Mathcad Professional 13.0 <description/> <author>Brian K. Johnson</author> <company/> <keywords/> <revisedBy>Brian K. Johnson</revisedBy> </userData> <identityInfo> <revision>2</revision> <documentID>c1fb88b0-6a44-4dc6-b677-40d820e95aaf</documentID> <versionID>a75fe904-0834-4730-b0cf-5dc6b50d061c</versionID> <parentVersionID>00000000-0000-0000-0000-000000000000</parentVersionID> <branchID>00000000-0000-0000-0000-000000000000</branchID> </identityInfo> </metadata> <settings> <presentation> <textRendering> <textStyles> <textStyle name="Normal"> <blockAttr margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="14" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Heading 1"> <blockAttr margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="18" font-weight="bold" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Heading 2"> <blockAttr margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="14" font-weight="bold" font-style="italic" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Heading 3"> <blockAttr margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="14" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Paragraph"> <blockAttr margin-left="0" margin-right="0" text-indent="21" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" 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font-charset="0" font-size="24" font-weight="bold" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Subtitle" base-style="Title"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="center" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="18" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> </textStyles> </textRendering> <mathRendering equation-color="#000"> <operators multiplication="narrow-dot" derivative="derivative" literal-subscript="small" definition="colon-equal" global-definition="triple-equal" local-definition="left-arrow" equality="bold-equal" symbolic-evaluation="right-arrow"/> <mathStyles> <mathStyle name="Variables" font-family="Times New Roman" font-charset="0" font-size="12" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="Constants" font-family="Times New Roman" font-charset="0" font-size="12" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 1" font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 2" font-family="Courier New" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 3" font-family="Arial" font-charset="0" font-size="10" font-weight="bold" font-style="normal" underline="false"/> <mathStyle name="User 4" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="italic" underline="false"/> <mathStyle name="User 5" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 6" font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 7" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="Math Text Font" font-family="Times New Roman" font-charset="0" font-size="12" font-weight="normal" font-style="normal" underline="false"/> </mathStyles> <dimensionNames mass="mass" length="length" time="time" current="charge" thermodynamic-temperature="temperature" luminous-intensity="luminosity" amount-of-substance="substance"/> <symbolics derivation-steps-style="vertical-insert" show-comments="false" evaluate-in-place="false"/> <results> <general precision="4" show-trailing-zeros="false" radix="dec" complex-threshold="10" exponential-threshold="4" imaginary-value="i" zero-threshold="15"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </results> </mathRendering> <pageModel show-page-frame="false" show-header-frame="true" show-footer-frame="false" header-footer-start-page="1" paper-code="1" orientation="landscape" print-single-page-width="false" page-width="792" page-height="612"> <margins left="57.6" right="57.6" top="64.656" bottom="64.656"/> <header use-full-page-width="false"> <left>{\rtf1\ansi\ansicpg1252\deff0\deflang1033{\fonttbl{\f0\fswiss\fprq15\fcharset0 Arial;}{\f1\fmodern\fprq9\fcharset0 Arial;}} \viewkind4\uc1\pard\f0\fs18 ECE423\par Power Systems Analysis\f1\par } </left> <center>{\rtf1\ansi\ansicpg1252\deff0\deflang1033{\fonttbl{\f0\fswiss\fprq15 Arial;}{\f1\fmodern\fprq9\fcharset0 Arial;}} \viewkind4\uc1\pard\qc\f0\fs18\par \f1\par \par } </center> <right>{\rtf1\ansi\ansicpg1252\deff0\deflang1033{\fonttbl{\f0\fswiss\fprq15\fcharset0 Arial;}{\f1\fswiss\fprq15 Arial;}{\f2\fmodern\fprq9\fcharset0 Arial;}} \viewkind4\uc1\pard\qr\f0\fs18 Session 34;\f1 Page \{n\}/\{nn\}\par \f0 Fall 2007\f1\par \f2\par \par } </right> </header> <footer use-full-page-width="false"/> </pageModel> <colorModel background-color="#fff" default-highlight-color="#ffff80"/> <language math="EN" UI="EN"/> </presentation> <calculation> <builtInVariables array-origin="0" convergence-tolerance="0.001" constraint-tolerance="0.001" random-seed="1" prn-precision="4" prn-col-width="8"/> <calculationBehavior automatic-recalculation="true" matrix-strict-singularity-check="true" optimize-expressions="false" exact-boolean="false" strings-use-origin="false" zero-over-zero="0"> <compatibility multiple-assignment="MC11" local-assignment="MC11"/> </calculationBehavior> <units> <currentUnitSystem name="si" customized="false"/> </units> </calculation> <editor protection-level="none" view-annotations="false" view-regions="false"> <ruler is-visible="false" ruler-unit="in"/> <plotTemplate> <xy item-idref="1"/> </plotTemplate> <grid granularity-x="6" granularity-y="6"/> </editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="false" save-text-images="false" screen-dpi="96"/> <miscellaneous> <handbook handbook-region-tag-ub="2749" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="1175" left="156" top="13.5" width="209.25" height="20.25" align-x="156" align-y="30" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Heading 1" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Zbus fault analysis example</p> </text> </region> <region region-id="9" left="12" top="48" width="72.75" height="15.75" align-x="12" align-y="60" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Define units: </p> </text> </region> <region region-id="10" left="96" top="48.75" width="88.5" height="15.75" align-x="132" align-y="60" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">MVA</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>1000</ml:real> <ml:id xml:space="preserve">kW</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="2"/> </region> <region region-id="169" left="96" top="72.75" width="68.25" height="15.75" align-x="126.75" align-y="84" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">MW</ml:id> <ml:id xml:space="preserve">MVA</ml:id> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="170" left="204" top="72.75" width="77.25" height="15.75" align-x="243.75" align-y="84" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">MVAr</ml:id> <ml:id