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AN ENGINEERING SELECTION FOR SIZE OF LONG CONDUCTORS CONSIDERING FACTORS IN ADDITION TO NEC Marcus O. Durham THEWAY Corp / U of Tulsa Robert A. Durham Radco Consulting Abstract Conductor – – – – Sizing Long conductor Voltage Drop Diameter, Length, # Phases Current, Temperature Conductor Sizing Common Part of Electrical Design NEC I = insulation temperature => I2R losses => heat For For runs < 100 ft runs > 100 ft, voltage drop begins dominate Conductor Sizing Impedance Zallowed = Vdrop allowed / Irequired Its the basics Conductor Small Size p d2 2 A(mil )= = 0.7854 d 2 4 A ( cmil ) = d 2 mil 2 = 0 .7854 cmil d = 10 mils A = 100 cmils = 78.54 mils2 Conductor Resistance Correct Base resistivity for temperature, mat’l, config. = annealed copper @ 20o C 234.5oC + T . r = 10.371 * 102 o 254.5 C r = 10 .786 W cmil / ft CU @ 25o C r = 17 .35 W cmil / ft AL @ 25o C Wire Dimensions First Pass - Resistance Only l R=r A A= rlI VD Wire Dimensions Resistance - Phase # - Distance A= r (D * # cond)(phasefactor * I ) VD 1 phase: ph factor = 1 # cond / ph = 2 3 phase: ph factor = 3 # cond / ph = 1 Voltage Drop Effect of Wire Dimensions & Distance VD = r (D * # cond)(phase factor * I ) A Manipulate area calculation Wire Dimensions AC -vs- DC Calculations are DC Sizes < 4/0 DC AC Larger conductors ZAC 1.3 * RDC Total Z has inductive & capacitive components Z = R + jX AC Considerations Inductive Wire dimensions reactance X L = 2 p f L = 377 L Skin effect negligible @ power frequency L = 4 * 10 Divide -7 d l 1 + 4 ln r by 2 for coax and transmission AC Considerations Capacitive 2p e l C= ln(d / r ) Parallel, round conductors Divide by 2 for 2 wires of single phase Xc negligible < 2400 V Yc very large for lines < 10 miles Ignore for cable Voltage Drop Based on Impedance VD =Z =R+ jX I VD rl d -7 = 2 + 2p f l * 13.816 * 10 ln I 4r r 2 Parallel 2 Conductors Neglect Capacitance Calculate VD straightforward 2 Length From Wire Dimensions - Voltage Drop Contains ‘r’ and ln (r) Can’t solve directly Make assumptions ‘d’ between conductors 3 * radius Equations for VD and A are radicals Comparison Conventional -vs- Dimensions For single load, > 100’ Determine size based on I & T, using NEC Calculate size based on V & Z, using technique Select size that is largest for I or V Summary Wire Size - Conductor Properties Consider resistance and inductance Correct resistivity for mat’l, config, T Calculate area from resistivity, length, phase, current, V drop Manipulate for voltage drop and distance It’s Radical Questions ? Questions ?