.MCAD 308000000 \  docDocumentMmcObject[  dim_formatTmasslengthtimecharge temperature luminosity substanceNumericalFormatQdii shpRectV S01mcDocumentObjectState\ mcPageModelK????mcHeaderFooterI@I |P CHeaderFooterJ@{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fnil\fprq15 Arial;}{\f3\fswiss\fprq15 Arial;}} {\colortbl\red0\green0\blue0;} \deflang1033\pard\plain\f3\fs18 \par } @{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fnil\fprq15 Arial;}{\f3\fswiss\fprq15 Arial;}} {\colortbl\red0\green0\blue0;} \deflang1033\pard\qc\plain\f3\fs18 \par } @{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fnil\fprq15 Arial;}{\f3\fswiss\fprq15 Arial;}} {\colortbl\red0\green0\blue0;} \deflang1033\pard\qr\plain\f3\fs18 \par } @J@{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fnil\fprq15 Arial;}{\f3\fswiss Arial;}{\f4\fswiss\fprq15 Arial;}} {\colortbl\red0\green0\blue0;} \deflang1033\pard\plain\f4\fs18 \par } @{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fnil\fprq15 Arial;}{\f3\fswiss Arial;}{\f4\fswiss\fprq15 Arial;}} {\colortbl\red0\green0\blue0;} \deflang1033\pard\qc\plain\f3\fs20 \par } @{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fnil\fprq15 Arial;}{\f3\fswiss Arial;}{\f4\fswiss\fprq15 Arial;}} {\colortbl\red0\green0\blue0;} \deflang1033\pard\qr\plain\f4\fs18 \par } @J@JMbP?MbP? TextState? TextStyle>@ ArialSerial_ParPropDefaultWNormal>@Arial@W Heading 1>@ Arial@W Heading 2>@ Arial@W Heading 3 >@ Arial@W Paragraph >@ Arial@WList >@ Arial@WIndent >@Times New Roman@W Title >@Times New Roman@W Subtitle font_style_listO font_styleP VariablesTimes New Roman@P ConstantsTimes New Roman@P TextArial@P Greek VariablesSymbol@P User 1Arial@P User 2 Courier New@P User 3System@P User 4Script@P User 5Roman@P User 6Modern@P User 7Times New Roman@PSymbolsSymbol@P Current Selection FontArial@P Undefined Font@P HeaderArial@P FooterArial@PRotated Math FontTimes New Roman TextRegion* docRegionGshpBoxU GG CharacterMap-RangeMap;@iTwo Source - One line Powere System for Fault Analysis File Name: L23.mcd Richard W. Wall March 10,2003 ChrPropMap777i RangeElem<7 ChrPropData8 RangeData=hArial<28nArial ParPropMap9$$Ei<$ ParPropData:@W   !"#$%&'()*+,-./0123Root EntryF ֽ8Ole CompObjqOlePres000 FMicrosoft Visio DrawingVISIO 4.0 ShapesVisio.Drawing.69qOh+'08DP\ht B* B*  N    - "-N$%L7" ,;L`t"7Laut`L;, uaL "-- ,"Arial-"System- . -!EsjO- - "-$vv-- %"Arial-- . -!Zse- - "-%LL- -- . -!Zf2I- - "- %]- - "- $!y>!-- - "-% KsK- -- . -!V1- - "->$o]pMr=w/}##/=M]n~}wr~pno]-- - "-J$#dO;)+ <Pdy );OdyydP<+yd-- -- . -!Rs1- - "-%oo]- - "->$ K : *    % - 5 = B G *J :K KJ [G kB y= 5 - %     y k [ K-- - "-J$# w b N ; +  , @ U i }   + ; N b w     } i U @ ,        w-- -- . -!Rr - - "-%K K K- - "-$***-- -- . - !ZL*mfdu- - "-$     -- -- . - ! ZL*(1-mf)d - - "-$     -- -- . -!ZrdQ - -- . - !Vs,Ism- -- . - !Vr,Ir~ - - "- $uuu-- - "-%u- --$)cc))-- -- . -!Isz- - "- $   -- - "-%  - --$$ )$ c c )$ )-- -- . -!Irz* - -- . -!Zf1- - "- % ]=  6 - -- $R ! ># R !