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Wall Oct 14, 1999 ChrPropMap6_#k RangeElem;# ChrPropData7 RangeData<hArial;7;7hArial;7;7hArial;7;7nArial; 7!;"7nArial#;$7!%; &7nArial#% ParPropMap8__ k';$( ParPropData9@V);*9@V'+;,9@V)-;.9@V+/;09@V-1;29@V/3; 49@V133EmbedMap05;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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Symmetrical Component Conversions6&@N;&@O7@K}8&@P;&@Q9@V0@R;.&@S;&@T/@NormalArial @U*@TX+?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$'50@f@G@g@G"@htree ? p@i? @h@j?d@ih@k?@i1@l*@T8#380 y@m@G@n@G"\\\-h = scale vactor68@o;@p9@V0@q;.@r;@s/@NormalArial @t@A@TB@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@*@TSws` 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@T(, @@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@T3~ 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@T093 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@TVC 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@TD A@GA@G"A? pA? AA?dAAbA?AA?p@AA?AA?tA1A?A3A?pAA?0AA?0AAA?0AAA?0AAA?0AAA?0AAA?0AAA?0AAA?0AAA?@AA?AA?dAaA?A2A?AaA?A1A?A1A?A1A?A1A?AaA?AA?dAaA?A2A?A1A*@T A@GA@G"-% 1.2.2 Transmission line calculations6%A;%A7A}8%A;%A9@V0A;.%A;%A/@NormalArial A*@T _ A@GA@G"WWW-( 1.2.1.1 Balanced line parameter matrix6&(A;A7AA;&A7A}AAA8(A;(A9@V0A;.(A;(A/@NormalArial A*@T#v30 ߄A@GA@G"fff-VT and CT Ratios68A;A9@V0A;.A;A/@NormalArial A@A@T$50 A@GA@G"A? pA? AA?dAVTRA?A3500A@A@T$50 A@GA@G"A? pA? AA?dACTRA?A320A@A@T(#oH>8 A@GA@G"A? pA? AA?dALLA?AA?tA1A?AA?dACTRA?AVTRA@A@TCkH A@GA@G"B? pB? BB?dBAcB?BB?p@BB?BB?tB1B?B3B?pBB ?0BB ?0AB B ?0AB B ?0AB B ?0AB B?0AB B?0ABB?0ABB?0ABB?@BB?B1B?B1B?B1B?BaB?B B?dBaB?B2B?B 1B?B B?dBaB?B2B?B aB?B 1B @A@TL|]%X B!@GB"@G"B#? pB$? B#B%?dB$ZL1B&?B$B'?p@B&B(?B'B)?tB(10B*?B(110iB+?B&LLB,@A@TL]X B-@GB.@G"B/? pB0? B/B1?dB0ZL0B2?pB0B3?B2B4?tB33B5?B3ZL1B6@A@Tt2 B7@GB8@G"B9? pB:? B9B;?dB:ZLabcB?pB<B?? B>B@?dB?ZL0BA?B?ZL1BB@A@T01 BC@GBD@G"BE? pBF?BEBG?dBFZLabcBH?BFBI?+@BHSerial_DisplayNodeWBJ?BHBK*@T BL@GBM@G"-. 1.2.2.2 Balanced line parameter computations6.BN;.BO7BK}8.BP;.BQ9@V0BR;..BS;.BT/@NormalArial BU@A@T1 BV@GBW@G"BX? pBY? BXBZ?dBYZL012B[?BYB\?dB[ Zabc_2_Z012B]?pB[B^?B]ZLabcB_@A@Tb,%  B`@GBa@G"Bb? pBc? BbBd?dBcZL0Be?BcBf?dBeZL012Bg? BeBh?tBg0Bi?Bg0Bj@A@T?C@( Bk@GBl@G"Bm? pBn?BmBo?dBnZL012Bp?BnBq?+@Bp@WBr?Bp2I0`Bs@A@T4bL%@ Bt@GBu@G"Bv? pBw? BvBx?dBwZL1By?BwBz?dByZL012B{? ByB|?tB{1B}?B{1B~*@T[3{h B@GB@G"++ + -$ 1.2.2.3 Set maximum torque angle 6# $B; B7B~}B;B7B~}BB;B7B~}BBB8$B;$B9@V0B;.