xml:space="preserve">MVA</ml:id> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="2405" left="336" top="72.75" width="37.5" height="15.75" align-x="357" align-y="84" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">pu</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="1171" left="12" top="105" width="65.25" height="37.5" align-x="26.25" align-y="138" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">a</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:imag symbol="j">1</ml:imag> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="1173" left="132" top="100.5" width="94.5" height="68.25" align-x="156" align-y="138" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">A1</ml:id> <ml:matrix rows="3" cols="3"> <ml:real>1</ml:real> <ml:real>1</ml:real> <ml:real>1</ml:real> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">a</ml:id> <ml:real>1</ml:real> <ml:id xml:space="preserve">a</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:matrix> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="2534" left="54" top="186" width="507" height="15.75" align-x="70.5" align-y="198" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Present this in terms of a series of examples. Use the system below (from the midterm exam). </p> </text> </region> <region region-id="2533" left="6" top="215.25" width="114" height="15.75" align-x="21.75" align-y="228" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">System Description:</p> </text> </region> <region region-id="2406" left="12" top="240" width="442.5" height="150.75" align-x="12" align-y="240" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{00020906-0000-0000-C000-000000000046}" type="embedded" item-idref="8"/> <rendering item-idref="9"/> </region> <region region-id="2408" left="6" top="396" width="57" height="15.75" align-x="12.75" align-y="408" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Set bases: </p> </text> </region> <region region-id="2409" left="24" top="420.75" width="77.25" height="15.75" align-x="45.75" align-y="432" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Sb</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>100</ml:real> <ml:id xml:space="preserve">MVA</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="2410" left="144" top="420.75" width="72.75" height="15.75" align-x="173.25" align-y="432" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Vb2</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>115</ml:real> <ml:id xml:space="preserve">kV</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="2411" left="240" top="420" width="195.75" height="15.75" align-x="248.25" align-y="432" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Use the line voltage as the reference</p> </text> </region> <region region-id="2412" left="144" top="442.5" width="102.75" height="33.75" align-x="173.25" align-y="462" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Vb1</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">Vb2</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="auto-select"/> <ml:real>13.8</ml:real> <ml:id xml:space="preserve">kV</ml:id> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:real>115</ml:real> <ml:id xml:space="preserve">kV</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="2517" left="408" top="442.5" width="102.75" height="33.75" align-x="437.25" align-y="462" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Vb3</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">Vb2</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="auto-select"/> <ml:real>13.2</ml:real> <ml:id xml:space="preserve">kV</ml:id> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:real>120</ml:real> <ml:id xml:space="preserve">kV</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="13"/> </region> <region region-id="2518" left="552" top="450.75" width="81" height="15.75" align-x="579.75" align-y="462" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Vb3</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">kV</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>12.65</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilovolt"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="14"/> </region> <region region-id="2413" left="288" top="456.75" width="75" height="15.75" align-x="315.75" align-y="468" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Vb1</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">kV</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>13.8</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilovolt"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="15"/> </region> <region region-id="2416" left="18" top="492" width="163.5" height="15.75" align-x="34.5" align-y="504" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Change of Base Calculations: </p> </text> </region> <region region-id="2417" left="30" top="516" width="71.25" height="15.75" align-x="52.5" align-y="528" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Generator 1: </p> </text> </region> <region region-id="2418" left="114" top="516.75" width="82.5" height="15.75" align-x="141" align-y="528" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Sg1</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>150</ml:real> <ml:id xml:space="preserve">MVA</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="16"/> </region> <region region-id="2419" left="228" top="516.75" width="90" height="15.75" align-x="280.5" align-y="528" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">XG11old</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>0.1</ml:real> <ml:id xml:space="preserve">pu</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="17"/> </region> <region region-id="2420" 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<ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">XT22</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">pu</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.087107750472589784</ml:real> </result> </ml:eval> </math> <rendering item-idref="51"/> </region> <region region-id="2457" left="120" top="1176.75" width="73.5" height="15.75" align-x="156" align-y="1188" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">XT20</ml:id> <ml:id xml:space="preserve">XT21</ml:id> </ml:define> </math> <rendering item-idref="52"/> </region> <region region-id="2458" left="234" top="1176.75" width="90.75" height="15.75" align-x="268.5" align-y="1188" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">XT20</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">pu</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.087107750472589784</ml:real> </result> </ml:eval> </math> <rendering item-idref="53"/> </region> <region region-id="2459" left="18" top="1206" width="71.25" height="15.75" align-x="40.5" align-y="1218" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Generator 2: </p> </text> </region> <region region-id="2460" left="102" top="1206.75" width="82.5" height="15.75" align-x="129" align-y="1218" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Sg2</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>100</ml:real> <ml:id xml:space="preserve">MVA</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="54"/> </region> <region