-- - "-%*KkK- - "-%K K- - "-% K K- - "-% K}K- -- . -!V2)- -- . -!V3 - -- . -!V4 - - "-N$%}K6! !4ETaj!o6qKo`jtaTE4! t`}K-- -- . -!Eri- - "-$ mm  -- -- . - !ZLs*mrd4- - "-$---- % Arial-- . -!Zt- - "- %-L- VisioDocumentCVisioInformation"SummaryInformation(Visio (TM) Drawing CR uA-d !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%wv4 S"|q@"];@ B `U ;@ !%U)15UC@=AUIMQUUpa%@U i!m"q#U$ %& @~ yJB ʏ}h1 /A~P (~` 1~  s~p !~  cu ~ 4ݿ(| UgX?xjQtCU&KPJ5xϊ} Ykߔm/F{ߍ~r [m~ڰ   (~ K]o~b ~;M_q~ w (~w+=Oa~w~w"/-/Z`aO贁Nk?.A&&HT /////f /0e?%2+?=?O?a?s?Q?2E?%2???? O//?4[OmOZaOOG3`OK\* @ROXNaX+v5 c(_rtavwTicPa<Vb'K2rR9p=qCfq璭Дc1j`aPV?zoU03b0f[*rcG !__@____2~bTqij)dxouogcS Beiqd0oBjOkehJ}ooo3<N$o@lo{oe# /ASn_o+ ń)Ϗ)h$GYk}wן :CUgf%˯_v#5TG&@Bɿ XV6Uf% ôOal]*V/RF.U4 \@abӼKfT) ;qDw@U@;FT L*H}hGTI(@ItA X??IB ?ss)IzbbK- !H!AnZsb ! %Rn   ;Ien]:G+ W C A:Kf 0s@jM?@Q1?@"?@@u # #?P It`: 1e ? t!Ԧ8cY##-"##V: *u`F 3u)9& Y4 %"T -S!w2.x22m0q2w2w222K"'1&*4|0H.2 (I 1,!C U/g/y/"Zp@@ #)&/,K*Jp$f+# ??@/?A?S?e90t0/x2 R0x2R2R* R RRR?J5/40?0A":I Qj~ʹ"?V @@M ?@m@@RUUWO%3_*F'yجjJsOOOOh2 n0|Pt0`bETl3!UPIa`c`0QgKbcgaWoyU&8}IagVozoyppT+ 4)HK!^{P_i%H\B@@ !H}0 /K@/ݕ_h_%| "* #vo*x2yhJCJo\onoofL!c10P!? ! BQ1$Qmb>^`FQoeoo}|}@ȻO[?@H6Yh]x"贁N7xk6ir A{t?@#}]xGz7x:mrU_9Ccp7xirD?@P̱n]]xK~7x],Œ_5a@S`##K'#i"X  օ }QH J? tzZ3%oS`찇CϦ޿~swddŻ?RzR7d1Cq); #Y$^x0\(/:"G/Y/k/}(~Ћ'#$)׭//$$/=0+ΏsMP VZl~>ֶt[@@ /K?@+1r?S!OQɷ?Jp$f12yh!3EW,$x//0/)#/UnFż'8[?@ҿi!贁Nˈe A{t?@ /bxqGzˈ ףp= Q@2ߞh$^ &"rߞh&ڠUy:ߞh_?bc{ߞhʅoϩhCϩhJ e/-Dfcj+O2M¯ԯ:Tl l >>t>=Oas$H FÏ}l&fL21Ќ#J5`U3*<sI[Ϳ/]+snʄmôßՐ ۔B?M%-O?FQ?F YJYJYG/n}`ށz Rri`\ 6P"'0uw>S X~CD2!FNQH@?ߏ~~4C\ Zy@@rqhq\n?<"~S;P=#2_M'v???OՐ"P۔Ab/0P&qSe"4FGPT*cAmGvgp_<͋PP #X/_A_п4?@`@r"rups_PbtU8;$_Z%Ưا?7"$Hn}r~QK~p8 Jy)#ԝVC? LR1CHi D23EWi{ Zr&{OOOO@ _uO/_'اD|/h0qz]So!zG6Sҩ.`iy- J9Aa G?Y?k?}8PƄboo(_1-mf) /"/4/F/G@k![\pR&0:)'t?@_Q1敁^'/& XQ*Ӧ8cYۯu/@38 1?oooy8"0p@ @b>@B'elU f qQ H T~f j/_,:}5O?@oSбGZTGP-DT! ZQ:!0u `u `-@u `u @<0߀@A `**5ҏ~7eč婘jMک}*p(e _jD@B"NH0|HF 5ZDbOT_f^ qp7OŽP4f fx/xacIذ]jè/,)/ܪ/?Tˏ':җ??????OO'O9OKO]Os_Aj-OQOuE__;'y__9_._z^]@ t̐| o. +Eo q_oqo }8Ycvoo -*? rxX.Zl~Bz@@1AL6/bb}?6%craՅ"4وnʄm`(:L^3|4"/XVs,Is#uw>S5GYT5n}@~@@pmK?@)\(3 pqRa\;BӤRRs4/F/X/j/|/h0dB/O///??&:r,IH?Z?l?~??ϵ?@ @@=?@36FdeeOB^ahP߸ DZqBnOOOOPbI[mߑߣpc eWfu~F?Y7"$\?P~c}sWz ¿R ˏݏSk 2?@ 8l@@ !𤳷9o->[N-UhFJK> ?5MoΟ1L=k0{q2Dv}߳ǯ䯜vW\ߢx ߦ=O?_|?a:֎Fj瘰㫿[ӎ;ܼBtgѐ#*  h`n/o$`'Zoll)|oo`r.$ .Pbt ߪ@РX2/6JPn /?/S8Md@P!Ȫ32M#-]Z\n[?'ʖh0dB/#/Rdvk/}/Р>o?8?+=???S?\0ڠẢc!21@K &фMAψOOOٝ1`PrzόϞ%_m__./RDV_Y5e{y?Ïe?^?Do>w0SMsa(\µ򼓥bl' qv(dBT!3`onČ "4 rBTPfx 2h5|Pobih/ݕ?@в?@"ٲߵհ곿ޟ !5tELBY11'F>Pbt󒰪OO__~F)uZ/&pᶤ=8\Qc!p>񇽫Ա η|ްØ՟ 16*U 7˦ٖDLqh|?`rτϖѯZLs*m&h5q5f2E8cQAJ@ǞE28U? SF0D:B7_I_[_Pbtfd_3j>f@Rְu4Y]ڵ؄yj6+u)EYn0E>wH$?.?@?SzW@?@\I?@_.֙?@FrS@lcse?~eX/P-SV@Wn??? OOGv`St?pϨFQol4;F??CbIO[OmOOOOOO_Вߏ[]_qy_V_g_ew_ H'DVh P~9+@mi`Amno~OH4 𮛿+Rk\oo-?EdK]oϥ!P׏S dQƒ` ?iFn߂ N`r*(FXjVtlQ^0>O?@/K?d> "8;WF}fÚ?2yhך +=O7@G=Df"0|ώx%Ϯ8-Z:"'Ȗu;@)HZl3ҋ͐@@ !86Cn7kFJp$#z//+/=/O/7r0?tBu////////??)?;?M0Na?s????;*??? c?>@Fifc;O? 2A%-iO OOOOO1K`?jrO __-_?_Q_c_u_____oo'oo_)o=+Lo^opoW e HxO6Գo1:Vo.,ք);M1̀?y -?Q u=,Ώ٣r  HFh?!C_ɟSOgn 1CUgyӯ-?