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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@VTitle =@Times New Roman@VSubtitle 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@ORotated Math FontTimes New Roman TextRegion* docRegionFshpBoxT  docRegionAttributeG@G"GG CharacterMap-RangeMap:@kTwo Source - One line Powere System for Fault Analysis File Name: 2SrcL1.mcd Richard W. Wall Oct 14, 1999 ChrPropMap6_#k RangeElem;# ChrPropData7 RangeData<hArial;7;7hArial;7;7hArial;7;7nArial; 7!;"7nArial#;$7!%; &7nArial#% ParPropMap8_Ok';$( ParPropData9@V);*9@V'+;,9@V)-;.9@V+/;09@V-1;29@V/3; 49@V131EmbedMap05;LinkMap.k6;k7LinkData/@NormalArial 8*@T7  9@G:@G"//P/P-AThis program computes the directional torque equations for relays Rs and Rr with various faults located at F1 and F2. 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 fro relay S. 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X5 7 9 1Gpxlm9mHairqShort Arial cke?redtop leftTim esConnectorUn3_03!) ) ) 3 3U9 9 9 9 U9 9 x9 h9 UX9 G9 49 $9 }9 3u Uu u u u Uu u ru du UUu Gu $D 'wԞ$l::})DB `d2FDثOʷ%?w' <@+" 5   - "-N$%>@@+FO[j{"+0+2@0U+i"}{j[O}Fi@U>@ "--  . ,"Arial-!Es^~"System- - "-$--  . %"Arial-!ZsY- - "-%@@- - "-%??-  . -!V1]- - "->$QA1#$#)1,A-Q,b)r$rbQ-- - "-J$#qXsCy/ %5 AK/PCRXPmKA5%ysmqX--  . -!Rsv- - "-%Q- - "-$--  . - !ZL*mfX-  . - !Vs,Isa- - "- $-- - "-%R- - "-$--  . -!Isn-  . -!Zf1T- - "- %Q - -- $2-- - "-%??- - "-%?@?-  . -!V2w-@C*@T y@D@G@E@G"-&Figure 1. System single line diagram.6&8&@F;&@G9@V0@H;.&@I;&@J/@NormalArial @K*@TW @L@G@M@G"-&1.1. Symmetrical Component Conversions6&@N;&@O7@K}8&@P;&@Q9@V0@R;.&@S;&@T/@NormalArial @U*@T`3?`(X y@V@G@W@G"$$-@Ia = 120 degree phase shift operator a2 = 240 degree phase shift operator6'&I@X;&@Y7@U@Z;@[7@U@ Arial@X@\;"@]7@U@Z@\@Z8%%$I@^;%@_9@V@`;$@a9@V@^@`@`0@b;.I@c;I@d/@NormalArial @eeqRegionA@T$/50Y @f@G@g@G"@htree ? p@i? @h@j?d@ih@k?@i1@l*@T@#3@0Z y@m@G@n@G"\\\-h = scale vactor68@o;@p9@V0@q;.@r;@s/@NormalArial @t@A@TJ@0[ @u@G@v@G"@w? p@x? @w@y?d@xa@z?@x@{?@@z@|?d@{cos@}?p@{@~?@}@?t@~2@?@~@?d@\p@?@3@?5@z@?@@@?d@sin@?p@@?@@?t@2@?@@?d@\p@?@3@?@1i@*@TSs`\ y@@G@@G" -4Phase to Symmetrical Component transformation matrix6484@;@9@V@;@9@V@@@0@;.4@;4@/@NormalArial @@A@T>"h] @@G@@G"@? p@? @@?d@A@?@@?p@@@?@@?t@1@?@3@?p@@?0@@?0A@@?0A@@?0A@@?0A@@?0A@@?0A@@?0A@@?0A@@?@@@?@a@?@@?d@a@?@2@?@1@?@@?d@a@?@2@?@a@?@1@?@1@?@1@?@1@@A@T#^ @@G@@G"@? p@? @@?@@@?d@ ZsZm_Z012@?p@@? @@?d@Zs@?