$B;$B/@NormalArial B@A@T|p6 B@GB@G"B? pB? BB?dBMTAB?BB?dBargB?pBB?BZL1B@A@T|7B@GB@G"B? pB?BB?dBMTAB?BB?+@B@WB?BdegB*@To B@GB@G"ggg-* 1.2.2.4 Asymmetrical compensation factor6*B;*B7B}8*B;*B9@V0B;.*B;*B/@NormalArial B@A@Ts, B@GB@G"B? pB? BB?dBk0B?BB?@BB?dBZL0B?BZL1B?BB?tB3B?BZL1B@A@T  B@GB@G"B? pB?BB?dBk0B?BB?+@B@WB?BB*@T[  B@GB@G"ASS-( 1.2.3 Default fault impedance matrices6(B;(B7B}8(B;(B9@V0B;.(B;(B/@NormalArial B@A@Tg1@ B@GB@G"B? pB? BB?dBZffB?pBB?0BB?0ABB?0ABB?0ABB?0ABB?0ABB?0ABB?0ABB?0ABB?@BB?BB?tB10B?B6B?B0B?B0B?B0B?BB?tB10B?B6B?B0B?B0B?B0B?BB?tB10B?B6B*@TF B@GB@G"A>>-$ 1.2.4 S voltage source impedance 6$B;$B7B}8$B;$B9@V0B;.$B;$B/@NormalArial B*@T0 B@GB@G"  -@zThe S end source has infinite zero zequence impedance so no zero sequence current can be supplied by the source generator.6z8zB;zB9@V0B;.zB;zB/@NormalArial B*@T B@GB@G"-Zero sequence addmitance68B;B9@V0C;.C;C/@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!?dC Zss1C"?pC C#?C"C$?tC#1C%?C#6iC&@A@T  C'@GC(@G"C)? pC*? C)C+?dC*Zss2C,?pC*C-?C,C.?tC-1C/?C-6iC0@A@TDUFP C1@GC2@G"C3? pC4? C3C5?dC4Zss012C6?C4C7?tC60.1C8?C6ZL012C9@A@T.kPC:@GC;@G"C?dC=Zss012C??C=C@?+@C?@WCA?C?CB@A@T4 CC@GCD@G"CE? pCF? CECG?dCFZssCH?CFCI?dCH Z012_2_ZabcCJ?pCHCK?CJZss012CL@A@T CM@GCN@G"CO? pCP?COCQ?dCPZssCR?CPCS?+@CR@WCT?CRCU*@TF CV@GCW@G"A>>-$ 1.2.5 R voltage source impedance 6$CX;$CY7CU}8$CZ;$C[9@V0C\;.$C];$C^/@NormalArial C_*@T% C`@GCa@G"9-@VThe R end source has zero sequence impedance equal to the positive sequence impedance.6V8VCb;VCc9@V0Cd;.VCe;VCf/@NormalArial Cg@A@T<NM0H Ch@GCi@G"Cj? pCk? CjCl?dCkZrrCm?CkZssCn@A@TD/UP Co@GCp@G"Cq? pCr? CqCs?dCrZrr012Ct?CrCu?dCt Zabc_2_Z012Cv?pCtCw?CvZrrCx@A@T~ Cy@GCz@G"C{? pC|?C{C}?p@C|C~?C}ZrrC?C|C?+@C@WC?CC@A@T  C@GC@G"C? pC?CC?dCZrr012C?CC?+@C@WC?CC@A@T& c H  C@GC@G"C? pC?CC?dCZss012C?CC?+@C@WC?CC@A@Tt  C@GC@G"C? pC? CC?dCZs2C?CC?dCZss012C? CC?tC2C?C2C@A@Tt X   C@GC@G"C? pC? CC?dCZr2C?CC?dCZrr012C? CC?tC2C?C2C*@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"vvv-Power system angle68C;C9@V0C;.C;C/@NormalArial C*@Tp 5K p(  C@GC@G"00-@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 4 RE <@  C@GC@G"C? pC? CC?dCangC?C45C@A@TP3 Z gH  C@GC@G"C? pC? CC?dCVgC?CC?tC120C?{CC?C3C*@TPc s Pp  ߄C@GC@G"-Power angle shift operator68C;C9@V0C;.C;C/@NormalArial C*@T8{ 8  ߄C@GC@G"fff-VT and CT Ratios68C;C9@V0C;.C;C/@NormalArial C@A@T@  N  C@GC@G"C? pC? CD?dC\dD?CD?@DD?dDcosD?pDD?DD?@DD?dD\pD?DangD ?D180D ?5DD ?@D D ?dD sinD ?pD D?D D?