Voltage Drop Calculations- Part Four


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:

  • Circular-mils method, 
  • Chapter (9) tables method. 

4- Approximate Mathematical method,

5- Quick On-Line method,

6- Ampere-Feet 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- Circular-mils 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(l-l) = √3 x 83.27A x .122ohms/1000ft x .200ft/1000ft = 3.5 V
Percent V.D = 3.5V / 208V = 1.7% 






5- Ampere-Feet Method







Ampere-Feet Method for Voltage Drop Calculation

  • You will find many manufacturers and city codes have tables (as in below image) that provide a quick reference for voltage drop calculations with ampere-feet values pre-calculated for 3% voltage drop.
  • The table values are provided for copper and Aluminum conductors and for single and three phases.


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 Amere-feet value from the given data, then select the next higher ampere-feet 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 Ampere-Feet Table for single phase 120 V, The Ampere-Feet 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

Ampere-feet = 200ft x 83.27 = 16,600 amp-ft

Lookup the above Ampere-Feet Table for 3 phase and find the next higher Ampere-Feet 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

  • You will find many manufacturers and city codes have lookup tables (as in below image) that provide a quick reference for voltage drop calculations with pre-calculated conductor sizes for certain Ampere load and conductor length for 3% voltage drop.
  • The table values are provided for copper and Aluminum conductors and for single and three phases.
  • there are many forms of Lookup Tables for Voltage drop calculations differ from each other according to the manufacturer or Authority that issue it.


How to use these tables:

1- To find the Minimum cable size which limit the VD to the table Value:

  1. Calculate the Ampere load from the given data,
  2. determine the suitable row for the next higher ampere load value
  3. determine the suitable column for the next higher conductor length
  4. Read the minimum conductor size will be at the crossing of steps 2 & 3.














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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