@Zm@?@@?@@@?@@@?d@Zabc@?p@@?0@@?0A@@?0A@@?0A@@?0A@@?0A@@?0A@@?0A@@?0A@@?@@@?@Zs@?@Zm@?@Zm@?@Zm@?@Zs@?@Zm@?@Zm@?@Zm@?@Zs@?@@?d@Z012@?@@?@@@?d@A@?@Zabc@?@@?d@A@?K@@?@1@?C@@?@Z012@@A@T04_ @@G@@G"@? p@? @@?@@@?d@ Z0Z1_Zabc@?p@@? @@?d@Z0@?@Z1@?@@?@@@?@@@?d@Z012@?p@@?0@@?0A@@?0A@@?0A@@?0A@@?0A@@?0A@A?0A@A?0AAA?@AA?AZ1A?A0A?@0A?@0A?@Z1A?@0A ?@0A ?@0A ?@Z0A ?@A ?dA ZabcA?A A?@AA?@AA?dAAA?KAA?A1A?AZ012A?AAA?C@A?AZabcA@A@T&3` A@GA@G"A? pA? AA?@AA?dA Zabc_2_Z012A?pAA ?AZabcA!?AA"?@A!A#?dA"Z012A$?A"A%?@A$A&?dA%AA'?A%ZabcA(?A$A)?dA(AA*?KA(A+?A*1A,?CA!A-?A,Z012A.@A@T8M3a A/@GA0@G"A1? pA2? A1A3?@A2A4?dA3 Z012_2_ZabcA5?pA3A6?A5Z012A7?A2A8?@A7A9?dA8ZabcA:?A8A;?@A:A?KA<A??A>1A@?A;Z012AA?A:AAB?CA7AC?ABZabcAD*@TCSP AE@GAF@G"A-1.2 Network impedance matrices6AG;AH7AD}8AI;AJ9@V0AK;.AL;AM/@NormalArial AN*@Tcsp AO@GAP@G"- 1.2.1 Network constants 6AQ;AR7AN}8AS;AT9@V0AU;.AV;AW/@NormalArial AX@A@TVI AY@GAZ@G"A[? pA\? A[A]?dA\AaA^?A\A_?p@A^A`?A_Aa?tA`1Ab?A`3Ac?pA^Ad?0AcAe?0AAdAf?0AAeAg?0AAfAh?0AAgAi?0AAhAj?0AAiAk?0AAjAl?0AAkAm?@AlAn?AlaAo?AkAp?dAoaAq?Ao2Ar?Aj1As?AiAt?dAsaAu?As2Av?AhaAw?Ag1Ax?Af1Ay?Ae1Az?Ad1A{*@T  ߄A|@GA}@G"@-@KThis matrix is used as a constant for building the system impedance matrix.6K8DDKA~;A9@VA;A9@VA~A;A9@VAA;A9@VAAA0A;.KA;KA/@NormalArial A@A@T}< A@GA@G"A? pA? AA?dAYnullA?pAA?0AA?0AAA?0AAA?0AAA?0AAA?0AAA?0AAA?0AAA?0AAA?@AA?A0A?A0A?A0A?A0A?A0A?A0A?A0A?A0A?A0A@A@TJ A@GA@G"A? pA? 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BEBG?dBFZLsBH?BFBI?@BHBJ?dBIZL0BK?BIBL?tBK2BM?BKZL1BN?BH3BO@A@TP BP@GBQ@G"BR? pBS?BRBT?dBSZLsBU?BSBV?+@BUSerial_DisplayNodeWBW?BUBX@A@TH1 BY@GBZ@G"B[? pB\?B[B]?dB\ZLabcB^?B\B_?+@B^@WB`?B^Ba@A@T0PQ Bb@GBc@G"Bd? pBe? BdBf?dBeZLmBg?BeBh?@BgBi?dBhZL0Bj?BhZL1Bk?Bg3Bl@A@TS Bm@GBn@G"Bo? pBp?BoBq?dBpZLmBr?BpBs?+@Br@WBt?BrBu*@To0 Bv@GBw@G"__-) 1.2.1.2 Unalanced line parameter matrix6')Bx;By7BuBz;'B{7Bu}BxBzBz8)B|;)B}9@V0B~;.)B;)B/@NormalArial B@A@T8T(8 B@GB@G"B? pB? BB?dB Line_LengthB?BB?tB25B?BB?dBCTRB?BVTRB@A@T;C(: B@GB@G"B? pB? BB?dBZLB?BB?p@BB?0BB?0ABB?0ABB?0ABB?0ABB?0ABB?0ABB?0ABB?0ABB?@BB?BB?tB0.2201B?B0.9608iB?BB?tB0.1175B?B0.4895iB?BB?tB0.1133B?B0.4608iB?BB?tB0.1175B?B0.4895iB?BB?tB0.2285B?B0.9575iB?BB?tB0.1175B?B0.4895iB?BB?tB0.1133B?B0.4608iB?BB?tB0.1175B?B0.4895iB?BB?tB0.2201B?B0.9608iB?B Line_LengthB@A@T M6< B@GB@G"B? pB?BB?dBZLB?BB?+@B@WB?BB*@T+ B@GB@G"-. 