@DD?dD\pD?DangD?D180D?D 1iD@A@T0 s Q  D@GD@G"D? pD? DD?dDVTRD?D3500D@A@T  D@GD@G"D? pD? DD ?dDCTRD!?D320D"*@T   D#@GD$@G"- 1.3.2 S end voltage source 6D%;D&7D"}8D';D(9@V0D);.D*;D+/@NormalArial D,@A@T@  U  D-@GD.@G"D/? pD0? D/D1?dD0EsD2?pD0D3?0D2D4?0AD3D5?0AD4D6?@D5D7?D5D8?dD7VgD9?D7aD:?D4D;?dD:VgD?D<2D??D3VgD@*@T+ ; 8  DA@GDB@G"- 1.3.3 R end voltage source 6DC;DD7D@}8DE;DF9@V0DG;.DH;DI/@NormalArial DJ@A@Th. k P DK@GDL@G"DM? pDN?DMDO?@DNDP?dDOAaDQ?DOEsDR?DNDS?+@DR@WDT?DRDU@A@T@I Sp  DV@GDW@G"DX? pDY? DXDZ?dDYErD[?pDYD\?0D[D]?0AD\D^?0AD]D_?@D^D`?D^Da?@D`Db?dDaVgDc?Da\dDd?D`aDe?D]Df?@DeDg?dDfVgDh?Df\dDi?DeDj?dDiaDk?Di2Dl?D\Dm?dDlVgDn?Dl\dDo*@T r   Dp@GDq@G"bbb-1.4 Subroutines6Dr;Ds7Do}8Dt;Du9@V0Dv;.Dw;Dx/@NormalArial Dy*@T    Dz@GD{@G"- 1.4.1 System Impedance matrix 6D|;D}7Dy}8D~;D9@V0D;.D;D/@NormalArial D*@T0 > 0  D@GD@G"<<-B 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 Zr: R end voltage source Impedance matrix1 ZL: Total length line impedance matrix1 Zff: Forward fault impedance matrix1 Zfr: Reverse fault impedance matrix1 mf: Percent of line length to forward2 mr: Percent of line length to reverse fault2 Notes: 1. [3X3] matrix of complex values 2. Scalar in range 0.0001 to 0.99996D;D7DD;D7DyDD;D7DDD;D7D_DD;-D7DDD;D7D_DD;(D7DDD;D7D_DD;%D7DDD;D7D_DD;$D7DDD;D7D_DD;&D7DDD;D7D_DD;,D7DDD;D7D_DD;ND7DDDD8#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@VDD;D9@VDD;"D9@VDD;#D9@VDDD0D;.D;D/@NormalArial D*@T Z   D@GD@G"JJJ-& 1.4.1.1 Impedance matrix description6&D;&D7D}8&D;&D9@V0D;.&D;&D/@NormalArial D*@T a+ (  D@GD@G"III-+ 1.4.1.2 System Impedance matrix subroutine6+D;+D7D}8+D;+D9@V0D;.+D;+D/@NormalArial D@A@T < P  D@GD@G"D? pD? DD?@DD?dDZsystemD?pDD? DD? @DD? @DD? @DD?dDZssD?DZrrD?DZLD?DZffD?DmD?DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DD?@DE?@DE?@EE?@EE?@EE?@EE?@EE?dEY11E?EE?@EE ?dEZssE ?KEE ?E 1E ?EE ?p@E E?E E?dEmE?EZLE?KE E?E1E?EE?dEY12E?KEE?EE?p@EE?EE?dEmE?EZLE?KEE?E1E?EE?dEY13E?EYnullE ?EE!?dE Y21E"?E Y12E#?EE$?dE#Y22E%?E#E&?@E%E'?@E&E(?p@E'E)?E(E*?dE)mE+?E)ZLE,?KE'E-?E,1E.?E&E/?p@E.E0?E/E1?p@E0E2?E1E3?tE21E4?E2mE5?E0ZLE6?KE.E7?E61E8?E%E9?dE8ZffE:?KE8E;?E:1E?KE<E??E>E@?p@E?EA?E@EB?p@EAEC?EBED?dEC1EE?ECmEF?EAZLEG?KE?EH?EG1EI?DEJ?dEIY31EK?EIY13EL?DEM?dELY32EN?ELY23EO?DEP?dEOY33EQ?EOER?@EQES?p@ERET?ESEU?p@ETEV?EUEW?dEV1EX?EVmEY?ETZLEZ?KERE[?EZ1E\?EQE]?dE\ZrrE^?KE\E_?E^1E`?DEa?dE`Y1Eb?E`Ec?dEbstackEd?pEbEe? EdEf?dEeY11Eg?EeY21Eh?DEi?dEhY1Ej?EhEk?dEjstackEl?pEjEm? ElEn?dEmY1Eo?EmY31Ep?DEq?dEpY2Er?EpEs?dErstackEt?pErEu? EtEv?dEuY12Ew?EuY22Ex?DEy?dExY2Ez?ExE{?dEzstackE|?pEzE}? E|E~?dE}Y2E?E}Y32E?DE?dEY3E?EE?dEstackE?pEE? EE?dEY13E?EY23E?DE?dEY3E?EE?dEstackE?pEE? EE?dEY3E?EY33E?DE?dEYE?EE?dEaugmentE?pEE? EE?dEY1E?EY2E?DE?dEYE?EE?dEaugmentE?pEE? EE?dEYE?EY3E?CDE?EE?dEYE?KEE?E1E*@TS.c` E@GE@G"-# 1.4.2 Compute system node voltages6#E;#E7E}8#E;#E9@V0E;.