1. 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 Marcus O. Durham THEWAY Corp / U of Tulsa Robert A. Durham Radco Consulting

2. Abstract u Conductor Sizing –Long conductor –Voltage Drop –Diameter, Length, # Phases –Current, Temperature

3. Conductor Sizing Common Part of Electrical Design u NEC = insulation temperature u I => I 2 R losses => heat u For runs < 100 ft u For runs > 100 ft, voltage drop begins dominate

4. Conductor Sizing Impedance Z allowed = V drop allowed / I required Its the basics

5. Conductor Small Size Amil d d( ). 2 2 2 4 07854   Acmild()  2 milcmil 2 07854 . d = 10 mils A = 100 cmils = 78.54 mils 2

6. Conductor Resistance u Correct resistivity for temperature, mat’l, config. u Base = annealed copper @ 20 o C u CU @ 25 o C u AL @ 25 o C           10371102 2345 2545.*... o o CT C  10786. cmil/ ft   1735. cmil/ ft 

7. Wire Dimensions First Pass - Resistance Only

8. Wire Dimensions Resistance - Phase # - Distance u 1 phase: ph factor = 1# cond / ph = 2 u 3 phase: ph factor = # cond / ph = 1  A DcondphasefactorI V D   *#*

9. Voltage Drop Effect of Wire Dimensions & Distance  V DcondphasefactorI A D   *#* Manipulate area calculation

10. Wire Dimensions AC -vs- DC u Calculations are DC u Sizes < 4/0 DC AC u Larger conductors Z AC 1.3 * R DC u Total Z has inductive & capacitive components u Z = R + jX

11. AC Considerations Inductive u Wire dimensions reactance u Skin effect negligible @ power frequency u Divide by 2 for coax and transmission XfLL L  2377  L d r               41014 7 *ln l

12. AC Considerations Capacitive u Parallel, round conductors u Divide by 2 for 2 wires of single phase u X c negligible < 2400 V u Y c very large for lines < 10 miles u Ignore for cable   C dr  2  l ln/

13. Voltage Drop Based on Impedance u Parallel Conductors u Neglect Capacitance u Calculate V D straightforward V I ZRjX D  V Ir f d r D                            2 2 2 7 2 4 21381610   l l*.*ln

14. Length From Wire Dimensions - Voltage Drop u Contains ‘r’ and ln (r) u Can’t solve directly u Make assumptions u ‘d’ between conductors 3 * radius u Equations for V D and A are radicals

15. Comparison Conventional -vs- Dimensions u For single load, > 100’ u Determine size based on I & T, using NEC u Calculate size based on V & Z, using technique u Select size that is largest for I or V

16. Summary Wire Size - Conductor Properties u Consider resistance and inductance u Correct resistivity for mat’l, config, T u Calculate area from resistivity, length, phase, current, V drop u Manipulate for voltage drop and distance It’s Radical

17. Questions ?