1.2.2.3 Balanced line parameter computations6.B;.B7B}8.B;.B9@V0B;..B;.B/@NormalArial B@A@T1, B@GB@G"B? pB? BB?dBZL012B?BB?dB Zabc_2_Z012B?pBB?BZLabcB@A@Tb%- B@GB@G"B? pB? BB?dBZL0B?BB?dBZL012B? BB?tB0B?B0B@A@TW@. B@GB@G"B? pB?BB?dBZL012B?BB?+@B@WB?B2I0`B@A@Tb%/ B@GB@G"B? pB? BB?dBZL1B?BB?dBZL012B? BB?tB1B?B1B*@T[;{h B@GB@G"++ -$ 1.2.2.4 Set maximum torque angle 6# $B; B7B}B;B7B}BB;B7B}BBB8$B;$C9@V0C;.$C;$C/@NormalArial C@A@T|x> C@GC@G"C? pC? CC ?dCMTAC ?CC ?dC argC ?pC C ?C ZL1C@A@T|* C@GC@G"C? pC?CC?dCMTAC?CC?+@C@WC?CdegC*@Tw! C@GC@G"gg-* 1.2.2.4 Asymmetrical compensation factor6*C;*C7C}8*C;*C9@V0C;.*C;*C /@NormalArial C!@A@T {4" C"@GC#@G"C$? pC%? C$C&?dC%k0C'?C%C(?@C'C)?dC(ZL0C*?C(ZL1C+?C'C,?tC+3C-?C+ZL1C.@A@T# C/@GC0@G"C1? pC2?C1C3?dC2k0C4?C2C5?+@C4@WC6?C4C7*@Tc $ C8@GC9@G"SS-( 1.2.3 Default fault impedance matrices6(C:;(C;7C7}8(C<;(C=9@V0C>;.(C?;(C@/@NormalArial CA@A@T g9@% CB@GCC@G"CD? pCE? CDCF?dCEZffCG?pCECH?0CGCI?0ACHCJ?0ACICK?0ACJCL?0ACKCM?0ACLCN?0ACMCO?0ACNCP?0ACOCQ?@CPCR?CPCS?tCR10CT?CR6CU?CO0CV?CN0CW?CM0CX?CLCY?tCX10CZ?CX6C[?CK0C\?CJ0C]?CI0C^?CHC_?tC^10C`?C^6Ca*@TsF Cb@GCc@G"A>-$ 1.2.4 S voltage source impedance 6$Cd;$Ce7Ca}8$Cf;$Cg9@V0Ch;.$Ci;$Cj/@NormalArial Ck*@T0 Cl@GCm@G" -@zThe S end source has infinite zero zequence impedance so no zero sequence current can be supplied by the source generator.6z8zCn;zCo9@V0Cp;.zCq;zCr/@NormalArial Cs*@T Ct@GCu@G"-Zero sequence addmitance68Cv;Cw9@V0Cx;.Cy;Cz/@NormalArial C{*@Tp C|@GC}@G"-Positive sequence addmitance68C~;C9@V0C;.C;C/@NormalArial C*@T0 C@GC@G"-Negitive sequence addmitance68C;C9@V0C;.C;C/@NormalArial C@A@T(fJ C@GC@G"C? pC? CC?dCZss0C?CC?tC10C?C6C@A@T- C@GC@G"C? pC? CC?dCZss1C?pCC?CC?tC1C?C6iC@A@T C@GC@G"C? pC? CC?dCZss2C?pCC?CC?tC1C?C6iC@A@T$ 5 F0  C@GC@G"C? pC? CC?dCZss012C?CC?tC0.1C?CZL012C@A@T$ 5 0  C@GC@G"C? pC?CC?dCZss012C?CC?+@C@WC?CC@A@T| 4  C@GC@G"C? pC? CC?dCZssC?CC?dC Z012_2_ZabcC?pCC?CZss012C@A@T|   C@GC@G"C? pC?CC?dCZssC?CC?+@C@WC?CC*@T   C@GC@G"{{-1.3 Voltage sources6C;C7C}8C;C9@V0C;.C;C/@NormalArial C*@T   C@GC@G"- 1.3.1 Generator constants 6C;C7C}8C;C9@V0C;.C;C/@NormalArial C*@T(  (  ߄C@GC@G"-Voltage Generator Voltage68C;C9@V0C;.C;C/@NormalArial C*@T f   ߄C@GC@G"vv-Power system angle68C;C9@V0C;.C;C/@NormalArial C*@Tp 5; p  C@GC@G"0-@SSpecify power angle in degress - positive for leading and negative for lagging,6S8==SC;"C9@VC;C9@VCC;C9@VCCC0C;.SC;SC/@NormalArial C@A@T $ R5 <0  C@GC@G"D? pD? DD?dDangD?D45D@A@TP# J g8  D@GD@G"D? pD? DD ?dDVgD ?DD ?tD 120D ?