-P\nvjM?@@u?@<&)ʶ.YY Y/AS[gt0? A{tϙϸ0 &/KB]8iߩ߂ɻOk?@rgڼOqɀ~ a@@?@hF_.|>.).@υ''?@WߧdSֱ`?@DﲰoK`m6S\FXdQƲ?@ /bͷ4D~P4@XBHGE3h>4@,PW?@܀9CqX}~4 :ڼ2@пʅCDΡ` @@LPL~iu @*?䈎IJ/8 'Gɨ/8y'aҟ1_9/8A'/z;rLɋR/8Af '.2]Qk/8/ _Xb[_}X*#_EGXO XOH{OHJCOegH O-/H?ppTppt<̯\$,|,D, ,@d@,@PPLPPjdld4dpttT&4/H.P l Kb"(\?@}¯څㅹBToldbt>!:ދ(uy 擏?uϖPϖG`Ѿ Esiн\v'0uw>SAÖ,D9cQL/P@&;˹Z99::fxѲ#5GYk}  wV?@P!a?` }E|?r)?` .D?~$ű@œ!+F/@]5Da)h2Pbd/V #$Z /&/IC/Š^/{//X0BSU/2PA:/%Z.` 2 ?$#?Ž>?P[?MO&P@@?Ś?!?s/H;SVgHHoHoX[sovGX#;o>XoX_X{t/)DDZE6k9Pf"lF?;)EIbpmfy0£P#3$(S1gff   &! -ݡ2JEQ3]i3u33333%3&'3)*)3+5,A32M3YJ;KRhAn2 cgmPQy¨0QfQ·0Q  !!--9ܢEEQQ]]iiuu))55AAMMYY*kkqq] <SR UG,>E6@h]?Rj#Page-1Black fill_White }uRed Green -Cya@Yellow GMnta3a=y(10% x line3 Long dash1"da%rI9e. X5 7 9 1Gpxlm9mHairqShort Arial cke?redtop leftTim esConnectorUn3_03!) ) ) 3 3U9 9 9 9 U9 9 x9 h9 UX9 G9 49 $9 }9 3u Uu u u u Uu u ru du UUu Gu 9@h)p>/`;2F4ʷ|@?wzA gT;˪ Cd;%*@U~ yA-&Figure 1. System single line diagram.7&&<&'8%n Arial9&(<&):@W1*</&+<&,0@NormalArial -*@Uyqq-&1.1. Symmetrical Component Conversions7&.<&/8-lArial9&0<&1:@W12</&3<&40@NormalArial 5*@Uq> y((-@Ia = 120 degree phase shift operator a2 = 240 degree phase shift operator7'&I6<&785n Arial8<985@ Arial6:<";85n Arial8:69I<</I? T A-1.2 Network impedance matrices7@<@8@lArial9@<@:@W1@</@<@0@NormalArial @*@UppR ߄@@-@KThis matrix is used as a constant for building the system impedance matrix.7K9KA@@dA= Line_LengthA?@@A=25A@@B@U(BbJpH AA@@ pAB@@ AAAC@@dABZLAD@@ABAE@@p@ADAF@@0AEAG@@0AAFAH@@0AAGAI@@0AAHAJ@@0AAIAK@@0AAJAL@@0AAKAM@@0AALAN@@0AAMAO@@@ANAP@@ANAQ@@tAP0.2201AR@@AP0.9608iAS@@AMAT@@tAS0.1175AU@@AS0.4895iAV@@ALAW@@tAV0.1133AX@@AV0.4608iAY@@AKAZ@@tAY0.1175A[@@AY0.4895iA\@@AJA]@@tA\0.2285A^@@A\0.9575iA_@@AIA`@@tA_0.1175Aa@@A_0.4895iAb@@AHAc@@tAb0.1133Ad@@Ab0.4608iAe@@AGAf@@tAe0.1175Ag@@Ae0.4895iAh@@AFAi@@tAh0.2201Aj@@Ah0.9608iAk@@AD Line_LengthAl*@U   F 1-. 1.2.2.2 Balanced line parameter computations7.Am<An8Al}Ao<,Ap8AllArialAmAoAm9.Aq<.Ar:@W1As</.At<.Au0@NormalArial Av@B@U ]E Aw@@ pAx@@ AwAy@@dAxZL012Az@@AxA{@@dAz Zabc_Z012A|@@pAzA}@@A|ZLA~@B@U KB A@@ pA@@ AA@@dAZL0A@@AA@@dAZL012A@@ AA@@tA0A@@A0A@B@U [A@@ pA@@AA@@dAZL012A@@AA@@+@ASerial_DisplayNodeXA@@AA@B@U KC A@@ pA@@ AA@@dAZL1A@@AA@@dAZL012A@@ AA@@tA1A@@A1A*@U/D@-$ 1.2.2.3 Set maximum torque angle 7$A<A8A}A<"A8AlArialAAA9$A<$A:@W1A</$A<$A0@NormalArial A@B@UPXnhA@@ pA@@ AA@@dAMTAA@@AA@@dAargA@@pAA@@AZL1A*@UI-* 1.2.2.4 Asymmetrical compensation factor7*A<A8A}A<(A8AlArialAAA9*A<*A:@W1A</*A<*A0@NormalArial A@B@U >A@@ pA@@ AA@@dAk0A@@AA@@p@AA@@AA@@dAZL0A@@AZL1A@@AA@@tA3A@@AZL1A@B@UmA@@ pA@@AA@@dAk0A@@AA@@+@A@XA@@AA*@UA-( 1.2.3 Default fault impedance matrices7(A<A8A}A<&A8AlArialAAA9(A<(A:@W1A</(A<(A0@NormalArial A@B@Ur=@A@@ pA@@ AA@@dAZffA@@pAA@@0AA@@0AAA@@0AAA@@0AAA@@0AAA@@0AAA@@0AAA@@0AAA@@0AAA@@@AA@@AA@@tA10A@@A8A@@A0A@@A0A@@A0A@@AA@@tA10A@@A8A@@A0A@@A0A@@A0A@@AA@@tA10A@@A8A@B@U0[F3@A@@ pA@@ AA@@dAZfrA@@AZffA*@UA-$ 1.2.4 S voltage source impedance 7$A<A8A}A<"A8AlArialAAA9$A<$A:@W1A</$A<$A0@NormalArial A*@U((-Zero sequence addmitance79A<A:@W1B</B<B0@NormalArial B*@U-Positive sequence addmitance79B<B:@W1B</B<B0@NormalArial B *@U@-Negitive sequence addmitance79B <B :@W1B </B <B0@NormalArial B@B@U8fB@@ pB@@ BB@@dBZss0B@@pBB@@BB@@tB1B@@B6iB@B@U]B@@ pB@@ BB@@dBZss1B@@pBB@@BB@@tB1B@@B6iB@B@UB @@ pB!