@@@?d@Asys@?@Zabc@?@@?d@Asys@?K@@?@1@?s@@?@Z012@@A@T @? p@? @@?@@@?d@ Z0Z1_Zabc@?p@@? @@?d@Z0@?@Z1@?@@?@@@?@@@?d@Z012@?p@@?0@@?0A@@?0A@@?0A@@?0A@@?0A@@?0A@@?0A@@?0A@@?@@@?@Z1@?@0@?@0@?@0@?@Z1@?@0@?@0@?@0@?@Z0@?@@?d@Zabc@?@@?@@@?d@Asys@?@Z012@?@@?d@Asys@?K@@?@1@?s@@?@Zabc@@A@T7Kq0 @? p@? @@?@@@?d@ Zabc_Z012@?p@@?@Zabc@?@@?@@@?d@Z012@?@@?@@@?d@Asys@?@Zabc@?@@?d@Asys@?K@@?@1@?s@@?@Z012@@A@TK0 @? p@? @@?@@@?d@ Z012_Zabc@?p@@?@Z012@?@@?@@@?d@Zabc@?@A?@@A?@AA?dAAsysA?KAA?A1A?AZ012A?@AsysA?s@A?AZabcA *@Tk{xA-1.2 Network impedance matrices6A ;A 7A }8A ;A 9@V0A;.A;A/@NormalArial A*@TA- 1.2.1 Network constants 6A;A7A}8A;A9@V0A;.A;A/@NormalArial A@A@T}<A? pA? AA?dAYnullA?pAA?0AA?0AAA ?0AAA!?0AA A"?0AA!A#?0AA"A$?0AA#A%?0AA$A&?0AA%A'?@A&A(?A&0A)?A%0A*?A$0A+?A#0A,?A"0A-?A!0A.?A 0A/?A0A0?A0A1*@T ߄  -@KThis matrix is used as a constant for building the system impedance matrix.6K8//KA2;/A39@VA4;A59@VA2A4A40A6;.KA7;KA8/@NormalArial A9@D@T@A:*@T#30-% 1.2.2 Transmission line calculations6%A;;%A<7A:}8%A=;%A>9@V0A?;.%A@;%AA/@NormalArial AB*@TCoSP1gg-* 1.2.1.1 Unbalanced line parameter matrix6(*AC;AD7ABAE;(AF7AB}ACAEAE8*AG;*AH9@V0AI;.*AJ;*AK/@NormalArial AL@A@T0t|AM? pAN? AMAO?dAN Line_LengthAP?AN25AQ@A@T^KAR? pAS? ARAT?dASZLAU?ASAV?p@AUAW?0AVAX?0AAWAY?0AAXAZ?0AAYA[?0AAZA\?0AA[A]?0AA\A^?0AA]A_?0AA^A`?@A_Aa?A_Ab?tAa0.2201Ac?Aa0.9608iAd?A^Ae?tAd0.1175Af?Ad0.4895iAg?A]Ah?tAg0.1133Ai?Ag0.4608iAj?A\Ak?tAj0.1175Al?Aj0.4895iAm?A[An?tAm0.2285Ao?Am0.9575iAp?AZAq?tAp0.1175Ar?Ap0.4895iAs?AYAt?tAs0.1133Au?As0.4608iAv?AXAw?tAv0.1175Ax?Av0.4895iAy?AWAz?tAy0.2201A{?Ay0.9608iA|?AU Line_LengthA}@A@T`t{ A~? pA? A~A?dAZLrA?AA?dAReA?pAA?AZLA@A@Tk. A? pA? AA?dAZLiA?AA?dAImA?pAA?AA?@AA?dAZLA?A1000A?A377A*@T1-. 1.2.2.2 Balanced line parameter computations6.A;.A7A}8.A;.A9@V0A;..A;.A/@NormalArial A@A@TH A? pA?AA?@AA?dAZLrA?A0.01A?AA?+@ASerial_DisplayNodeWA?AA@A@T oX A? pA?AA?@AA?dAZLiA?A0.01A?AA?+@A@WA?AA@A@T13 A? pA? AA?dAZL012A?AA?dA Zabc_Z012A?pAA?AZLA@A@T?(4 A? pA?AA?dAZL012A?AA?+@A@WA?AA@A@Tb%5 A? pA? AA?dAZL0A?AA?dAZL012A? AA?tA0A?A0A@A@TH%  A? pA?AA?@AA?dAZLrA?A0.99A?AA?+@A@WA?AA@A@T o%X  A? pA?AA?@AA?dAZLiA?A0.99A?AA?+@A@WA?AA@A@T$b<%06 A? pA? AA?dAZL1A?AA?dAZL012A? AA?tA1A?A1A@A@T$507 A? pA? AA?dAZL2A?AZL1A*@TSrc`8 jjj-$ 1.2.2.3 Set maximum torque angle 6# $A; A7A}A;A7A}AA;A7A}AAA8$A;$A9@V0A;.$A;$A/@NormalArial A@A@TH\m{h A? pA?AA?@AA?dAZLrA?A0.8A?AA?+@A@WA?AA@A@T \imRh A? pA?AA?@AA?dAZLiA?A0.8A?AA?+@A@WB?AB@A@Ttn49 B? pB? BB?dBMTA1B?BB?dBargB?pBB?BZL1B @A@Tt: B ? pB ? B B ?dB MTA2B ?B MTA1B@A@TtV; B? pB? BB?dBMTA0B?BB?dBargB?pBB?BZL0B*@To< Igg-* 1.2.2.4 Asymmetrical compensation factor6*B;*B7B}8*B;*B9@V0B;.*B;*B/@NormalArial B@A@TH{ B? pB ?BB!?@B B"?dB!ZLrB#?B!0.2B$?B B%?+@B$@WB&?B$B'@A@T iR B(? pB)?B(B*?@B)B+?dB*ZLiB,?B*0.2B-?B)B.?+@B-@WB/?B-B0@A@T},= B1? pB2? B1B3?dB2k0B4?B2B5?p@B4B6?B5B7?dB6ZL0B8?B6ZL1B9?B4B:?tB93B;?B9ZL1B<@A@T*> B=? pB>?B=B??dB>k0B@?B>BA?+@B@@WBB?B@BC@A@TH{ BD? pBE?BDBF?@BEBG?dBFZLrBH?BF0.1BI?BEBJ?+@BI@WBK?BIBL@A@T iR BM? pBN?BMBO?@BNBP?dBOZLiBQ?BO0.1BR?BNBS?+@BR@WBT?BRBU*@T[? ASS-( 1.2.3 Default fault impedance matrices6(BV;(BW7BU}8(BX;(BY9@V0BZ;.(B[;(B\/@NormalArial B]@A@T _28@ B^? pB_? B^B`?dB_Zf1Ba?pB_Bb?0BaBc?0ABbBd?0ABcBe?0ABdBf?0ABeBg?0ABfBh?0ABgBi?0ABhBj?0ABiBk?@BjBl?BjBm?tBl10Bn?Bl8Bo?Bi0Bp?Bh0Bq?Bg0Br?BfBs?tBr10Bt?Br8Bu?Be0Bv?Bd0Bw?Bc0Bx?BbBy?tBx10Bz?Bx8B{@A@T,=8A B|? pB}? B|B~?dB}Zf2B?B}Zf1B@A@T8,n=R8B B? pB? BB?dBZf3B?BZf1B*@T+;8D -No faults for pre-fault case68B;B9@V0B;.B;B/@NormalArial B@A@TH<M{H B? pB?BB?@BB?dBZLrB?B0.9B?BB?+@B@WB?BB@A@T <iMRH B? pB?BB?@BB?dBZLiB?B0.9B?BB?+@B@WB?BB@D@Tp@xpB*@TFA>>-$ 1.2.4 S voltage source impedance 6$B;$B7B}8$B;$B9@V0B;.$B;$B/@NormalArial B*@T-@zThe S end source has infinite zero sequence impedance so no zero sequence current can be supplied by the source generator.6z8zB;zB9@V0B;.zB;zB/@NormalArial B*@T -Zero sequence admittance68B;B9@V0B;.B;B/@NormalArial B*@Tm -Positive sequence admittance68B;B9@V0B;.B;B/@NormalArial B*@T1 -Negative sequence admittance68B;B9@V0B;.B;B/@NormalArial B@A@TV: B? pB? BB?dBZss0B?BB?tB10B?B6B@A@T B? pB? BB?dBZss1B?pBB?BB?tB1B?B6iB@A@T B? pB? BB?dBZss2B?pBB?BB?tB1B?B6iB@A@T;F  B? pB? BB?dBZss012B?pBB?0BB?0ABB?0ABB?0ABB?0ABB?0ABB?0ABB?0ABB?0ABB?@BB?BZss2B?B0B?B0B?B0B?BZss1B?B0B?B0B?B0B?BZss0B@A@TTe4` B? pB? BB?dBZssB?BB?dB Z012_ZabcB?pBB?BZss012B@A@TT e` B? pB?BB?dBZssB?BB?+@B@WB?BB*@Tv Ann-, 1.2.5 Relay S bus Delta - Wye Transformer 6,B;,B7B}8,B;,C9@V0C;.,C;,C/@NormalArial C*@T   -@ Node 2 is connected to the a grounded Y transformer with very high 1K ohm reactance positive sequence and 10 ohms zero sequence impedance.68C;C9@V0C;.C;C /@NormalArial C *@T  -Zero sequence admittance68C ;C 9@V0C ;.C;C/@NormalArial C*@Tm  -Positive sequence admittance68C;C9@V0C;.C;C/@NormalArial C@A@T8%]  C? pC? CC?dCZST0C?CC?tC0.6C?C10iC@A@T ;%   C? pC? CC ?dCZST1C!?5CC"?@C!C#?tC"10C$?C"6C%?C!1iC&@A@Tx/; E C'? pC(? C'C)?dC(ZST012C*?pC(C+?0C*C,?0AC+C-?0AC,C.?0AC-C/?0AC.C0?0AC/C1?0AC0C2?0AC1C3?0AC2C4?@C3C5?C3ZST1C6?C20C7?C10C8?C00C9?C/ZST1C:?C.0C;?C-0C@A@TP%o F C?? pC@? C?CA?dC@ZSTCB?C@CC?dCB Z012_ZabcCD?pCBCE?CDZST012CF@A@TlM}6xG CG? pCH?CGCI?dCHZSTCJ?CHCK?+@CJ@WCL?CJCM*@TFA>>-$ 1.2.6 R voltage source impedance 6$CN;$CO7CM}8$CP;$CQ9@V0CR;.