{D D ?D 3D*@TPS c P`  ߄D@GD@G"-Power angle shift operator68D;D9@V0D;.D;D/@NormalArial D*@T8k { 8x  ߄D@GD@G"ff-VT and CT Ratios68D;D9@V0D;.D;D/@NormalArial D@A@T@r  N  D@GD @G"D!? pD"? D!D#?dD"\dD$?D"D%?@D$D&?dD%cosD'?pD%D(?D'D)?@D(D*?dD)\pD+?D)angD,?D(180D-?5D$D.?@D-D/?dD.sinD0?pD.D1?D0D2?@D1D3?dD2\pD4?D2angD5?D1180D6?D-1iD7@A@T0 s Q  D8@GD9@G"D:? pD;? D:D@A@T  D?@GD@@G"DA? pDB? DADC?dDBCTRDD?DB320DE*@T   DF@GDG@G"- 1.3.2 S end voltage source 6DH;DI7DE}8DJ;DK9@V0DL;.DM;DN/@NormalArial DO@A@T@  U  DP@GDQ@G"DR? pDS? DRDT?dDSEsDU?pDSDV?0DUDW?0ADVDX?0ADWDY?@DXDZ?DXD[?dDZVgD\?DZaD]?DWD^?dD]VgD_?D]D`?dD_aDa?D_2Db?DVVgDc*@T r   Dd@GDe@G"bb-1.4 Subroutines6Df;Dg7Dc}8Dh;Di9@V0Dj;.Dk;Dl/@NormalArial Dm*@T    Dn@GDo@G"- 1.4.1 System Impedance matrix 6Dp;Dq7Dm}8Dr;Ds9@V0Dt;.Du;Dv/@NormalArial Dw*@T0 > 0  Dx@GDy@G"-A Zsystem Definitions Output: Z: System impedance matrix For this system - the result is a [12X12] matrix of complex variables Input: Zs: S end voltage source Impedance matrix1 ZL: Total length line impedance matrix1 Zff: Forward fault impedance matrix1 m: Percent of line length to forward2 Notes: 1. [3X3] matrix of complex values 2. Scalar in range 0.0001 to 0.999963Dz;D{7DwD|;D}7DwyDzD~;D7DwD|D;D7Dw_D~D;)D7DwDD;D7Dw_DD;%D7DwDD;D7Dw_DD;%D7DwDD;D7Dw_DD;ND7DwDDD|8^^#D;D9@VD;D9@VDD;D9@VDD;1D9@VDD;D9@VDD;D9@VDD;D9@VDD;-D9@VDD;)D9@VDD;&D9@VDD;&D9@VDD;D9@VDD;D9@VDD;"D9@VDD;#D9@VDDD0D;.D;D/@NormalArial D*@T Z   D@GD@G"JJ-& 1.4.1.1 Impedance matrix description6&D;&D7D}8&D;&D9@V0D;.&D;&D/@NormalArial D*@T a   D@GD@G"II-+ 1.4.1.2 System Impedance matrix subroutine6+D;+D7D}8+D;+D9@V0D;.+D;+D/@NormalArial D@A@T , e @  D@GD@G"D? pD? DD?@DD?dDZsystemD?pDD? DD? @DD? @DD?dDZssD?DZLD?DZffD?DmD?DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?dDY11D?DD?@DD?dDZssD?KDD?D1D?DD?p@DD?DD?dDmD?DZLD?KDD?D1D?DD?dDY12D?KDD?DD?p@DD?DD?dDmD?DZLD?KDD?D1D?DD?dDY21D?DY12D?DD?dDY22D?DD?@DD?p@DD?DD?dDmD?DZLD?KDD?D1E?DE?dEZffE?KEE?E1E?DE?dEY1E?EE?dEstackE?pEE ? EE ?dE Y11E ?E Y21E ?DE ?dE Y2E?E E?dEstackE?pEE? EE?dEY12E?EY22E?DE?dEYE?EE?dEaugmentE?pEE? EE?dEY1E?EY2E?CDE?EE?dEYE?KEE ?E1E!*@T 6 M E"@GE#@G"-# 1.4.2 Compute system node voltages6#E$;#E%7E!}8#E&;#E'9@V0E(;.