#E;#E/@NormalArial E*@TkKx E@GE@G";;l;l-B4 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 mf: Percent of line length to forward4 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 4E;E7EE; E7EyEE;E7EEE;E7E_EE;#E7EEE;E7E_EE;E7EEE;E7E_EE;+E7EEE;E7E_EE;-E7EEE;E7E_EE;(E7EEE;E7E_EE;%E7EEE;E7E_EE;$E7EEE;E7E_EE;&E7EEE;E7E@ ArialEE;,E7EEE;E7E_EE;6E7EEE;E7E_EE;_E7EEEE8#4E;"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@VEF;F9@VEF;F9@VFF;0F9@VFF;F9@VFF;"F 9@VFF ;#F 9@VFF F 0F ;.4F ;4F/@NormalArial F@A@T F@GF@G"F? pF? FF?@FF?dFSolve_Node_VoltagesF?pFF? FF? @FF? @FF? @FF? @FF? @FF?dFEsF?FErF?FZssF ?FZrrF!?FZLF"?FZffF#?FmF$?FF%?@F$F&?@F%F'?@F&F(?@F'F)?@F(F*?@F)F+?dF*ZF,?F*F-?dF,ZsystemF.?pF,F/? F.F0? @F/F1? @F0F2? @F1F3?dF2ZssF4?F2ZrrF5?F1ZLF6?F0ZffF7?F/mF8?F)F9?dF8NullSrcF:?pF8F;?0F:F?@F=F??F=0F@?F<0FA?F;0FB?F(FC?dFBIgenFD?FBFE?@FDFF?dFEZssFG?KFEFH?FG1FI?FDEsFJ?F'FK?dFJIgenFL?FJFM?dFLstackFN?pFLFO? FNFP?dFOIgenFQ?FONullSrcFR?F&FS?dFRIgenFT?FRFU?dFTstackFV?pFTFW? FVFX?dFWIgenFY?pFWFZ?FYF[?@FZF\?dF[ZrrF]?KF[F^?F]1F_?FZErF`?F%Fa?dF`VFb?F`Fc?dFbZFd?FbIgenFe?CF$Ff?FeVFg*@T Fh@GFi@G"- 1.4.3 Compute relay currents6Fj;Fk7Fg}8Fl;Fm9@V0Fn;.Fo;Fp/@NormalArial Fq*@TC Fr@GFs@G";;(;(-A Solve_currents Definitions Output: Ib: Branch currents1 IS - Send relay current IR - R end relay currents 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. 1X6 Column vector = [IS : IR]T 2. [1X12] column vector = [V1 : V2 : V3 : V4]T 3. 3X3 matrix of complex values 4. Scalar in range 0.0001 to 0.99996]Ft;Fu7FqFv;Fw7FqyFtFx;Fy7FqFvFz;F{7Fq@ ArialFxF|;xF}7FqFzF~;F7Fq_F|F;(F7FqF~F;F7Fq_FF;&F7FqFF;F7Fq@ ArialFF;)F7FqFF;F7Fq_FF;0F7FqFF;F7Fq_FF;EF7FqFFFv8#F;F9@VF;F9@VFF;F9@VFF;F9@VFF;F9@VFF;F9@VFF;F9@VFF;$F9@VFF;F9@VFF;)F9@VFF;'F9@VFF;F9@VFF;F9@VFF;$F9@VFF;0F9@VFF; F9@VFF;#F9@VFFF0F;.F;F/@NormalArial F@A@T$m F@GF@G"F? pF? FF?@FF?dFSolve_currentsF?pFF? FF? @FF?dFVF?FZLF?FmF?FF?@FF?@FF?@FF?@FF?dFIsF?FF?@FF?p@FF?FF?dFmF?FZLF?KFF?F1F?pFF?FF?@FF?dF submatrixF?pFF? FF? @FF? @FF? @FF?dFVF?F0F?F2F?F0F?F0F?FF?dF submatrixF?pFF? FF? @FF? @FF? @FF?dFVF?F3F?F5F?F0F?F0F?FF?dFIrF?FF?@FF?p@FF?FF?p@FF?FF?tF1F?FmF?FZLF?KFF?F1F?pFF?FF?@FF?dF submatrixF?pFF? FF? @FG? @FG? @GG?dGVG?G6G?G8G?F0G?F0G?FG?dG submatrixG ?pGG ? G G ? @G G ? @G G ? @G G?dG VG?G 3G?G 5G?G 0G?G 0G?FG?dGIbG?GIsG?FG?dGIbG?GG?dGstackG?pGG? GG?dGIbG?GIrG?CFG?GIbG *@T$ G!