region-id="2461" left="216" top="1206.75" width="90" height="15.75" align-x="268.5" align-y="1218" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">XG21old</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>0.2</ml:real> <ml:id xml:space="preserve">pu</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="55"/> </region> <region region-id="2462" left="102" top="1230.75" width="75" height="15.75" align-x="130.5" align-y="1242" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Vg2</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>13.2</ml:real> <ml:id xml:space="preserve">kV</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="56"/> </region> <region region-id="2463" left="102" top="1253.25" width="175.5" height="39" align-x="139.5" align-y="1278" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">XG21</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">XG21old</ml:id> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">Vg2</ml:id> <ml:id xml:space="preserve">Vb3</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">Sb</ml:id> <ml:id xml:space="preserve">Sg2</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="57"/> </region> <region region-id="2464" left="294" top="1266.75" width="92.25" height="15.75" align-x="330" align-y="1278" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">XG21</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">pu</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.21776937618147449</ml:real> </result> </ml:eval> </math> <rendering item-idref="58"/> </region> <region region-id="2465" left="102" top="1302.75" width="76.5" height="15.75" align-x="139.5" align-y="1314" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">XG22</ml:id> <ml:id xml:space="preserve">XG21</ml:id> </ml:define> </math> <rendering item-idref="59"/> </region> <region region-id="2466" left="240" top="1302.75" width="92.25" height="15.75" align-x="276" align-y="1314" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">XG22</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">pu</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.21776937618147449</ml:real> </result> </ml:eval> </math> <rendering item-idref="60"/> </region> <region region-id="2467" left="108" top="1332.75" width="136.5" height="15.75" align-x="159" align-y="1344" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">ZG20old</ml:id> <ml:apply> <ml:plus/> <ml:real>10.0</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:mult style="default"/> <ml:imag symbol="j">1</ml:imag> <ml:real>0.05</ml:real> </ml:apply> <ml:id xml:space="preserve">pu</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="61"/> </region> <region region-id="2468" left="108" top="1361.25" width="172.5" height="39" align-x="144" align-y="1386" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">ZG20</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">ZG20old</ml:id> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">Vg2</ml:id> <ml:id xml:space="preserve">Vb3</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">Sb</ml:id> <ml:id xml:space="preserve">Sg2</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="62"/> </region> <region region-id="2469" left="108" top="1410.75" width="155.25" height="15.75" align-x="142.5" align-y="1422" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">ZG20</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">pu</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:complex> <ml:real>10.888468809073723</ml:real> <ml:imag>0.054442344045368622</ml:imag> </ml:complex> </result> </ml:eval> </math> <rendering item-idref="63"/> </region> <region region-id="2470" left="12" top="1458" width="225.75" height="15.75" align-x="29.25" align-y="1470" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Heading 3" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Positive Sequence Network (unreduced): </p> </text> </region> <region region-id="2471" left="24" top="1482" width="340.5" height="107.25" align-x="24" align-y="1482" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{00045C6C-0000-0000-C000-000000000046}" type="embedded" item-idref="64"/> <rendering item-idref="65"/> </region> <region region-id="2472" left="6" top="1596" width="300.75" height="15.75" align-x="26.25" align-y="1608" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="inherit" list-style-type="disc" tabs="inherit">Calculate reduced equivalent for each fault location</p> </text> </region> <region region-id="2529" left="18" top="1626" width="434.25" height="31.5" align-x="38.25" align-y="1638" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Parallel impedance branches: general equation as a function of location on line 1:</p> </text> </region> <region region-id="2474" left="12" top="1655.25" width="441.75" height="39" align-x="78.75" align-y="1680" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Z1equiv</ml:id> <ml:boundVars> <ml:id xml:space="preserve">M</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:imag symbol="j">1</ml:imag> <ml:id xml:space="preserve">XG11</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:imag symbol="j">1</ml:imag> <ml:id xml:space="preserve">XT11</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:imag symbol="j">1</ml:imag> <ml:id xml:space="preserve">XL11</ml:id> </ml:apply> <ml:id xml:space="preserve">M</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:imag symbol="j">1</ml:imag> <ml:id xml:space="preserve">XL11</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">M</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:imag symbol="j">1</ml:imag> <ml:id xml:space="preserve">XT21</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:imag symbol="j">1</ml:imag> <ml:id xml:space="preserve">XG21</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:real>-1</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="66"/> </region> <region region-id="2475" left="12" top="1710" width="83.25" height="15.75" align-x="20.25" align-y="1722" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Fault at Bus 2: </p> </text> </region> <region region-id="2476" left="42" top="1734.75" width="115.5" height="15.75" align-x="93.75" align-y="1746" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Z1equiv2</ml:id> <ml:apply> <ml:id xml:space="preserve">Z1equiv</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="67"/> </region> <region region-id="2477" left="192" top="1734.75" width="109.5" height="15.75" align-x="242.25" align-y="1746" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Z1equiv2</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">pu</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:complex> <ml:real>5.7425341315559508E-18</ml:real> <ml:imag>0.093785796776763672</ml:imag> </ml:complex> </result> </ml:eval> </math> <rendering item-idref="68"/> </region> <region region-id="2478" left="6" top="1758" width="83.25" height="15.75" align-x="14.25" align-y="1770" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Fault at Bus 