#E);#E*/@NormalArial E+*@TS(N E,@GE-@G";;-A Solve_Node_Voltages Definitions Output: Vn: Vnode voltages1 Input: Es: S end voltage source2 Zs: S end voltage source Impedance matrix3 ZL: Total length line impedance matrix3 Zff: Forward fault impedance matrix3 m: Percent of line length to forward4 Notes: 1. [1X6] column vector = [V1 : V2 ]T 2. [1X3] column vector 3. [3X3] matrix of complex values 4. Scalar in range 0.0001 to 0.99996/ E.;E/7E+E0; E17E+yE.E2;E37E+E0E4;E57E+_E2E6;"E77E+E4E8;E97E+_E6E:;,E;7E+E8E<;E=7E+_E:E>;)E?7E+EEB;%EC7E+E@ED;EE7E+_EBEF;%EG7E+EDEH;EI7E+@ ArialEFEJ;+EK7E+EHEL;EM7E+_EJEN;_EO7E+ELENE08kk#EP;"EQ9@VER;ES9@VEPET;EU9@VEREV;EW9@VETEX;EY9@VEVEZ;-E[9@VEXE\;)E]9@VEZE^;&E_9@VE\E`;&Ea9@VE^Eb;Ec9@VE`Ed;&Ee9@VEbEf;Eg9@VEdEh;"Ei9@VEfEj;#Ek9@VEhEjEj0El;.Em;En/@NormalArial Eo@A@T$0P Ep@GEq@G"Er? pEs? ErEt?@EsEu?dEtSolve_Node_VoltagesEv?pEtEw? EvEx? @EwEy? @ExEz? @EyE{?dEzEsE|?EzZssE}?EyZLE~?ExZffE?EwmE?EsE?@EE?@EE?@EE?@EE?@EE?dEZE?EE?dEZsystemE?pEE? EE? @EE? @EE?dEZssE?EZLE?EZffE?EmE?EE?dENullSrcE?pEE?0EE?0AEE?0AEE?@EE?E0E?E0E?E0E?EE?dEIgenE?EE?@EE?dEZssE?KEE?E1E?EEsE?EE?dEIgenE?EE?dEstackE?pEE? EE?dEIgenE?ENullSrcE?EE?dEVE?EE?dEZE?EIgenE?CEE?EVE*@T+;8W E@GE@G"- 1.4.3 Compute relay currents6E;E7E}8E;E9@V0E;.E;E/@NormalArial E*@TKKcXX E@GE@G";;-A| Solve_currents Definitions Output: Ib: Branch currents1 IS - Send relay current Input: V: Node voltage vector computed by Solve_Node_Voltages2 ZL: Total length line impedance matrix3 m: Percent of line length to forward4 Notes: 1. 1X6 Column vector = [IS : IR]T 2. [1X12] column vector = [V1 : V2]T 3. 3X3 matrix of complex values 4. Scalar in range 0.0001 to 0.999967|E;E7EE;E7EyEE;E7EEE;E7E@ ArialEE;]E7EEE;E7E_EE;(E7EEE;E7E_EE;%E7EEE;E7E@ ArialEE;)E7EEE;E7E_EE;&E7EEE;E7E_EE;EE7EEEE8YY#|E;E9@VE;E9@VEE;E9@VEE;E9@VEE;E9@VEE;E9@VEE;$E9@VEE;E9@VEE;)E9@VEE;&E9@VEE;E9@VEE;E9@VEE;$E9@VEE;&E9@VEE; E9@VEE;#E9@VEEE0E;.|E;|E/@NormalArial F@A@Tt-Y F@GF@G"F? pF? FF?@FF?dFSolve_currentsF?pFF? FF ? @FF ?dF VF ?F ZLF ?FmF ?FF?@F F?dFIsF?FF?@FF?p@FF?FF?dFmF?FZLF?KFF?F1F?pFF?FF?@FF?dF submatrixF?pFF? FF? @FF? @FF ? @FF!?dF VF"?F 0F#?F2F$?F0F%?F0F&?FF'?dF& submatrixF(?pF&F)? F(F*? @F)F+? @F*F,? @F+F-?dF,VF.?F,3F/?F+5F0?F*0F1?F)0F2?CF F3?F2IsF4*@T, F5@GF6@G"-& 1.4.4 Rectangular to polar conversion6&F7;&F87F4}8&F9;&F:9@V0F;;.&F<;&F=/@NormalArial F>@A@T5_ F?@GF@@G"FA? pFB? FAFC?@FBFD?dFC rect2polarFE?pFCFF?FERFG?FBFH?@FGFI?@FHFJ?@FIFK?@FJFL?@FKFM?@FLFN?dFMmFO?{FMFP?FOFQ?dFPRFR?FPiFS?FLFT?dFS\aFU?FSFV?@FUFW?dFVargFX?pFVFY?FXFZ?dFYRF[?FYiF\?FUF]?tF\180F^?F\\pF_?FKF`?dF_pFa?pF_Fb?0FaFc?0AFbFd?@FcFe?Fc\aFf?FbmFg?IFJFh?@FgFi?dFhPolFj?FhpFk?)FgFl?dFkiFm?Fk1Fn?IFIFo?@FnFp?dFoPolFq?FoFr?dFqstackFs?pFqFt? FsFu?dFtPolFv?FtpFw?