$CS;$CT/@NormalArial CU*@T%9-@VThe R end source has zero sequence impedance equal to the positive sequence impedance.6V8VCV;VCW9@V0CX;.VCY;VCZ/@NormalArial C[@A@T# ( C\? pC]? C\C^?dC]ZrrC_?pC]C`?0C_Ca?0AC`Cb?0ACaCc?0ACbCd?0ACcCe?0ACdCf?0ACeCg?0ACfCh?0ACgCi?@ChCj?ChCk?tCj1Cl?Cj6iCm?Cg0Cn?Cf0Co?Ce0Cp?CdCq?tCp1Cr?Cp6iCs?Cc0Ct?Cb0Cu?Ca0Cv?C`Cw?tCv1Cx?Cv6iCy@A@TH  Cz? pC{?CzC|?@C{C}?dC| Zabc_Z012C~?pC|C?C~ZrrC?C{C?+@C@WC?CC@D@T( @0 ( C*@T; K H [ A{{-1.3 Voltage sources6C;C7C}8C;C9@V0C;.C;C/@NormalArial C*@TS c ` \ A- 1.3.1 Generator constants 6C;C7C}8C;C9@V0C;.C;C/@NormalArial C*@T s ] ߄-Voltage Generator Voltage68C;C9@V0C;.C;C/@NormalArial C*@Ts ^ ^ ߄vv-Power system angle68C;C9@V0C;.C;C/@NormalArial C*@Th{ + h _ 00-@SSpecify power angle in degrees - positive for leading and negative for lagging,6S8SC;SC9@V0C;.SC;SC/@NormalArial C@A@T Q 4 ` C? pC? CC?dCangC?KCC?C15C@A@TH  _ a C? pC? CC?dCVgC?CC?tC120C?{CC?C3C*@TH  H b ߄q-Power angle shift operator68C;C9@V0C;.C;C/@NormalArial C*@T0 0 c ߄)ff-VT and CT Ratios68C;C9@V0C;.C;C/@NormalArial C@A@T8  F d C? pC? CC?dC\dC?CC?@CC?dCcosC?pCC?CC?@CC?dC\pC?CangC?C180C?5CC?@CC?dCsinC?pCC?CC?@CC?dC\pC?CangC?C180C?C1iC@A@T( Y I e C? pC? CC?dCVTRC?C1C@A@Th  f C? pC? CC?dCCTRC?C1C*@T #  g A- 1.3.2 S end voltage source 6C;C7C}8C;C9@V0C;.C;C/@NormalArial C@A@T8* o MP k C? pC? CC?dCEsC?pCC?0CC?0ACC?0ACC?@CC?CC?dCVgC?CaC?CC?dCVgC?CC?dCaC?C2C?CVgC*@T{  l A- 1.3.3 R end voltage source 6C;C7C}8C;C9@V0D;.D;D/@NormalArial D@A@T8 K m D? pD? DD?dDErD?pDD?0DD ?0ADD ?0AD D ?@D D ?D D ?@D D?dD VgD?D \dD?D aD?D D?@DD?dDVgD?D\dD?DD?dDaD?D2D?DD?dDVgD?D\dD@D@T @ D*@T r  Abb-1.4 Subroutines6D;D7D}8D;D 9@V0D!;.D";D#/@NormalArial D$*@T   A- 1.4.1 System Impedance matrix 6D%;D&7D$}8D';D(9@V0D);.D*;D+/@NormalArial D,*@T# Z3 0  AJJ-& 1.4.1.1 Impedance matrix description6&D-;&D.7D,}8&D/;&D09@V0D1;.&D2;&D3/@NormalArial D4*@T; _ H  $$-A Znet Definitions Output: Z: System impedance matrix For this system - the result is a [12X12] matrix of complex variables Input: Zs: S end voltage source Impedance matrix Zr: R end voltage source Impedance matrix ZL: Total length line impedance matrix Zff: Forward fault impedance matrix Zfr: Reverse fault impedance matrix mf: Percent of line length to forward mr: Percent of line length to reverse fault Notes: 1. [3X3] matrix of complex values 2. Scalar in range 0.0001 to 0.99996D5;D67D4D7;D87D4yD5D9;D:7D4D7D;;D<7D4D9D=;%D>7D4D;D?;(D@7D4D=DA;%DB7D4D?DC;$DD7D4DADE;%DF7D4DCDG;DH7D4DEDI;&DJ7D4DGDK;DL7D4_DIDM;LDN7D4_DKDMD78DO;DP9@V0DQ;.DR;DS/@NormalArial DT*@Ts Q  AII-+ 1.4.1.2 System Impedance matrix subroutine6+DU;+DV7DT}8+DW;+DX9@V0DY;.+DZ;+D[/@NormalArial D\@A@T l3  n D]? pD^? D]D_?@D^D`?dD_ZnetDa?pD_Db? DaDc? @DbDd? @DcDe? @DdDf? @DeDg? @DfDh? @DgDi? @DhDj? @DiDk?dDjZsDl?DjZtDm?DiZrDn?DhZLDo?DgZf1Dp?DfZf2Dq?DeZf3Dr?Ddm1Ds?Dcm2Dt?Dbm3Du?D^Dv?@DuDw?@DvDx?@DwDy?@DxDz?@DyD{?@DzD|?@D{D}?@D|D~?@D}D?@D~D?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?dDY11D?DD?@DD?@DD?dDZsD?KDD?D1D?DD?dDZf3D?KDD?D1D?DD?p@DD?DD?dDm3D?DZLD?KDD?D1D?DD?dDY12D?KDD?DD?p@DD?DD?dDm3D?DZLD?KDD?D1D?DD?dDY13D?DYnullD?DD?dDY14D?DYnullD?DD?dDY15D?DYnullD?DD?dDY21D?DY12D?DD?dDY22D?pDD?DD?@DD?@DD?@DD?p@DD?DD?dDm1D?DZLD?KDD?D1D?DD?p@DD?DD?dDm2D?DZLD?KDD?D1D?DD?p@DD?DD?dDm3D?DZLD?KDD?D1D?DD?dDZtD?KDD?D1D?DD?dDY23D?KDD?DD?p@DD?DD?dDm1D?DZLD?KDD?D1D?DD?dDY24D?DYnullD?DD?dDY25D?KDD?DD?p@DE?DE?dEm2E?EZLE?KDE?E1E?DE?dEY31E?EY13E?DE ?dEY32E ?EY23E ?DE ?dE Y33E ?pE E?E E?@EE?@EE?p@EE?EE?dEm1E?EZLE?KEE?E1E?EE?p@EE?EE?p@EE?EE?tE1E?Em1E?EZLE?KEE ?E1E!?EE"?dE!Zf1E#?KE!E$?E#1E%?DE&?dE%Y34E'?KE%E(?E'E)?p@E(E*?E)E+?p@E*E,?E+E-?dE,1E.?E,m1E/?E*ZLE0?KE(E1?E01E2?DE3?dE2Y35E4?E2YnullE5?DE6?dE5Y41E7?E5Y14E8?DE9?dE8Y42E:?E8Y24E;?DE?DE??dE>Y44E@?pE>EA?E@EB?@EAEC?@EBED?p@ECEE?EDEF?p@EEEG?EFEH?dEG1EI?EGm1EJ?EEZLEK?KECEL?EK1EM?EBEN?p@EMEO?ENEP?p@EOEQ?EPER?dEQ1ES?EQm2ET?EOZLEU?KEMEV?EU1EW?EAEX?dEWZrEY?KEWEZ?EY1E[?DE\?dE[Y45E]?KE[E^?E]E_?p@E^E`?E_Ea?p@E`Eb?EaEc?dEb1Ed?Ebm2Ee?E`ZLEf?KE^Eg?Ef1Eh?DEi?dEhY51Ej?EhY15Ek?DEl?dEkY52Em?EkY25En?DEo?dEnY53Ep?EnY35Eq?DEr?dEqY54Es?EqY45Et?DEu?dEtY55Ev?pEtEw?EvEx?@EwEy?@ExEz?p@EyE{?EzE|?p@E{E}?E|E~?dE}1E?E}m2E?E{ZLE?KEyE?E1E?ExE?p@EE?EE?dEm2E?EZLE?KEE?E1E?EwE?dEZf2E?KEE?E1E?DE?dEY1E?EE?dEstackE?pEE? EE?dEY11E?EY21E?DE?dEY1E?EE?dEstackE?pEE? EE?dEY1E?EY31E?DE?dEY1E?EE?dEstackE?pEE? EE?dEY1E?EY41E?DE?dEY1E?EE?dEstackE?pEE? EE?dEY1E?EY51E?DE?dEY2E?EE?dEstackE?pEE? EE?dEY12E?EY22E?DE?dEY2E?EE?dEstackE?pEE? EE?dEY2E?EY32E?DE?dEY2E?EE?dEstackE?pEE? EE?dEY2E?EY42E?DE?dEY2E?EE?dEstackE?pEE? EE?dEY2E?EY52E?DE?dEY3E?EE?dEstackE?pEE? EE?dEY13E?EY23E?DE?dEY3E?EE?dEstackE?pEE? EE?dEY3E?EY33E?DE?dEY3E?EE?dEstackE?pEE? EE?dEY3E?EY43E?DE?dEY3E?EE?dEstackE?pEE? EE?dEY3E?EY53E?DE?dEY4E?EE?dEstackE?pEE? EE?dEY14E?EY24E?DE?dEY4E?EE?dEstackE?pEE? EE?dEY4E?EY34E?DE?dEY4F?EF?dFstackF?pFF? FF?dFY4F?FY44F?D~F?dFY4F?FF ?dFstackF ?pFF ? F F ?dF Y4F ?F Y54F?D}F?dFY5F?FF?dFstackF?pFF? FF?dFY15F?FY25F?D|F?dFY5F?FF?dFstackF?pFF? FF?dFY5F?FY35F?D{F?dFY5F ?FF!?dF stackF"?pF F#? F"F$?dF#Y5F%?F#Y45F&?DzF'?dF&Y5F(?F&F)?dF(stackF*?pF(F+? F*F,?dF+Y5F-?F+Y55F.?DyF/?dF.YF0?F.F1?dF0augmentF2?pF0F3? F2F4?dF3Y1F5?F3Y2F6?DxF7?dF6YF8?F6F9?dF8augmentF:?pF8F;? F:F?DwF??dF>YF@?F>FA?dF@augmentFB?pF@FC? FBFD?dFCYFE?FCY4FF?DvFG?dFFYFH?FFFI?dFHaugmentFJ?pFHFK? FJFL?dFKYFM?FKY5FN?sDuFO?FNFP?dFOYFQ?KFOFR?FQ1FS@D@T@@H@FT*@TK[X A-# 1.4.2 Compute system node voltages6#FU;#FV7FT}8#FW;#FX9@V0FY;.