@@ B B"@@dB!Zss2B#@@pB!B$@@B#B%@@tB$1B&@@B$6iB'@B@U(Lh(B(@@ pB)@@ B(B*@@dB)Zss012B+@@pB)B,@@0B+B-@@0AB,B.@@0AB-B/@@0AB.B0@@0AB/B1@@0AB0B2@@0AB1B3@@0AB2B4@@0AB3B5@@@B4B6@@B4Zss2B7@@B30B8@@B20B9@@B10B:@@B0Zss1B;@@B/0B<@@B.0B=@@B-0B>@@B,Zss0B?@B@U0pUW B@@@ pBA@@ B@BB@@dBAZssBC@@BABD@@dBC Z012_ZabcBE@@pBCBF@@BEZss012BG@B@UXN{X BH@@ pBI@@BHBJ@@dBIZssBK@@BIBL@@+@BK@XBM@@BKBN*@U7 L H A-$ 1.2.6 R voltage source impedance 7$BO<BP8BN}BQ<"BR8BNlArialBOBQBO9$BS<$BT:@W1BU</$BV<$BW0@NormalArial BX*@U[ -k h 9-@VThe R end source has zero sequence impedance equal to the positive sequence impedance.7V9VBY8C:yC;C?<C@8C:C=CA<CB8C:_C?CC<CD8C:CACE<+CF8C:CCCG<CH8C:_CECI<(CJ8C:CGCK<CL8C:_CICM<%CN8C:CKCO<CP8C:_CMCQ<$CR8C:COCS<CT8C:_CQCU<&CV8C:CSCW<CX8C:_CUCY<CZ8C:CWC[<+C\8C:CYC]<C^8C:_C[C]C=9C_<C`:@W1Ca</Cb<Cc0@NormalArial Cd*@U }  b Auu-& 1.4.1.1 Impedance matrix description7&Ce<Cf8Cd}Cg<$Ch8Cdl ArialCeCgCe9&Ci<&Cj:@W1Ck</&Cl<&Cm0@NormalArial Cn*@U  w 00-@LNotes: 1. [3X3] matrix of complex values 2. Scalar in range 0.0001 to 0.99997L9LCo@@dD=Y1D?@@D=D@@@dD?stackDA@@pD?DB@@ DADC@@dDBY11DD@@DBY21DE@@CDF@@dDEY1DG@@DEDH@@dDGstackDI@@pDGDJ@@ DIDK@@dDJY1DL@@DJY31DM@@CDN@@dDMY1DO@@DMDP@@dDOstackDQ@@pDODR@@ DQDS@@dDRY1DT@@DRY41DU@@CDV@@dDUY2DW@@DUDX@@dDWstackDY@@pDWDZ@@ DYD[@@dDZY12D\@@DZY22D]@@CD^@@dD]Y2D_@@D]D`@@dD_stackDa@@pD_Db@@ DaDc@@dDbY2Dd@@DbY32De@@CDf@@dDeY2Dg@@DeDh@@dDgstackDi@@pDgDj@@ DiDk@@dDjY2Dl@@DjY42Dm@@CDn@@dDmY3Do@@DmDp@@dDostackDq@@pDoDr@@ DqDs@@dDrY13Dt@@DrY23Du@@CDv@@dDuY3Dw@@DuDx@@dDwstackDy@@pDwDz@@ DyD{@@dDzY3D|@@DzY33D}@@CD~@@dD}Y3D@@D}D@@dDstackD@@pDD@@ DD@@dDY3D@@DY43D@@CD@@dDY4D@@DD@@dDstackD@@pDD@@ DD@@dDY14D@@DY24D@@CD@@dDY4D@@DD@@dDstackD@@pDD@@ DD@@dDY4D@@DY34D@@CD@@dDY4D@@DD@@dDstackD@@pDD@@ DD@@dDY4D@@DY44D@@CD@@dDYD@@DD@@dDaugmentD@@pDD@@ DD@@dDY1D@@DY2D@@CD@@dDYD@@DD@@dDaugmentD@@pDD@@ DD@@dDYD@@DY3D@@CD@@dDYD@@DD@@dDaugmentD@@pDD@@ DD@@dDYD@@DY4D@@sCD@@DD@@dDYD@@KDD@@D1D*@U(Od(`d Att-# 1.4.2 Compute system node voltages7#D<D8D}D<"D8DlArialDDD9#D<#D:@W1D</#D<#D0@NormalArial D*@U kis x III-A Solve_Node_Voltages Definitions Output: Vn: Vnode voltages1 Input: Es: S end voltage source2 Er: R end voltage source2 Zs: S end voltage source Impedance matrix3 Zr: R end voltage source Impedance matrix3 ZL: Total length line impedance matrix3 Zff: Forward fault impedance matrix3 Zfr: Reverse fault impedance matrix3 mf: Percent of line length to forward4 mr: Percent of line length to reverse fault47 D<D8DD< D8DyDD<D8DDD<D8D_DD<D8DDD< D8DDD<D8DDD<D8D_DD<D8DDD<D8DDD<D8DDD<D8D_DD<+D8DDD<D8D_DD<D8DDD<+D8DDD<D8D_DD<(D8DDD<D8D_DD<%D8DDD<D8D_DD<$D8DDD<D8D_DD<&D8DDD<D8D@ ArialDD<D8DDD<+D8DDD<D8D_DDD9D<D:@W1D</E<E0@NormalArial E*@Uxox( *TT-@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 0.9999754E<4E8EE<E8E_EE<_E8EEEE9E <E :@W,1E </E <E 0@NormalArial E@B@U  E@@ pE@@ EE@@@EE@@dESolve_Node_VoltagesE@@pEE@@ EE@@ @EE@@ @EE@@ @EE@@ @EE@@ @EE@@ @EE@@ @EE@@dEEsE@@EErE@@EZsE@@EZrE @@EZLE!