.MCAD 306000000 \  docDocumentMmcObject[  dim_formatTmasslengthtimecharge temperature luminosity substanceNumericalFormatQdii shpRectVA+]+mcDocumentObjectState\ mcPageModelKL?L???mcHeaderFooterI@I |P ComputeEngineNBuiltInsS SerialAnyvalY@@Y @@Y@YMbP?@Y units_classR TextState? TextStyle>@ Times New RomanNormal>@Times New Roman Heading 1>@ Arial Heading 2>@Times New Roman Heading 3 >@ Arial Paragraph >@ ArialList >@ ArialIndent >@Times New RomanTitle >@Times New RomanSubtitle 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 Roman TextRegion* docRegionGshpBoxUx#=x87YY CharacterMap-RangeMap;EE421 Unbalanced Line Example ChrPropMap7 ParPropMap9 RangeElem< ParPropData: RangeData=EmbedMap1<LinkMap/<LinkData0@ Heading 1Times New Roman*@UYlh`-Define transformation79<:1</<0@NormalTimes New Roman eqRegionB@U(~u7Dtree@ p@@ @@da@@@@t1 @@!@@d e"@@ #@@t"1j$@@"%@@@$&@@t%2'@@%\p(@@$3)@B@Ul*@@ p+@@ *,@@d+A1-@@p+.@@0-/@@0A.0@@0A/1@@0A02@@0A13@@0A24@@0A35@@0A46@@0A57@@@68@@69@@d8a:@@82;@@5a<@@41=@@3a>@@2?@@d>a@@@@>2@A@@11@B@@01@C@@/1@D@@.1@E*@U4Xjj-Define Constants:79@F<@G:1@H</@I<@J0@NormalTimes New Roman @K@B@U(:?@L@@ p@M@@ @L@N@@d@M\r@O@@@M@P@@5@@O@Q@@t@P100@R@@@Pohm@S@@@Om@T@B@U @U@@ p@V@@ @U@W@@d@Vfreq@X@@5@V@Y@@t@X60@Z@@@XHz@[@B@U((Q@@7@\@@ p@]@@ @\@^@@d@]\mo@_@@5@]@`@@@@_@a@@@@`@b@@t@a4@c@@@a\p@d@@@`@e@@t@d10@f@@K@d@g@@@f7@h@@@_@i@@d@hH@j@@@hm@k@B@U'OR)@@l@@ p@m@@ @l@n@@d@mIcons@o@@@m@p@@d@o\mo@q@@@o@r@@t@q2@s@@@q\p@t@B@U0h+@u@@ p@v@@ @u@w@@d@vCarsonsResistConst@x@@5@v@y@@5@@x@z@@t@y9.869@{@@@y@|@@t@{10@}@@K@{@~@@@}7@@@@x@@@d@ohm@@@@@@@d@m@@@@Hz@@B@Ui7@@@ p@@@ @@@@d@ De_const@@@@@@@t@2160@@@@@@@@@@@@d@ft@@@@@@@d@Hz@@@@0.5@@@@@@@p@@@@@@@@@d@ohm@@@@m@@@@0.5@*@U(8(HH&&-@Compute the series impedance matrix for the line configuration of Figure P4.4 where the conductor is 336,400 CM, 26/7 Strand ACSR. Assume line is 50 miles long79@<@:1@</@<@0@NormalTimes New Roman @ COleDocItemDocItem @U``+bbࡱ> @\B  !"#$%&'()*+,-./012345679:;<=>?[DEFGHIJLMNOPQRTUVWXYZ^_`abcdefghijklmnopqrstuvwxyz{|}~Root Entry F<PAData |k1Table8CompObjj|kDd`   c |AXC:\bj\cour\EE\523\Spring02\hws\hw5\p4-4.bmpbj"7B}idjDn\j"7B}iPNG  IHDR`gAMA IDATx$Yc,v]wg F@,Re:2#"bQb &B$@XRi+( F`aXťIϓ<}8;RiByjaaPm8VY~wՒʖv `&^pyD]Vl[b8"ceZA`w==Upmm#54 ɼCV B (@5 A )#2Bc#k.:6`5=6wܯ}f oh2!SXr] /pnpv~\`gg'N$TꔬX$5l # !p 0~Pptm82jp%^%{c0)St=0GB̽^yG{VDeHܗjAs?OpW5(C\5J-԰& 9d!'h+(ΰ5z0"$[avwR8x%Ɣ~?L瞈ԃ!^sl[؝"`Xqh Q>Z݆MiX4ҋLgBvOCaW@P@4b*#"Z9+ima`8lK.k -sǬ k˒A(@GyVҊh$uI݆}[ƣpQҩb~g;kSc2eswþNmy(.#^n`nɎ%j+@N}XWǭy wI{ؖ B@ˣDwC35~ƹtA+CFFc-lR"*%xƻU9cXv!s[6rHۡl/Zװ[d6'8at.n/{ݪP0-WLv6"Wh&g^P 2@N FV:at=N;r'F|9u4rHR~f5_3,N.E:9ީ50\'h_ ;v[08 (A5keemم_Wfs?GE9z \wݽt!kt<<ڗvu-?H.b^,KԻWםU:Nk~P'Fի7*B)ƪ@ c8ԌZspv~ڴ˻7epﺗ{x1EYď.Q.yH])~){i\Hque?kT4Yr}:c!6ᦻ;4w}OKET_7U]LUĜ0".-8˅ *`ˍk[%2ErJو &>Wd\-d/AU .gtxLºwòQ&0pw_K˴fHBxL$enrkwD9ڡ"YsClU[s6[ݫ@,7aكװH->[jNb1`j`,~go' Μ%p4̗_!/ VR.$91ZY>.g9 1ݻn;ݨw;IkpM%dZleLq1 qUWt03a|<\t&Hltk8m+Gr[7 PpPvSL,xur QU+oX1ԡֽx+ IHPXi, ץ}d"j29S3 (t H"*@@m@H$"D(`rQow( ag,fW ! O\z_\tshm:OR\׼b |RO8& \j5XxUDa(xv<:ΆBk:7V zb ':xJ<QpmVf?ƫѹ@;6}rOS$G]zmRo]Kfm7P=]Ŋ-6.J7Bn yiPUp8bk"UWaHu27}\skKX3~j3ݦx}^ 7#%?Z3\2!