(FnFx?dFwiFy?Fw0Fz?FHF{?dFziF|?FzF}?tF|0F~?F|2F?CFGF?FPolF*@T8F8 F@GF@G"-@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 variables6*F;*F7FyF;F7FFF;F7FyFF;F7FyFF;F7F@ ArialFF;F7FFF;!F7FyFF;F7F@ ArialFF;F7FFF;F7FyFF;F7FFF;F7FyFF;F7FFF;#F7FyFFF8#F;+F9@VF;F9@VFF;F9@VFF;#F9@VFF;F9@VFF;F9@VFF;F9@VFF;#F9@VFFF0F;.F;F/@NormalArial F*@TkU{x] F@GF@G"==-21.6 Calculate faulted system voltages and currents62F;2F7F}82F;2F9@V0F;.2F;2F/@NormalArial F*@T I ^ F@GF@G"))p-BThe second calculation is for an faulted system. The locations of the forward is establisted by setting the value of mf as a decimal fraction of the total line length. If mf equalt 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 mr shown as ZLs in Figure 1. The amount of impedance added is determined by Zls = mr*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 mr to add no additional impedance to the source impedance.68F;F9@V0F;.F;F/@NormalArial F@A@T =$_ F@GF@G"F? pF? FF?dFrF?F0.8F*@TH H` yF@GF@G"EE- Relay reach6 8 F; F9@V0F;. F; F/@NormalArial F*@T3E@a F@GF@G"--p-BjThe parameters associated with the forward and reverse fault matrix are illustrated in Figure 2. Use impedance values of 106 for open circuits. Phase to phase faults are generated by setting Zab, Zbc, and / or Zac to small values. Phase to ground faults are generated by setting Zaa, Zbb, and / or Zcc to small values. The minimum fault impedance should be limited to 0.0001. Fault impedances can be complex. Not specifying a fault impedance defaults to an open circuit fault matrix. Chaning the left hand variable fro Zff to Zfr moves the fault matrix to the Zf2 position making the fault matrix behind Relay S.6y|jF;|F7FF;F7F@ ArialFF;F7F` ArialFF;F7F` ArialFFF8jF;jF9@V0F;.jF;jF/@NormalArial F@Tb F@GF@G"HHࡱ>    !"Root EntryFU#?Ole CompObjrOlePres000z FMicrosoft Visio DrawingVISIO 4.0 ShapesVisio.Drawing.119qOh+'08DP\htcKC;@cKC;@ b   -  "-$%% "--n"Arial-"System- . -!Zab- -  "-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$                       --VisioDocumentN)VisioInformation"SummaryInformation(Visio (TM) Drawing N)R(6d !fffMMM333<q0<T d Arial)-": -3Times New Roman5T?? 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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$()*+,%&'" -01C_  !- %    #  t#Dv@@  !"! ` hl 2@B;u's<D g (5m@(n84$s  RL8TW@{}N&B!