@@EZffE"@@EZfrE#@@EmfE$@@EmrE%@@EE&@@@E%E'@@@E&E(@@@E'E)@@@E(E*@@@E)E+@@@E*E,@@@E+E-@@dE,ZE.@@E,E/@@dE.ZsystemE0@@pE.E1@@ E0E2@@ @E1E3@@ @E2E4@@ @E3E5@@ @E4E6@@ @E5E7@@dE6ZsE8@@E6ZrE9@@E5ZLE:@@E4ZffE;@@E3ZfrE<@@E2mfE=@@E1mrE>@@E+E?@@dE>NullSrcE@@@E>EA@@p@E@EB@@0EAEC@@0AEBED@@0AECEE@@@EDEF@@ED0EG@@EC0EH@@EB0EI@@E*EJ@@dEIIgenEK@@EIEL@@@EKEM@@dELZsEN@@KELEO@@EN1EP@@EKEsEQ@@E)ER@@dEQIgenES@@EQET@@dESstackEU@@pESEV@@ EUEW@@dEVIgenEX@@EVNullSrcEY@@E(EZ@@dEYIgenE[@@EYE\@@dE[stackE]@@pE[E^@@ E]E_@@dE^IgenE`@@E^NullSrcEa@@E'Eb@@dEaIgenEc@@EaEd@@dEcstackEe@@pEcEf@@ EeEg@@dEfIgenEh@@pEfEi@@EhEj@@@EiEk@@dEjZrEl@@KEjEm@@El1En@@EiErEo@@E&Ep@@dEoVEq@@EoEr@@dEqZEs@@EqIgenEt@@sE%Eu@@EtVEv*@U(T( A,,- 1.4.3 Compute relay currents7Ew<Ex8Ev}Ey<Ez8EvlArialEwEyEw9E{<E|:@W1E}</E~<E0@NormalArial E*@U(c( ;;(;(-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. 1X9 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 0.99997`E<E8EE<E8EyEE<E8EEE<E8E@ ArialEE<E8EEE<5E8EEE@@pF<F?@@F>RF@@@F;FA@@@F@FB@@@FAFC@@@FBFD@@@FCFE@@@FDFF@@@FEFG@@dFFmFH@@{FFFI@@FHFJ@@dFIRFK@@FIiFL@@FEFM@@dFL\aFN@@FLFO@@@FNFP@@dFOargFQ@@pFOFR@@FQFS@@dFRRFT@@FRiFU@@FNFV@@tFU180FW@@FU\pFX@@FDFY@@dFXpFZ@@pFXF[@@0FZF\@@0AF[F]@@@F\F^@@F\\aF_@@F[mF`@@IFCFa@@@F`Fb@@dFaPolFc@@FapFd@@)F`Fe@@dFdiFf@@Fd1Fg@@IFBFh@@@FgFi@@dFhPolFj@@FhFk@@dFjstackFl@@pFjFm@@ FlFn@@dFmPolFo@@FmpFp@@(FgFq@@dFpiFr@@Fp0Fs@@FAFt@@dFsiFu@@FsFv@@tFu0Fw@@Fu2Fx@@sF@Fy@@FxPolFz*@U3-@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 variables7i+F{<+F|8FzyF}<F~8FzyF{F<F8FzyF}F<F8Fz@ ArialFF<#F8FzyFF<F8Fz@ ArialFF@@@G=G?@@dG> rect2polarG@@@pG>GA@@G@VS_012GB@@G=GC@@+@GB@XGD@@GBGE@B@U(kkGF@@ pGG@@ GFGH@@dGGVR1polGI@@GGGJ@@dGIVR_012GK@@GI1GL@B@UY50p GM@@ pGN@@GMGO@@@GNGP@@dGO rect2polarGQ@@pGOGR@@GQVR_012GS@@GNGT@@+@GS@XGU@@GSGV*@U8q 8w y1- Extract Relay and fault currents7 GW< GX8GVn Arial9 GY< GZ:@W1G[</ G\< G]0@NormalArial G^@B@U0[Qx G_@@ pG`@@ G_Ga@@dG`IbrGb@@G`Gc@@dGbSolve_currentsGd@@pGbGe@@ GdGf@@ @GeGg@@dGf VprefaultGh@@GfZLGi@@GemfGj@B@U0Dy Gk@@ pGl@@ GkGm@@dGl ISprefaultGn@@GlGo@@dGn submatrixGp@@pGnGq@@ GpGr@@ @GqGs@@ @GrGt@@ @GsGu@@dGtIbrGv@@Gt0Gw@@Gs2Gx@@Gr0Gy@@Gq0Gz@B@U0Fz G{@@ pG|@@ G{G}@@dG| IRprefaultG~@@G|G@@dG~ submatrixG@@pG~G@@ GG@@ @GG@@ @GG@@ @GG@@dGIbrG@@G3G@@G5G@@G0G@@G0G*@U8 8~ y1JJ-2Display Relay and fault currents in polar notation72G<2G8Gn Arial92G<2G:@W1G</2G<2G0@NormalArial G@B@U0*|X| G@@ pG@@GG@@@GG@@dG rect2polarG@@pGG@@G ISprefaultG@@GG@@+@G@XG@@GG@B@U0}} G@@ pG@@GG@@@GG@@dG rect2polarG@@pGG@@G IRprefaultG@@GG@@+@G@XG@@GG*@U   ]Azz-,1.6 Calculate prefault voltages and currents7,G<,G8GlArial9,G<,G:@W1G</,G<,G0@NormalArial G*@U0Y0 Q))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.79G<G:@W1G</G<G0@NormalArial G@B@UHZRG@@ pG@@ GG@@dGrG@@G0.8G*@USyRR- Relay reach7 G< G8Gn Arial9 G< G:@W1G</ G< G0@NormalArial G*@U8e38L--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.7y|jG<|G8GG<G8G@ ArialGG<G8G@ ArialGG<G8G@ ArialGGG9jG    !"Root EntryF ֽ8Ole CompObjqOlePres000z FMicrosoft Visio DrawingVISIO 4.0 ShapesVisio.Drawing.69qOh+'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&!  