Advanced Voltage Drop Calculations for 600 volt Building Wire
by Gerald Newton
April 24, 2003

The Problem:
The resistance's from Table 8, Chapter 9 of the NEC are for 75 degrees Centigrade.  There are methods of correcting these values for other temperatures using the equation at the bottom of the table, but no method is given for determining the conductor temperature.  Resistance of aluminum and copper decreases  with temperature, and conductor operating temperature decreases non linearly with a decrease in amperes due to the I square R heating effect.  In most cases, conductor operating temperature is not 75 degrees C. but at some lower temperature.   For example, a 12 AWG copper with 75 degree insulation has an ampacity of 25 amperes in Table 310.16.  This means that with 3 current carrying conductors in a raceway in an ambient temperature of 30 degrees C. the 12 AWG will reach 75 degrees C. when 25 amperes is applied.  However, in most cases the 12 AWG will be on a 20 ampere circuit breaker and will operate at 16 amperes maximum when continuously loaded.  With 16 amperes the approximate operating temperature of the 12 AWG is 46.8 degrees C. and not 75 degrees C.  Additionally, if the ambient temperature is at room temperature of 72 degrees F. the 12 AWG operating temperature is approximately  38.5 degrees C.


K Factor
Similar problems occur when using the k factor method of calculating voltage drop.  At 75 degrees C. K=12.9 ohms.  At 46.8 degrees C. K=11.7  and at 38.5 degrees C. K=11.35.  


Determining Conductor Operating Temperature


Approximate conductor operating temperature can be determined using the fourier heat transfer equation.  Both Samuel Rosch and Neher-McGrath used variations of this equation to determine ampacities.  Ampacity tables are created using the heat transfer equation.  The general equation is given in equation 1.

nm equation
equation 1

i = kiloamperes
tc = conductor temperature in degrees C.
ta = ambient temperature in degrees C.
rdc = resistance of one foot of conductor in microhms
rca = thermal resistance in thermal ohm feet
1+yc = multiplier for converting rdc to ac resistance and accounts for proximal heating effect from adjacent conductors.


By solving for rca(1+yc) given in equation 2 and using values for Table 310.16 and Table 8 of Chapter 9 of the NEC a table
of rca(1+yc) values can be found.
We can estimate the rca(1+Yc) values by using the current values (i) from the 75 degree columns for copper and aluminum in NEC Table 310.16.
For rdc we can use Table 8 in Chapter 9 of the NEC and move the decimal place three places to the left in the ohms/1000 ft
column to get microhms per foot. tc = 75 degrees C and ta = 30 degrees C.  We can then develop a table of rca(1+yc values
for the respective wire sizes for copper and aluminum.

rca
equation 2


Let rca' represent the values found in equation 2 for use in equation 4.

rcaprime .

We need one more equation before we can find tc, the conductor temperature.  That is the equation for rdc in terms of tc.  See equation 3.


rdc
equation 3

rdc = ohms
pc = circular mil ohms per foot of conductor at 20 degrees C. (10.371 ohms for 100% IACS copper, 17.002 ohms for 61% IACS aluminum)
tah = absolute value of inferred temperature of zero resistance. (234.5 degrees C. for copper and 228.1 degrees C. for aluminum)
cma = circular mil area of conductor from Chapter 9 Table 8 of NEC
tc = conductor temperature in degrees C.

Next we substitute equation 3 for rdc into equation 1 and solve for tc to get equation 4 where i is in amperes.

tcprime
 
equation 4


We find the tc for the given i and ta and then find K using equation 5.

k
equation 5

Next we find voltage drop using the standard voltage drop equation in 6.

vd
equation 6

l = conductor length in feet

Advanced Voltage Drop Calculator by electrician.com

Also use ampacity tables to select correct size conductor.
This calculator only determines voltage drop for a given conductor.

Select Material
Select Size

Select Voltage
and Phase
Select Ambient
Temperature C
(use 30 C if unsure)


Degrees F
Enter 1-way circuit
length in feet

Enter Load
in amperes
Voltage
drop
Voltage at load
end of circuit
Per Cent
voltage drop
Conductor Temperature
  Degrees C.

Data
(Conductor temperature should not exceed temperature for which
insulation is rated)
cma of
conductor
RCA
thermal
tah
Temp
Pc
resistance
Conductor
Temp
K for
temp



Reference Charts




k

Caution

When using the calculator the conductor's insulation temperature should not be exceeded
that would be a maximum of 90 degrees C plus 5 degrees for rounding off since the calculator is intended to
solve voltage drop problems for building wire listed in Table 310.16 of the NEC.
For practical NEC applications any voltage drop calculation must
also be complimented with an ampacity determination usually done by looking up ampacity in Table 310.16.
The calculator was designed for Table 310.16 conductors only and is an approximation since
RCA is calculated using only the 75 degree columns. The conductor temperature should
not exceed the respective temperature for the insulations listed that are 60 degrees C,
75 degrees C. and 90 degrees C. Also the thermal resistance values used in the calculator
were determined using only the 75 degree column. This is not exactly correct for the 60 and
90 degree columns since the ampacity in the 75 degree column that was used in this reverse
calculation method is actually a rounded off value, rounded to the nearest 5 amperes.
A more accurate method would be to determine the thermal resistances from all three columns,
60, 75, and 90 degrees C and then find the average value. Howerver, if the respective
ampacities from each of the columns is used in the advanced calculator the 60, 75, and
90 degree temperatures are fairly accurate. For instance for No. 4 Aluminum 65 amperes
calculates to 75 degrees C, 55 amperes results in 60.7 degrees C, and 75 amperes results
in 93.5 degrees C as the conductor temperatures.


The State of Washington Labor and Industries will not allow the use of this calculator.
They require using the k method with copper K = 12.9
and Aluminum K = 21.2 that assumes a conductor operating temperature of 75 degrees C.