`va:I62t)zF@ɮ *. IsG"-ǃn7ab'uDh2_yitKnq}rtbdUh2k|Mf,LNLzuOgFL$0v7hn NF{*XD{I!WB nכw}מ[HxU'V]J$NT}GФ:C5dډb@(KoXaX|j#{2n-<+ҝ~NvmX7L±,p_S/~bt&Hu /vRȈ._:TT PʨmVLw `Z8zX\SbN/D;HX\6`BQ'۟FhxJzuMwCrMw:zzHi\=AXf \;u."l}[ M:9eB!2PElf=@@j~?aOsئt5t1;?A,c2p_j%^s3V|zq +>R.j/$uB iG)6nNR4S LIGB{W?ߨwRu|=+x6Xݫ^9wn|Qr~=%00Vo̰b;iI7+@'\UvgOp@ͣWSE@Th7lWS67Hrc|O>=dp"&Zk cܷŽa=y 5ң;>Bi=C |ږ'šk qWZ1(@-6:.'\k~*zJ/5c֭0veY?Y %;{րlD+xjׂi.[A<MٲC]銳 9[T]dg0U7FG2 x=zwZ~{+n,чK!PlMz)zrsedj/o|L-'24v5pVh.1Np(A+ yEOrXruZlKuz.bfV!j'A454;2kzw/'?\tw/}_ۇ|Sozg2?rX9]gfS``AkJ۱ո VH J SAVb0+H)sPIK"&}L&#0;"5Aٝ]Sx8[q|WS:n" &s%\}`fφ@|E.ʡrXy U_ѰWD̃ +W03ZB.S7Z,g,4ʒd@#3&\{uc\7B6-v=zDx sZcF\yOrj/E)@0mm iibQ[Lo6]Qb~궒@]+1 woaM5ܦ>du}dƀ652%d' nqLxx䇏08pܭq:w;z[plOnց&wG89lԲ$붦R P̽KՓmN[?JP#mIj:gN m."c~qTtUemL'\zzU_?^~?]Tsh|S;۵90or9N0 &0)ӍJP I}HM={qnew0\(\-ԗ' oǎE~CA.G~S .GR&7>g~kWv] K6=lZ/ SYBXя }C=6Hhu>kX@j"= ]}b ~v-@*<ݲ~಄<ku_[q{KsNͷlI>]OoyPh궜1XqefzRC)K\!wv{j@ gmOx)C>vk)P <|zt@@:0UT"U`V3G7&t||Y|Y?QsSWr8jaZ/wa$'a)|१\7zO{IOӯq*AKVu<蛒bm~KS2`kօT=u@(.&+@PzQN:ղYnW@ ӽ)ȓu+û n^AC=xsۮ/Uj6Z]o=N?h[HBVDo9!]uos醙)5[5T!@(#"z5m^]2?'o}ZGR[\w )`;xm\ObG,l5;)]{\\}[>?aV%`,#@,̹vb-^MKջ:G0P @LѡɺE񘨍upծ_Fczx3mm`3]*$?im[:Ն/rݢ&?׮n'?olvn7BX#M`­ PT)'4@MsOԙyB"e)(W4_Y }cr@:yZ_:>_L0(\΃6n2Cw}="<-,2ۯ?\} xOݧ,L mr<=́6o~e\.9STգAa d1 9" Sz >.r{"$Rqd3[ nڤav#$~ Q__bР&vt~  s%7m X_c@{׿~w_3$"%?h{kxX1Օɒ#AUhîȰ\LsIE)TjUY D4O]t8;^?@Zv20ݱƖDDkpEu4{כ:<ʾ)P =oV(+ x*SG{Ȩ ؘPޭ;":p+Tn8պp^y|G2 IDAT>p+/mJ \)}e|8{tu0Q㵯C!w@#2x;N%0׹gI㱋sEo ?ozsO_3^K}]*ԗ>kP_W*T/$4z pA#2"x@ م؂ 2X!O=4= t:x?i:T?o~g|A2<K>~~c0Sj`1kbuEW1ؘKPu fI&$jvKw}6"q4]aTO >HK_~ІTw=OxyI7? /Kd2>]o/fؗxuexцu({52!( 8*25h⨜{aHzBe]-ck=@\1V'.QY|QUf>S基|⥞ɉOU/Uy5ec.෩X$;?,ɐc/RRN Uy*Tf#y8ܹ?~c; Rxh>n?fdo گClHj JD m -#Cr$Gopw0M!|E>y4DPfZV wi\ƚ]?7S`zytH^a&k[TCU>ZNE "! 9`Uoy LجʠO'^T*PX8;=p5> [#h-?xR]V.P$G6*_7~Ov0u m8@- ̈́D"PCp؃:n"n<$ <^{X&.:[U p b!!KՆ]E\B!v%J7n]!±{`Ì@͵??+ǵj4M<dVǃǠSO9B`\sňTt7R5t}sGEס8Aw0J]/45S*s`§>uA;cQ t9t @G)Jnn2,>FV秶>`'^J}ƾDٯQ`H}&?v҇$cnZZw^>xu؝\w~?ÍzvjKWvWp lo\2PGƍxd1f ,F/ \ϓ<(WD H>ş8PqPZ'_[݆?ß. n<̑mp{NUPH!083)xM9G 9BC3).NpXFHSv:Mg*7|M$At5ZKyu;tiks綰;WwQT,>FVפXIͼD f%*cLe Iq&%"K+_UM]X8`T ۟jqSːvGRjEXy wNKyZh!o^|UU~j1@$SQs H n0a& *pZ?;˞r KVc{m/|MOCRqv:ħ~|CaMiPW6NE_]S˞k*4o`Ы;3] XJOm< j8A7=# |]x烁0{>ٍŗ6-3=<֭SHUdn0)C¿x aZO+1bYf,J[oY ] h+fE0  yp!n=!es/?x aM[eu <9 +N\$u۟)~é`'zы>;mag PaN'Bj* 'y""mk/Gj lՕ>ҟ/nCdLݢ?]y?ny\(RiioǗq۷giǕ!}u'}=W ^v9ة4a6UDD \i7-0Xj3~upaJ9m=>QC z~Wlc{K?ggN`{N1`wzX_yj|7Y_"TGذ9 th`ڈ3 0PzO:?~+:Ș#4l?x+!}o!.òKF 6i瞌aIן״<ZkLJ"6VTԖ7J$TMKCmK)mt7&$Eb# FH"c h;k۝8|'_ǿa,g Ǣ|Io>N9wEikLB0W^AFUwڦ^af;kny)yВVd|yڟ[?Mv-nϟ]z7P:zЖ<Tl [OsނjO^ n%R lD  PK٫ĭs#Z*H04XKoI46_M0_~7a>x2?5p2Az׃R;ߘ>g[U hJ ؘ5'!1DѠ޶nzRz} *78ID?|+uzgQR|{ӬwOܟlX\M2LrhU;/*zn-ҋBY--KӉ#T`a@ @ &r-c {ݵ`̥뫧x@oO-@?+uu~{-ci=͜&XF9½FhPɆ'Kͣ)"c`0*IX9AWXNѐ+®!/SRuxϞcn+pxg(W~iTSߣ/lOtX>1OlP4 O8CՄtHsIؠ*34w++2K^aO'Nna6׫Zz.Bd?n,J 'Їm}~?6y9E[𡼲?3!VH!9sw~ c;W]W,lKUٚ%T2TJ:@P( лTFC_@a=Qeƛ4++ RϫgoPrexh]92OOeO~۷z?>"Kr"hكrϳ =#p-,(,ht.njm+R^̃\ i_nùߴ}): 7kRwsW~{*YG]{X$\.Cc>2|,-.M_&i>\B췆R2vR^LF-tUԘZs9C@S3iXٜC<uvyZǹ`^6 k4z\N{o3Ю4l:;Ex5`idq/{۲V-캣m0@ɕԪ{5Xn?oG-𶧗o_<ӽ8MuQi7lRh;Rz`]BEC۫l!_xhYmRq!CFJl2C!qr.#d`9f|EiI4\$uuUL',_{sY¯ggn.