< 5D@ wl<O$P 'w,h$9@,O)/`<l2FL W&?w' <(`C*4!F*@Tc yF@GF@G"- Figure 2. Fault matrix diagram.6 8 F; F9@V0F;. F; F/@NormalArial F@A@T8pT F@GF@G"F? pF? FF?dFZaaF?FF?tF10F?F6F@A@Te F@GF@G"F? pF? FF?dFZbbF?FF?tF10G?F6G@A@Tf G@GG@G"G? pG? GG?dGZccG?GG?tG10G ?G6G @A@T8qUg G @GG @G"G ? pG? G G?dGZabG?GG?tG10G?G6G@A@TT G@GG@G"G? pG? GG?dGZbcG?GG?tG10G?G6G@A@T i G@GG@G"G? pG ? GG!?dG ZacG"?G 10G#@A@T0:/Ij G$@GG%@G"G&? pG'? G&G(?dG'YffG)?pG'G*?0G)G+?0AG*G,?0AG+G-?0AG,G.?0AG-G/?0AG.G0?0AG/G1?0AG0G2?0AG1G3?@G2G4?pG2G5?G4G6?@G5G7?@G6G8?dG7ZccG9?KG7G:?G91G;?G6G?G=1G??G5G@?dG?ZbcGA?KG?GB?GA1GC?KG1GD?GCGE?dGDZbcGF?KGDGG?GF1GH?KG0GI?GHGJ?dGIZacGK?KGIGL?GK1GM?KG/GN?GMGO?dGNZbcGP?KGNGQ?GP1GR?pG.GS?GRGT?@GSGU?@GTGV?dGUZbbGW?KGUGX?GW1GY?GTGZ?dGYZabG[?KGYG\?G[1G]?GSG^?dG]ZbcG_?KG]G`?G_1Ga?KG-Gb?GaGc?dGbZabGd?KGbGe?Gd1Gf?KG,Gg?GfGh?dGgZacGi?KGgGj?Gi1Gk?KG+Gl?GkGm?dGlZabGn?KGlGo?Gn1Gp?pG*Gq?GpGr?@GqGs?@GrGt?dGsZaaGu?KGsGv?Gu1Gw?GrGx?dGwZabGy?KGwGz?Gy1G{?GqG|?dG{ZacG}?KG{G~?G}1G@A@T8T~mQhk G@GG@G"G? pG? GG?dGZffG?GG?dGYffG?KGG?G1G@A@T\mhl G@GG@G"G? pG?GG?dGZffG?GG?+@G@WG?GG@A@Th\mhm G@GG@G"G? pG?GG?dGYffG?GG?+@G@WG?GG*@Tn G@GG@G"->1.7 Compute relay voltages and currents for the faulted system6>G;G7G}G;:G7G}GGG8>G;>G9@V0G;.>G;>G/@NormalArial G*@To yG@GG@G"-Location of forward fault68G;G9@V,0G;.G;G/@NormalArial G@A@Tp G@GG@G"G? pG? GG?dGmG?G.55G*@Tq yG@GG@G"-Compute node voltages68G;G9@V0G;.G;G/@NormalArial G@A@T DCr G@GG@G"G? pG? GG?dGVnodeG?GG?dGSolve_Node_VoltagesG?pGG? GG? @GG? @GG? @GG?dGEsG?GZssG?GZLabcG?GZffG?GmG@A@T ,=68s G@GG@G"G? pG? GG?dGVsG?GG?dG submatrixG?pGG? GG? @GG? @GG? @GG?dGVnodeG?G0G?G2G?G0G?G0G@A@T L]5Xt G@GG@G"G? pG? GG?dGVfG?GG?dG submatrixG?pGG? GG? @GG? @GG? @GG?dGVnodeG?G3G?G5G?G0G?G0G@A@T`\mh ͠G@GG@G"G? pG?GG?@GG?dG rect2polarG?pGG?GVsG?GG?+@G@WG?GH@A@Td|}@x} H@GH@G"H? pH? HH?dHVs012H?HH?@HH?dHAH ?KHH ?H 1H ?HVsH @A@T|;~ H @GH@G"H? pH? HH?dHVsabH?HH?@HH?dHVsH?H0H?HH?dHVsH?H1H@A@T H@GH@G"H? pH? HH?dHVsbcH?HH ?@HH!?dH VsH"?H 1H#?HH$?dH#VsH%?H#2H&@A@TK  H'@GH(@G"H)? pH*? H)H+?dH*VscaH,?H*H-?@H,H.?dH-VsH/?H-2H0?H,H1?dH0VsH2?H00H3@A@T` ͠H4@GH5@G"H6? pH7?H6H8?@H7H9?dH8 rect2polarH:?pH8H;?H:VfH?H<H?*@T  H@@GHA@G"- 1.7.1 Extract Relay Currents6HB;HC7H?}HD;HE7H?}HBHDHB8HF;HG9@V0HH;.HI;HJ/@NormalArial HK@A@T%  HL@GHM@G"HN? pHO?HNHP?dHOMTAHQ?HOHR?+@HQ@WHS?HQdegHT@A@T-'( HU@GHV@G"HW? pHX? HWHY?dHXIbrHZ?HXH[?dHZSolve_currentsH\?pHZH]? H\H^? @H]H_?dH^VnodeH`?H^ZLabcHa?H]mHb@A@T4E"@ Hc@GHd@G"He? pHf? HeHg?dHfIsHh?HfHi?dHh submatrixHj?pHhHk? HjHl? @HkHm? @HlHn? @HmHo?dHnIbrHp?Hn0Hq?Hm2Hr?Hl0Hs?Hk0Ht@A@Tdh|/p Hu@GHv@G"Hw? pHx? HwHy?dHxIsabHz?HxH{?