#FZ;#F[/@NormalArial F\*@T k[ x ;;;-Bs Solve_Node_Voltages Definitions Output: Vn: Vnode voltages1 Input: Es: S end voltage source2 Er: R end voltage source2 Zs: S end voltage source Impedance matrix3 Zr: R end voltage source Impedance matrix3 ZL: Total length line impedance matrix3 Zff: Forward fault impedance matrix3 Zfr: Reverse fault impedance matrix3 m1: Percent of line length to forward for Line #14 m2: Percent of line length to forward for Line #24 mr: Percent of line length to reverse fault4 Notes: 1. [1X12] column vector = [V1 : V2 : V3 : V4]T 2. [1X3] column vector 3. [3X3] matrix of complex values 4. Scalar in range 0.0001 to 0.99996 sF];F^7F\F_; F`7F\yF]Fa;Fb7F\F_Fc;Fd7F\_FaFe;Ff7F\FcFg; Fh7F\FeFi;Fj7F\FgFk;Fl7F\_FiFm;Fn7F\FkFo;Fp7F\FmFq;Fr7F\FoFs;Ft7F\_FqFu;+Fv7F\FsFw;Fx7F\_FuFy;Fz7F\FwF{;+F|7F\FyF};F~7F\_F{F;(F7F\F}F;F7F\_FF;%F7F\FF;F7F\_FF;$F7F\FF;F7F\_FF;2F7F\FF;F7F\@ ArialFF;1F7F\FF;F7F\_FF;F7F\FF;+F7F\FF;F7F\_FF;F7F\_FF; F7F\_FF;)F7F\FF;F7F\_FF;_F7F\_FFF_8sF;~F9@VF;3F9@VFF;F9@VFFF0F;.sF;sF/@NormalArial F@A@T(!  F? pF? FF?@FF?dFSolve_Node_VoltagesF?pFF? FF? @FF? @FF? @FF?dFEsF?FErF?FZssF?FZrrF?FZsysF?FF?@FF?@FF?@FF?@FF?@FF?@FF?@FF?dFNullSrcF?pFF?0FF?0AFF?0AFF?@FF?F0F?F0F?F0F?FF?dFIgenF?FF?@FF?dFZssF?KFF?F1F?FEsF?FF?dFIgenF?FF?dFstackF?pFF? FF?dFIgenF?FNullSrcF?FF?dFIgenF?FF?dFstackF?pFF? FF?dFIgenF?FNullSrcF?FF?dFIgenF?FF?dFstackF?pFF? FF?dFIgenF?pFF?FF?@FF?dFZrrF?KFF?F1F?FErF?FF?dFIgenF?FF?dFstackF?pFF? FF?dFIgenF?FNullSrcF?FF?dFVF?FF?dFZsysF?FIgenF?sFG?FVG@D@T@G*@T#  A- 1.4.3 Compute relay currents6G;G7G}8G;G9@V0G;.G;G /@NormalArial G *@T3Sk@ ;;8;8-A Solve_currents Definitions Output: Ib: Branch currents1 Is - Send relay current Ir - R end relay currents Iflt - F1 fault current Input: V: Node voltage vector computed by Solve_Node_Voltages2 ZL: Total length line impedance matrix3 mf: Percent of line length to forward4 Notes: 1. 1X9 Column vector = [Is : Ir : IST]T 2. [1X12] column vector = [V1 : V2 : V3 : V4]T 3. 3X3 matrix of complex values 4. Scalar in range 0.0001 to 0.99996G ;G 7G G ;G7G yG G;G7G G G;G7G @ ArialGG;G7G GG;G7G GG;G7G _GG;G7G GG;'G7G GG;G7G _GG;G 7G GG!;%G"7G GG#;G$7G @ ArialG!G%;G&7G G#G';G(7G _G%G);G*7G _G'G+;&G,7G G)G-;G.7G _G+G/;G07G G-G1;,G27G G/G3;G47G _G1G5;G67G G3G7;G87G _G5G9;BG:7G _G7G9G 8#G;;G<9@VG=;)G>9@VG;G?;'G@9@VG=GA;GB9@VG?GC;aGD9@VGAGE; GF9@VGCGG;#GH9@VGEGGGG0GI;.GJ;GK/@NormalArial GL@A@Tt\! GM? pGN? GMGO?@GNGP?dGOSolve_currentsGQ?pGOGR? GQGS? @GRGT? @GSGU?dGTVGV?GTZtGW?GSZLGX?GRm1GY?GNGZ?@GYG[?@GZG\?@G[G]?@G\G^?@G]G_?@G^G`?dG_IsGa?G_Gb?@GaGc?p@GbGd?GcGe?dGdm1Gf?GdZLGg?KGbGh?Gg1Gi?pGaGj?GiGk?@GjGl?dGk submatrixGm?pGkGn? GmGo? @GnGp? @GoGq? @GpGr?dGqVGs?Gq3Gt?Gp5Gu?Go0Gv?Gn0Gw?GjGx?dGw submatrixGy?pGwGz? GyG{? @GzG|? @G{G}? @G|G~?dG}VG?G}6G?G|8G?G{0G?Gz0G?G^G?dGIrG?GG?@GG?p@GG?GG?p@GG?GG?tG1G?Gm1G?GZLG?KGG?G1G?pGG?GG?@GG?dG submatrixG?pGG? GG? @GG? @GG? @GG?dGVG?G9G?G11G?G0G?G0G?GG?dG submatrixG?pGG? GG? @GG? @GG? @GG?dGVG?G6G?G8G?G0G?G0G?G]G?dGIstG?GG?@GG?p@GG?GZtG?KGG?G1G?pGG?GG?dG submatrixG?pGG? GG? @GG? @GG? @GG?dGVG?G3G?G5G?G0G?G0G?G\G?dGIbG?GIsG?G[G?dGIbG?GG?dGstackG?pGG? GG?dGIbG?GIrG?GZG?dGIbG?GG?dGstackG?pGG? GG?dGIbG?KGG?GIstG?sGYG?GIbG@D@T(@0(G*@T;$KHA-& 1.4.4 Rectangular to polar conversion6&G;&G7G}8&G;&G9@V0G;.&G;&G/@NormalArial G@A@TT-W` G? pG? GG?@GG?dG rect2polarG?pGG?GRG?GG?@GG?@GG?@GG?@GG?@GG?@GG?dGmG?{GG?GG?dGRG?GiG?GG?dG\aG?GG?@GG?dGargG?pGG?GG?dGRG?GiG?GG?tG180G?G\pG?GG?dGpG?pGH?0GH?0AHH?@HH?H\aH?HmH?IGH?@HH?dHPolH?HpH ?)HH ?dH iH ?H 1H ?IGH ?@H H?dH PolH?H H?dHstackH?pHH? HH?dHPolH?HpH?(H H?dHiH?H0H?GH?dHiH?HH?tH0H?H2H?sGH?HPolH*@T8kF8x -@Rectangular to polar coordinate conversion Output: [V or I : Angle]1 Input: [V or I complex variables]2 Notes: 1.3X2 matrix of scalar values 2.[3X1] vector of complex variables6i+H ;+H!7HyH";H#7HyH H$;H%7HyH"H&;H'7H@ ArialH$H(;#H)7HyH&H*;H+7H@ ArialH(H,;JH-7HyH*H,H 8H.;H/9@V0H0;.H1;H2/@NormalArial H3*@T# o A-,1.5 Calculate prefault voltages and currents6,H4;,H57H3}8,H6;,H79@V0H8;.,H9;,H:/@NormalArial H;*@T+k8p @@-BThe first calculation is for an unfaulted system. The locations of the forward (m1) and reverse (m2 and m3) faults doesn't matter at this point because the fault matrix represents essentially and open circuit. "Vprevault" is a matrix of node voltages for the prefault condition "Ibr" extracts the three phase Relay S and R currents as well as the total three phase forward fault current. "Vs_abc", "Vr_abc", and "VFabc" are 1x3 column vectors for the voltages seen by Relay S, Relay R and at the point of the forward fault. 68H<;H=9@V0H>;.H?;H@/@NormalArial HA*@Tsq y)-!Default location of Line #1 fault6!8!HB;!HC9@V0HD;.!HE;!HF/@NormalArial HG@A@Ttr HH? pHI? HHHJ?dHIm1HK?HI0.5HL*@T{Bs 9* * -@kAll fault locations are specifired as a portion of the line length and must be in the range 0.0 < m < 1.0. 