%.PF!0㮡J]ϹuЂUR.9)ub )tl'pJ@s] >& @QW++`%~7BʳA읨㭃o酜 $d0_g_ν-6OR^l5IMg-r[D(M'N\]Vp:nNʵPr¸d,L`J--1t1fTen{>v X|=s>%V|^''S{З\{/Hh=du:l] &vBɡ*Wm6>mY!e. a(Q5smhK.EHB$ᆰ=xɇm~+gsH{@roFkץsgsws_z &|9+Nn}KANe;^nMLpEok\w°SZF$ 0Ű#A(=8 hb:i7{y8Nw>n3?>۩s@}qԐ m5d6wMa ݹ>˜k,zNQfbXac4Z[,J?]>P$8:>h o (3+.''.auJ_|oΡa7l䖩_D/ #ǒَ^hm hZM1 dB 9|#?XS>nxKn'z7К W[= /#-`S1c).{at%a_h }N[O_A2 H LIBnn *D0pB5d`W (Rx m{1ɶqa1v^o;m&iu5GKQ=MWY&*{3cSnV.qs1Uw?ju(5#݂Eel ˸z["WzQӇ۱ֺ,CKHt+QK !ulP:VcA•t HF[;OL6xxw799 8.Y}5rM +a}ٽJ@{w24R{;"M\M]pPW{ & RlLr ;͐)miXxj}~x87Jׇ'%?_e?E޿V1t.&y. |]ےP,k=8TV!dh a" w}a+&/_9 "x:tr` NϯggqW#x̝qdΑkr OÚZb];i4BXi#ӊ\T4TCA Xj1ҭC.0ۻ-yaГ6/K\a.Vn:" ^^0^Mh* OoW¹M \6&]ig"ֲlXP%lت1oQE Dlٷޠr`R/bXVGk{9>~@( j܏@y,)n ?s_?ƿ [>Z\}Ub֩s$mbK%U6E:qlz[`)WjA.%Uɘ\f4)te 63(1Iנ@n.PY6ALWە)O p1a|0=ި͏#b)q2{6~=k'_?цD[F_d~l=p,KxSfԠE rl Pf\vMA ,TE :flEQ2l%xN@%]eԢu,4} xl;E&gM߭)Z%ת 04E2Bv`j: ڟXj*s O Lv0|(b OZ?$ޏchm6<>v2r`j1@w8C05o $5! 5 f4TQjK;(;ө1c_)6k}w|zS .y驟~KB˺Փq]ٺCu쥭nϟxv-/S yô32')jٺ3C  To^:jU2W<>7!^^k臨BvfQ]q~3M_I+@7Ɨ.G^tD1'Kd:eUL.?_|gjG@ MrLD@ =)_}u//jcKrI PX̌\F/oč҄"$l]0}h;]Fi@QxAm} o[X0+ZR0nҕuK̩6_' 5xFʥ_#&P"qXA OF*B\XjI ƨSsp Y)m!cms70Ԇq^7%AuCs 7 1DŽ 3dž??{_S).A XAri f3$j hSGX>URg,]\q5X񐉌.[p+ sB#0,T6X7GXɔ 0"iƮ_F}\3LJkm&k5qT 6OZ khߕb:,70j@EcZqѸcؤ1mH $XlݭGx}/Ǹ 'MӞXJF[4x<_~gw6z{i6WedU fZG*[p)oSک.Rနll:ad aG(b1՚:=xW;ZAz tVsA @^:Q;Y P(iHmA`-`Jk ,D@:k}\g0Y֦Z5osO0U\XHjFe3KJ#3ˑ _uw]nn %>A eX8 0@1(!?toj|'1VUJJg]H2wg(e`{ Ipt+N@_cQDj>uȚ Z u6"`6*)"9e\LM P&!8rA{Ĭد :_ )šZsX"PbՌ p(l$ 1`ج*39vsyQkl G=J[9ܙ:}hէDٌk~ק?' .mm 0פb)@M;V6wbp#I`9bi7cb$PsƲ 8cjʱ[ݭٻZ8#g}NXtKcJZS@Pvb{K]a  f%qJ(V! Yn~e"%ރXzs|[1HGLe)j3\z8R2MW+C[EUe4 uMЁԊz- FPHi+V5'aŊZn0FNLM :G8b9#FzCW[vJ{^aFXn dڡ0 VQL0"!PrټBs(4`JF3\2GCsd6RȪmRd'px*R{E Yk׉T^r{Z{mʱu&OڱDڼPETZ1 337 (4 %ZA`B#A* `8IdžaM5Ca kTHv*:Oss0k_k22>j?b0t_#Gu福|&[W)ci)6N G5ek(@؀*@Cpw +Ș7/BNŠ9/=lnG3IGo9l>2𠷇ߴC!>X8haꇭ[qv0mU2gF\UG`lS 4D21(b3Ɔb,o)fJCGͩ%g+Kkq]A6lYX w1Vumjy#$QZ!Gܫ|Vr b)eNpj=1#c;H@57(DECZ{9ڎAmuc Q;t:-5EpZ2<-`>]v{1>]ЈUqbD5Y|htE=oІ [_5Q+;4@EcPWmAdkGd/iiC]s/}i}pX 0^zbAչR,Aq.O}~^,1Z~GP^;!vSJqBmpTe#f7fBF=ԭCkrWfޠe8 %q/ոoAue9u8n:ӵS+F*rT'Ȁ[1cI FDSc7Qnʔto7mZ<ݒ\{vTaolLe0Ϙx7.q]<|p[_cCUL(Pv썉{0МNPr0̆(GX,N!C 5lռA?n,5 k 3mlb]N9A[( [9 ;-hg y0q?B\cv 0ݸ&Qi Wľ6 %pXhKSW4C7p{{^Oa=ĭ\/cۆuSmr-]tPk-ЍYxn(4̇.U 9lߊ\j14l-N%HzGF "wT! βa |Ȑ`%,W7{e"3/m5i o `ڮ5 `{ʬ[x 3'p(-DVkp`b/P a3 YZ4\ Ry UwrX&;ڋٰswJg{N{B3kamx0%3mHj 9 :Kufdj55 $w 6/˹^:^T4(3(Ԁ20Hvd`g~E[2xA5APD]Azj&5bAt-GHބ-2d:^ F![(G~fvQt #AZ~5F[љ^{.mN! &l}5"@/jbsPR kzdxH"hAJ@l+oJd^ 4 N{Go!5m/pB8%@.ƹDRAJ:uG u'5hqNHБer6P#C?ipЇNh JwE! ,´d+ d/ (QߠM& NCac,/+ (^Ɲ])uU4tC E6 kMXh,١-g#X́ S*0݆.Ԧb$v yZdilr8X\)`1p8@dC`$fvaG@':vXPH FBث֡yZz?x`rࢤP5{4_K_j< t+^{3My`iP%ѻ]r(^b: R KvWsg$}>_,b1u6owX &=tf;wI дfgIL~dx&`p]BNJɺ9;[arZcQMMi2Ґ6 ޗd&yIþH()x\C?`2QB+jjF!A Mv7պ \.w^[%y4w ۮКܵ1/9Dmzz[l , vMjfzht-2= C{ĵP)kw^*&,O,I*Xض|R Ӧu &q JE7Oؤ+n(l&65hbI5Dc-@m, |S/}H<9,ض|_ك2vQvG״e6no t+@)r0v].͝kػh C)`"[fXs89H n=D] *L*(XiP$-$%9<3?*0fXHl] 1i FPo}eS9tZsy%ajUS[i-R%6lpNjWJ97{{U7eEzhEN`Tů֎a4S0?xB q(=:>\{LN[j )h!x##G#D䤑bxC4%0,2{f}~u}<x>g` ? m傻wdՇ,l"\YVzv~mJfn.Of}~'k׼FrS\TｿWNNͧ)L2{^KW_|b LyQ=޿zi<~ : fG,șQ/CRl~|=cI/~Tr[گ޳8iAFW[(8|߿VG?}2s^pi\r}PoBj䶾AI+ R{|R岾ˋN:;+(jժQ# Ҕ)DDނJwL.O2L)OڅBrBU5Fgz9 ^pmmVNjE\;7{$ 'I7%2q2ݼvܦcmH˲Sֳ:Ἤ#3 xaE.Qי5-QN%#1+Vʌ8cY2#%Ռ4wq!X,L#n3}f5#%٘2MAlbHe_Ytm{9{]r=$,Xm_0%Fy]RjyÅ/K]EhWY|t <$nZU628»& Rv'$G 9 ORyCD*"PҔq;Ql#ZngT! ۍ&dF.