3: </p> </text> </region> <region region-id="2479" left="36" top="1782.75" width="115.5" height="15.75" align-x="87.75" align-y="1794" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Z1equiv3</ml:id> <ml:apply> <ml:id xml:space="preserve">Z1equiv</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="69"/> </region> <region region-id="2480" left="186" top="1782.75" width="103.5" height="15.75" align-x="236.25" align-y="1794" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Z1equiv3</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">pu</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:complex> <ml:real>1.0717480601566344E-17</ml:real> <ml:imag>0.17503552171052769</ml:imag> </ml:complex> </result> </ml:eval> </math> <rendering item-idref="70"/> </region> <region region-id="2481" left="6" top="1812" width="185.25" height="15.75" align-x="14.25" align-y="1824" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Fault at Bus M (midpoint of line):</p> </text> </region> <region region-id="2482" left="36" top="1842.75" width="129" height="15.75" align-x="92.25" align-y="1854" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Z1equivM</ml:id> <ml:apply> <ml:id xml:space="preserve">Z1equiv</ml:id> <ml:real>0.5</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="71"/> </region> <region region-id="2483" left="192" top="1842.75" width="114" height="15.75" align-x="246.75" align-y="1854" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Z1equivM</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">pu</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:complex> <ml:real>1.015448656183232E-17</ml:real> <ml:imag>0.16584082762819269</ml:imag> </ml:complex> </result> </ml:eval> </math> <rendering item-idref="72"/> </region> <region region-id="2484" left="6" top="1944" width="230.25" height="15.75" align-x="6" align-y="1956" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Heading 3" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Negative Sequence Network (unreduced): </p> </text> </region> <region region-id="2485" left="30" top="1974" width="271.5" height="105.75" align-x="30" align-y="1974" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{00045C6C-0000-0000-C000-000000000046}" type="embedded" item-idref="73"/> <rendering item-idref="74"/> </region> <region region-id="2486" left="6" top="2118" width="300.75" height="15.75" align-x="26.25" align-y="2130" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="inherit" list-style-type="disc" tabs="inherit">Calculate reduced equivalent for each fault location</p> </text> </region> <region region-id="2487" left="6" top="2142" width="440.25" height="15.75" align-x="6" align-y="2154" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit">Parallel impedance branches: general equation as a function of location on line 1</p> </text> </region> <region region-id="2488" left="6" top="2171.25" width="441.75" height="39" align-x="72.75" align-y="2196" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Z2equiv</ml:id> <ml:boundVars> <ml:id xml:space="preserve">M</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:imag symbol="j">1</ml:imag> <ml:id xml:space="preserve">XG12</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:imag symbol="j">1</ml:imag> <ml:id xml:space="preserve">XT12</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:imag symbol="j">1</ml:imag> <ml:id xml:space="preserve">XL12</ml:id> </ml:apply> <ml:id xml:space="preserve">M</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:imag symbol="j">1</ml:imag> <ml:id xml:space="preserve">XL12</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">M</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:imag symbol="j">1</ml:imag> <ml:id xml:space="preserve">XT22</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:imag symbol="j">1</ml:imag> <ml:id xml:space="preserve">XG22</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:real>-1</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="75"/> </region> <region region-id="2489" left="6" top="2232" width="83.25" height="15.75" align-x="14.25" align-y="2244" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Fault at Bus 2: </p> </text> </region> <region region-id="2490" left="36" top="2256.75" width="115.5" height="15.75" align-x="87.75" align-y="2268" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Z2equiv2</ml:id> <ml:apply> <ml:id xml:space="preserve">Z2equiv</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="76"/> </region> <region region-id="2491" left="162" top="2256.75" width="109.5" height="15.75" align-x="212.25" align-y="2268" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Z2equiv2</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">pu</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:complex> <ml:real>5.7425341315559508E-18</ml:real> <ml:imag>0.093785796776763672</ml:imag> </ml:complex> </result> </ml:eval> </math> <rendering item-idref="77"/> </region> <region region-id="2492" left="6" top="2280" width="83.25" height="15.75" align-x="14.25" align-y="2292" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Fault at Bus 3: </p> </text> </region> <region region-id="2493" left="30" top="2304.75" width="115.5" height="15.75" align-x="81.75" align-y="2316" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Z2equiv3</ml:id> <ml:apply> <ml:id xml:space="preserve">Z2equiv</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="78"/> </region> <region region-id="2494" left="162" top="2304.75" width="103.5" height="15.75" align-x="212.25" align-y="2316" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Z2equiv3</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">pu</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:complex> <ml:real>1.0717480601566344E-17</ml:real> <ml:imag>0.17503552171052769</ml:imag> </ml:complex> </result> </ml:eval> </math> <rendering item-idref="79"/> </region> <region region-id="2495" left="6" top="2334" width="185.25" height="15.75" align-x="14.25" align-y="2346" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Fault at Bus M (midpoint of line):</p> </text> </region> <region region-id="2496" left="30" top="2358.75" width="129" height="15.75" align-x="86.25" align-y="2370" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Z2equivM</ml:id> <ml:apply> <ml:id xml:space="preserve">Z2equiv</ml:id> <ml:real>0.5</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="80"/> </region> <region region-id="2497" left="168" top="2358.75" width="114" height="15.75" align-x="222.75" align-y="2370" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Z2equivM</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">pu</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:complex> <ml:real>1.015448656183232E-17</ml:real> <ml:imag>0.16584082762819269</ml:imag> </ml:complex> </result> </ml:eval> </math> <rendering item-idref="81"/> </region> <region region-id="2498" left="12" top="2430" width="209.25" height="15.75" align-x="12" align-y="2442" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Heading 3" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Zero Sequence Network (unreduced): </p> </text> </region> <region region-id="2499" left="12" top="2454" width="465" height="117.75" align-x="12" align-y="2454" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{00045C6C-0000-0000-C000-000000000046}" type="embedded" item-idref="82"/> <rendering item-idref="83"/> </region> <region region-id="2500" left="12" top="2580" width="300.75" height="15.75" align-x="32.25" align-y="2592" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="inherit" list-style-type="disc" tabs="inherit">Calculate reduced equivalent for each fault location</p> </text> </region> <region region-id="2501" left="18" top="2610" width="440.25" height="15.75" align-x="18" align-y="2622" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit">Parallel impedance branches: general equation as a function of location on line 1</p> </text> </region> <region region-id="2502" left="12" top="2639.25" width="342.75" height="39" align-x="78.75" align-y="2664" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Z0equiv</ml:id> <ml:boundVars> <ml:id xml:space="preserve">M</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:imag symbol="j">1</ml:imag> <ml:id xml:space="preserve">XT10</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:imag symbol="j">1</ml:imag> <ml:id xml:space="preserve">XL10</ml:id> </ml:apply> <ml:id xml:space="preserve">M</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:imag symbol="j">1</ml:imag> <ml:id xml:space="preserve">XL10</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">M</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:imag symbol="j">1</ml:imag> <ml:id xml:space="preserve">XT20</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:real>-1</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="84"/> </region> <region region-id="2503" left="12" top="2706" width="83.25" height="15.75" align-x="20.25" align-y="2718" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Fault at Bus 2: </p> </text> </region> <region region-id="2504" left="42" top="2730.75" width="115.5" height="15.75" align-x="93.75" align-y="2742" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Z0equiv2</ml:id> <ml:apply> <ml:id xml:space="preserve">Z0equiv</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="85"/> </region> <region region-id="2505" left="168" top="2730.75" width="109.5" height="15.75" align-x="218.25" align-y="2742" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Z0equiv2</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">pu</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:complex> <ml:real>2.9139171474352888E-18</ml:real> <ml:imag>0.047589450084756575</ml:imag> </ml:complex> </result> </ml:eval> </math> <rendering item-idref="86"/> </region> <region region-id="2506" left="12" top="2772" width="83.25" height="15.75" align-x="20.25" align-y="2784" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Fault at Bus 3: </p> </text> </region> <region region-id="2507" left="36" top="2796.75" width="115.5" height="15.75" align-x="87.75" align-y="2808" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Z0equiv3</ml:id> <ml:apply> <ml:id xml:space="preserve">Z0equiv</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="87"/> </region> <region region-id="2508" left="168" top="2796.75" width="109.5" height="15.75" align-x="218.25" align-y="2808" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Z0equiv3</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">pu</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:complex> <ml:real>4.8856577060066328E-18</ml:real> <ml:imag>0.079791480597123737</ml:imag> </ml:complex> </result> </ml:eval> </math> <rendering item-idref="88"/> </region> <region region-id="2509" left="12" top="2826" width="185.25" height="15.75" align-x="20.25" align-y="2838" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Fault at Bus M (midpoint of line):</p> </text> </region> <region region-id="2510" left="30" top="2850.75" width="129" height="15.75" align-x="86.25" align-y="2862" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Z0equivM</ml:id> <ml:apply> <ml:id xml:space="preserve">Z0equiv</ml:id> <ml:real>0.5</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="89"/> </region> <region region-id="2511" left="174" top="2850.75" width="114" height="15.75" align-x="228.75" align-y="2862" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Z0equivM</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">pu</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:complex> <ml:real>1.5855285133493978E-17</ml:real> <ml:imag>0.25894500847565755</ml:imag> </ml:complex> </result> </ml:eval> </math> <rendering item-idref="90"/> </region> <region region-id="2536" left="12" top="2915.25" width="366" height="15.75" align-x="27" align-y="2928" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Create Ybus Matrices for Positive, Negative and Zero Sequences</p> </text> </region> <region region-id="2537" left="18" top="2951.25" width="409.5" height="150.75" align-x="41.25" align-y="3030" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIFunction" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Y1</ml:id> <ml:matrix rows="4" cols="4"> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:imag font="0" symbol="j">1</ml:imag> <ml:id xml:space="preserve">XG11</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:imag font="0" symbol="j">1</ml:imag> <ml:id xml:space="preserve">XT11</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>-1</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:imag font="0" symbol="j">1</ml:imag> <ml:id xml:space="preserve">XT11</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:div/> <ml:real>-1</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:imag font="0" symbol="j">1</ml:imag> <ml:id xml:space="preserve">XT11</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:imag font="0" symbol="j">1</ml:imag> <ml:id xml:space="preserve">XT11</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:imag symbol="j">1</ml:imag> <ml:id xml:space="preserve">XL11</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>-1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:imag symbol="j">1</ml:imag> <ml:id xml:space="preserve">XL11</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:div/> <ml:real>-1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:imag symbol="j">1</ml:imag> <ml:id xml:space="preserve">XL11</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:imag font="0" symbol="j">1</ml:imag> <ml:id xml:space="preserve">XT21</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:imag symbol="j">1</ml:imag> <ml:id xml:space="preserve">XL11</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>-1</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:imag font="0" symbol="j">1</ml:imag> <ml:id