@GG"@G"A-& 1.4.4 Rectangular to polar conversion6&G#;&G$7G }8&G%;&G&9@V0G';.&G(;&G)/@NormalArial G*@A@T-W G+@GG,@G"G-? pG.? G-G/?@G.G0?dG/ rect2polarG1?pG/G2?G1RG3?G.G4?@G3G5?@G4G6?@G5G7?@G6G8?@G7G9?@G8G:?dG9mG;?{G9G?G<iG??G8G@?dG?\aGA?G?GB?@GAGC?dGBargGD?pGBGE?GDGF?dGERGG?GEiGH?GAGI?tGH180GJ?GH\pGK?G7GL?dGKpGM?pGKGN?0GMGO?0AGNGP?@GOGQ?GO\aGR?GNmGS?IG6GT?@GSGU?dGTPolGV?GTpGW?)GSGX?dGWiGY?GW1GZ?IG5G[?@GZG\?dG[PolG]?G[G^?dG]stackG_?pG]G`? G_Ga?dG`PolGb?G`pGc?(GZGd?dGciGe?Gc0Gf?G4Gg?dGfiGh?GfGi?tGh0Gj?Gh2Gk?CG3Gl?GkPolGm*@T0>k0 Gn@GGo@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*Gp;*Gq7GmyGr;Gs7GmGpGt;Gu7GmyGrGv;Gw7GmyGtGx;Gy7Gm@ ArialGvGz;G{7GmGxG|;!G}7GmyGzG~;G7Gm@ ArialG|G;G7GmG~G;G7GmyGG;G7GmGG;G7GmyGG;G7GmGG;#G7GmyGGGp8#G;+G9@VG;G9@VGG;G9@VGG;#G9@VGG;G9@VGG;G9@VGG;G9@VGG;#G9@VGGG0G;.G;G/@NormalArial G*@TE G@GG@G"A==-21.6 Calculate faulted system voltages and currents62G;2G7G}82G;2G9@V0G;.2G;2G/@NormalArial G*@T9; G@GG@G"))p)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.68G;G9@V0G;.G;G/@NormalArial G@A@TT-e` G@GG@G"G? pG? GG?dGrG?G0.8G*@T8S}c8` yG@GG@G"EEE- Relay reach6 8 G; G9@V0G;. G; G/@NormalArial G*@T{5 G@GG@G"--p-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|jG;|G7GG;G7G@ ArialGG;G7G` ArialGG;G7G` ArialGGG8jG;jG9@V0G;.jG;jG/@NormalArial G@TxxG@GG@G"HHࡱ>    !"Root EntryFJ>1@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?? Y@-1,,J/T  hTJbOSS0{Gz?@CPjV]uVbUUO OS? T666 NP U    UvPaC G#G#G#G#G#G#xG &#O`$$!N=4!>7i>}p'0U2?E! 67gjP>603206&0B!4?6@27Tg2k=\- g2 VT @9ܯ6L^pu )5,2?Op??ZX F&m0#P@w?l_?VCG MO_N9{OOOOOo2qG`?FoXf.Xf RrjrjrgF_ _) ]__qgaopsoon# h0T_o?u5e%wv4R#|q@"];@ B `U ;@ !%U)15UC@=AUIMQUUpa%@U i!m"q#U$ %}&' ~ yJB Ώ}h1 !3E ~P ~` #5~ w~p  %(~ gy(~ 8| YkX?DxjtCU&KPJ5|ώ } ]oPm3Jߑ~v  _q(~ް  ~ Oas~f ~ ?Qcu(~w ~w/ASe~w~w/1/Z`aO贁Nk?2A&& LT /////f/ 0e?)2/?A?S?e?w?Q? 2!E?)2????O/??4_OqOZa(OOG7dOK\ @R_XNa\+z5 c(_tavwTigPa<Vb/'2rR9p=qGfq뒱Дg1Sj`aPV?~ovU03b0f[rgG !______6~fT q ij-d|oyo$ggSBeiud4oFjSkihJooo 7@R(opooe#!3EWroo/ Ʉ-ӏ@ -h$K]o{۟#>GYkf%ϯczP'9K&@B)ͿXV:Uj%øOaXp].ϑ3RJṇU4\DaӼOfX) 'ÿ ϒɟP&:A,A@[7cr{ύϫ`F hTA@* ?<I?NXfx** <Ebb{b b NeH u w wp&8J\nw QGeneric box with text and connection points. 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&!  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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 M #),W3 )̀ )HD S+)\۫S)H+E,D@@$ ,D@@% <@BT$t'zSI uD$C [x?R! 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"$%I&g'+ (a )i *q +, -*2Aw a IK jy{@4@!?!EE?P 6F F0B?