6k8kHM;kHN9@V0HO;.kHP;kHQ/@NormalArial HR*@Tt y)-!Default location of Line #2 fault6!8!HS;!HT9@V0HU;.!HV;!HW/@NormalArial HX@A@Tu HY? pHZ? HYH[?dHZm2H\?HZ0.1H]*@Tv y)-!Default location of reverse fault6!8!H^;!H_9@V0H`;.!Ha;!Hb/@NormalArial Hc@A@Tw Hd? pHe? HdHf?dHem3Hg?He0.01Hh*@Tx *~~-@rThe distance to fault location have no affect for prefault calculations because the fault matrix is high impedance6r8rHi;rHj9@V0Hk;.rHl;rHm/@NormalArial Hn*@Ty y)-@DCalculate system impedance matrix and compute prefault node voltages6D8DHo;DHp9@V0Hq;.DHr;DHs/@NormalArial Ht@A@TC3z Hu? pHv? HuHw?dHvZsysHx?HvHy?dHxZnetHz?pHxH{? HzH|? @H{H}? @H|H~? @H}H? @H~H? @HH? @HH? @HH? @HH?dHZssH?HZSTH?HZrrH?HZLH?HZf1H?HZf2H?H~Zf3H?H}m1H?H|m2H?H{m3H@A@TDI{ H? pH? HH?dH VprefaultH?HH?dHSolve_Node_VoltagesH?pHH? HH? @HH? @HH? @HH?dHEsH?HErH?HZssH?HZrrH?HZsysH*@TX;#X | y1-(Display Relay voltages in polar notation6(8(H;(H9@V0H;.(H;(H/@NormalArial H*@T+;8} y1-Extract Relay voltages68H;H9@V0H;.H;H/@NormalArial H@A@TDUhP~ H? pH? HH?dHVs_abc_prefaultH?HH?dH submatrixH?pHH? HH? @HH? @HH? @HH?dH VprefaultH?H3H?H5H?H0H?H0H@A@TXD UP H? pH?HH?@HH?dH rect2polarH?pHH?HVs_abc_prefaultH?HH?+@H@WH?HH@A@T\mfh H? pH? HH?dHVr_abc_prefaultH?HH?dH submatrixH?pHH? HH? @HH? @HH? @HH?dH VprefaultH?H6H?H8H?H0H?H0H*@T y1-%Determine the Relay sequence voltages6%8%H;%H9@V0H;.%H;%H/@NormalArial H@A@TX  H? pH?HH?@HH?dH rect2polarH?pHH?HVr_abc_prefaultH?HH?+@H@WH?HH@D@T@H@A@T0JH? pH? HH?dHV012sH?HH?dHAsysH?HVs_abc_prefaultH@A@Tf6KH? pH? HH?dHVS1polH?HH?dHV012sH?H1H@A@T.LH? pH? HH?dHV012rH?HH?dHAsysH?HVr_abc_prefaultH@A@TX%  H? pH?HH?@HH?dH rect2polarH?pHI?HV012sI?HI?+@I@WI?II@A@Te47(MI? pI? II?dIVR1polI?II ?dIV012rI ?I1I *@TC P\APP-@Currents for Relay S and R are computed from the node voltages and impedance to the fault at F1 as set my m1. The zero sequence trans- former current is computed from V2 node voltage and the transformer impedance.68//I ;/I 9@VI;I9@VI II0I;.I;I/@NormalArial I@A@TXl}x I? pI?II?@II?dI rect2polarI?pII?IV012rI?II?+@I@WI?II*@TWy1- Extract Relay and fault currents6 8 I; I9@V0I ;. I!; I"/@NormalArial I#*@T`C` y1-(Display Relay currents in polar notation6(8(I$;(I%9@V0I&;.(I';(I(/@NormalArial I)@A@TXI*? pI+? I*I,?dI+IbrI-?I+I.?dI-Solve_currentsI/?pI-I0? I/I1? @I0I2? @I1I3?dI2 VprefaultI4?I2ZSTI5?I1ZLI6?I0m1I7@A@TDYI8? pI9? I8I:?dI9 ISprefaultI;?I9I? I=I?? @I>I@? @I?IA? @I@IB?dIAIbrIC?IA0ID?I@2IE?I?0IF?I>0IG@A@TP IH? pII?IHIJ?@IIIK?dIJ rect2polarIL?pIJIM?IL ISprefaultIN?IIIO?+@IN@WIP?INIQ@A@TEZIR? pIS? IRIT?dIS IRprefaultIU?ISIV?dIU submatrixIW?pIUIX? IWIY? @IXIZ? @IYI[? @IZI\?dI[IbrI]?I[3I^?IZ5I_?IY0I`?IX0Ia*@TP&+P 00-@bThese currents reflect the currents caused by system power transfer set by the system power angle6b8bIb;bIc9@V0Id;.bIe;bIf/@NormalArial Ig@A@TL[Ih? pIi? IhIj?dIi ISTprefaultIk?IiIl?dIk submatrixIm?pIkIn? ImIo? @InIp? @IoIq? @IpIr?dIqIbrIs?Iq6It?Ip8Iu?Io0Iv?In0Iw@A@T<MHSIx? pIy?IxIz?@IyI{?dIz rect2polarI|?pIzI}?I| ISTprefaultI~?IyI?+@I~@WI?I~I@A@TP<MH I? pI?II?@II?dI rect2polarI?pII?I IRprefaultI?II?+@I@WI?II@D@Tx@xI*@TBKA::-31.6 Specify the system fault structure and location63I;3I7I}83I;3I9@V0I;.3I;3I/@NormalArial I*@T L``-BThe second calculation is for an faulted system. The locations of the forward is established by setting the value of mf as a decimal fraction of the total line length. If m1 equal 0.25, then the fault is located 0.25 * the line length from Relay S toward Relay R. Line impedance is added to the source impedance by adjusting the value of m3 shown as ZLs in Figure 1. The amount of impedance added is determined by Zls = m3*ZL where ZL is the system line impedance. This allows faults to be placed behind Relay S but still forward of relay R. Use small nonzero positive values (0.0001) for m3 to add an insignificant amount of additional impedance to the source impedance.68I;I9@V0I;.I;I/@NormalArial I@A@T 5 I? pI? II?dIrI?I0.8I*@T@ @ yll-Default relay reach68I;I9@V0I;.I;I/@NormalArial I*@T)<8 -Fault Matrix Specifications6I;I7I| 8I;I9@V0I;.I;I/@NormalArial I*@TCP PP-BThe parameters associated with the fault matrix are illustrated in Figure 2. The fault matrix is placed at location m1, m2, or m3 by changing the name of the fault matrix variable to Zf1, Zf2, or Zf3 respectively. Use impedance values of 106 for open circuits. Phase to phase faults are generated by setting Zab, Zbc, and / or Zac to small appropriate values. Phase to ground faults are generated by setting Zaa, Zbb, and / or Zcc to small appropriate values. The minimum fault impedance should be limited to 0.00001. Fault impedances can be complex. Not specifying a fault impedance defaults to an open circuit prefault fault matrix used above. 6 NI;NI7II;I7I@ ArialII;I7III;I7I_II;I7III;I7I@ ArialII;I7I@ ArialIII8I;I9@V0I;.I;I/@NormalArial I@Tf J"Jࡱ>    !"#Root EntryFpsQOle CompObjqOlePres000~ FMicrosoft Visio DrawingVISIO 4.0 ShapesVisio.Drawing.69qOh+'08DP\htcKC;DcKC;D b   (-  "-$%% "-- . n"Arial-!Zab"System- -  "-b$/"{/b?KS7h%  $ >V%l7Kb{ 9PldVv>$ hvSd?P/9" -- . -!A- -  "-b$/!*{7bGK[7p%  , F ^ %t 7 K b {       9 Pt d^ vF ,  pv[dGP79* !-- . -!B- -  "-b$/!#)2{?bOKc7x% 4 Nf%|7Kb{ 9P|dfvN4xvcdOP?92 )#!-- . -!C- (-  "-$ --  -- . -!Zbc - (-  "-$%u u %%u-- . -!Zac- (-  "-$} } %%} -- . -!Zaa- (-  "-$%} } %%%%} -- . -!Zbb- (-  "-$-} } %-%-} ---- . -!Zcc&- -  "-%- -  "-%%- -  "-%  - -  "-%-!