}iR7%l\7Hݣ*^J;:Li9x.n5x9lJ398SPpƒHcvqA֌r `IOVkփ>q|,=)C~/Œ%SS^LO%m l$p&T")N^2'Xڜ(Sgz J yT' WKO'׷RGe9հ:\ SGޘz5ꞧkWwWqn7u.-l@TPβIԤ. Pw>lIb o9$ :W$9JjL Z6Ó"#'7u/ m]ˌŖNIp]%V ZQTDrL(!ij`:ՇAYzP!Vct9k̜}E"# 3)RT]EFQh1Ij ,S\$W@{%[g3"Y۶N"60s{rΠM@j|hM+4Y}_Rcv~f$=YrzE7Nb$IPA'L/$_{iR6k0yE\\3eQlQu]T[% {K&1#Q_.Z2PՑXPd&xP̖(s569ݓr!2j9d6;x\M(O}Anl.[_OٗP!e\$ ,*k_륕|P^J S+[ZbH5N[RlD(XF3R:|5鞡L$ҏ|Yڥqrs]%9'eNgYa'q6FݤJXoI`{. %GK7(ȒxIңu 8@:^e"蒊r!TY IDAT<2pVaQ9VsuT(mBl:6޾|9/|4|ƧwΛL~KtPsAWM RlH :9/1 0{CgIa"ug5$ds!Ϛ`IQwo~Wؙs1gn?*<)s/!欤)%C9HD'%7X1&;"CP blqpፁâ֗ +DY^Eŷaold]}oD_srNzs$L ,7mp5GKHbGhQ :Z˘8轻#k`fh%/Nut異s;/im$2‹ϔ7rY @ ?˯z+п"?z!X7ۗ7^b흣ʟCY~a]Ssz;5$LfG\ 8c2 (ϐesFc.Xd9_yW4&ռ_sn~n^'~O). BJV@խ(45s0/>i'Oԑ]D*Gs|hʺ/R‘lW#ħrGulܟGq2|?{o2D, bn:^}ܭmEX(χPک٨!Bdl(s!V*! t՞/~}9W$qm&m[J) Wp"~8oٛq yo~ӟHwilD h!q*.վ :;`iQK h @u.Ǩ]]9L6<8e1&>f[+0lw5 {LHN?azo_.<~]wat5MrEfA;؁K1$P 9#E FM]}Qϒޚh(oz^)=ʖ,2Q b@@o% _~|[a9̛m/+_ۿ S*i2ə1CD3; Y}?I:; Ŧn2ھt4w-{7^czf M\"`ۘXzݣpSrT$wF`NT!ū=I(#H ,Y.@*r0nvQk=\]&goQi[" 4R)3Pŗ&./;:_1sިz @)(F]x#Dd:ݙBrJITTu\PӽzH|. eo UbQhI\伋&g17C4h55JG0t2x8gYuJƀE H.935 Bh1 @@`" f-9t쇀n}s)/>@Lv5 ݙ#b޼Y8rvlDpCtV đ F LI@'BŚnhYFۋG@4c\zuu&xBK>RhֱhΡ.TS ̝} CuFI"<e驑*Y"Ӆh0d !C ?Ҩہv Xb%vخr[+S$ dQ5&jZeb+WIa!A lK"@Ji줱xaX4%k`b% CXkxzF9٥)S2x/i7J;GŨsV^)eʡ;Y,yu5{c1.ѺŨn$U&egQ8THjҵ#{]\*L#8Bb#R"^%#AJ4v 8{uʌ_Ζ]WTd.9rKsT1ySVOꬣzSLɠQQG{.`25 $Af1M3TD0$^ P+hZbCeIENDB` [0@0Normalx CJmH nH DD Heading 1$$xx@& CJKHnH @@ Heading 2$<@& ;CJnH << Heading 3$<@&6nH <A@<Default Paragraph Font.. BullitList1nH22 BullitList2  & F,,Author$CJnH F"Fabstract keywords $xCJnH 2B22 Body TextB*nH DCBDBody Text Indent $xnH 61R6caption$<<CJDbD References$<<CJnH JrJ ContractInfod h@ 5CJnH4P4 Body Text 2 dx Y96>zamxmhho(. hhOJQJo( hhOJQJo(xxxxzaY9Y9Y9@`@GTimes New Roman5Symbol3& Arial"0heF0Brian K Johnson  FMicrosoft Word Document MSWordDocWord.Document.89qObjectPoolPPWordDocument CSummaryInformation(KDocumentSummaryInformation8Sq bjbjt+t+  AA]  h\HV *P   jU/ =!"#$% Oh+'0T   (4<DLssBrian K JohnsonriariaNormal orm1rmMicrosoft Word 8.0@@44 P ՜.+,D՜.+,D hp  Dell Computer Corporation\1  TitleL(RZ _PID_GUID _PID_HLINKSAN{8BEF73A2-6D08-11D6-A34A-444553540000}AZ,C:\bj\cour\EE\523\Spring02\hws\hw5\p4-4.bmpOle OlePres000]Х R6R&WordMicrosoft Word  @Times New Roman- &6RC ((  !!!"""###$$$%%%&&&'''((()))***+++,,,---...///000111222333444555666777888999:::;;;<<<===>>>???@@@AAABBBCCCDDDEEEFFFGGGHHHIIIJJJKKKLLLMMMNNNOOOPPPQQQRRRSSSTTTUUUVVVWWWXXXYYYZZZ[[[\\\]]]^^^___```aaabbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwxxxyyyzzz{{{|||}}}~~~hnoyw]YZsWiX^TP|ynqkυ|TWmߕmׅߞpUSkviwkgSctvqXN`^^XiهӒvY]TURe`Xlgր謹xX\|ρzadncŔ藣XhkqiZ~m\lfhhkչ\s|ѿ~y~q幃t畸ݒ꫻ӭlhge鬟귊}xy颰Д祰ѝ䮵迨唹q֜c^敮ᚺːݞʠ᭦ʟϣTyhe藫媛Ƀy|ēٚʟҟᰢyg~z`om~ᵗۑ伖ۢ೚ʟ{ZYofW]p}{fapmWZwx}LcXlxm÷q¼ś\ʥvcѣƦxź}mcfPUZYOaLP]\lSXX^dTZUeZ^W\WWNYSUO]WWTccUTiO`UPYOLmdUUNHCUXUUXPROXSPPUTRTNTUOKSPTTXS`Y`\aXY]\PcRKNWLLNUYTYlZaaaaWZYUYSPYTWTXUaSLLSRTSPRRRKTTURY]]p\~ʲrRycrLTKېXYt\TXSq\ܫ{`ڜYYڧUڥYڔX֙lӔiٗ`ۇ]؅Y؊cӄl֏hzi]\YއطU|lvkh֔k݅߉|䣥؂z|z˂]c\ӄ\RܿcpistfpRzʘ^x~ez^gNطfǧPYia~UW`aw\ݨScY]dWYXWYܺ٠YꢕLT埨U쨐LȒ٬N輑쟽\XN\GəSq`Pƛ|O{\]LsvO`