~FzA +  B A @1 }+ l3!UF_M._XYPDYP0YP + @(4._@LOqgnyB)F"M|0A O GPI"OVFUI aIt`g`,g`:g`a i+!o4'2KaگfzAB)m .ZabC :0h??UB?M E+v5w4OwPOkJ~p~OOO̴FSBr$ODOVCW4=vGwF?_)BThWuZcQ]_1Wbgy ayXt ftdc@ko}ooon AC :ހo n;N+=;OBdvu|Oj0CB BFB~sf@Rbv@fLۆDfTfS aTSH a`hoȧ˟ݟBC @8P,!oT"DVhzՎį֯{ BL `AX+=OsͿ}RLۏ#GkLLSX aXϤ 0CS:j|ߎ!OO*OaO sO+|KcO_M___q^1C/_S[___Vv{.oUdo"p4FXoZbcSd85Ң5.@ROO ///.1;_V/Sƀw///Z?/QDh@<3kc90P|3B?T?f?)Sj!?? ??OYd0OBOTOfOdrrNrOOOO__ /.ZaN_Sm/w_;GtLGt_nNy@Ny_H_Ul81?o%o7oy?*baS[omo=oooOoo(DCbbYk}ů/.n#"S9K[[~bb\֏ 0B5b*S W osz۬П&42}^^Cbvmۯ/.76S M_oovvƿp꿀 2DVψ4c1 @Z>Нȋ𗓈&He!u `u `bu `u  " @ MX_u` oWuv Vb5  ]a0BTrp!Z` @z3@ $p2I  H$0}z<>q Cb!(?(ѯ>Ք)a' Ka-!2 aPup/N-b+ nH  .@Rdv 22( ' /AB AO@d1wBVwOv2C3O2CG3J1DaR@R/!/3/y/W/i/u_//±" //R/ ??0?B?T?f?x????? P r0??‚(h0N/or o@pBrVv rs s rws _qhBB+_=_O_a______" __ o(o:oLo^opoooooooo  :-?x"U 0N/ @0BӢVӯv:9:3C9.Bhp3pYk}Տŏѿ"%7(? dĀXŀ{Æ 0@GJ\<^ا˿ݼ܀ $-T1 ąASeIϝϯ .ߩVhzߌߞ߰D0T<_ hp7I"V!hz-DT!ß՟L^p840Im UuD9E8Y NKW/v ЖA"{/E#/0#'*\r*2 ~*2 !]IH#"4FXj|.0t"R//?s7K;!7KM'Asa._v$R{_%"RS!S_0"RcW+S!j?*QrXb`~XbA?S?e?w????o??;? OOI 3R??OQOcOuOOOOOOOO_/(p=P1_C_'#e{;!e{M's$ʦPR鏺%PO0PI)YODoXrI~ooooooooo;);M|,]~~u~~ 2;VJ~_q}evesR"ӠŐd+Ὼ!euҵ"~1}"2πF~]=LJchşן "4=Wi{1Lү,>Pb\А@U\7FҼd+7E["8FcCiϵ3EQ]o߁ߴ 2DVhtb',-&Ҽ d+?%%a">/Fi#I'o*"%/9KQcuM|2Kҵ$)uu&7P:66G15GG3%J\nth0%ToB{%///??84=`=A_;4?F?V9%pi?{?M|A?B}vD$6H?OQOxPSbO6f ٰO$ vbOsc/PFb{s[wcz޳F/OO@O8_ V_h_F___\ ut^X;o!o3oEoWoio{oooyXoo b7Cv'А=WՀO"f!E%K @$6LYPk}\cU^ҏ,>Pbx"J$ ffܚ h/xóLqJIO"f!JSn@ȯpwR #(5G\[¡UXrҿ,~ЍYki 0c2z 2/yŅLqO"f!8J\nߴ@:XX=%]D!5o2?)y^#hq}yPB "< ې ' -8T9 Y0T(@1.[/Nq1//'/; ,  h@ D@$%&'()*+,-0#4@B:$9>{@$?RQdPage-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$()*+,%&'" -01C_  !- %    #  t#Dv@@  !"! ` hl 2@B;u's<D g (5m@(n84$s  RL8TW@{}N&B!< 5D@ wl<O$P 'w,h$9@,O)/`<l2FL W&?w' <(`C*4!G*@Tv yG@GG@G"- Figure 2. Fault matrix diagram.6 8 G; G9@V0G;. G; G/@NormalArial G@A@T(TD G@GG@G"G? pG? GG?dGZaaG?G2G@A@Tx G@GG@G"G? pG? GG?dGZbbG?GG?tG10G?G6G@A@T G@GG@G"G? pG? GG?dGZccG?GG?tG10G?G6G@A@T(aE G@GG@G"G? pG? GG?dGZabG?GG?tG10G?G6G@A@Tx G@GG@G"H? pH? HH?dHZbcH?HH?tH10H?H6H@A@T H@GH@G"H ? pH ? H H ?dH ZacH ?H H ?tH 10H?H 6H@A@T "*w9P H@GH@G"H? pH? HH?dHYffH?pHH?0HH?0AHH?0AHH?0AHH?0AHH?0AHH?0AHH?0AHH?0AHH?@HH ?pHH!?H H"?@H!H#?@H"H$?dH#ZccH%?KH#H&?H%1H'?H"H(?dH'ZacH)?KH'H*?H)1H+?H!H,?dH+ZbcH-?KH+H.?H-1H/?KHH0?H/H1?dH0ZbcH2?KH0H3?H21H4?KHH5?H4H6?dH5ZacH7?KH5H8?H71H9?KHH:?H9H;?dH:ZbcH?pHH??H>H@?@H?HA?@H@HB?dHAZbbHC?KHAHD?HC1HE?H@HF?dHEZabHG?KHEHH?HG1HI?H?HJ?dHIZbcHK?KHIHL?HK1HM?KHHN?HMHO?dHNZabHP?KHNHQ?HP1HR?KHHS?HRHT?dHSZacHU?KHSHV?HU1HW?KHHX?HWHY?dHXZabHZ?KHXH[?HZ1H\?pHH]?H\H^?