.MCAD 304020000 1 77 572 0 .CMD PLOTFORMAT 0 0 1 1 1 0 0 1 1 0 0 1 1 1 0 0 1 1 0 1 0 0 1 1 NO-TRACE-STRING 0 0 0 0 0 0 2 1 0 1 1 NO-TRACE-STRING 0 3 2 0 1 1 NO-TRACE-STRING 0 4 3 0 1 1 NO-TRACE-STRING 0 1 4 0 1 1 NO-TRACE-STRING 0 2 5 0 1 1 NO-TRACE-STRING 0 3 6 0 1 1 NO-TRACE-STRING 0 4 0 0 1 1 NO-TRACE-STRING 0 1 1 0 1 1 NO-TRACE-STRING 0 2 2 0 1 1 NO-TRACE-STRING 0 3 3 0 1 1 NO-TRACE-STRING 0 4 4 0 1 1 NO-TRACE-STRING 0 1 5 0 1 1 NO-TRACE-STRING 0 2 6 0 1 1 NO-TRACE-STRING 0 3 0 0 1 1 NO-TRACE-STRING 0 4 1 0 1 1 NO-TRACE-STRING 0 1 1 21 15 0 0 3 .CMD PLOTFORMAT 0 0 1 1 1 0 0 1 1 0 0 1 1 1 0 0 1 1 0 1 0 0 1 1 NO-TRACE-STRING 0 0 0 0 0 0 2 1 0 1 1 NO-TRACE-STRING 0 3 2 0 1 1 NO-TRACE-STRING 0 4 3 0 1 1 NO-TRACE-STRING 0 1 4 0 1 1 NO-TRACE-STRING 0 2 5 0 1 1 NO-TRACE-STRING 0 3 6 0 1 1 NO-TRACE-STRING 0 4 0 0 1 1 NO-TRACE-STRING 0 1 1 0 1 1 NO-TRACE-STRING 0 2 2 0 1 1 NO-TRACE-STRING 0 3 3 0 1 1 NO-TRACE-STRING 0 4 4 0 1 1 NO-TRACE-STRING 0 1 5 0 1 1 NO-TRACE-STRING 0 2 6 0 1 1 NO-TRACE-STRING 0 3 0 0 1 1 NO-TRACE-STRING 0 4 1 0 1 1 NO-TRACE-STRING 0 1 1 21 15 0 1 3 .CMD FORMAT rd=d ct=10 im=i et=3 zt=15 pr=5 mass length time charge temperature tr=0 vm=0 .CMD SET ORIGIN 0 .CMD SET TOL 0.000001000000000 .CMD SET PRNCOLWIDTH 8 .CMD SET PRNPRECISION 6 .CMD PRINT_SETUP 0.984252 0.984252 0.984252 0.984252 0 .CMD HEADER_FOOTER 1 1 *empty* *empty* *empty* 0 1 *empty* *empty* *empty* .CMD HEADER_FOOTER_FONT fontID=14 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1 .CMD HEADER_FOOTER_FONT fontID=15 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1 .CMD DEFAULT_TEXT_PARPROPS 0 0 1744450612 .CMD DEFINE_FONTSTYLE_NAME fontID=0 name=Variables .CMD DEFINE_FONTSTYLE_NAME fontID=1 name=Constants .CMD DEFINE_FONTSTYLE_NAME fontID=2 name=Text .CMD DEFINE_FONTSTYLE_NAME fontID=4 name=User^1 .CMD DEFINE_FONTSTYLE_NAME fontID=5 name=User^2 .CMD DEFINE_FONTSTYLE_NAME fontID=6 name=User^3 .CMD DEFINE_FONTSTYLE_NAME fontID=7 name=User^4 .CMD DEFINE_FONTSTYLE_NAME fontID=8 name=User^5 .CMD DEFINE_FONTSTYLE_NAME fontID=9 name=User^6 .CMD DEFINE_FONTSTYLE_NAME fontID=10 name=User^7 .CMD DEFINE_FONTSTYLE fontID=0 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=2 .CMD DEFINE_FONTSTYLE fontID=1 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1 .CMD DEFINE_FONTSTYLE fontID=2 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1 .CMD DEFINE_FONTSTYLE fontID=4 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1 .CMD DEFINE_FONTSTYLE fontID=5 family=Courier^New points=10 bold=0 italic=0 underline=0 colrid=-1 .CMD DEFINE_FONTSTYLE fontID=6 family=System points=10 bold=0 italic=0 underline=0 colrid=-1 .CMD DEFINE_FONTSTYLE fontID=7 