In article " Voltage drop calculations Part One ", I indicated that there are eight methods for Voltage Drop Calculations as follows:
1 Ohm’s Law Method,
2 European method,
3 U.S method which divided to:
 Circularmils method,
 Chapter (9) tables method.
4 Approximate Mathematical method,
5 Quick OnLine method,
6 AmpereFeet method,
7 Lookup tables,
8 Excel spreadsheets.
And I explained the first two methods: Ohm’s Law Method and European method in this Article.
And, I explained the third method: U.S Method Circularmils method In Article" Voltage drop calculations Part Two ".
Also, I explained the third method: U.S Method Chapter (9) tables method In Articles:
Today I will continue explaining other methods for Voltage Drop Calculations as follows.
4 Approximate Mathematical Method
Approximate Mathematical Method for Voltage Drop Calculation
The Approximate
formulas for calculating voltage drop are as follows:
Voltage Drop 3Ø
= √3 I (R cos θ + X sin θ) L
Voltage Drop 1Ø
= 2 I (R cos θ + X sin θ) L
Where:
Voltage Drop =
in volts (V)
I = Current in
amperes
R= Conductive
resistance in ohms/ 1000 ft.
X= Conductor
inductive reactance in ohms/1000 ft.
L= one way
length of circuit (source to load) in thousands of feet (K ft.)
θ = Phase angle
of load
and if:
Z = R cos θ + X
sin θ
Where:
Z = Complex
impedance ohms/ 1000 ft. obtain from Manufacturers Tables.
Then,
Voltage Drop 3Ø
= √3 I (Z) L
Voltage Drop 1Ø =
2 I (Z) L

Example#1:
30KVA load, 3 phases, 208V, 200 feet, 1/0 cable. What is the voltage drop knowing that the impedance = .122 ohms/1000ft?
Solution:
I = 30KVA / (1.73 x 208) = 83.27amp
Voltage Drop 3Ø = √3 I (Z) L
Vd(ll) = √3 x 83.27A x .122ohms/1000ft x .200ft/1000ft = 3.5 V Percent V.D = 3.5V / 208V = 1.7%
5 AmpereFeet Method
AmpereFeet Method for Voltage Drop Calculation
How to use these
tables:
1 To find the maximum
distance in feet for each conductor which limit the VD to the table Value.
Divide the table
value by the total circuit Amperes to obtain the maximum distance in feet for
each conductor.
2 To find the
Minimum cable size which limit the VD to the table Value.
Calculate the
Amerefeet value from the given data, then select the next higher amperefeet
value from the table.

Example#2:
A 10A load at 120V, using #14 wire what will be maximum distance in feet for each conductor which limit the VD to 3%?
Solution:
From the above AmpereFeet Table for single phase 120 V, The AmpereFeet value = 604
The maximum distance = 604 ÷ 10 A = 60.4 ft. max. For a 3% voltage drop.
Example#3:
30KVA load, 3 phases, 208V, 200 feet. What is the required cable size to limit voltage drop to 3%?
Solution: (see image in example#2)
I = 30KVA / (1.73 x 208) = 83.27amp
Amperefeet = 200ft x 83.27 = 16,600 ampft
Lookup the above AmpereFeet Table for 3 phase and find the next higher AmpereFeet value under 208 V Column
It will be 16,865 for size cable is #1/0
6 Lookup Tables Method
Lookup Tables Method For Voltage Drop Calculation
How to use these
tables:
1 To find the
Minimum cable size which limit the VD to the table Value:

Example#4:
20KVA load, single phases, 220 V, 130 feet. what is the minimum conductor size to limit voltage drop to 3%?
Solution:
Step#1: Calculate the Ampere load from the given data,
I = 10KVA / 220 = 45.45 amp
Step#2: determine the suitable row for the next higher ampere load value
It is the 50 A Copper Row.
Step#3: determine the suitable column for the next higher conductor length
It is the 150 feet Column.
Step#4: Read the minimum conductor size will be at the crossing of steps 2 & 3.
It is 4 AWG.
In the next Article, I will continue explaining Other Methods for Voltage Drop Calculations. Please, keep following.
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