@H]H_?@H^H`?dH_ZaaHa?KH_Hb?Ha1Hc?H^Hd?dHcZabHe?KHcHf?He1Hg?H]Hh?dHgZacHi?KHgHj?Hi1Hk@A@T(nA" Hl@GHm@G"Hn? pHo? HnHp?dHoZffHq?HoHr?dHqYffHs?KHqHt?Hs1Hu@A@T@0 Hv@GHw@G"Hx? pHy?HxHz?dHyZffH{?HyH|?+@H{@WH}?H{H~@A@TXNp1 H@GH@G"H? pH?HH?dHYffH?HH?+@H@WH?HH*@T H@GH@G"->1.7 Compute relay voltages and currents for the faulted system6>H;H7H}H;:H7H}HHH8>H;>H9@V0H;.>H;>H/@NormalArial H*@T+( yH@GH@G"-Location of forward fault68H;H9@V,0H;.H;H/@NormalArial H@A@T-( H@GH@G"H? pH? HH?dHmH?H0.63H*@T;KH yH@GH@G"-Compute node voltages68H;H9@V0H;.H;H/@NormalArial H@A@TTkeC` H@GH@G"H? pH? HH?dHVnodeH?HH?dHSolve_Node_VoltagesH?pHH? HH? @HH? @HH? @HH? @HH? @HH?dHEsH?HErH?HZssH?HZrrH?HZLabcH?HZffH?HmH@A@T t6 H@GH@G"H? pH? HH?dHVsH?HH?dH submatrixH?pHH? HH? @HH? @HH? @HH?dHVnodeH?H0H?H2H?H0H?H0H@A@T 5 H@GH@G"H? pH? HH?dHVfH?HH?dH submatrixH?pHH? HH? @HH? @HH? @HH?dHVnodeH?H3H?H5H?H0H?H0H@A@Tx< ͠H@GH@G"H? pH?HH?@HH?dH rect2polarH?pHH?HVsH?HH?+@H@WH?HH@A@T 4 H@GH@G"H? pH? HH?dHVrH?HH?dH submatrixH?pHH? HH? @HH? @HH? @HH?dHVnodeH?H6H?H8I?H0I?H0I@A@T nH I@GI@G"I? pI? II?dIVs012I?II ?dIAI ?IVsI @A@T Cv I @GI @G"I? pI? II?dIVsabI?II?@II?dIVsI?I0I?II?dIVsI?I1I@A@Tw I@GI@G"I? pI? II?dIVsbcI?II?@II ?dIVsI!?I1I"?II#?dI"VsI$?I"2I%@A@TSx I&@GI'@G"I(? pI)? I(I*?dI)VscaI+?I)I,?@I+I-?dI,VsI.?I,2I/?I+I0?dI/VsI1?I/0I2@A@Tx4G ͠I3@GI4@G"I5? pI6?I5I7?@I6I8?dI7 rect2polarI9?pI7I:?I9VrI;?I6I@A@T j%F  I?@GI@@G"IA? pIB? IAIC?dIBVr012ID?IBIE?dIDAIF?IDVrIG@A@Tx;[@H ͠IH@GII@G"IJ? pIK?IJIL?@IKIM?dIL rect2polarIN?pILIO?INVfIP?IKIQ?+@IP@WIR?IPIS*@Tcsp IT@GIU@G"- 1.7.1 Extract Relay Currents6IV;IW7IS}IX;IY7IS}IVIXIV8IZ;I[9@V0I\;.I];I^/@NormalArial I_@A@T|2 I`@GIa@G"Ib? pIc?IbId?dIcMTAIe?IcIf?+@Ie@WIg?IedegIh@A@T  Ii@GIj@G"Ik? pIl? IkIm?dIlIbrIn?IlIo?dInSolve_currentsIp?pInIq? IpIr? @IqIs?dIrVnodeIt?IrZLabcIu?IqmIv@A@T! Iw@GIx@G"Iy? pIz? IyI{?dIzIsI|?IzI}?dI| submatrixI~?pI|I? I~I? @II? @II? @II?dIIbrI?I0I?I2I?I0I?I0I@A@T " I@GI@G"I? pI? II?dIIrI?II?dI submatrixI?pII? II? @II? @II? @II?dIIbrI?I3I?I5I?I0I?I0I@A@T`'# I@GI@G"I? pI? II?dIIsabI?II?@II?dIIsI?I0I?II?dIIsI?I1I@A@Tpt I@GI@G"I? pI? II?dIIsbcI?II?@II?dIIsI?I1I?II?dIIsI?I2I@A@T/s I@GI@G"I? pI? II?dIIscaI?II?@II?dIIsI?I2I?II?dIIsI?I0I@A@TB( I@GI@G"I? pI? II?dIIsaI?II?dIIsI?I0I@A@TXq I@GI@G"I? pI? II?dIIsbI?II?dIIsI?I1I@A@T I@GI@G"I? pI? II?dIIscI?II?dIIsI?I2I@A@Th ͠I@GI@G"I? pI?II?@II?dI rect2polarI?pII?IIsI?II?+@I@WI?II@A@T R2 I@GI@G"I? pI? II?dIIr012I?II?dIAI?IIrI@A@Th  I@GI@G"I? pI? II?dIIs012I?II?dIAI?IIsI@A@T,M=!8 I@GI@G"I? pI? II?dIIfJ?IJ?dJIsJ?JIrJ@A@Th. kP ͠J@GJ@G"J? pJ?JJ?