xml:space="preserve">XT21</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:div/> <ml:real>-1</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:imag font="0" symbol="j">1</ml:imag> <ml:id xml:space="preserve">XT21</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:imag font="0" symbol="j">1</ml:imag> <ml:id xml:space="preserve">XT21</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:imag font="0" symbol="j">1</ml:imag> <ml:id xml:space="preserve">XG21</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:matrix> </ml:define> </math> <rendering item-idref="91"/> </region> <region region-id="1840" left="12" top="3127.5" width="66" height="21" align-x="39.75" align-y="3144" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Z_1</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">Y1</ml:id> <ml:real>-1</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="92"/> </region> <region region-id="1841" left="6" top="3185.25" width="228" height="78.75" align-x="32.25" align-y="3228" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Z_1</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:matrix rows="4" cols="4"> <ml:complex> <ml:imag>0.055798489433155317</ml:imag> </ml:complex> <ml:complex> <ml:imag>0.051538263570767663</ml:imag> </ml:complex> <ml:complex> <ml:imag>0.025976908396441688</ml:imag> </ml:complex> <ml:complex> <ml:imag>0.018554934568886926</ml:imag> </ml:complex> <ml:complex> <ml:imag>0.05153826357076767</ml:imag> </ml:complex> <ml:complex> <ml:imag>0.093785796776763686</ml:imag> </ml:complex> <ml:complex> <ml:imag>0.047270996012739715</ml:imag> </ml:complex> <ml:complex> <ml:imag>0.033764997151956945</ml:imag> </ml:complex> <ml:complex> <ml:imag>0.025976908396441688</ml:imag> </ml:complex> <ml:complex> <ml:imag>0.0472709960127397</ml:imag> </ml:complex> <ml:complex> <ml:imag>0.17503552171052775</ml:imag> </ml:complex> <ml:complex> <ml:imag>0.125025372650377</ml:imag> </ml:complex> <ml:complex> <ml:imag>0.018554934568886926</ml:imag> </ml:complex> <ml:complex> <ml:imag>0.033764997151956938</ml:imag> </ml:complex> <ml:complex> <ml:imag>0.125025372650377</ml:imag> </ml:complex> <ml:complex> <ml:imag>0.15152365937354773</ml:imag> </ml:complex> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="93"/> </region> <region region-id="2401" left="354" top="3216" width="245.25" height="15.75" align-x="354" align-y="3228" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Note that Z_1 is no longer a sparse matrix.....</p> </text> </region> <region region-id="1847" left="12" top="3396" width="103.5" height="15.75" align-x="12" align-y="3408" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Negative sequence:</p> </text> </region> <region region-id="1958" left="6" top="3437.25" width="409.5" height="150.75" align-x="29.25" align-y="3516" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Y2</ml:id> <ml:matrix rows="4" cols="4"> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:imag font="0" symbol="j">1</ml:imag> <ml:id xml:space="preserve">XG12</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:imag font="0" symbol="j">1</ml:imag> <ml:id xml:space="preserve">XT12</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>-1</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:imag font="0" symbol="j">1</ml:imag> <ml:id xml:space="preserve">XT12</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:div/> <ml:real>-1</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:imag font="0" symbol="j">1</ml:imag> <ml:id xml:space="preserve">XT12</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:imag font="0" symbol="j">1</ml:imag> <ml:id xml:space="preserve">XT12</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:imag symbol="j">1</ml:imag> <ml:id xml:space="preserve">XL12</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>-1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:imag symbol="j">1</ml:imag> <ml:id xml:space="preserve">XL12</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:div/> <ml:real>-1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:imag symbol="j">1</ml:imag> <ml:id xml:space="preserve">XL12</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:imag font="0" symbol="j">1</ml:imag> <ml:id xml:space="preserve">XT22</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:imag symbol="j">1</ml:imag> <ml:id xml:space="preserve">XL12</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>-1</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:imag font="0" symbol="j">1</ml:imag> <ml:id xml:space="preserve">XT22</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:div/> <ml:real>-1</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:imag font="0" symbol="j">1</ml:imag> <ml:id xml:space="preserve">XT22</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:imag font="0" symbol="j">1</ml:imag> <ml:id xml:space="preserve">XT22</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:imag font="0" symbol="j">1</ml:imag> <ml:id xml:space="preserve">XG22</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:matrix> </ml:define> </math> <rendering item-idref="94"/> </region> <region region-id="1848" left="18" top="3619.5" width="66" height="21" align-x="45.75" align-y="3636" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Z_2</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">Y2</ml:id> <ml:real>-1</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="95"/> </region> <region region-id="1849" left="12" top="3677.25" width="228" height="78.75" align-x="38.25" align-y="3720" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Z_2</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:matrix rows="4" cols="4"> <ml:complex> <ml:imag>0.055798489433155317</ml:imag> </ml:complex> <ml:complex> <ml:imag>0.051538263570767663</ml:imag> </ml:complex> <ml:complex> <ml:imag>0.025976908396441688</ml:imag> </ml:complex> <ml:complex> <ml:imag>0.018554934568886926</ml:imag> </ml:complex> <ml:complex> <ml:imag>0.05153826357076767</ml:imag> </ml:complex> <ml:complex> <ml:imag>0.093785796776763686</ml:imag> </ml:complex> <ml:complex> <ml:imag>0.047270996012739715</ml:imag> </ml:complex> <ml:complex> <ml:imag>0.033764997151956945</ml:imag> </ml:complex> <ml:complex> <ml:imag>0.025976908396441688</ml:imag> </ml:complex> <ml:complex> <ml:imag>0.0472709960127397</ml:imag> </ml:complex> <ml:complex> <ml:imag>0.17503552171052775</ml:imag> </ml:complex> <ml:complex> <ml:imag>0.125025372650377</ml:imag> </ml:complex> <ml:complex> <ml:imag>0.018554934568886926</ml:imag> </ml:complex> <ml:complex> <ml:imag>0.033764997151956938</ml:imag> </ml:complex> <ml:complex> <ml:imag>0.125025372650377</ml:imag> </ml:complex> <ml:complex> <ml:imag>0.15152365937354773</ml:imag> </ml:complex> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="96"/> </region> <region region-id="1853" left="24" top="3876" width="446.25" height="31.5" align-x="24" align-y="3888" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">The zero sequence matrix will be different, since there are more open connections</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">and shorts to ground.