family=Script points=10 bold=0 italic=0 underline=0 colrid=-1 .CMD DEFINE_FONTSTYLE fontID=8 family=Roman points=10 bold=0 italic=0 underline=0 colrid=-1 .CMD DEFINE_FONTSTYLE fontID=9 family=Modern points=10 bold=0 italic=0 underline=0 colrid=-1 .CMD DEFINE_FONTSTYLE fontID=10 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1 .CMD UNITS U=1 .CMD DIMENSIONS_ANALYSIS 0 0 .CMD COLORTAB_ENTRY 0 0 0 .CMD COLORTAB_ENTRY 128 0 0 .CMD COLORTAB_ENTRY 0 128 0 .CMD COLORTAB_ENTRY 128 128 0 .CMD COLORTAB_ENTRY 0 0 128 .CMD COLORTAB_ENTRY 128 0 128 .CMD COLORTAB_ENTRY 0 128 128 .CMD COLORTAB_ENTRY 128 128 128 .CMD COLORTAB_ENTRY 192 192 192 .CMD COLORTAB_ENTRY 255 0 0 .CMD COLORTAB_ENTRY 0 255 0 .CMD COLORTAB_ENTRY 255 255 0 .CMD COLORTAB_ENTRY 0 0 255 .CMD COLORTAB_ENTRY 255 0 255 .CMD COLORTAB_ENTRY 0 255 255 .CMD COLORTAB_ENTRY 255 255 255 .TXT 2 1 427 0 0 0 Cg a48.500000,48.500000,48 {\rtf1\ansi \deff0{\fonttbl{\f0\fcharset0\fnil Arial;}}{\stylesheet{\f0 \fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\fs22\b Magnetic Field due to Three-phase Parallel Wires}} .TXT 3 0 456 0 0 0 Cg a73.700000,73.700000,464 {\rtf1\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1 This sheet will calculate magnetic field (flux density) in a plane a specified distance away from a cable carrying three-phase current. The default geometry is a trefoil (triangular) structure of three wires, but you can modify this to any geometry you choose simply by setting the co-ordinates of the three wires. The default is perfect balance (all three phases equal amplitude and 120 degrees apart) but again you can modify this to see the effect of imbalance.}} .TXT 13 0 497 0 0 0 Cg a77.400000,77.400000,24 {\rtf1\ansi \deff0{\fonttbl{\f0\fcharset0\fnil Arial;}}{\stylesheet{\f0 \fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard Absolute current in amps} .EQN 0 20 483 0 1 0 {0:I}NAME:470 .TXT 0 14 569 0 0 0 Cg a17.000000,17.000000,41 {\rtf1\ansi \deff0{\fonttbl{\f0\fcharset0\fnil Arial;}}{\stylesheet{\f0 \fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard Relative Current magnitudes (three phase)} .EQN 0 20 462 0 0 0 {0:I2}NAME:1*(-{0:cos}NAME(({0:\p}NAME)/(3))-1i*{0:sin}NAME(({0:\p}NAME)/(3))) .TXT 3 -54 498 0 0 0 Cg a34.400000,34.400000,44 {\rtf1\ansi \deff0{\fonttbl{\f0\fcharset0\fnil Arial;}}{\stylesheet{\f0 \fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard Proportionality constant,\par amps to microtesla} .EQN 0 48 463 0 0 0 {0:I1}NAME:1 .EQN 1 -28 482 0 0 0 {0:k}NAME:0.2 .EQN 1 34 464 0 0 0 {0:I3}NAME:1*(-{0:cos}NAME(({0:\p}NAME)/(3))+1i*{0:sin}NAME(({0:\p}NAME)/(3))) .TXT 2 -20 570 0 0 0 Cg a43.400000,43.400000,44 {\rtf1\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1\fs18 (Modify these to\par change the 3-phase\par balance)}} .TXT 1 -34 499 0 0 0 Cg a73.000000,73.000000,38 {\rtf1\ansi \deff0{\colortbl;\red255\green0\blue0;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard Grid resolution: \par ({\cf1 all dims in metres}) } .EQN 0 20 481 0 0 0 {0:dx}NAME:.1 .TXT 5 -20 500 0 0 0 Cg a73.000000,73.000000,11 {\rtf1\ansi \deff0{\fonttbl{\f0\fcharset0\fnil Arial;}}{\stylesheet{\f0 \fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard Index Range} .EQN 0 20 480 0 0 0 {0:ii}NAME:0;100 .TXT 3 -20 501 0 0 0 Cg a77.400000,77.400000,53 {\rtf1\ansi \deff0{\fonttbl{\f0\fcharset0\fnil Arial;}}{\stylesheet{\f0 \fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard Frig factor (to prevent\par singularities at wire centre)} .EQN 1 20 479 0 0 0 {0:dd}NAME:.01 .TXT 1 14 571 0 0 0 Cg a26.000000,26.000000,76 {\rtf1\ansi \deff0{\fonttbl{\f0\fcharset0\fnil Arial;}}{\stylesheet{\f0 \fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard Location of parallel trefoil wires 6cm apart perpendicular to the x-y plane} .EQN 1 29 442 0 0 0 {0:sep}NAME:0.06 .TXT 3 -63 502 0 0 0 Cg a22.900000,22.900000,59 {\rtf1\ansi \deff0{\fonttbl{\f0\fcharset0\fnil Arial;}}{\stylesheet{\f0 \fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard Observation plane (select y for closest distance to cables)} .TXT 1 34 572 0 0 0 Cg a42.400000,42.400000,67 {\rtf1\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard {\cf1\fs18 (Modify these to\par change the geometry\par of the three phase\par conductors)}} .EQN 2 18 520 0 0 0 {0:x1}NAME:(-{0:sep}NAME)/(2)*{0:cos}NAME(({0:\p}NAME)/(3)) .EQN 0 14 521 0 0 0 {0:y1}NAME:0 .EQN 2 -66 503 0 0 0 ({0:x}NAME)[({0:ii}NAME):({0:dx}NAME*{0:ii}NAME)-5 .EQN 0 20 488 0 1 0 {0:y}NAME:1.0 .EQN 4 32 522 0 0 0 {0:x2}NAME:({0:sep}NAME)/(2)*{0:cos}NAME(({0:\p}NAME)/(3)) .EQN 0 14 523 0 0 0 {0:y2}NAME:({0:sep}NAME)/(2) .TXT 6 -66 537 0 0 0 Cg a39.000000,39.000000,36 {\rtf1\ansi \deff0{\fonttbl{\f0\fcharset0\fnil Arial;}}{\stylesheet{\f0 \fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard Magnitude of each contributing field} .EQN 0 52 524 0 0 0 {0:x3}NAME:({0:sep}NAME)/(2)*{0:cos}NAME(({0:\p}NAME)/(3)) .EQN 0 14 525 0 0 0 {0:y3}NAME:(-{0:sep}NAME)/(2) .EQN 6 -66 531 0 0 0 {0:Bmag1}NAME({0:x}NAME,{0:y}NAME):({0:k}NAME*{0:I1}NAME*{0:I}NAME)/(\((({0:x}NAME-{0:x1}NAME))^(2)+(({0:y}NAME-{0:y1}NAME))^(2)+{0:dd}NAME)) .EQN 9 0 532 0 0 0 {0:Bmag2}NAME({0:x}NAME,{0:y}NAME):({0:k}NAME*{0:I2}NAME*{0:I}NAME)/(\((({0:x}NAME-{0:x2}NAME))^(2)+(({0:y}NAME-{0:y2}NAME))^(2)+{0:dd}NAME)) .EQN 9 0 534 0 0 0 {0:Bmag3}NAME({0:x}NAME,{0:y}NAME):({0:k}NAME*{0:I3}NAME*{0:I}NAME)/(\((({0:x}NAME-{0:x3}NAME))^(2)+(({0:y}NAME-{0:y3}NAME))^(2)+{0:dd}NAME)) .TXT 13 9 560 0 0 0 Cg a19.000000,19.000000,24 {\rtf1\ansi \deff0{\fonttbl{\f0\fcharset0\fnil Arial;}}{\stylesheet{\f0 \fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard Net B Field calculation } .EQN 0 25 553 0 0 0 {0:B}NAME({0:x}NAME,{0:y}NAME):({3,1}ö0ö{0:Bmag1}NAME({0:x}NAME,{0:y}NAME)*({0:x}NAME-{0:x1}NAME)/(\((({0:x}NAME-{0:x1}NAME))^(2)+(({0:y}NAME-{0:y1}NAME))^(2)+{0:dd}NAME)){54}{0:Bmag2}NAME({0:x}NAME,{0:y}NAME)*({0:x}NAME-{0:x2}NAME)/(\((({0:x}NAME- {0:x2}NAME))^(2)+(({0:y}NAME-{0:y2}NAME))^(2)+{0:dd}NAME)){54}{0:Bmag3}NAME({0:x}NAME,{0:y}NAME)*({0:x}NAME-{0:x3}NAME)/(\((({0:x}NAME-{0:x3}NAME))^(2)+(({0:y}NAME-{0:y3}NAME))^(2)+{0:dd}NAME))ö{0:Bmag1}NAME({0:x}NAME,{0:y}NAME)*(({0:y}NAME-{0:y1}NAME)*( -1))/(\((({0:x}NAME-{0:x1}NAME))^(2)+(({0:y}NAME-{0:y1}NAME))^(2)+{0:dd}NAME)){54}{0:Bmag2}NAME({0:x}NAME,{0:y}NAME)*(({0:y}NAME-{0:y2}NAME)*(-1))/(\((({0:x}NAME-{0:x2}NAME))^(2)+(({0:y}NAME-{0:y2}NAME))^(2)+{0:dd}NAME)){54}{0:Bmag3}NAME({0:x}NAME, {0:y}NAME)*(({0:y}NAME-{0:y3}NAME)*(-1))/(\((({0:x}NAME-{0:x3}NAME))^(2)+(({0:y}NAME-{0:y3}NAME))^(2)+{0:dd}NAME))) .TXT 7 -25 559 0 0 0 Cg a24.400000,24.400000,13 {\rtf1\ansi \deff0{\fonttbl{\f0\fcharset0\fnil Arial;}}{\stylesheet{\f0 \fs20 Normal;}}\plain\fs20 \pard\plain\s0\f0\fs20 \pard Sample result} .EQN 4 0 558 0 0 0 |({0:B}NAME(0,2.5))={0}?_n_u_l_l_ .EQN 20 -9 562 0 0 0 6&-0.5&(_n_u_l_l_&_n_u_l_l_)&|({0:B}NAME(({0:x}NAME)[({0:ii}NAME),{0:y}NAME)),{0:y1}NAME,{0:y2}NAME,{0:y3}NAME@&&(_n_u_l_l_&_n_u_l_l_)&({0:x}NAME)[({0:ii}NAME),{0:x1}NAME,{0:x2}NAME,{0:x3}NAME 0 1 1 0 0 10 0 1 1 Horizontal distance, m 0 1 1 1 1 0 0 1 1 MicroTesla (cable position, m) 0 1 0 0 2 2 Mag field 0 0 0 1 1 5 0 1 0 2 2 Wire 1 5 0 2 0 2 2 Wire 2 5 0 3 0 2 2 Wire 3 0 1 4 0 1 1 NO-TRACE-STRING 0 2 5 0 1 1 NO-TRACE-STRING 0 3 6 0 1 1 NO-TRACE-STRING 0 4 0 0 1 1 NO-TRACE-STRING 0 1 1 0 1 1 NO-TRACE-STRING 0 2 2 0 1 1 NO-TRACE-STRING 0 3 3 0 1 1 NO-TRACE-STRING 0 4 4 0 1 1 NO-TRACE-STRING 0 1 5 0 1 1 NO-TRACE-STRING 0 2 6 0 1 1 NO-TRACE-STRING 0 3 0 0 1 1 NO-TRACE-STRING 0 4 1 0 1 1 NO-TRACE-STRING 1 0 1 59 43 12 0 3 Magnetic flux, y m from 3-phase cable .TXT 88 1 564 0 1 0 Cg a76.400000,76.400000,229 {\rtf1\ansi \deff0{\fonttbl{\f0\fcharset0\fnil Arial;}{\f1\fcharset0 \fnil Courier New;}}{\stylesheet{\f0\fs20 Normal;}}\plain\fs20 \pard \plain\s0\f0\fs20 \pard {\fs16 This worksheet is provided by Elmac Services. Every effort is taken to achieve accuracy but no responsibility\par can be accepted for the consequences of errors. \par For other EMC-related Mathcad worksheets, visit }{\f1\fs16 http://www.elmac.co.uk}}