C  *B  /-,>b/t-!-/&// rrC 01_#0#0h:qr 4% W//S `/r?(*/'.P??/O/k@tk@<k@}%-$FG@#) W3Q ),C, ]\GD/S+)~u`u Qu qbb @wS% )&B BBH 6#6/ L@ A`9Copyright 1995 Visio Corporation. All s reserved.r`Shape.hlp!#15000bKlU%a+ ### ,^*?+ 's N NWaE.],E!qO&[`(4/-=/ rrs \0`1/,V!?? ߊ'q 4% (F-]( 8W?/"?(OV/LH=8*OtMrA//tOW@t@<@ }p-F M #),W3 )̀ )HD S+)\۫S)H+E,D@@$ ,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$9@,O)/`<l2FL W&?w' <(`C*4!G*@Uy yA- Figure 2. Fault matrix diagram.7 G< G8Gn Arial9 G< G:@W1G</ G< G0@NormalArial G@B@UH6o0 G@@ pG@@ GG@@dGZaaG@@GG@@tG10G@@G6G@B@U60 G@@ pG@@ GG@@dGZbbG@@GG@@tG10G@@KGG@@G6G@B@U86_0 G@@ pG@@ GG@@dGZccG@@GG@@tG10G@@G6G@B@U60 G@@ pG@@ GG@@dGZabG@@GG@@tG10G@@G6G@B@UY600 G@@ pG@@ GG@@dGZbcG@@GG@@tG10G@@G6G@B@Up60 G@@ pG@@ GG@@dGZacH@@GH@@tH10H@@KHH@@H6H*@U(S,cB` - 79H<H:@W1H</H<H 0@NormalArial H @B@U L? H @@ pH @@ H H @@dH ZfH@@H H@@p@HH@@0HH@@0AHH@@0AHH@@0AHH@@0AHH@@0AHH@@0AHH@@0AHH@@0AHH@@@HH@@pHH@@HH@@@HH@@@HH@@dHZccH@@KHH @@H1H!@@HH"@@dH!ZacH#@@KH!H$@@H#1H%@@HH&@@dH%ZbcH'@@KH%H(@@H'1H)@@KHH*@@H)H+@@dH*ZbcH,@@KH*H-@@H,1H.@@KHH/@@H.H0@@dH/ZacH1@@KH/H2@@H11H3@@KHH4@@H3H5@@dH4ZbcH6@@KH4H7@@H61H8@@pHH9@@H8H:@@@H9H;@@@H:H<@@dH;ZbbH=@@KH;H>@@H=1H?@@H:H@@@dH?ZabHA@@KH?HB@@HA1HC@@H9HD@@dHCZbcHE@@KHCHF@@HE1HG@@KHHH@@HGHI@@dHHZabHJ@@KHHHK@@HJ1HL@@KHHM@@HLHN@@dHMZacHO@@KHMHP@@HO1HQ@@KHHR@@HQHS@@dHRZabHT@@KHRHU@@HT1HV@@pHHW@@HVHX@@@HWHY@@@HXHZ@@dHYZaaH[@@KHYH\@@H[1H]@@HXH^@@dH]ZabH_@@KH]H`@@H_1Ha@@HWHb@@dHaZacHc@@KHaHd@@Hc1He@@KHHf@@He1Hg@B@U(mK Hh@@ pHi@@ HhHj@@dHiZfrHk@@HiZfHl*@U -@EChange the assignment variable from "Zff" to "Zfr" for reverse faults7EHm1.7 Compute relay voltages and currents for the faulted system7>Hu<>Hv8HtlArial9>Hw<>Hx:@W1Hy</>Hz<>H{0@NormalArial H|*@U A S P y)-Location of forward fault7H}<H~8H|n Arial9H<H:@W,1H</H<H0@NormalArial H@B@U@ !V P H@@ pH@@ HH@@dHmfH@@H0.15H*@U8A S 8P y-Reverse fault location7H<H8Hn Arial9H<H:@W1H</H<H0@NormalArial H@B@U@ 9V P H@@ pH@@ HH@@dHmrH@@H0.0001H@B@U0x 2 k +H@@ pH@@ HH@@dHVnodeH@@HH@@dHSolve_Node_VoltagesH@@pHH@@ HH@@ @HH@@ @HH@@ @HH@@ @HH@@ @HH@@ @HH@@ @HH@@dHEsH@@HErH@@HZssH@@HZrrH@@HZLH@@HZffH@@HZfrH@@HmfH@@HmrH*@U0  0 ,Arr-' 1.7.1 Extract Relay and fault voltages7'H<H8H}H<&H8HlArialHHH9'H<'H:@W1H</'H<'H0@NormalArial H@B@U0 F k -H@@ pH@@ HH@@dHVSabcH@@HH@@dH submatrixH@@pHH@@ HH@@ @HH@@ @HH@@ @HH@@dHVnodeH@@H3H@@H5H@@H0H@@H0H@B@U0 Q m /H@@ pH@@ HH@@dHVRabcH@@HH@@dH submatrixH@@pHH@@ HH@@ @HH@@ @HH@@ @HH@@dHVnodeH@@H9H@@H11H@@H0H@@H0H@B@U0!.!m(!0H@@ pH@@ HH@@dHVS012H@@HH@@dHAH@@HVSabcH*@Up!