- -  "- %I%I- -  "- % II- -  "-%%- -  "-%%- -  "-%%- -  "-%}  - -  "-%}  - -  "-%}  - -  "- %   - -  "-%  - -  "-%,  - -  "-%wr X r - -  "-% 2 - - "-2$                       --VisioDocument*VisioInformation"SummaryInformation(Visio (TM) Drawing *Rsp)/d !fffMMM333<q0<T d Arial)-": -3Times New Roman5T?? 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Can be stretched toy dimwenss.mb?7io68?k?4 H"'}hTM@?,544?P +qu u Gu` Zu qbb (J* **%L@_ A`9Copyright 1995 Visio Corporation. All |s reserved.r`Shape.hlp!#150002lUXBa 5*Z&!  C  *B  /-,>b/t-!-/&// rrC 01_#0#0h:qr 4% W//S `/r?(*/'.P??/O/k@tk@<k@}%-$Fx #B< Q ;$udC\G@|OYC+;OC3H+ C$%F hTA@* ?<I?NXfx** <Ebb{b b NeH 1 #wwx wp wp5 wwwwp PWPNRpps~yph\VB[5p'.' H  ;Generic circle or ellipse with text and connection points.b?7i6E8?4 H"w'}hT@?, =zOP +qu >~u`u Qu qbb @wS% )&B BBH 6#6/ L@ A`9Copyright 1995 Visio Corporation. All s reserved.r`Shape.hlp!#15000bKlU%a+ ### ,^*?+ 's N NWaE.],E!qO&[`(4/-=/ rrs \0`1/,V!?? ߊ'q 4% (F-]( 8W?/"?(OV/LH=8*OtMrA//tOW@t@<@ }p-F #B< U ;d/CFG@/$+;٫%c)H+/NcE,D@@$ ,D@@% <@B$L,zS  u@İ{ ,?R?P! eqDw@U@FT L*hGTۼID{@z@??I ?sJsIzIb^b:- !H!AnZs.b (! n   IenLsHJC" gD!+ L#C"C"C""D!* C"2O D!: C"B C"J rC"RD!ZC"wbC"jC"rg D!zC"C"D!C"C"]C"C"o D!C"K0010U0000U000z0Ur0j0b0Z0UR0J0B0:0U20*0"000 00In*M"$%I&g'+ (a )i *q +, -*2Aw a IK jy{@4@!?!EE?P 6F F10B?FzA + B A @1 W"l^3!UF_ ]B_WXmPDmP0mP] + @(4._@Lqgny)F"M|0A" O G`I"OVF eI aI_t`{`,{`u{`a i+!o4'2aگTfzAB)m] ZabC :0?>UB%?ME?vIw4O%wPOkJpO0OOFcBr@@C%FOVWWHQv[wFS_=VT|WZcǏQ]_EW%bgy ay2ht ftxc@oooon AC :o >;N?Q;OVxuj0CB BFB"~ s(0zTfv@f֏Lࢿ 1/Xfhfc" a"hcH a@|oȻ͟ߟBC @8P,!&T"Xj|բƯد{ B``Al?QcϿῑR L7[``cl alϸ 2DCg:~?!OO*OaO@sOO/Az_wOO._/b_t_]1k/_go___ fƟBo exo6HZloZbcgмh-QҢE0BTfx0JO#/_3/E/W.1w_~/g%ƀ///jO?Q#h<@d3kAca03j?|??)gЅj??'| OO-OmdXOjO|OЎOO}rrrO__)_;_M___d__g/_Ot`t_yy__e*&#l#8Y?OoPaoso??bagooQooo>O.@RdvZ((b¢#5 GrgǻƻΏ©©&8J\n5bg k Òʟ DVhzŔ4~}rrbͯ߯)'9K@]oįg ÿ*N`rτPϨϺϰ4c1 Q+0瓈=H$e a] a! pfӧN-+qtH c' L^p$.0+VB7I[r8u2 r7BOBOVB#SUC"$_!VBOS/W_CUZJ/^AaROPl!Ru///////_??)2 /?S?Rr????????OO&O8O\`+reOwO[҂)hNr RrQs"R!r}]sx_q}l!____o@_o3oEo)2 ]oooooooooo 0BTf+xY"͙N RKK"!貫l!яM+=Ias)2ȋ(V8U?d%%ԀgLУՀIw*f*֗Ǘŀq+¯ԯ\ 1CȖ`@RdϜ]T'9K];p߂ߔ!+(:וP`a"Δp1$-?DT!);M_KHDYDl"'婇 uDE&1j K/ sQ2*?Ul"93k#:?l"e3E7u#k:Կt!걢2e02k}Yk˙LmAEWi#//*/PbtΠԀ׏vs"K=+Y21uoJ52K2ϾõD@  +=O@s#bMϯL&8J\nȿڿ\8ƯFJu_+_ƯEQK2@-?Qߗu߇k߽ɢ{,>Pbto$" ,8ƥ&J ue"+e/Ʒ%W"#K2/"#' #*2!3EW{q?Dɢ|XHKJf4um66GP:%.F{, RF1G300TB/$/*$ >5G?Y?k?}??GH=Az_2K??9p??|OBvATTBTfxOO`˄.r/ _/&Fgv N"QOǐv.rs-s.rsw7svz+VF?F_X_j__@__oo+o=luV\nnhSKoooooooЀ`=O/ N"b2v'HρM"!ê.@Rv%я=lfs \e\n8J\nȟڟ隰 + ޸1 ޷T b൧x;3q["\!‡gÍ b@fxB =l\emh&8J\nπϒϤ@d$ay gsЪz byGq%"&!Q1W , mh0B*=ei`!!q~1 E)g {ROy}qxt~P{#R SK-ğ@&5(-PHo(WT 0T'(A.9/prrqy"A|/~?!75("?,I( /,s0s0?h@ D@$%&'()*+,-0#4@Bk%9>@e%?RdPage-1Black fill}White uRed Greeun -Cya@Yellow GMnta3ay(10% x line3 Long dash1"darI9e. X5 7 9 1pxlm9mHairqShort Arial ckeredtop leftT/imesConnector 8ptBox!Coircl!J.E".3M'4X!< S.5i 6m$7m$8m$9IQ#2733 U | s Ug Y N F U0 !   w3 3 U U x h X UG 4 $  U ә U Ur d U G U< -  ?.-{1CUgy$()*+,%&'" -01C_  !- %    #  t#Dv@@  !"! ` hl 2@B(s<Ds g(5m@(?V?:4?pIJ??J>J@?@J?JA?@J@JB?dJAZaaJC?KJAJD?JC1JE?J@JF?dJEZabJG?KJEJH?JG1JI?J?JJ?dJIZacJK?KJIJL?JK1JM?KIJN?JM1JO*@T#  y)UU-Fault locations68JP;JQ9@V,0JR;.JS;JT/@NormalArial JU@A@T(%  JV? pJW? JVJX?dJWm1JY?JW0.4JZ@A@TX%o  J[? pJ\? J[J]?dJ\m2J^?J\0.999J_@A@T%  J`? pJa? J`Jb?dJam3Jc?Ja0.001Jd@A@T9%"  Je? pJf? JeJg?dJfZf1Jh?JfZfJi*@TH#H  zRR-Set Fault type68Jj;Jk9@V0Jl;.Jm;Jn/@NormalArial Jo@D@T8@@8 Jp*@TK[X[A->1.7 Compute relay voltages and currents for the faulted system6>Jq;Jr7Jp}Js;:Jt7Jp}JqJsJq8>Ju;>Jv9@V0Jw;.>Jx;>Jy/@NormalArial Jz*@Tk{xty)-Compute node voltages68J{;J|9@V0J};.J~;J/@NormalArial J@A@TC3uJ? pJ? JJ?dJZsysJ?JJ?dJZnetJ?pJJ? JJ? @JJ? @JJ? @JJ? @JJ? @JJ? @JJ? @JJ? @JJ?dJZssJ?JZSTJ?JZrrJ?JZLJ?JZf1J?JZf2J?JZf3J?Jm1J?Jm2J?Jm3J@A@T6;vJ? pJ? JJ?dJVnodeJ?JJ?dJSolve_Node_VoltagesJ?pJJ? JJ? @JJ? @JJ? @JJ?dJEsJ?JErJ?JZssJ?JZrrJ?JZsysJ*@T*wA-' 1.7.1 Extract Relay and fault voltages6'J;J7J}J; J7J}JJJ8'J;'J9@V0J;.'J;'J/@NormalArial J@A@T@xJ? pJ? JJ?dJVs_abcJ?JJ?dJ submatrixJ?pJJ? JJ? @JJ? @JJ? @JJ?dJVnodeJ?J3J?J5J?J0J?J0J*@TX+Xy1-'Display fault voltage in polar notation6'8'J;'J9@V0J;.'J;'J/@NormalArial J@A@T>yJ? pJ? JJ?dJVr_abcJ?JJ?dJ submatrixJ?pJJ? JJ? @JJ? @JJ? @JJ?dJVnodeJ?J9J?J11J?J0J?J0J@A@T >zJ? pJ? JJ?dJVf_abcJ?JJ?dJ submatrixJ?pJJ? JJ? @JJ? @JJ? @JJ?dJVnodeJ?J6J?J8J?J0J?J0J@A@TH  J? pJ?JJ?@JJ?dJ rect2polarJ?pJJ?JVf_abcJ?JJ?+@J@WJ?JJ@A@T%8 {J? pJ? JJ?dJV012sJ?JJ?dJAsysJ?JVs_abcJ@A@T,=68|J? pJ? JJ?dJV012rJ?JK?dJAsysK?JVr_abcK*@T K[ Xy1-@UDisplay Relay voltages in polar notation using phase and symmetrical component format6U8UK;UK9@V0K;.UK;UK/@NormalArial K@A@T|v K ? pK ?K K ?@K K ?dK rect2polarK ?pK K?K Vs_abcK?K K?+@K@WK?KK@A@TH| K? pK?KK?@KK?dK rect2polarK?pKK?KV012sK?KK?+@K@WK?KK@A@Tt K? pK?KK?@KK ?dK rect2polarK!?pKK"?K!Vr_abcK#?KK$?+@K#@WK%?K#K&@A@TH K'? pK(?K'K)?@K(K*?dK) rect2polarK+?pK)K,?K+V012rK-?K(K.?+@K-@WK/?K-K0@D@T@!K1*@T DA<<-, 1.7.2 Extract Relay and polarizing currents6,K2;K37K1}K4;%K57K1}K2K4K28,K6;,K79@V0K8;.,K9;,K:/@NormalArial K;@A@Th  HK?dK=MTA1K??K=K@?+@K?