@JJ ?dJ rect2polarJ ?pJJ ?J IrJ ?JJ ?+@J @WJ?J J@A@TLb]:X J@GJ@G"J? pJ? JJ?dJIsa012J?JJ?dJAaJ?JIsJ@A@TL]XN J@GJ@G"J? pJ? JJ?dJIsb012J?JJ?dJAbJ ?JIsJ!@A@TLR]*XP J"@GJ#@G"J$? pJ%? J$J&?dJ%Isc012J'?J%J(?dJ'AcJ)?J'IsJ*@A@Tnx ͠J+@GJ,@G"J-? pJ.?J-J/?@J.J0?dJ/ rect2polarJ1?pJ/J2?J1Isa012J3?J.J4?+@J3@WJ5?J3J6@A@ThvF ͠J7@GJ8@G"J9? pJ:?J9J;?@J:J?J=IfJ??J:J@?+@J?@WJA?J?JB@A@TycJC@GJD@G"JE? pJF?JEJG?@JFJH?dJG rect2polarJI?pJGJJ?JIIsb012JK?JFJL?+@JK@WJM?JKJN@A@TX* JO@GJP@G"JQ? pJR?JQJS?@JRJT?dJS rect2polarJU?pJSJV?JUIsc012JW?JRJX?+@JW@WJY?JWJZ@A@T$5*0= ͠J[@GJ\@G"J]? pJ^?J]J_?dJ^VsabJ`?J^Ja?+@J`@WJb?J`Jc@A@T$#50 ͠Jd@GJe@G"Jf? pJg?JfJh?dJgVsbcJi?JgJj?+@Ji@WJk?JiJl@A@TX$5y0 ͠Jm@GJn@G"Jo? pJp?JoJq?dJpVscaJr?JpJs?+@Jr@WJt?JrJu@A@TDzU&P? ͠Jv@GJw@G"Jx? pJy?JxJz?dJyIsabJ{?JyJ|?+@J{@WJ}?J{J~@A@TDUP ͠J@GJ@G"J? pJ?JJ?dJIsbcJ?JJ?+@J@WJ?JJ@A@TXDUuP ͠J@GJ@G"J? pJ?JJ?dJIscaJ?JJ?+@J@WJ?JJ@A@Tg%x J@GJ@G"J? pJ? JJ?dJRabJ?JJ?@JJ?dJImJ?pJJ?JJ?dJVsabJ?JJ?p@JJ?JJ?dJIsabJ?JMTAJ?JJ?dJImJ?pJJ?JJ?p@JJ?JJ?@JJ?tJ1J?{JJ?J3J?JJ?dJIsc012J?J2J?JJ?p@JJ?JJ?dJIsabJ?JMTAJ@A@T,y J@GJ@G"J? pJ?JJ?{@JJ?JRabJ?JJ?+@J@WJ?JJ@A@T+| J@GJ@G"J? pJ? JJ?dJRab1J?JJ?@JJ?dJImJ?pJJ?JJ?dJVsabJ?JJ?p@JJ?JJ?dJIsabJ?JMTAJ?JJ?dJImJ?pJJ?JJ?p@JJ?JJ?@JJ?@JJ?tJ1J?JJ?dJaJ?J2J?{JJ?J3J?JJ?dJIsa012J?J2J?JJ?p@JJ?JJ?dJIsabJ?JMTAJ@A@T* J@GJ@G"J? pJ?JJ?{@JJ?JRab1J?JJ?+@J@WJ?JJ@A@T#%q J@GJ@G"J? pJ? JJ?dJRbcJ?JJ?@JJ?dJImJ?pJJ?JJ?dJVsbcJ?JJ?p@JJ?JJ?dJIsbcJ?JMTAJ?JK?dJImK?pJK?KK?p@KK?KK?@KK?tK1K?{KK?K3K ?KK ?dK Isa012K ?K 2K ?KK ?p@K K?K K?dKIsbcK?KMTAK@A@T  K@GK@G"K? pK?KK?{@KK?KRbcK?KK?+@K@WK?KK@A@T7k$P K@GK@G"K? pK? KK ?dKRcaK!?KK"?@K!K#?dK"ImK$?pK"K%?K$K&?dK%VscaK'?K%K(?p@K'K)?K(K*?dK)IscaK+?K)MTAK,?K!K-?dK,ImK.?pK,K/?K.K0?p@K/K1?K0K2?@K1K3?tK21K4?{K2K5?K43K6?K1K7?dK6Isb012K8?K62K9?K/K:?p@K9K;?K:K@A@TT e` K?@GK@@G"KA? pKB?KAKC?{@KBKD?KCRcaKE?KBKF?+@KE@WKG?KEKH@A@T* KI@GKJ@G"KK? pKL? 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L L ?dL RcgL ?L L?@L L?dLImL?pLL?LL?@LL?dLVsL?L2L?pLL?LL?p@LL?LL?dLZL1L?pLL?LL?@LL?dLIsL?L2L?LL ?dLk0L!?LL"?dL!Isa012L#?L!0L$?L L%?dL$ImL&?pL$L'?L&L(?p@L'L)?L(L*?p@L)L+?L*L,?tL+3L-?L+2L.?pL)L/?L.L0?@L/L1?dL0Isc012L2?L00L3?L/L4?dL3Isc012L5?L32L6?pL'L7?L6L8?p@L7L9?L8L:?dL9ZL1L;?pL9L?dL=IsL??L=2L@?Lx LX@GLY@G"LZ? pL[? LZL\?dL[Ir2L]?L[L^?dL]Ir012L_?L]2L`@A@Tl } x צLa@GLb@G"Lc? pLd?LcLe?dLdIr2Lf?LdLg?+@Lf@WLh?LfLi@A@Tl < x Lj@GLk@G"Ll? pLm? LlLn?dLmIs2Lo?LmLp?dLoIs012Lq?Lo2Lr@A@TXl } {x צLs@GLt@G"Lu? pLv?LuLw?{@LvLx?LwIs2Ly?LvLz?+@Ly@WL{?LyL|@A@T0 " L}@GL~@G"L? pL? LL?@LL?dLlocateL?pLL? 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