+!p(!h y1MM-2Display Relay and fault voltages in polar notation72H<2H8Hn Arial92H<2H:@W1H</2H<2H0@NormalArial H@B@U00!F!o@!2H@@ pH@@ HH@@dHVR012H@@HH@@dHAH@@HVRabcH@B@U0X!r!qh!3H@@ pH@@ HH@@dHVS0polH@@HH@@dHVS012H@@H0H@B@Ux6!!h!i H@@ pH@@HH@@@HH@@dH rect2polarH@@pHH@@HVSabcH@@HH@@+@H@XH@@HH@B@U0x!!s!6I@@ pI@@ II@@dIVR0polI@@II@@dIVR012I@@I0I@B@U0!!q! I@@ pI@@ II @@dIVS2polI @@II @@dI VS012I @@I 2I @B@U0!!s! I@@ pI@@ II@@dIVR2polI@@II@@dIVR012I@@I2I@B@Ux!! ! I@@ pI@@II@@@II@@dI rect2polarI@@pII@@IVRabcI@@II@@+@I@XI@@II*@Ug"|"x"A-, 1.7.2 Extract Relay and polarizing currents7,I<I 8I}I!<+I"8IlArialII!I9,I#<,I$:@W1I%</,I&<,I'0@NormalArial I(@B@U"'"1"I)@@ pI*@@ I)I+@@dI*IbrI,@@I*I-@@dI,Solve_currentsI.@@pI,I/@@ I.I0@@ @I/I1@@dI0VnodeI2@@I0ZLI3@@I/mfI4@B@U""E"I5@@ pI6@@ I5I7@@dI6ISabcI8@@I6I9@@dI8 submatrixI:@@pI8I;@@ I:I<@@ @I;I=@@ @I@@ @I=I?@@dI>IbrI@@@I>0IA@@I=2IB@@I<0IC@@I;0ID@B@U""G"IE@@ pIF@@ IEIG@@dIFIRabcIH@@IFII@@dIH submatrixIJ@@pIHIK@@ IJIL@@ @IKIM@@ @ILIN@@ @IMIO@@dINIbrIP@@IN3IQ@@IM5IR@@IL0IS@@IK0IT*@U"""% y1JJ-2Display Relay and fault currents in polar notation72IU<2IV8ITn Arial92IW<2IX:@W1IY</2IZ<2I[0@NormalArial I\@B@U"#G#I]@@ pI^@@ I]I_@@dI^IS012I`@@I^Ia@@dI`AIb@@I`ISabcIc@B@Ux"<##& Id@@ pIe@@IdIf@@@IeIg@@dIf rect2polarIh@@pIfIi@@IhISabcIj@@IeIk@@+@Ij@XIl@@IjIm@B@U#&#I # In@@ pIo@@ InIp@@dIoIR012Iq@@IoIr@@dIqAIs@@IqIRabcIt@B@UH#b#KX#"Iu@@ pIv@@ IuIw@@dIvIS0polIx@@IvIy@@dIxIS012Iz@@Ix0I{@B@Uh##Mx#$I|@@ pI}@@ I|I~@@dI}IR0polI@@I}I@@dIIR012I@@I0I@B@UxR###' I@@ pI@@II@@@II@@dI rect2polarI@@pII@@IIRabcI@@II@@+@I@XI@@II@B@U##K# I@@ pI@@ II@@dIIS2polI@@II@@dIIS012I@@I2I@B@U##M#! I@@ pI@@ II@@dIIR2polI@@II@@dIIR012I@@I2I*@U$ $$-@I 1.7.4 Compute symmetrical component polarizing torque directional values7II<I8I}I@@{J=J?@@J>J@@@dJ?IR012JA@@J?0JB@@J<2JC@B@U'z'0' JD@@ pJE@@JDJF@@dJEZ32RV0JG@@JEJH@@+@JG@XJI@@JGJJ*@U(%(( -@E 1.7.4.6.3 Relay S negative sequence voltage polarized torque value7EJK<JL8JJ}JM@@K<0K?@@K+3K@@B@U0+dK+e8+ KA@@ pKB@@ KAKC@@dKBVRc1KD@@KBKE@@p@KDKF@@KEKG@@@KFKH@@@KGKI@@dKHVRabc_prefaultKJ@@KH2KK@@KGKL@@dKKaKM@@KKKN@@dKMVRabc_prefaultKO@@KM0KP@@KFKQ@@p@KPKR@@KQKS@@dKRaKT@@KR1KU@@KPKV@@dKUVRabc_prefaultKW@@KU1KX@@KD3KY*@U w+&+ + - 1.8.3 Sending end reach7KZ<K[8KY|9K\<K]:@W,1K^</K_<K`0@NormalArial Ka*@Uw+)++ iii- 1.8.4 Receiving end reach7Kb<Kc8Ka|9Kd<Ke:@W,1Kf</Kg<Kh0@NormalArial Ki*@UP++P+g N -Ground Elements7Kj<Kk8KinArial9Kl<Km:@W1Kn</Ko<Kp0@NormalArial Kq@B@U++A+] Kr@@ pKs@@ KrKt@@dKsmsagKu@@KsKv@@@KuKw@@tKvReKx@@pKvKy@@KxKz@@@KyK{@@dKzVSabcK|@@Kz0K}@@KyK~@@dK}VSa1K@@KuK@@dKReK@@pKK@@pKK@@KK@@@KK@@dKZL1K@@pKK@@KK@@@KK@@dKISabcK@@K0K@@KK@@@KK@@dK3K@@Kk0K@@KK@@dKIS012K@@K0K@@KK@@dKVSa1K@B@U++++^ K@@ pK@@ KK@@dKmragK@@KK@@@KK@@tKReK@@pKK@@KK@@@KK@@dKVRabcK@@K0K@@KK@@dKVRa1K@@KK@@dKReK@@pKK@@pKK@@KK@@@KK@@dKZL1K@@pKK@@KK@@@KK@@dKIRabcK@@K0K@@KK@@@KK@@dK3K@@Kk0K@@KK@@dKIR012K@@K0K@@KK@@dKVRa1K@B@U,D,B(,_ K@@ pK@@ KK@@dKmsbgK@@KK@@@KK@@tKReK@@pKK@@KK@@@KK@@dKVSabcK@@K1K@@KK@@dKVSb1K@@KK@@dKReK@@pKK@@pKK@@KK@@@KK@@dKZL1K@@pKK@@KK@@@KK@@dKISabcK@@K1K@@KK@@@KK@@tK3K@@Kk0K@@KK@@dKIS012K@@K0K@@KK@@dKVSb1K@B@U,-D,(,` K@@ pK@@ KK@@dKmrbgK@@KK@@@KK@@tKReK@@pKK@@KK@@@KK@@dKVRabcK@@K1K@@KK@@dKVRb1K@@KK@@dKReK@@pKK@@pKK@@KK@@@KK@@dKZL1K@@pKK@@KK@@@KK@@dKIRabcK@@K1K@@KK@@@KK@@tK3K@@Kk0K@@KK@@dKIR012K@@K0K@@KK@@dKVRb1K@B@UJ,,Ap,a K@@ pK@@ KL@@dKmscgL@@KL@@@LL@@tLReL@@pLL@@LL@@@LL@@dLVSabcL@@L2L @@LL @@dL VSc1L @@LL @@dL ReL @@pL L@@pL L@@LL@@@LL@@dLZL1L@@pLL@@LL@@@LL@@dLISabcL@@L2L@@LL@@@LL@@tL3L@@Lk0L@@LL@@dLIS012L@@L0L@@LL@@dLVSc1L @B@UJ,+,p,b L!