aYy>΢X`SZFHºRPPiXmd]lO\FUTPLä䏺їL`Pǧ\aUƮ\YNR溧sXTx^RmX躬Yͣz弮HPPUW^kmz`sglskdNKpwr^iksn`hdvh]edcTdg\CGY辩kt^D]a\mWLUX|NP鼸ZYRnd^\DlZާLKaLhUUYcRKw^w]ߛTPihofk}YSP]K^n`o|^`a]˛Aq\a`TRcy`pqhgA]FUYeLG\fch]Z\`oZ}lUdcnCܱgTZPqSRۀPWUWe`}먴^gYXGeyXzݐTwLRNpzfpT\cUkSS\YzT\RhXnnZP۵e]lLTWPLpPm`To]PZ^٧OwTdf`zTmvSRR\kUiCPactO~cgʣK\RAa}cYkƱXncm¥OPRwfhXWچʷgRST^sphehU~`nZlraT|ىw\za~YXPTtXlceXi`{XznRoPpenXil^`sUgTiapwXgc}ZfTqTxYܐrąpRYec^RgY\W`aNFc\iX|ӘcYLe^atywPXGXWUz~h\cfYPNу\KكRYWO|afWXxhxސWZw\RqXNTC]OUUPa~RXWFh^]N\XSmORvkzڭ\\Gn`cYSZsZ]hΑxeavcgTNSp{NY}tFRkXHnhY]~h]\{]co˨gkT߾Xe\rk]cdgL]\֔d]NWOTTNTWpffggifkwgklSKW]ZqlwWwcxgzzgqg{}remkcplrON\hUa``DNC\cyXaUNePYfp݀Yd}cLWOdgc\WPAXdp李dcPg\`LOcLm뜉WRy\Z`DRacW]R\dPLedKXHei\YoꪗWcTvHUPlihwWq`^`h뷎RO^TaWSYqaepnaT\HavohLZLܗN\`ooֺY`UOS`twdTSNUsSaRrsKlWPoeZܷF׹O`^^]`tlPSn`fafzWSZ^\^}ZمUh}nsoZzGPZTcT\l^cZ\eTapfLZWY^^dYSDaqcdvfeezNed`cognKmgRYocxS`SkraW{SNrlX\khTSKaTYSii^YhaUHTXokgfv{qggocfxq{^W\rrcccZavrgdhhaU\c^OUXS`hXU]c\Zaehr]keascP`Xkg\TaUOT ƺǷʺø˼ȿήeĿOON´nfnWWZ^haWnO`iXTX`NWo&'Courier New-@*@U( (KH-$Define heights relative to the earth7$9$@<$@:1@</$@<$@0@NormalTimes New Roman @@B@U0.T(M@@@ p@@@ @@@@d@Hgw@@@@@@@5@@@@@t@36@@@@ft@@@5@@@@t@11@@@@ft@@B@U0:NHHS@@@ p@@@ @@@@d@Ha@@@@@@@d@Hgw@@@5@@@@t@6.5@@@@ft@@B@U:)NHT@@@ p@@@@@@@d@Ha@@@@@@@+@@Serial_DisplayNodeX@@@@ft@@B@U0ZonIhU@@@ p@@@ @@@@d@Hb@@@5@@@@t@36@@@@ft@@B@U0zIV@@@ p@@@ @@@@d@Hc@@@@@@@d@Ha@@@5@@@@t@8@@@@ft@@B@UzW@@@ p@@@@@@@d@Hc@@@@@@@+@@@X@@@@ft@*@U((YH-@ODefine horizontal position relative to center of the tower (some are negative).7O9O@@@A=A?@@dA>DbcA@@@A>AA@@+@A@@XAB@@A@ftAC*@UH -@PGMR and Rac from table B.8 (entry for Linnet in Appendix 8 of Bergen and Vittal)7P9PAD*@U-from table B.8 at 25C and 60Hz79B?<B@:1BA</BB<BC0@NormalTimes New Roman BD@B@U0_BE@@ pBF@@ BEBG@@dBFGMR3BH@@5BFBI@@tBH0.006BJ@@BHftBK@B@UQBL@@ pBM@@ BLBN@@dBM diameter3BO@@5BMBP@@tBO0.502BQ@@BOinBR*@U$ $`-Spacing between conductors79BS<BT:1BU</BV<BW0@NormalTimes New Roman BX*@U(1D(@&@lt-Within the bundle:79BY<BZ:1B[</B\<B]0@NormalTimes New Roman B^@B@U0Rf]` B_@@ pB`@@ B_Ba@@dB`Da1a2Bb@@5B`Bc@@tBb1.0Bd@@BbftBe@B@URf` Bf@@ pBg@@ BfBh@@dBgDb1b2Bi@@5BgBj@@tBi1.0Bk@@BiftBl@B@U8Rfg` Bm@@ pBn@@ BmBo@@dBnDc1c2Bp@@5BnBq@@tBp1.0Br@@BpftBs*@U `&(#-@Calculate geometric mean radius of the bundle and use the 3x3 matrix method. The is an approximation of the 6x6 matrix approach. 79Bt<Bu:1Bv</Bw<Bx0@NormalTimes New Roman By@B@U8uBz@@ pB{@@ BzB|@@dB{ RsbundleB}@@{B{B~@@B}B@@dB~GMR3B@@B~Da1a2B@B@U@  P B@@ pB@@ BB@@dBLperlength_altB@@BB@@dBIconsB@@pBB@@0BB@@0ABB@@0ABB@@0ABB@@0ABB@@0ABB@@0ABB@@0ABB@@0ABB@@@BB@@BB@@dBlnB@@pBB@@BB@@dBDeB@@B RsbundleB@@BB@@dBlnB@@pBB@@BB@@dBDeB@@BDbcB@@BB@@dBlnB@@pBB@@BB@@dBDeB@@BDacB@@BB@@dBlnB@@pBB@@BB@@dBDeB@@BDbcB@@BB@@dBlnB@@pBB@@BB@@dBDeB@@B RsbundleB@@BB@@dBlnB@@pBB@@BB@@dBDeB@@BDabB@@BB@@dBlnB@@pBB@@BB@@dBDeB@@BDacB@@BB@@dBlnB@@pBB@@BB@@dBDeB@@BDabB@@BB@@dBlnB@@pBB@@BB@@dBDeB@@B RsbundleB*@U(1 D (@ o-@SThe resistance matrix must also be modified since there are now parallel conductors7S9SB ~8 C=@@ pC>@@ C=C?