@WKA?K?degKB@A@T$50z KC? pKD? KCKE?dKDIbrKF?KDKG?dKFSolve_currentsKH?pKFKI? KHKJ? @KIKK? @KJKL?dKKVnodeKM?KKZSTKN?KJZLKO?KIm1KP@A@T<M4H{ KQ? pKR? KQKS?dKRIs_abcKT?KRKU?dKT submatrixKV?pKTKW? KVKX? @KWKY? @KXKZ? @KYK[?dKZIbrK\?KZ0K]?KY2K^?KX0K_?KW0K`@A@T<AMH| Ka? pKb? KaKc?dKbI012sKd?KbKe?dKdAsysKf?KdIs_abcKg*@T`CS`Py```-7Display transformer neutral currents in polar notation6787Kh;7Ki9@V0Kj;.7Kk;7Kl/@NormalArial Km@A@TTe2`} Kn? pKo? KnKp?dKoIr_abcKq?KoKr?dKq submatrixKs?pKqKt? KsKu? @KtKv? @KuKw? @KvKx?dKwIbrKy?Kw3Kz?Kv5K{?Ku0K|?Kt0K}@A@TT=e`~ K~? pK? K~K?dKI012rK?KK?dKAsysK?KIr_abcK@A@Tl}?x K? pK? KK?dK Ipol_abcK?KK?dK submatrixK?pKK? KK? @KK? @KK? @KK?dKIbrK?K6K?K8K?K0K?K0K@A@TD K? pK? KK?dK Ispol_012K?KK?dKAsysK?K Ipol_abcK@A@T  K? pK?KK?@KK?dK rect2polarK?pKK?K Ipol_abcK?KK?+@K@WK?KK@A@Tv2 K? pK? KK?dKIs_polK?KK?dK Ispol_012K?K0K*@T" y-@VDisplay Relay currents in polar notation using phase and symmetrical component format6V8VK;VK9@V0K;.VK;VK/@NormalArial K@A@TzK? pK?KK?@KK?dK rect2polarK?pKK?KIs_abcK?KK?+@K@WK?KK@A@Tx K? pK?KK?@KK?dK rect2polarK?pKK?KI012sK?KK?+@K@WK?KK@A@T4 E x@ K? pK?KK?@KK?dK rect2polarK?pKK?KIr_abcK?KK?+@K@WK?KK@A@Tx4 E @ K? pK?KK?@KK?dK rect2polarK?pKK?KI012rK?KK?+@K@WK?KK@D@T` @h ` K*@T{   -9 1.7.3 Compute cross polarizing directional torque values69K;K7K}K;2K7K}KKK89K;9K9@V0K;.9K;9K/@NormalArial K*@T   -: 1.7.3.1 Compute phase to phase voltages at Relay S and R6 :K; K7K}K;0K7K}KKK8:K;:K9@V0K;.:K;:K/@NormalArial K@A@T 2 K? pK? KK?dKVs_abK?KK?@KK?dKVs_abcK?K0K?KK?dKVs_abcK?K1K@A@T W K? pK? KK?dKVs_bcK?KK?@KL?dKVs_abcL?K1L?KL?dLVs_abcL?L2L@A@T`   L? pL? LL?dLVs_caL ?LL ?@L L ?dL Vs_abcL ?L 2L ?L L?dL Vs_abcL?L 0L@A@T 0 L? pL? LL?dLVr_abL?LL?@LL?dLVr_abcL?L0L?LL?dLVr_abcL?L1L@A@T Q L? pL? LL?dLVr_bcL?LL ?@LL!?dL Vr_abcL"?L 1L#?LL$?dL#Vr_abcL%?L#2L&@A@T`   L'? pL(? L'L)?dL(Vr_caL*?L(L+?@L*L,?dL+Vr_abcL-?L+2L.?L*L/?dL.Vr_abcL0?L.0L1*@T !! -= 1.7.3.2 Compute cross polarized torque values Relay S and R6 =L2; L37L1}L4;3L57L1}L2L4L28=L6;=L79@V0L8;.=L9;=L:/@NormalArial L;@A@T !$!*! L?dL=TSxaL??L=L@?@L?LA?{@L@LB?LAVs_bcLC?{L@LD?LCLE?p@LDLF?LEIs_abcLG?LD0LH?L?LI?dLHcosLJ?pLHLK?LJLL?@LKLM?dLLargLN?pLLLO?5LNLP?dLOVs_bcLQ?LO1iLR?pLKLS?LRLT?@LSLU?dLTargLV?pLTLW?LVLX?dLWIs_abcLY?LW0LZ?LSMTA1L[@A@T !0!! L\? pL]?L\L^?dL]TSxaL_?L]L`?+@L_@WLa?L_Lb@A@T,!D!+8! Lc? pLd? LcLe?dLdTSxbLf?LdLg?@LfLh?{@LgLi?LhVs_caLj?{LgLk?LjLl?dLkIs_abcLm?Lk1Ln?LfLo?dLncosLp?pLnLq?LpLr?@LqLs?dLrargLt?pLrLu?5LtLv?dLuVs_caLw?Lu1iLx?pLqLy?LxLz?@LyL{?dLzargL|?pLzL}?L|L~?dL}Is_abcL?L}1L?LyMTA1L@A@T,!1=!8! L? pL?LL?dLTSxbL?LL?+@L@WL?LL@A@TL!d!*X! L? pL? LL?dLTSxcL?LL?@LL?{@LL?LVs_abL?{LL?LL?dLIs_abcL?L2L?LL?dLcosL?pLL?LL?@LL?dLargL?pLL?5LL?dLVs_abL?L1iL?pLL?LL?@LL?dLargL?pLL?LL?dLIs_abcL?L2L?LMTA1L@A@TL!0]!X! L? pL?LL?dLTSxcL?LL?+@L@WL?LL@A@Tl!!+x!L? pL? LL?dLTRxaL?LL?@LL?{@LL?LVr_bcL?{LL?LL?dLIr_abcL?L0L?LL?dLcosL?pLL?LL?@LL?dLargL?pLL?5LL?dLVr_bcL?L1iL?pLL?LL?@LL?dLargL?pLL?LL?dLIr_abcL?L0L?LMTA1L@A@Tl!1}!x!L? pL?LL?dLTRxaL?LL?+@L@WL?LL@A@T!!,!L? pL? LL?dLTRxbL?LL?@LL?{@LL?LVr_caL?{LL?LL?dLIr_abcL?L1L?LL?dLcosL?pLL?LL?@LL?dLargL?pLL?5LL?dLVr_caL?L1iL?pLL?LL?@LL?dLargL?pLL?LL?dLIr_abcL?L1L?LMTA1L@A@T!2!!L? pL?LL?dLTRxbL?LL?+@L@WL?LL@A@T!!+!L? pL? LL?dLTRxcL?LL?@LM?{@LM?MVr_abM?{LM?MM?dMIr_abcM?M2M?LM?dMcosM?pMM ?MM ?@M M ?dM argM ?pM M ?5M M?dM Vr_abM?M 1iM?pM M?MM?@MM?dMargM?pMM?MM?dMIr_abcM?M2M?MMTA1M@A@T!1!!M? pM?MM?dMTRxcM?MM?+@M@WM?MM *@T!!!-@I 1.7.4 Compute symmetrical component polarizing torque directional values6IM!;M"7M }M#;BM$7M }M!M#M!8IM%;IM&9@V0M';.IM(;IM)/@NormalArial M**@T! C""PP-BiThe torque equation is generically - T = |Ipol| |Iphase| cos(angle(Ipol) - angle(Iphase)). For line to ground faults, the zero sequence current is in phase with the faulted phase. This works for two line to single and two line to ground faults but not for balanced three phase to ground faults nor for phase to phase faults since these faults do not normally generate zero sequence currents. This will only work for Relay S because only Relay S has zero sequence current source to get the polarizing zero sequence current from (IST0pol). ISTpol is generated from the grounded wye transformer model at Relay S bus. 6i8ZiM+;M,9@VM-;ZM.9@VM+M-M-0M/;.iM0;iM1/@NormalArial M2*@TS"c"`" -@M 1.7.4.2 Compute zero sequence current polarized torque values Relay S and R6 MM3; M47M2}M5;CM67M2}M3M5M38MM7;MM89@V0M9;.MM:;MM;/@NormalArial M<@A@Tl""1x" M=? pM>? M=M??dM>Is_resM@?pM>MA?M@MB?@MAMC?@MBMD?dMCIs_abcME?MC0MF?MBMG?dMFIs_abcMH?MF1MI?MAMJ?dMIIs_abcMK?MI2ML*@Tk"{"x" a-+Compute the residual current into the line.6+8+MM;+MN9@V0MO;.+MP;+MQ/@NormalArial MR@A@T"L"." MS? pMT? MSMU?dMTT32IsMV?MTMW?@MVMX?{@MWMY?MXIs_polMZ?{MWM[?MZIs_resM\?MVM]?dM\cosM^?pM\M_?M^M`?@M_Ma?dM`argMb?pM`Mc?MbIs_polMd?M_Me?dMdargMf?pMdMg?MfIs_resMh@A@T"4"" Mi? pMj?MiMk?dMjT32IsMl?MjMm?+@Ml@WMn?MlMo@D@T"@""Mp*@T""" -@Q 1.7.4.3 Compute zero sequence voltage polarized torque values for Relay S and R6 QMq; Mr7Mp}Ms;GMt7Mp}MqMsMq8QMu;QMv9@V0Mw;.QMx;QMy/@NormalArial Mz*@T"#" @@-AThe torque equation is generically - T = -|Vpol| |Iphase| cos(angle(a*Vpol) - angle(Iphase)) where a is the 120 degree operator and p is 0 for phase a, 2 for phase b, and 1 for phase c. For line to ground faults, the zero sequence voltage is 180 degrees out of phase with the voltage of the faulted phase. This works for two line to line and two line to ground faults but not for balanced three phase to ground faults nor for phase to phase faults.68M{;M|9@V0M};.M~;M/@NormalArial M@A@T$#<#:0# M? pM? MM?dMT32VsM?MM?