<sp count="2"/> </p> </text> </region> <region region-id="1961" left="6" top="3953.25" width="304.5" height="150.75" align-x="29.25" align-y="4032" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIFunction" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Y0</ml:id> <ml:matrix rows="4" cols="4"> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">ZG10</ml:id> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:imag font="0" symbol="j">1</ml:imag> <ml:id xml:space="preserve">XT10</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:imag symbol="j">1</ml:imag> <ml:id xml:space="preserve">XL10</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>-1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:imag symbol="j">1</ml:imag> <ml:id xml:space="preserve">XL10</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:div/> <ml:real>-1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:imag symbol="j">1</ml:imag> <ml:id xml:space="preserve">XL10</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:imag font="0" symbol="j">1</ml:imag> <ml:id xml:space="preserve">XT20</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:imag symbol="j">1</ml:imag> <ml:id xml:space="preserve">XL10</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">ZG20</ml:id> </ml:apply> </ml:matrix> </ml:define> </math> <rendering item-idref="97"/> </region> <region region-id="2139" left="18" top="4171.5" width="66" height="21" align-x="45.75" align-y="4188" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Z_0</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">Y0</ml:id> <ml:real>-1</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="98"/> </region> <region region-id="1860" left="24" top="4229.25" width="327" height="78.75" align-x="50.25" align-y="4272" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Z_0</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:matrix rows="4" cols="4"> <ml:complex> <ml:real>3.0497794580970385</ml:real> <ml:imag>0.030497794580970385</ml:imag> </ml:complex> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:complex> <ml:imag>0.047589450084756575</ml:imag> </ml:complex> <ml:complex> <ml:imag>0.0041995516103749339</ml:imag> </ml:complex> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:complex> <ml:imag>0.0041995516103749339</ml:imag> </ml:complex> <ml:complex> <ml:imag>0.079791480597123737</ml:imag> </ml:complex> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:complex> <ml:real>10.888468809073725</ml:real> <ml:imag>0.054442344045368636</ml:imag> </ml:complex> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="99"/> </region> <region region-id="1862" left="24" top="4356" width="318" height="15.75" align-x="24" align-y="4368" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">So for a SLG fault at bus 2, with prefault voltage of 1.0pu:</p> </text> </region> <region region-id="1866" left="60" top="4380.75" width="70.5" height="17.25" align-x="84.75" align-y="4392" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Zf0</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z_0</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="100"/> </region> <region region-id="2550" left="186" top="4380.75" width="75.75" height="15.75" align-x="209.25" align-y="4392" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Zf0</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:complex> <ml:imag>0.047589450084756575</ml:imag> </ml:complex> </result> </ml:eval> <resultFormat> <general precision="4" show-trailing-zeros="false" radix="dec" complex-threshold="10" exponential-threshold="4"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true"/> </resultFormat> </math> <rendering item-idref="101"/> </region> <region region-id="1870" left="60" top="4404.75" width="70.5" height="17.25" align-x="84.75" align-y="4416" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Zf1</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z_1</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="102"/> </region> <region region-id="2551" left="186" top="4404.75" width="75.75" height="15.75" align-x="209.25" align-y="4416" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Zf1</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:complex> <ml:imag>0.093785796776763686</ml:imag> </ml:complex> </result> </ml:eval> <resultFormat> <general precision="4" show-trailing-zeros="false" radix="dec" complex-threshold="10" exponential-threshold="4"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true"/> </resultFormat> </math> <rendering item-idref="103"/> </region> <region region-id="1874" left="60" top="4428.75" width="70.5" height="17.25" align-x="84.75" align-y="4440" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Zf2</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z_2</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="104"/> </region> <region region-id="2552" left="186" top="4428.75" width="75.75" height="15.75" align-x="209.25" align-y="4440" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Zf2</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:complex> <ml:imag>0.093785796776763686</ml:imag> </ml:complex> </result> </ml:eval> <resultFormat> <general precision="4" show-trailing-zeros="false" radix="dec" complex-threshold="10" exponential-threshold="4"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true"/> </resultFormat> </math> <rendering item-idref="105"/> </region> <region region-id="1912" left="36" top="4464" width="431.25" height="31.5" align-x="36" align-y="4476" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">For comparison, if we had done the normal circuit reduction for this fault point we would have:</p> </text> </region> <region region-id="1913" left="54" top="4506.75" width="102.75" height="15.75" align-x="104.25" align-y="4518" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Z1equiv2</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:complex> <ml:real>5.7425341315559508E-18</ml:real> <ml:imag>0.093785796776763672</ml:imag> </ml:complex> </result> </ml:eval> <resultFormat> <general precision="4" show-trailing-zeros="false" radix="dec" complex-threshold="10" exponential-threshold="4"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true"/> </resultFormat> </math> <rendering item-idref="106"/> </region> <region region-id="1914" left="198" top="4506.75" width="102.75" height="15.75" align-x="248.25" align-y="4518" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Z2equiv2</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:complex> <ml:real>5.7425341315559508E-18</ml:real> <ml:imag>0.093785796776763672</ml:imag> </ml:complex> </result> </ml:eval> <resultFormat> <general precision="4" show-trailing-zeros="false" radix="dec" complex-threshold="10" exponential-threshold="4"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true"/> </resultFormat> </math> <rendering item-idref="107"/> </region> <region