@@dC>DmC@@@C>CA@@p@C@CB@@CACC@@@CBCD@@dCCDabCE@@CCDbcCF@@CBDacCG@@C@CH@@tCG1CI@@CG3CJ@B@UX* > u8 CK@@ pCL@@CKCM@@dCLDmCN@@CLCO@@+@CN@XCP@@CNftCQ@B@UXP y ph CR@@ pCS@@ CRCT@@dCSL1CU@@CSCV@@dCUIconsCW@@CUCX@@dCWlnCY@@pCWCZ@@CYC[@@dCZDmC\@@CZGMRC]@B@UPX  gp C^@@ pC_@@C^C`@@dC_L1Ca@@C_Cb@@+@Ca@XCc@@CaCd@@dCcmHCe@@CcmiCf@B@UX @ p Cg@@ pCh@@ CgCi@@dChZ1Cj@@ChCk@@p@CjCl@@CkCm@@dClRacCn@@ClCo@@@CnCp@@@CoCq@@@CpCr@@tCq1jCs@@Cq2Ct@@Cp\pCu@@CofreqCv@@CnL1Cw@@CjLengthCx@B@UP  g Cy@@ pCz@@CyC{@@dCzZ1C|@@CzC}@@+@C|@XC~@@C|ohmC@B@U g C@@ pC@@CC@@dC Z012_p4_34C@@CC@@+@C@XC@@CCJ0C*@U8)o<8847?- Similarly 7 9 C< C:1C</ C< C0@NormalTimes New Roman C@B@U`H^XC@@ pC@@ CC@@dC GMRbundleC@@{CC@@CC@@dCGMR3C@@CDa1a2C@B@U@J^XC@@ pC@@CC@@dC GMRbundleC@@CC@@+@C@XC@@CftC@B@UHuC@@ pC@@ CC@@dCL1bunC@@CC@@dCIconsC@@CC@@dClnC@@pCC@@CC@@dCDmC@@C GMRbundleC@B@U@lC@@ pC@@CC@@dCL1bunC@@CC@@+@C@XC@@CC@@dCmHC@@CmiC@B@UHcuC@@ pC@@ CC@@dCZ1bunC@@5CC@@p@CC@@CC@@@CC@@dCRac3C@@C2C@@CC@@@CC@@@CC@@@CC@@tC1jC@@C2C@@C\pC@@CfreqC@@CL1bunC@@CLengthC@B@UC@@ pC@@CC@@dCZ1bunC@@CC@@+@C@XC@@CohmC*@U vUj^LeF-A2Consider an untransposed line described in problem 4.4 and Figure P4.4. Let the ground wire be 1/0 ACSR and recalculate the phase impedance matrix Zabc, the sequence impedance matrix Z012, and the unbalance factors. Compare with previous results from problem 4.20 for the same line without the ground wire.7292C<2C:1C</2C<2C0@NormalTimes New Roman C*@U(i|(xoqx-Ground wire data: 79C<C:1C</C<C0@NormalTimes New Roman C@B@U@xC@@ pC@@ CC@@dCRac_gwC@@5CC@@tC0.888C@@CC@@dCohmC@@CmiC*@U-Table B.8, at 25C and 60Hz79C<C:1C</C<C0@NormalTimes New Roman C@B@U@C@@ pC@@ CC@@dCGMR_gwC@@5CC@@tC.00446C@@CftC@B@UHC@@ pC@@ CC@@dC diameter_gwC@@5CC@@tC.398C@@CinC@B@U(R(C@@ pC@@ CC@@dC Rperlength_gwC@@pCC@@0CC@@0ACC@@0ACC@@0ACC@@0ACC@@0ACC@@0ACD@@0ACD@@0ADD@@0ADD@@0ADD@@0ADD@@0ADD@@0ADD@@0ADD@@0ADD @@@DD @@DD @@dD Rac_gwD @@D RdD @@DRdD@@DRdD@@DRdD@@DRdD@@DD@@dDRacD@@DRdD@@DRdD@@DRdD@@DRdD@@CRdD@@CD@@dDRacD@@DRdD@@CRdD@@CRdD@@CRdD@@CRdD@@CD @@dDRacD!@@DRdD"@B@U(D#@@ pD$@@D#D%@@dD$ Rperlength_gwD&@@D$D'@@+@D&@XD(@@D&D)@@dD(ohmD*@@D(mi4J0D+*@U((op-@B@U@BVePD?@@ pD@@@ D?DA@@dD@XgwDB@@5D@DC@@tDB0DD@@DBftDE*@UATP-(horizontal position is at our zero point7(9(DF<(DG:1DH</(DI<(DJ0@NormalTimes New Roman DK*@U(i|(xH-@HNow calculate distance between conductors (be careful of negative signs)7H9HDLReduce to equivalent 3x3 matrix by removing 4th row and column7>9>E=<>E>:1E?</>E@<>EA0@NormalTimes New Roman EB@B@U8OEC@@ pED@@ ECEE@@dEDZaEF@@EDEG@@dEF submatrixEH@@pEFEI@@ EHEJ@@ @EIEK@@ @EJEL@@ @EKEM@@dELZabc_gwEN@@EL0EO@@EK2EP@@EJ0EQ@@EI2ER@B@UxU$ES@@ pET@@ ESEU@@dETZbEV@@ETEW@@dEV submatrixEX@@pEVEY@@ EXEZ@@ @EYE[@@ @EZE\@@ @E[E]@@dE\Zabc_gwE^@@E\0E_@@E[2E`@@EZ3Ea@@EY3Eb@B@U8P Ec@@ pEd@@ EcEe@@dEdZcEf@@EdEg@@dEf submatrixEh@@pEfEi@@ EhEj@@ @EiEk@@ @EjEl@@ @EkEm@@dElZabc_gwEn@@El3Eo@@Ek3Ep@@Ej0Eq@@Ei2Er@B@UxU&Es@@ pEt@@ EsEu@@dEtZdEv@@EtEw@@dEv submatrixEx@@pEvEy@@ ExEz@@ @EyE{@@ @EzE|@@ @E{E}@@dE|Zabc_gwE~@@E|3E@@E{3E@@Ez3E@@Ey3E@B@U8j"E@@ pE@@ EE@@dEZabceqE@@EE@@dEZaE@@EE@@@EE@@dEZbE@@EE@@dEZdE@@KEE@@E1E@@EZcE@B@U82Fi@#E@@ pE@@EE@@dEZabceqE@@EE@@+@E@XE@@EE*@U  w-In problem 4.20 we