# AN ENGINEERING SELECTION FOR SIZE OF LONG CONDUCTORS CONSIDERING FACTORS IN

```AN ENGINEERING SELECTION FOR
SIZE OF LONG CONDUCTORS
CONSIDERING FACTORS IN
Marcus O. Durham THEWAY Corp / U of Tulsa
Robert A. Durham
Abstract
 Conductor
–
–
–
–
Sizing
Long conductor
Voltage Drop
Diameter, Length, # Phases
Current, Temperature
Conductor Sizing
Common Part of Electrical Design
 NEC
I
= insulation temperature
=&gt; I2R losses =&gt; heat
 For
 For
runs &lt; 100 ft
runs &gt; 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 &amp; Distance
VD =
r (D * # cond)(phase factor * I )
A
Manipulate area calculation
Wire Dimensions
AC -vs- DC
 Calculations
are DC
 Sizes &lt; 4/0 DC  AC
 Larger conductors ZAC
1.3 * RDC
 Total Z has inductive &amp; 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 &lt; 2400 V
Yc very large for lines &lt; 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, &gt; 100’
Determine size based on I &amp; T, using NEC
Calculate size based on V &amp; 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