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Voltage Drop Calculation 
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This article is the first of a series in the selection of electrical cables.
Cable selection is an important part of electrical installation design. Selecting the correct size of cable could lower initial cost, lower operating cost, better voltage regulation notwithstanding the safety factor.
Cable parameters are provided in values per unit length, usually ohms per kilometer(Ω/km) for IEC or miles(Ω/mi) for North American Standards.
The following table illustrate the typical parameters for industrial cables
Nominal conductor area (mm^{2}) 
Single cores in trefoil 
3 cores  Approximate armouring resistance 


Resistance at 90^{o}C (ohm/km) 
Reactance at 50Hz 
Resistance at 90^{o}C (ohm/km) 
Reactance at 50Hz 
GSWB at 60^{o}C 3Ã¢Â€Â“4 cores (ohm/km) 

1.5  15.6  0.185  15.6  0.118  46.2 
2.5  9.64  0.173  9.64  0.111  51.3 
4  5.99  0.163  5.99  0.108  60.3 
6  3.97  0.153  3.97  0.105  30.5 
10  2.35  0.148  2.35  0.0983  36.7 
16  1.48  0.134  1.48  0.0933  23.1 
25  0.936  0.125  0.936  0.0892  28.1 
35  0.674  0.121  0.674  0.0867  10.43 
50  0.499  0.118  0.499  0.0858  11.81 
70  0.344  0.112  0.344  0.0850  13.61 
95  0.271  0.108  0.271  0.0825  10.87 
120  0.214  0.106  0.214  0.0808  11.92 
150  0.175  0.105  0.175  0.0808  7.38 
185  0.140  0.105  0.140  0.0808  8.15 
240  0.108  0.103  0.108  0.0800  8.94 
300  0.087  0.101  0.087  0.0800  10.10 
400  0.069  0.0992  0.069  0.0795  10.00 
Derivation of Voltage Drop Formula
A short cable voltage drop in AC systems is provided by the formula
V_{d} = IR cosØ + IX sinØ
where:
V_{d} = Voltage drop per phase, volts
Ø = Load power factor angle
IR cosØ = Voltage drop component on the cable resistance
IX sinØ = Voltage drop component on the cable reactance
You might be wondering where this formula came from. Actually, this formula is just an approximation. We shall going through the process of deriving this formula to better understand it.
Considering the following vector diagram:
where:
V_{s} = Sending end voltage per phase
V_{r} = Receiving end voltage per phase
I = Load current
R = Cable resistance
X = Cable reactance
Ø = Load power factor angle
AB = IR cosØ
BE = CF = IR cosØ
BC = EF = IX sinØ
DF = IX cosØ
AC = AB + BC = AB + EF
AC = IR cosØ + IX sinØ
DC = DF  CF = DF  BE
DC = IX cosØ  IR sinØ
V_{s} = OD = √(OA + AB + BC)^{2} + (DF  BE)^{2}
Unless the cable is very long, the imaginary axis component of the voltage is very small compared to the real axis component.
(OA + AB + BC) >> (DF  BE)
thus the sending end voltage will be
V_{s} = (OA + AB + BC)
V_{s} = V_{r} + IR cosØ + IX sinØ volts/phase
From the above formula, the voltage drop on a per phase basis will be
V_{d} = V_{s}  V_{r}
V_{d} = IR cosØ + IX sinØ volts/phase per unit length
That is how the voltage drop formula was derived.
Normally, voltage drop is expressed as a percentage of the sending end linetoline voltage. The formula will be
where:
V = sending end linetoline voltage
R = rl, where r is the unit resistance in ohms/km
X = xl, where x is the unit reactance in ohms/km
as published in cable data publications.
For Part 2, we shall be providing real world examples on voltage drop calculations.
References:
 Handbook of Electrical Engineering For Practitioners in the Oil, Gas and Petrochemical Industry
Alan L. Sheldrake  Electrical Engineer's Reference Book Sixteenth edition
M. A. Laughton
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