.MCAD 309000000 \  docDocument MmcObject[  dim_formatTmasslengthtimecharge temperature luminosity substanceNumericalFormatQdii shpRectV+ } mcDocumentObjectState\ mcPageModelKL?L???mcHeaderFooterI@I |P CHeaderFooterJA{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fnil\fprq14 Arial;}{\f3\fswiss\fprq15 Arial;}} {\colortbl\red0\green0\blue0;} \deflang1033\pard\plain\f3\fs18 EE525/504 \par Power Systems Protection \par } @{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fnil\fprq14 Arial;}{\f3\fswiss\fprq15 Arial;}} {\colortbl\red0\green0\blue0;} \deflang1033\pard\qc\plain\f3\fs18 \par } A {\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fnil\fprq14 Arial;}{\f3\fswiss\fprq15 Arial;}} {\colortbl\red0\green0\blue0;} \deflang1033\pard\qr\plain\f3\fs18 Session 10; Page \{n\}/\{nn\} \par Fall 2002 \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>@ Times New RomanSerial_ParPropDefaultW?Normal>@Times New Roman@W? Heading 1>@ Arial@W Heading 2>@Times New Roman@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 3Arial@P User 4Times New Roman@P User 5Times New Roman@P User 6Arial@P User 7Times New Roman@P SymbolsSymbol@P Current Selection FontArial@P Undefined Font@P HeaderArial@P FooterArial@P Rotated Math FontTimes New RomanK TextRegion* docRegionGshpBoxUh-h(// CharacterMap-RangeMap;EE 525/504: HW #4 Solutions ChrPropMap7 ParPropMap9 RangeElem< ParPropData: RangeData=@WEmbedMap1<LinkMap/<LinkData0@ Heading 1Times New Roman*@UI\X~-$Define constants and Transformations7$9$<$:@W1</$<$0@NormalTimes New Roman *@U(q(`-Define transformation79<:@W1</<0@NormalTimes New Roman eqRegionB@U0}?!tree@ p"@@ !#@@d"a$@@"%@@t$1&@@$'@@d&e(@@&)@@t(1j*@@(+@@@*,@@t+2-@@+\p.@@*3/*@U~-Problem 1: Solve the following:70<1 ChrPropData8/nTimes New Roman2<38/nTimes New Roman02094<5:@W16</7<80@NormalTimes New Roman 9*@UC$ D^++-@XA. Find the symmetrical components referenced to phase "A", and phase "B" and phase "C" 7X:<;89mTimes New Roman<@@@ p@@@@@@@{@@@@@@VA0@@@@@@@+@@@X@@@@@@B@U@@@ p@@@@@@@@@@@@d@arg@@@p@@@@@VA0@@@@@@@+@@@X@@@@@@B@U>@@@ p@@@@@@@{@@@@@@VA1@@@@@@@+@@@X@@@@@@B@U+@@@ p@@@@@@@@@@@@d@arg@@@p@@@@@VA1@@@@@@@+@@@X@@@@deg@@B@U.>(@@@ p@@@@@@@{@@@@@@VA2@@@@@@@+@@@X@@@@@@B@U3.(A@@ pA@@AA@@@AA@@dAargA@@pAA@@AVA2A@@AA@@+@A@XA@@AdegA *@U i| xT-Phase B Symmetrical Components79A <A :@W1A </A <A0@NormalTimes New Roman A*@U  Tee-;Define a new transform or a way to modify the existing one:7;9;A<;A:@W1A</;A<;A0@NormalTimes New Roman A@B@UHbA@@ pA@@,AA@@dAVBA@@AA@@@AA@@dAVB0A@@AVB1A@@AVB2A@B@UHjA@@ pA @@,AA!@@dA VA1A"@@A A#@@dA"aA$@@A"VB1A%*@U-and79A&<A':@W1A(</A)<A*0@NormalTimes New Roman A+@B@U= A,@@ pA-@@,A,A.@@dA-VA2A/@@A-A0@@@A/A1@@dA0aA2@@A02A3@@A/VB2A4*@Uhh-and 79A5<A6:@W1A7</A8<A90@NormalTimes New Roman A:@B@UA;@@ pA<@@,A;A=@@dA<VA0A>@@A<VB0A?