@@ pL"@@ L!L#@@dL"mrcgL$@@L"L%@@@L$L&@@tL%ReL'@@pL%L(@@L'L)@@@L(L*@@dL)VRabcL+@@L)2L,@@L(L-@@dL,VRc1L.@@L$L/@@dL.ReL0@@pL.L1@@pL0L2@@L1L3@@@L2L4@@dL3ZL1L5@@pL3L6@@L5L7@@@L6L8@@dL7IRabcL9@@L72L:@@L6L;@@@L:L<@@tL;3L=@@L;k0L>@@L:L?@@dL>IR012L@@@L>0LA@@L2LB@@dLAVRc1LC*@UX,,X,f N-Phase Elements7LD<LE8LCnArial9LF<LG:@W1LH</LI<LJ0@NormalArial LK@B@U,,J, LL@@ pLM@@ LLLN@@dLMmsabLO@@LMLP@@@LOLQ@@tLPReLR@@pLPLS@@LRLT@@p@LSLU@@LTLV@@@LULW@@dLVVSabcLX@@LV0LY@@LULZ@@dLYVSabcL[@@LY1L\@@pLSL]@@L\L^@@@L]L_@@K@L^L`@@L_1iLa@@L^VSc1Lb@@LOLc@@dLbReLd@@pLbLe@@pLdLf@@LeLg@@@LfLh@@dLgZL1Li@@pLgLj@@LiLk@@@LjLl@@dLkISabcLm@@Lk0Ln@@LjLo@@dLnISabcLp@@Ln1Lq@@pLfLr@@LqLs@@K@LrLt@@5LsLu@@tLt1iLv@@LtVSc1Lw@B@U,',, Lx@@ pLy@@ LxLz@@dLymrabL{@@LyL|@@@L{L}@@tL|ReL~@@pL|L@@L~L@@p@LL@@LL@@@LL@@dLVRabcL@@L0L@@LL@@dLVRabcL@@L1L@@pLL@@LL@@@LL@@K@LL@@L1iL@@LVRc1L@@L{L@@dLReL@@pLL@@pLL@@LL@@@LL@@dLZL1L@@pLL@@LL@@@LL@@dLIRabcL@@L0L@@LL@@dLIRabcL@@L1L@@pLL@@LL@@K@LL@@5LL@@tL1iL@@LVRc1L@B@U-D-J(- L@@ pL@@ LL@@dLmsbcL@@LL@@@LL@@tLReL@@pLL@@LL@@p@LL@@LL@@@LL@@dLVSabcL@@L1L@@LL@@dLVSabcL@@L2L@@pLL@@LL@@@LL@@K@LL@@L1iL@@LVSa1L@@LL@@dLReL@@pLL@@pLL@@LL@@@LL@@dLZL1L@@pLL@@LL@@@LL@@dLISabcL@@L1L@@LL@@dLISabcL@@L2L@@pLL@@LL@@K@LL@@5LL@@tL1iL@@LVSa1L@B@U-'D-(- L@@ pL@@ LL@@dLmrbcL@@LL@@@LL@@tLReL@@pLL@@LL@@p@LL@@LL@@@LL@@dLVRabcL@@L1L@@LL@@dLVRabcL@@L2L@@pLL@@LL@@@LL@@K@LL@@L1iL@@LVRa1L@@LL@@dLReL@@pLL@@pLL@@LL@@@LL@@dLZL1L@@pLL@@LL@@@LL@@dLIRabcL@@L1L@@LL@@dLIRabcL@@L2L@@pLL@@LL@@K@LL@@5LL@@tL1iL@@LVRa1L@B@UJ--Ip- L@@ pL@@ LL@@dLmscaL@@LM@@@LM@@tMReM@@pMM@@MM@@p@MM@@MM@@@MM@@dMVSabcM@@M2M @@MM @@dM VSabcM @@M 0M @@pMM @@M M@@@M M@@K@MM@@M1iM@@MVSb1M@@LM@@dMReM@@pMM@@pMM@@MM@@@MM@@dMZL1M@@pMM@@MM@@@MM@@dMISabcM@@M2M@@MM@@dMISabcM @@M0M!@@pMM"@@M!M#@@K@M"M$@@5M#M%@@tM$1iM&@@M$VSb1M'@B@UJ-'-p- M(@@ pM)@@ M(M*@@dM)mrcaM+@@M)M,@@@M+M-@@tM,ReM.@@pM,M/@@M.M0@@p@M/M1@@M0M2@@@M1M3@@dM2VRabcM4@@M22M5@@M1M6@@dM5VRabcM7@@M50M8@@pM/M9@@M8M:@@@M9M;@@K@M:M<@@M;1iM=@@M:VRb1M>@@M+M?@@dM>ReM@@@pM>MA@@pM@MB@@MAMC@@@MBMD@@dMCZL1ME@@pMCMF@@MEMG@@@MFMH@@dMGIRabcMI@@MG2MJ@@MFMK@@dMJIRabcML@@MJ0MM@@pMBMN@@MMMO@@K@MNMP@@5MOMQ@@tMP1iMR@@MPVRb1MS@B@U---C MT@@ pMU@@MTMV@@dMUmsagMW@@MUMX@@+@MW@XMY@@MWMZ@B@U--F-= M[@@ pM\@@M[M]@@dM\mragM^@@M\M_@@+@M^@XM`@@M^Ma@B@U.B&. .S Mb@@ pMc@@MbMd@@dMcmsbgMe@@McMf@@+@Me@XMg@@MeMh@B@U...G(.T Mi@@ pMj@@MiMk@@dMjmrbgMl@@MjMm@@+@Ml@XMn@@MlMo@B@U8.N.H.U Mp@@ pMq@@MpMr@@dMqmscgMs@@MqMt@@+@Ms@XMu@@MsMv@B@U@.V.FP.V Mw@@ pMx@@MwMy@@dMxmrcgMz@@MxM{@@+@Mz@XM|@@MzM}@B@Uh.~.x.W M~@@ pM@@M~M@@dMmsabM@@MM@@+@M@XM@@MM@B@Up.~.G.X M@@ pM@@MM@@dMmrabM@@MM@@+@M@XM@@MM@B@U...Y M@@ pM@@MM@@dMmsbcM@@MM@@+@M@XM@@MM@B@U.~.G.Z M@@ pM@@MM@@dMmrbcM@@MM@@+@M@XM@@MM@B@U.J..[ M@@ pM@@MM@@dMmscaM@@MM@@+@M@XM@@MM@B@U..F.\ M@@ pM@@MM@@dMmrcaM@@MM@@+@M@XM@@M