found:79E<E:1E</E<E0@NormalTimes New Roman E@B@U8z\E@@ pE@@EE@@dEZabcE@@EE@@+@E@XE@@EE*@U (mmrmi-B&Comparing results: (a) The resistance terms are larger, due to folding in the resistance of the ground wire (b) The self inductance terms are smaller (in Xaa, Xbb, Xcc) since the phase conductors are coupling with a grounded conductor that is much closer than the earth. (c) The inductive reactance of the off-diagonal terms are also smaller.7&9&E<&E:1E</&E<&E0@NormalTimes New Roman E*@U 3 *w"-+Now find the symmetrical components matrix:7+9+E<+E:1E</+E<+E0@NormalTimes New Roman E@B@U0,E@@ pE@@ EE@@dE Z012_p4_40E@@EE@@@EE@@@EE@@dEA1E@@KEE@@E1E@@EZabceqE@@EA1E@B@U0BVP-E@@ pE@@EE@@dE Z012_p4_40E@@EE@@+@E@XE@@EE*@U/r{-and earlier we had:79E<E:1E</E<E0@NormalTimes New Roman E@B@U80E@@ pE@@EE@@dE Z012_p4_20E@@EE@@+@E@XE@@EE*@U9H2-CComparing results: (a) The resistance terms are only larger in the zero sequence terms, since the ground conductor only carries zero sequence currents (b) The self inductance terms X1 and X2 are basically the same, but X0 is smaller for the case with the ground wire. Again, coupling to a closer ground conductor. (c) The off-diagonal terms that couple the zero sequence show differences, those that couple positve to negative are essentially the same. (d) So all of the difference seen in the Zabc matrices are basically in the zero sequence related terms. 79>>E<>E:E<E:EEE1E</E<E0@NormalTimes New Roman E*@U -Capacitance Matrix Calculations79E<E:1E</E<E0@NormalTimes New Roman E@B@U(Q5@E@@ pE@@ EE@@dE\e_oE@@5EE@@@EE@@tE8.854E@@EE@@tE10E@@KEE@@E12E@@EE@@dEFE@@EmE@B@U1RF @E@@ pE@@ EE@@dECconsE@@EE@@@EE@@tE2E@@E\pE@@E\e_oE@B@U(jx~IxE@@ pE@@ EE@@dEHaaiE@@EE@@tE2E@@EHaE@B@Uj~xE@@ pE@@EE@@dEHaaiF@@EF@@+@F@XF@@FftF@B@U js~CxF@@ pF@@ FF@@dFHbbiF@@FF@@tF2F @@FHbF @B@Uj~xF @@ pF @@F F @@dF HbbiF@@F F@@+@F@XF@@FftF@B@U({KF@@ pF@@ FF@@dFHcciF@@FF@@tF2F@@FHcF@B@UF@@ pF@@FF@@dFHcciF@@FF@@+@F@XF@@FftF@B@U(JF @@ pF!@@ F F"@@dF!HabiF#@@{F!F$@@F#F%@@@F$F&@@p@F%F'@@F&F(@@dF'HaF)@@F'HbF*@@F%2F+@@F$F,@@p@F+F-@@F,F.@@dF-XaF/@@F-XbF0@@F+2F1@B@U@aF2@@ pF3@@F2F4@@dF3HabiF5@@F3F6@@+@F5@XF7@@F5ftF8@B@U(JF9@@ pF:@@ F9F;@@dF:HaciF<@@{F:F=@@F@@@F=F?@@p@F>F@@@F?FA@@dF@HaFB@@F@HcFC@@F>2FD@@F=FE@@p@FDFF@@FEFG@@dFFXaFH@@FFXcFI@@FD2FJ@B@U@aFK@@ pFL@@FKFM@@dFLHaciFN@@FLFO@@+@FN@XFP@@FNftFQ@B@U(6K0FR@@ pFS@@ FRFT@@dFSHbciFU@@{FSFV@@FUFW@@@FVFX@@p@FWFY@@FXFZ@@dFYHbF[@@FYHcF\@@FW2F]@@FVF^@@p@F]F_@@F^F`@@dF_XbFa@@F_XcFb@@F]2Fc@B@U@"6b0Fd@@ pFe@@FdFf@@dFeHbciFg@@FeFh@@+@Fg@XFi@@FgftFj*@UYlhH~-GMR from table B.879Fk<Fl:1Fm</Fn<Fo0@NormalTimes New Roman Fp@B@U0iFq@@ pFr@@ FqFs@@dFr diameterFt@@5FrFu@@tFt0.721Fv@@FtinFw@B@Ux1Fx@@ pFy@@ FxFz@@dFyrF{@@FyF|@@dF{ diameterF}@@F{2F~@B@UsHF@@ pF@@ FF@@dFLengthF@@5FF@@tF50F@@FmiF@B@U=)`F@@ pF@@ FF@@dFPF@@5FF@@@FF@@tF1F@@FCconsF@@pFF@@0FF@@0AFF@@0AFF@@0AFF@@0AFF@@0AFF@@0AFF@@0AFF@@0AFF@@@FF@@FF@@dFlnF@@pFF@@FF@@dFHcciF@@FrF@@FF@@dFlnF@@pFF@@FF@@dFHbciF@@FDbcF@@FF@@dFlnF@@pFF@@FF@@dFHaciF@@FDacF@@FF@@dFlnF@@pFF@@FF@@dFHbciF@@FDbcF@@FF@@dFlnF@@pFF@@FF@@dFHbbiF@@FrF@@FF@@dFlnF@@pFF@@FF@@dFHabiF@@FDabF@@FF@@dFlnF@@pFF@@FF@@dFHaciF@@FDacF@@FF@@dFlnF@@pFF@@FF@@dFHabiF@@FDabF@@FF@@dFlnF@@pFF@@FF@@dFHaaiF@@FrF@B@UpHq`F@@ pF@@FF@@dFPF@@FF@@+@F@XF@@FF@@dFmF@@FpFCJ0F@B@UkF@@ pF@@ FF@@dF CapperlengthF@@FF@@dFPF@@KFF@@F1F@B@Ud:F@@ pF@@FF@@dF CapperlengthF@@FF@@+@F@XF@@FF@@dFnFF@@FmiF@B@UBV6PF@@ pF@@ FF@@dFCabcF@@FF@@dF CapperlengthF@@FLengthF@B@UBKV%PF@@ pF@@FF@@dFCabcF@@FF@@+@F@XF@@FnFCJ0F*@UX1@@@-A4.34 Consider the line configuration shown in Figure P4.4. Instead of using a single conductor of 336,400 CM ACSR in each phase, with current carrying capacity of 530 amperes, suppose that each phase consists of a two-conductor bundle of two 3/0 ACSR conductors with capacity of 300 amperes/conductor. Let the two conductors of each bundle be seperated by 1.0ft vertically. Compute the capacitance matrix Cabc for the bundled conductor configuration and compare with the previous solution (problem 4.20).79F<F:1F</F<F0@NormalTimes New Roman F*@U 9L H-@CSince 4.20 neglects the ground wire, it will be neglected here too.7C9CFm8G8@@ pG9@@ G8G:@@dG9 RsbundleG;@@{G9G<@@G;G=@@dG<r3G>@@G<Da1a2G?@B@U0{{G@@@ pGA@@ G@GB@@dGA PequivbundGC@@GAGD@@@GCGE@@tGD1GF@@GDCconsGG@@pGCGH@@0GGGI@@0AGHGJ@@0AGIGK@@0AGJGL@@0AGKGM@@0AGLGN@@0AGMGO@@0AGNGP@@0AGOGQ@@@GPGR@@GPGS@@dGRlnGT@@pGRGU@@GTGV@@dGUHcciGW@@GU RsbundleGX@@GOGY@@dGXlnGZ@@pGXG[@@GZG\@@dG[HbciG]@@G[DbcG^@@GNG_@@dG^lnG`@@pG^Ga@@G`Gb@@dGaHaciGc@@GaDacGd@@GMGe@@dGdlnGf@@pGdGg@@GfGh@@dGgHbciGi@@GgDbcGj@@GLGk@@dGjlnGl@@pGjGm@@GlGn@@dGmHbbiGo@@Gm RsbundleGp@@GKGq@@dGplnGr@@pGpGs@@GrGt@@dGsHabiGu@@GsDabGv@@GJGw@@dGvlnGx@@pGvGy@@GxGz@@dGyHaciG{@@GyDacG|@@GIG}@@dG|lnG~@@pG|G@@G~G@@dGHabiG@@GDabG@@GHG@@dGlnG@@pGG@@GG@@dGHaaiG@@G RsbundleG@B@U0#>k8G@@ pG@@ GG@@dGCabc_buG@@GG@@@GG@@dG PequivbundG@@KGG@@G1G@@GLengthG@B@U02Fj@G@@ pG@@GG@@dGCabc_buG@@GG@@+@G@XG@@GnFG*@UyiYj-6Now if we compare the original Cabc with the Cabc_bu: 7696G<6G:1G</6G<6G0@NormalTimes New Roman G@B@U@eG@@ pG@@GG@@dGCabcG@@GG@@+@G@XG@@GnFG*@U  ( ri-AObservations: (1) The self-capacitance terms are larger with the bundled conductors, capacitance is proportional to the natural log of conductor diameter (2) The off-diagonal capacitance terms also increase. However, if we looked at the offdiagonal terms in the P-matrices at the right, we see that they are nearly identical, so the differences in the capacitance matrices are from the inversion.79G<G:G<G:GG<G:GGG1G</G<G0@NormalTimes New Roman G@B@U q G@@ pG@@ GG@@dG C012_p4_20G@@GG@@@GG@@@GG@@dGA1G@@KGG@@G1G@@GCabcG@@GA1G@B@U8   G@@ pG@@ GG@@dG C012_p4_34G@@GG@@@GG@@@GG@@dGA1G@@KGG@@G1G@@GCabc_buG@@GA1G@B@U !`!G@@ pG@@GG@@dG C012_p4_20G@@GG@@+@G@XG@@GnFCJ0G@B@U0?!~!NX!G@@ pG@@ GG@@dGc_1G@@GG@@p@GG@@GG@@@GG@@@GG@@tG2G@@G\pG@@G\e_oG@@GG@@dGlnG@@pGG@@GG@@dGDmG@@GrG@@GLengthG@B@UJ!+^!X!G@@ pG@@GG@@dGc_1G@@GG@@+@G@XG@@GnF3J0G*@U!!!"(-0Note that c_1 does not match the matrix term....7090G<0G:1G</0G<0G0@NormalTimes New Roman G@B@U!~"X"G@@ pG@@GG@@dG C012_p4_34G@@GG@@+@G@XG@@GnFCJ0G@B@UHO""fh"G@@ pG@@ GG@@dGc_1G@@GG@@p@GG@@GG@@@GG@@@GG@@tG2H@@G\pH@@G\e_oH@@GH@@dHlnH@@pHH@@HH@@dHDmH@@H RsbundleH@@GLengthH @B@U8Z"{n"Uh"H @@ pH @@H H @@dH c_1H @@H H@@+@H @XH@@H nF