@MM?{@MM?MM?dMV012sM?M0M?{MM?MM?tM3M?MM?dMI012sM?M0M?MM?dMcosM?pMM?MM?@MM?dMargM?pMM?KMM?MM?dMV012sM?M0M?pMM?MM?@MM?dMargM?pMM?MM?dMI012sM?M0M?MMTA0M@A@T$#5#0# թM? pM?MM?dMT32VsM?MM?+@M@WM?MM@A@TD#\#8P#! M? pM? MM?dMT32VrM?MM?@MM?{@MM?MM?dMV012rM?M0M?{MM?MM?dM3M?MM?dMI012rM?M0M?MM?dMcosM?pMM?MM?@MM?dMargM?pMM?KMM?MM?dMV012rM?M0M?pMM?MM?@MM?dMargM?pMM?MM?dMI012rM?M0M?MMTA0M@A@TD#U#P#" թM? pM?MM?dMT32VrM?MM?+@M@WM?MM*@Tc#s#p# -@N 1.7.4.4 Compute negative sequence current polarized torque for Relay S and R6 NM; M7M}M;DM7M}MMM8NM;NM9@V0M;.NM;NM/@NormalArial M*@T{# ## @@-AThe torque equation is generically - T = -|Vpol| |Iphase| cos(angle(apVpol) - angle(Iphase)) where a is the 120 degree operator and p is 0 for phase a, 2 for phase b, and 1 for phase c. For line to ground faults, the zero sequence voltage is 180 degrees out of phase with the voltage of the faulted phase. This works for two line to ground and two line to ground faults but not for balanced three phase to ground faults nor for phase to phase faults.6FEM;EM7MM;M7M@ ArialMM;}M7MMMM8M;M9@V0M;.M;M/@NormalArial M*@T#6## ˚9& & -@60036 - "Comparing Ground Directional Element Performance using Field Data", K. Zimmerman and J.Mooney, WPRC, 1993, and 6012-"Limits to the Sensitivity of Gnd Dir and Dist Ele."68M;M9@V0M;.M;M/@NormalArial M@A@T# $;$ M? pM? MM?dMT32QsM?MM?@MM?{@MM?MM?dMV012sM?M2M?{MM?MM?tM3M?MN?dMI012sN?M2N?MN?dNcosN?pNN?NN?@NN?dNargN?pNN ?KNN ?N N ?dN V012sN ?N 2N ?pNN?N N?@NN?dNargN?pNN?NN?dNI012sN?N2N?NMTA2N@A@T# $$ թN? pN?NN?dNT32QsN?NN?+@N@WN?NN@A@T$,$9 $ N? pN? NN ?dNT32QrN!?NN"?@N!N#?{@N"N$?N#N%?dN$V012rN&?N$2N'?{N"N(?N'N)?dN(3N*?N(N+?dN*I012rN,?N*2N-?N!N.?dN-cosN/?pN-N0?N/N1?@N0N2?dN1argN3?pN1N4?KN3N5?N4N6?dN5V012rN7?N52N8?pN0N9?N8N:?@N9N;?dN:argN?dN=I012rN??N=2N@?N9MTA2NA@A@T$-$($ թNB? pNC?NBND?dNCT32QrNE?NCNF?+@NE@WNG?NENH*@T;$2K$H$# @***-8These equations do not appear to work for reverse faults6888NI;8NJ9@V0NK;.8NL;8NM/@NormalArial NN@A@TT$l$7`$ NO? pNP? NONQ?dNPT32s_aNR?NPNS?@NRNT?{@NSNU?NTNV?dNUI012sNW?NU2NX?{NSNY?NXNZ?dNYIs_abcN[?NY0N\?NRN]?dN\cosN^?pN\N_?N^N`?@N_Na?dN`argNb?pN`Nc?NbNd?dNcI012sNe?Nc2Nf?pN_Ng?NfNh?@NgNi?dNhargNj?pNhNk?NjNl?dNkIs_abcNm?Nk0Nn?Ng0No@A@TT$e$`$ Np? pNq?NpNr?dNqT32s_aNs?NqNt?+@Ns@WNu?NsNv@A@Tt$$8$ Nw? pNx? NwNy?dNxT32s_bNz?NxN{?@NzN|?{@N{N}?N|N~?dN}I012sN?N}2N?{N{N?NN?dNIs_abcN?N1N?NzN?dNcosN?pNN?NN?@NN?dNargN?pNN?NN?dNI012sN?N2N?pNN?NN?@NN?dNargN?pNN?NN?dNIs_abcN?N1N?N0N@A@Tt$$$ N? pN?NN?dNT32s_bN?NN?+@N@WN?NN@A@T$$7$ N? pN? NN?dNT32s_cN?NN?@NN?{@NN?NN?dNI012sN?N2N?{NN?NN?dNIs_abcN?N2N?NN?dNcosN?pNN?NN?@NN?dNargN?pNN?NN?dNI012sN?N2N?pNN?NN?@NN?dNargN?pNN?NN?dNIs_abcN?N2N?N0N@A@T$$$ N? pN?NN?dNT32s_cN?NN?+@N@WN?NN@A@T$}$5$ N? pN? NN?dNT32r_aN?NN?@NN?{@NN?NN?dNI012rN?N2N?{NN?NN?dNIr_abcN?N0N?NN?dNcosN?pNN?NN?@NN?dNargN?pNN?NN?dNI012rN?N2N?pNN?NN?@NN?dNargN?pNN?NN?dNIr_abcN?N0N?N0N@A@T$$$ N? pN?NN?dNT32r_aN?NN?+@N@WN?NN@A@T$~$6$ N? pN? NN?dNT32r_bN?NN?@NN?{@NN?NN?dNI012rN?N2N?{NN?NN?dNIr_abcN?N1N?NN?dNcosN?pNN?NO?@NO?dOargO?pOO?OO?dOI012rO?O2O?pNO?OO?@OO ?dOargO ?pOO ?O O ?dO Ir_abcO ?O 1O?O0O@A@T$$$ O? pO?OO?dOT32r_bO?OO?+@O@WO?OO@A@T$} %5% O? pO? OO?dOT32r_cO?OO?@OO?{@OO?OO?dOI012rO?O2O ?{OO!?O O"?dO!Ir_abcO#?O!2O$?OO%?dO$cosO&?pO$O'?O&O(?@O'O)?dO(argO*?pO(O+?O*O,?dO+I012rO-?O+2O.?pO'O/?O.O0?@O/O1?dO0argO2?pO0O3?O2O4?dO3Ir_abcO5?O32O6?O/0O7@A@T$%% O8? pO9?O8O:?dO9T32r_cO;?O9O@D@T %@(% %O?*@T+%;%8%5 -@N 1.7.4.5 Compute negative sequence voltage polarized torque for Relay S and R6 NO@; OA7O?}OB;DOC7O?}O@OBO@8NOD;NOE9@V0OF;.NOG;NOH/@NormalArial OI*@TK%{%X%6 00-A2The torque equation is generically - T = -|Vpol| |Iphase| cos(angle(apVneg) - angle(Iabc) - MTA) where a is the 120 degree operator and p is 0 for phase a, 2 for phase b, and 1 for phase c. This works for two line to ground and two line to ground faults but not for balanced three phase to ground faults.6FE2OJ;EOK7OIOL;OM7OI@ ArialOJON;OO7OIOLONOL82OP;2OQ9@V0OR;.2OS;2OT/@NormalArial OU*@T%K%%7 y;;;-Bus S68OV;OW9@V0OX;.OY;OZ/@NormalArial O[@A@T%%9%8 O\? pO]? O\O^?dO]T32sQaO_?O]O`?@O_Oa?K@O`Ob?{OaOc?ObOd?dOcV012sOe?Oc2Of?{O`Og?OfOh?dOgIs_abcOi?Og0Oj?O_Ok?dOjcosOl?pOjOm?OlOn?@OmOo?dOnargOp?pOnOq?OpOr?dOqV012sOs?Oq2Ot?pOmOu?OtOv?@OuOw?dOvargOx?pOvOy?OxOz?dOyIs_abcO{?Oy0O|?OuMTA2O}@A@T%%% O~? pO?O~O?dOT32sQaO?OO?+@O@WO?OO@A@T%%:%: O? pO? OO?dOT32sQbO?OO?@OO?K@OO?{OO?OO?dOV012sO?O2O?{OO?OO?dOIs_abcO?O1O?OO?dOcosO?pOO?OO?@OO?dOargO?pOO?OO?p@OO?OO?dOaO?OV012sO?O2O?pOO?OO?@OO?dOargO?pOO?OO?dOIs_abcO?O1O?OMTA2O@A@T% % % O? pO?OO?dOT32sQbO?OO?+@O@WO?OO@A@T%%9%< O? pO? OO?dOT32sQcO?OO?@OO?K@OO?{OO?OO?dOV012sO?O2O?{OO?OO?dOIs_abcO?O2O?OO?dOcosO?pOO?OO?@OO?dOargO?pOO?OO?@OO?dOaO?O2O?OO?dOV012sO?O2O?pOO?OO?@OO?dOargO?pOO?OO?dOIs_abcO?O2O?OMTA2O@A@T%%% O? pO?OO?dOT32sQcO?OO?+@O@WO?OO*@T%K &&> y;;;-Bus R68O;O9@V0O;.O;O/@NormalArial O@A@T&,&7 &? O? pO? OO?dOT32rQaO?OO?@OO?K@OO?{OO?OO?dOV012rO?O2O?{OO?OO?dOIr_abcO?O0O?OO?dOcosO?pOO?OO?@OO?dOargO?pOO?OO?dOV012rO?O2O?pOO?OO?