*@Uhyh -or 79A@<AA:@W1AB</AC<AD0@NormalTimes New Roman AE@B@U <& AF@@ pAG@@,AFAH@@dAGVAAI@@AGAJ@@@AIAK@@dAJVB0AL@@AJAM@@dALaAN@@ALVB1AO@@AIAP@@@AOAQ@@dAPaAR@@AP2AS@@AOVB2AT@B@UH;VjPAU@@ pAV@@,AUAW@@dAVVC1AX@@AVAY@@@AXAZ@@dAYaA[@@AY2A\@@AXVB1A]*@UATP-and 79A^<A_:@W1A`</Aa<Ab0@NormalTimes New Roman Ac@B@UBDVPAd@@ pAe@@,AdAf@@dAeVC2Ag@@AeAh@@dAgaAi@@AgVB2Aj*@UhAThP -and 79Ak<Al:@W1Am</An<Ao0@NormalTimes New Roman Ap@B@UBVPAq@@ pAr@@,AqAs@@dArVC0At@@ArVB0Au@B@Uc@~xAv@@ pAw@@,AvAx@@dAwVCAy@@AwAz@@@AyA{@@dAzVB0A|@@AzA}@@@A|A~@@dA}aA@@A}2A@@A|VB1A@@AyA@@dAaA@@AVB2A*@U(d(L<<- such that: 7 9 A< A:@W1A</ A< A0@NormalTimes New Roman A*@U``T++-define: 79A<A:@W1A</A<A0@NormalTimes New Roman A@B@U([A@@ pA@@,AA@@p@AA@@0AA@@0AAA@@0AAA@@@AA@@AVCA@@AVBA@@AVAA@@AA@@p@AA@@0AA@@0AAA@@0AAA@@0AAA@@0AAA@@0AAA@@0AAA@@0AAA@@0AAA@@@AA@@AaA@@A1A@@AA@@dAaA@@A2A@@AA@@dAaA@@A2A@@A1A@@AaA@@A1A@@A1A@@A1A@@pAA@@0AA@@0AAA@@0AAA@@@AA@@AVB2A@@AVB1A@@AVB0A@B@UA@@ pA@@ AA@@dAB1A@@pAA@@0AA@@0AAA@@0AAA@@0AAA@@0AAA@@0AAA@@0AAA@@0AAA@@0AAA@@@AA@@AaA@@A1A@@AA@@dAaA@@A2A@@AA@@dAaA@@A2A@@A1A@@AaA@@A1A@@A1A@@A1A*@U9'LH\-+so the phase B symmetrical components are: 7+9+A<+A:@W1A</+A<+A0@NormalTimes New Roman A@B@U [vWpA@@ pA@@ AA@@dAV_B012A@@AA@@@AA@@dAB1A@@KAA@@A1A@@AVabcA@B@Un*A@@ pA@@ AA@@dAVB0A@@AA@@dAV_A012A@@A0A@B@U A@@ pA@@AA@@dAVB0A@@AA@@+@A@XA@@AA@B@Un*A@@ pA@@ AA@@dAVB1A@@AA@@dAV_A012A@@A1A@B@UoA@@ pA@@AB@@dAVB1B@@AB@@+@B@XB@@BB@B@Un* B@@ pB@@ BB@@dBVB2B@@BB @@dBV_A012B @@B2B @B@Uv!B @@ pB @@B B@@dB VB2B@@B B@@+@B@XB@@BB@B@U=B@@ pB@@BB@@{@BB@@BVB0B@@BB@@+@B@XB@@BB@B@UB@@ pB@@BB@@@BB@@dBargB@@pBB @@BVB0B!@@BB"@@+@B!@XB#@@B!B$@B@U6=0B%@@ pB&@@B%B'@@{@B&B(@@B'VB1B)@@B&B*@@+@B)@XB+@@B)B,@B@U"*60B-@@ pB.@@B-B/@@@B.B0@@dB/argB1@@pB/B2@@B1VB1B3@@B.B4@@+@B3@XB5@@B3degB6@B@U;V=PB7@@ pB8@@B7B9@@{@B8B:@@B9VB2B;@@B8B<@@+@B;@XB=@@B;B>@B@UB2VPB?@@ pB@@@B?BA@@@B@BB@@dBAargBC@@pBABD@@BCVB2BE@@B@BF@@+@BE@XBG@@BEdegBH*@U%3v-,Transformation matrix for Phase C components7,9,BI<,BJ:@W1BK</,BL<,BM0@NormalTimes New Roman BN@B@U(=A4BO@@ pBP@@ BOBQ@@dBPC1BR@@pBPBS@@0BRBT@@0ABSBU@@0ABTBV@@0ABUBW@@0ABVBX@@0ABWBY@@0ABXBZ@@0ABYB[@@0ABZB\@@@B[B]@@B[1B^@@BZB_@@dB^aB`@@B^2Ba@@BYaBb@@BX1Bc@@BWaBd@@BVBe@@dBdaBf@@Bd2Bg@@BU1Bh@@BT1Bi@@BS1Bj@B@Ur 5Bk@@ pBl@@ BkBm@@dBlV_C012Bn@@BlBo@@@BnBp@@dBoC1Bq@@KBoBr@@Bq1Bs@@BnVabcBt@B@URoi+`6Bu@@ pBv@@ BuBw@@dBvVC0Bx@@BvBy@@dBxV_C012Bz@@Bx0B{@B@US!nh7B|@@ pB}@@B|B~@@dB}VC0B@@B}B@@+@B@XB@@BB@B@U`Snh8B@@ pB@@BB@@{@BB@@BVC0B@@BB@@+@B@XB@@BB@B@UZgnIh9B@@ pB@@BB@@@BB@@dBargB@@pBB@@BVC0B@@BB@@+@B@XB@@BB@B@Uro+:B@@ pB@@ BB@@dBVC1B@@BB@@dBV_C012B@@B1B@B@Us);B@@ pB@@BB@@dBVC1B@@BB@@+@B@XB@@BB@B@U`s<B@@ pB@@BB@@{@BB@@BVC1B@@BB@@+@B@XB@@BB@B@UzI=B@@ pB@@BB@@@BB@@dBargB@@pBB@@BVC1B@@BB@@+@B@XB@@BdegB@B@Uo+>B@@ pB@@ BB@@dBVC2B@@BB@@dBV_C012B@@B2B@B@U)?B@@ pB@@BB@@dBVC2B@@BB@@+@B@XB@@BB@B@U`@B@@ pB@@BB@@{@BB@@BVC2B@@BB@@+@B@XB@@BB@B@UIAB@@ pB@@BB@@@BB@@dBargB@@pBB@@BVC2B@@BB@@+@B@XB@@BdegB*@UMCEE-@_Notice that the magnitudes of the symmetrical components stay the same, only the angles change.7_9_B<_B:@W1B</_B<_B0@NormalTimes New Roman