region-id="1915" left="336" top="4506.75" width="102.75" height="15.75" align-x="386.25" align-y="4518" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Z0equiv2</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:complex> <ml:real>2.9139171474352888E-18</ml:real> <ml:imag>0.047589450084756575</ml:imag> </ml:complex> </result> </ml:eval> <resultFormat> <general precision="4" show-trailing-zeros="false" radix="dec" complex-threshold="10" exponential-threshold="4"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true"/> </resultFormat> </math> <rendering item-idref="108"/> </region> <region region-id="2553" left="24" top="4554" width="327" height="15.75" align-x="24" align-y="4566" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">And for a SLG fault at bus 3, with prefault voltage of 1.0pu:</p> </text> </region> <region region-id="2554" left="60" top="4578.75" width="76.5" height="17.25" align-x="90.75" align-y="4590" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Zf03</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z_0</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>2</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="109"/> </region> <region region-id="2555" left="186" top="4578.75" width="81.75" height="15.75" align-x="215.25" align-y="4590" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Zf03</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:complex> <ml:imag>0.079791480597123737</ml:imag> </ml:complex> </result> </ml:eval> <resultFormat> <general precision="4" show-trailing-zeros="false" radix="dec" complex-threshold="10" exponential-threshold="4"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true"/> </resultFormat> </math> <rendering item-idref="110"/> </region> <region region-id="2556" left="60" top="4602.75" width="76.5" height="17.25" align-x="90.75" align-y="4614" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Zf13</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z_1</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>2</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="111"/> </region> <region region-id="2557" left="186" top="4602.75" width="75.75" height="15.75" align-x="215.25" align-y="4614" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Zf13</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:complex> <ml:imag>0.17503552171052775</ml:imag> </ml:complex> </result> </ml:eval> <resultFormat> <general precision="4" show-trailing-zeros="false" radix="dec" complex-threshold="10" exponential-threshold="4"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true"/> </resultFormat> </math> <rendering item-idref="112"/> </region> <region region-id="2558" left="60" top="4626.75" width="76.5" height="17.25" align-x="90.75" align-y="4638" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Zf23</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z_2</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>2</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="113"/> </region> <region region-id="2559" left="186" top="4626.75" width="75.75" height="15.75" align-x="215.25" align-y="4638" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Zf23</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:complex> <ml:imag>0.17503552171052775</ml:imag> </ml:complex> </result> </ml:eval> <resultFormat> <general precision="4" show-trailing-zeros="false" radix="dec" complex-threshold="10" exponential-threshold="4"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true"/> </resultFormat> </math> <rendering item-idref="114"/> </region> <region region-id="2560" left="36" top="4662" width="431.25" height="31.5" align-x="36" align-y="4674" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">For comparison, if we had done the normal circuit reduction for this fault point we would have:</p> </text> </region> <region region-id="2561" left="54" top="4704.75" width="96.75" height="15.75" align-x="104.25" align-y="4716" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Z1equiv3</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:complex> <ml:real>1.0717480601566344E-17</ml:real> <ml:imag>0.17503552171052769</ml:imag> </ml:complex> </result> </ml:eval> <resultFormat> <general precision="4" show-trailing-zeros="false" radix="dec" complex-threshold="10" exponential-threshold="4"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true"/> </resultFormat> </math> <rendering item-idref="115"/> </region> <region region-id="2562" left="198" top="4704.75" width="96.75" height="15.75" align-x="248.25" align-y="4716" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Z2equiv3</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:complex> <ml:real>1.0717480601566344E-17</ml:real> <ml:imag>0.17503552171052769</ml:imag> </ml:complex> </result> </ml:eval> <resultFormat> <general precision="4" show-trailing-zeros="false" radix="dec" complex-threshold="10" exponential-threshold="4"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true"/> </resultFormat> </math> <rendering item-idref="116"/> </region> <region region-id="2563" left="336" top="4704.75" width="102.75" height="15.75" align-x="386.25" align-y="4716" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Z0equiv3</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:complex> <ml:real>4.8856577060066328E-18</ml:real> <ml:imag>0.079791480597123737</ml:imag> </ml:complex> </result> </ml:eval> <resultFormat> <general precision="4" show-trailing-zeros="false" radix="dec" complex-threshold="10" exponential-threshold="4"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true"/> </resultFormat> </math> <rendering item-idref="117"/> </region> <region region-id="2564" left="36" top="4746" width="104.25" height="15.75" align-x="36" align-y="4758" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">So we're consistent</p> </text> </region> <region region-id="2566" left="12" top="4842" width="177.75" height="15.75" align-x="22.5" align-y="4854" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">SLG current for a fault at bus 2: </p> </text> </region> <region region-id="1876" left="30" top="4870.5" width="173.25" height="35.25" align-x="57" align-y="4890" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Iaf0</ml:id> <ml:apply> <ml:div/> <ml:real>1.0</ml:real> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z_0</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z_1</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z_2</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="118"/> </region> <region region-id="1926" left="246" top="4878.75" width="84.75" height="15.75" align-x="271.5" align-y="4890" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Iaf0</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:complex> <ml:imag>-4.2524050094715653</ml:imag> </ml:complex> </result> </ml:eval> </math> <rendering item-idref="119"/> </region> <region region-id="2576" left="348" top="4878.75" width="55.5" height="15.75" align-x="375" align-y="4890" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-ca