@OO?dOargP?pOP?PP?dPIr_abcP?P0P?OMTA2P@A@T&%& & P? pP?PP?dPT32rQaP ?PP ?+@P @WP ?P P @A@T4&L&8@&A P ? pP? P P?dPT32rQbP?PP?@PP?K@PP?{PP?PP?dPV012rP?P2P?{PP?PP?dPIr_abcP?P1P?PP?dPcosP?pPP?PP?@PP ?dPargP!?pPP"?P!P#?dP"aP$?P"P%?dP$V012rP&?P$2P'?pPP(?P'P)?@P(P*?dP)argP+?pP)P,?P+P-?dP,Ir_abcP.?P,1P/?P(MTA2P0@A@T4&E&@& P1? pP2?P1P3?dP2T32rQbP4?P2P5?+@P4@WP6?P4P7@A@TL&l&7`&C P8? pP9? P8P:?dP9T32rQcP;?P9P?{P=P??P>P@?dP?V012rPA?P?2PB?{P<PC?PBPD?dPCIr_abcPE?PC2PF?P;PG?dPFcosPH?pPFPI?PHPJ?@PIPK?dPJargPL?pPJPM?PLPN?@PMPO?dPNaPP?PN2PQ?PMPR?dPQV012rPS?PQ2PT?pPIPU?PTPV?@PUPW?dPVargPX?pPVPY?PXPZ?dPYIr_abcP[?PY2P\?PUMTA2P]@A@TT&e&`& P^? pP_?P^P`?dP_T32rQcPa?P_Pb?+@Pa@WPc?PaPd@A@Ts&8&&/ Pe? pPf? PePg?dPf\aPh?Pf0.99Pi@A@T&D&3&0 Pj? pPk? PjPl?dPkT32sQPm?KPkPn?PmPo?dPnRePp?pPnPq?PpPr?p@PqPs?PrPt?@PsPu?dPtV012sPv?Pt2Pw?PsPx?@PwPy?dPx\aPz?PxZL2P{?PwP|?dP{I012sP}?P{2P~?PqP?p@P~P?PP?dPZL2P?PP?dPI012sP?P2P@A@T& &&1 P? pP?PP?dPT32sQP?PP?+@P@WP?PP@A@T&}&X&2 P? pP?PP?@PP?dPargP?pPP?PP?dPV012sP?P2P?PP?+@P@WP?PdegP@A@T&K&&&3 P? pP?PP?@PP?dPargP?pPP?PP?@PP?dP\aP?PZL2P?PP?dPI012sP?P2P?PP?+@P@WP?PdegP@A@Th&&&4 P? pP?PP?@PP?dPargP?pPP?PP?p@PP?PP?dPZL2P?PP?dPI012sP?P2P?PP?+@P@WP?PdegP*@T&/&& '''-= 1.7.4.6 Zero sequence voltage polarized directional element6=P;=P7P}8=P;=P9@V0P;.=P;=P/@NormalArial P*@T&'' H  -@Reference equations - 6026 "New Ground Direction Elements Operate Reliably for Changing System Conditions", A. Guzman, J. Roberts, and D. Hou. These algorithms should be used for ground faults only.68P;P9@V0P;.P;P/@NormalArial P@D@T('@0'('P*@T;'IK'H' AAA-@D 1.7.4.6.1 Relay S zero sequence voltage polarized impedance value6 DP; P7P}P;7P7P}PPP8DP;DP9@V0P;.DP;DP/@NormalArial P@A@T ['H'J' P? pP? PP?dPZ32VsP?PP?K@PP?pPP?PP?dPReP?pPP?PP?@PP?tP3P?PP?dPV012sP?P0P?PP?p@PP?PP?@PP?p@PP?PP?dPZL0P?{PP?PZL0P?P3P?PP?dPI012sP?P0P?PP?p@PP?{PP?PP?tP3P?PP?dPI012sP?P0P?P2P@A@T''' P? pP?PP?dPZ32VsP?PP?+@P@WP?PP*@T'G'' ???-@D 1.7.4.6.2 Relay R zero sequence voltage polarized impedance value6 DP; Q7P}Q;7Q7P}PQP8DQ;DQ9@V0Q;.DQ;DQ/@NormalArial Q@A@T'F/(@( Q ? pQ ? Q Q ?dQ Z32VrQ ?Q Q ?K@Q Q?pQ Q?QQ?dQReQ?pQQ?QQ?p@QQ?QQ?p@QQ?QQ?dQ3Q?QV012rQ?Q0Q?QQ?p@QQ?QQ?@QQ?p@QQ?QQ ?dQZL0Q!?{QQ"?Q!ZL0Q#?Q3Q$?QQ%?dQ$I012rQ&?Q$0Q'?Q Q(?p@Q'Q)?{Q(Q*?Q)Q+?tQ*3Q,?Q*Q-?dQ,I012rQ.?Q,0Q/?Q'2Q0@A@T((( Q1? pQ2?Q1Q3?dQ2Z32VrQ4?Q2Q5?+@Q4@WQ6?Q4Q7*@T[(k(h(G -@E 1.7.4.6.3 Relay S negative sequence voltage polarized torque value6 EQ8; Q97Q7}Q:;8Q;7Q7}Q8Q:Q88EQ<;EQ=9@V0Q>;.EQ?;EQ@/@NormalArial QA@A@T {(Y(K(H QB? pQC? QBQD?dQCZ32QsQE?QCQF?K@QEQG?pQFQH?QGQI?dQHReQJ?pQHQK?QJQL?@QKQM?p@QLQN?QMQO?dQN3QP?QNV012sQQ?QL2QR?QKQS?p@QRQT?QSQU?p@QTQV?QUQW?dQVZL1QX?{QVQY?QXZL1QZ?QTQ[?p@QZQ\?Q[Q]?dQ\3Q^?Q\I012sQ_?QZ2Q`?QEQa?p@Q`Qb?{QaQc?QbQd?tQc3Qe?QcQf?dQeI012sQg?Qe2Qh?Q`2Qi@A@T( ((I Qj? pQk?QjQl?dQkZ32QsQm?QkQn?+@Qm@WQo?QmQp*@T(((J -@E 1.7.4.6.4 Relay R negative sequence voltage polarized torque value6 EQq; Qr7Qp}Qs;8Qt7Qp}QqQsQq8EQu;EQv9@V0Qw;.EQx;EQy/@NormalArial Qz@A@T (]G)I()K Q{? pQ|? Q{Q}?dQ|Z32QrQ~?Q|Q?K@Q~Q?pQQ?QQ?dQReQ?pQQ?QQ?p@QQ?QQ?p@QQ?QQ?dQ3Q?QV012rQ?Q2Q?QQ?p@QQ?QQ?p@QQ?QQ?dQZL1Q?{QQ?QZL1Q?QQ?p@QQ?QQ?dQ3Q?QI012rQ?Q2Q?Q~Q?p@QQ?{QQ?QQ?p@QQ?QQ?dQ3Q?QI012rQ?Q2Q?Q2Q@A@T$)5)0)L Q? pQ?QQ?dQZ32QrQ?QQ?+@Q@WQ?QQ@D@TX)@`)X)Q*@Tk){)x)M www-9 1.7.4.7 Positive sequence torque for three phase faults69Q;9Q7Q}89Q;9Q9@V0Q;.9Q;9Q/@NormalArial Q@A@T))B)N Q? pQ? QQ?dQTS32PQ?QQ?@QQ?{@QQ?QQ?tQ3Q?QQ?dQV012sQ?Q1Q?{QQ?QQ?tQ3Q?QQ?dQI012sQ?Q1Q?QQ?dQcosQ?pQQ?QQ?@QQ?dQargQ?pQQ?QQ?dQV012sQ?Q1Q?pQQ?QQ?@QQ?dQargQ?pQQ?QQ?dQI012sQ?Q1Q?QMTA1Q@A@T)))O Q? pQ?QQ?dQTS32PQ?QQ?+@Q@WQ?QQ@A@T))C)P Q? pQ? QQ?dQTR32PQ?QQ?@QQ?{@QQ?QQ?tQ3Q?QQ?dQV012rQ?Q1Q?{QQ?QQ?tQ3Q?QQ?dQI012rQ?Q1Q?QQ?dQcosQ?pQQ?QQ?@QQ?dQargQ?pQQ?QQ?dQV012rQ?Q1Q?pQQ?QQ?@QQ?dQargR?pQR?RR?dRI012rR?R1R?QMTA1R@A@T)))Q R? pR?RR?dRTR32PR ?RR ?+@R @WR ?R R *@T)t))R lll-@K 1.7.4.8 Positive sequence torque for three phase faults using V1 prefault6KR ;KR7R }8KR;KR9@V0R;.KR;KR/@NormalArial R@A@T)*C)S R? pR? RR?dRTS32PmR?RR?@RR?{@RR?RR?tR3R?RR?dRV012sR?R1R ?{RR!?R R"?tR!3R#?R!R$?dR#I012sR%?R#1R&?RR'?dR&cosR(?pR&R)?R(R*?@R)R+?dR*argR,?pR*R-?R,R.?dR-V012sR/?R-1R0?pR)R1?R0R2?@R1R3?dR2argR4?pR2R5?R4R6?dR5I012sR7?R51R8?R1MTA1R9@A@T)**T R:? pR;?R:R?+@R=@WR??R=R@@A@T *$*D*U RA? pRB? RARC?dRBTR32PmRD?RBRE?@RDRF?{@RERG?RFRH?tRG3RI?RGRJ?dRIV012rRK?RI1RL?{RERM?RLRN?tRM3RO?RMRP?dROI012rRQ?RO1RR?RDRS?dRRcosRT?pRRRU?RTRV?@RURW?dRVargRX?pRVRY?RXRZ?dRYV012rR[?RY1R\?pRUR]?R\R^?@R]R_?dR^argR`?pR^Ra?R`Rb?dRaI012rRc?Ra1Rd?R]MTA1Re@A@T*%* *V Rf? pRg?RfRh?dRgTR32PmRi?RgRj?+@Ri@WRk?RiRl@D@T0*@8*0*Rm*@TC*dS*P* \\\-@O1.8 Distance element polarized by prefault positive sequence voltage for r=0.86ORn;Ro7Rm}Rp;:Rq7Rm}RnRpRn8ORr;ORs9@V0Rt;.ORu;ORv/@NormalArial Rw@A@T`**1x* Rx? pRy? RxRz?dRyTSAGR{?RyR|?p@R{R}?R|R~?@R}R?@R~R?dRrR?RZL1R?pR~R?RR?@RR?dRIs_abcR?R0R?RR?@RR?dR3R?Rk0R?RR?dRI012sR?R0R?R}R?dRVs_abcR?R0R?R{R?p@RR?RR?@RR?dRaR?R0R?RVS1polR@A@Tl*O}*8x*X ȖR? pR?RR?@RR?dRReR?pRR?RTSAGR?RR?+@R@WR?RR@A@T**/* R? pR? RR?dRTSBGR?RR?p@RR?RR?@RR?@RR?dRrR?RZL1R?pRR?RR?@RR?dRIs_abcR?R1R?RR?@RR?dR3R?Rk0R?RR?dRI012sR?R0R?RR?dRVs_abcR?R1R?RR?p@RR?RR?@RR?dRaR?R2R?RVS1polR@A@T*M*6*Y ȖR? pR?RR?@RR?dRReR?pRR?RTSBGR?RR?+@R@WR?RR@A@T**/* R? pR? 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