@HzH|?dH{IsH}?H{0H~?HzH?dH~IsH?H~1H@A@Txd|p H@GH@G"H? pH? HH?dHIsbcH?HH?@HH?dHIsH?H1H?HH?dHIsH?H2H@A@Td7|p H@GH@G"H? pH? HH?dHIscaH?HH?@HH?dHIsH?H2H?HH?dHIsH?H0H@A@Tp|j H@GH@G"H? pH?HH?dHIbrH?HH?+@H@WH?HH@A@TJ0 H@GH@G"H? pH? HH?dHIsaH?HH?dHIsH?H0H@A@T`y H@GH@G"H? pH? HH?dHIsbH?HH?dHIsH?H1H@A@T H@GH@G"H? pH? HH?dHIscH?HH?dHIsH?H2H@A@TH ͠H@GH@G"H? pH?HH?@HH?dH rect2polarH?pHH?HIsH?HH?+@H@WH?HH@A@TpB H@GH@G"H? pH? HH?dHIsa012H?HH?dHAaH?HIsH@A@Tx H@GH@G"H? pH? HH?dHIsb012H?HH?dHAbH?HIsH@A@T0 H@GH@G"H? pH? HH?dHIsc012H?HH?dHAcH?HIsH@A@T-( ͠H@GH@G"H? pH?HH?@HH?dH rect2polarH?pHH?HIsa012H?HH?+@H@WH?HH@A@T$p5Y0 H@GH@G"H? pH?HH?@HH?dH rect2polarH?pHH?HIsb012H?HH?+@H@WH?HH@A@TtoX H@GI@G"I? pI?II?@II?dI rect2polarI?pII?IIsc012I?II?+@I@WI ?II @A@TZ! I @GI @G"I ? pI? I I?dIIabI?II?@II?dIIsI?I0I?II?dIIsI?I1I@A@T`y I@GI@G"I? pI? II?dIIbcI?II?@II?dIIsI ?I1I!?II"?dI!IsI#?I!2I$@A@T  I%@GI&@G"I'? pI(? I'I)?dI(IcaI*?I(I+?@I*I,?dI+IsI-?I+2I.?I*I/?dI.IsI0?I.0I1@A@Tn- I2@GI3@G"I4? pI5? I4I6?dI5VabI7?I5I8?@I7I9?dI8VsI:?I80I;?I7I@A@Tp I?@GI@@G"IA? pIB? IAIC?dIBVbcID?IBIE?@IDIF?dIEVsIG?IE1IH?IDII?dIHVsIJ?IH2IK@A@T5 IL@GIM@G"IN? pIO? INIP?dIOVcaIQ?IOIR?@IQIS?dIRVsIT?IR2IU?IQIV?dIUVsIW?IU0IX@A@T4 IY@GIZ@G"I[? pI\? I[I]?dI\IaI^?I\I_?dI^IsI`?I^0Ia@A@T8eK Ib@GIc@G"Id? pIe? IdIf?dIeIbIg?IeIh?dIgIsIi?Ig1Ij@A@Thz Ik@GIl@G"Im? pIn? ImIo?dInIcIp?InIq?dIpIsIr?Ip2Is@A@T It@GIu@G"Iv? pIw? IvIx?dIwVaIy?IwIz?dIyVsI{?Iy0I|@A@T  I}@GI~@G"I? pI? II?dIVbI?II?dIVsI?I1I@A@TL. I@GI@G"I? pI? II?dIVcI?II?dIVsI?I2I@A@TXt I@GI@G"I? pI? II?dIIresI?II?p@II?II?dIAaI?IIsI?I0I@A@T I@GI@G"I? pI?II?dIIresI?II?+@I@WI?II@A@T8'( I@GI@G"I? pI? II?dImaI?II?@II?dIImI?pII?II?@II?p@II?IVaI?II?dIIaI?II?p@II?II?dIIaI?II?dIk0I?IIresI?II?dIIaI?II?dIImI?pII?IZL1I@A@T-( I@GI@G"I? pI?II?dImaI?II?+@I@WI?II@A@T@$50 ͠I@GI@G"I? pI?II?@II?dI rect2polarI?pII?IVsI?II?+@I@WI?II@A@T7x(h I@GI@G"I? pI? II?dImbI?II?@II?dIImI?pII?II?@II?dIVbI?II?dIIbI?II?p@II?II?dIIbI?II?dIk0I?IIresI?II?dIIbI?II?dIImI?pII?IZL1I@A@T\mh I@GI@G"I? pI?II?dImbI?II?+@I@WI?II@A@T@ ͠I@GI@G"I? pI?II?@IJ?dI rect2polarJ?pIJ?JIsJ?IJ?+@J@WJ?JJ@A@Tw' J@GJ@G"J ? pJ ? J J ?dJ mcJ ?J J ?@J J?dJ ImJ?pJ J?JJ?@JJ?dJVcJ?JJ?dJIcJ?JJ?p@JJ?JJ?dJIcJ?JJ?dJk0J?JIresJ?JJ?dJIcJ?J J?dJImJ ?pJJ!?J ZL1J"@A@T J#@GJ$@G"J%? pJ&?J%J'?dJ&mcJ(?J&J)?+@J(@WJ*?J(J+@A@T. J,@GJ-@G"J.? pJ/? 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