This short article will summarise voltage drop calculation formulas derivation from vector theory. Finally, an example of cable voltage drop calculation is provided.
• Voltage Drop in Electrical Cable
Actual voltage received at the electrical consumer’s terminals i.e. distribution transformers, motors, lighting fixture, analyzer package, etc. must be taken into account when selecting a suitable size of cable. There is voltage drop on electrical cable due to its characteristics, for example, cable resistance and reactance, load power factor. The bigger cable size, the lower voltage drop is on same cable length.
• Allowable Voltage Drop
There are numerous standards regulate allowable voltage drop all cross the world. Below are of most used allowable voltage drop.
International standards (IEC 60364-5-52) has specified voltage drop between the origin of an installation and any load point should not be greater below table:
NFPA NEC 70 2020 recommends the following allowable voltage drop of branch in articles 210.19(A) Note 3 and feeder in 215.2(A) Note 2.
|NEC ALLOWABLE VOLTAGE DROP|
|Combined feeder and branch at end user||5%|
• Formula development
Basic inputs to evaluate voltage drop calculation is:
- Data of cable (resistance R ohms, reactance X ohms, and cable length from power origin to loads),
- Consumer load (load rating power in kW and power factor).
The voltage drop formulas could be verified by the vector analysis figure below. Obviously, both accurate or approximate voltage drop is easy to obtain. However, in a practical project, an approximately calculated voltage drop is sufficient for calculation purposes. The assumption of approximate formulas is the angle between voltage received (VR) and voltage sent (VS) is small so that error of estimation could be ignored.
• Voltage Drop Formulas
Three-phase circuit voltage drop formula:
Single phase circuit voltage drop formula:
DC circuit voltage drop formula:
|VD||:||Voltage drop, in volts|
|cosΦ||:||Load power factor|
|R||:||Resistance of cable, in ohms per phase per 1000m|
|X||:||Reactance of cable, in ohms per phase per 1000m|
|I||:||Load current, in amperes|
|L||:||Total length of cable, in meter|
• An example of cable voltage drop calculation
4 runs of 120 mm2 3-core 6/10 (12) kV XLPE insulated cable 200 m in length feeds a 3kV 4000kW Medium Voltage Switchboard that has a full-load current of 855 amps, power factor is 0.9 lagging. Also, specific resistance R and reactance X for the cable are 0.196 and 0.099 ohm/km respectively at 90 oC and 50 Hz.
Let evaluate voltage drop on this cable:
|R||=||0,196 ohms per phase per 1000m|
|X||=||0,099 ohms per phase per 1000m|
Since there are 4 runs of cable, total resistance and reactance will be divided by 4 accordingly. Therefore, the voltage drop on this cable is:
VD = 1,73 x 855 x (0,196/4 x 0,9 + 0,99/4 x 0,4) x 200 / 1000 = 16V
Above manual calculation is an exercise of how to apply voltage drop formula. In order to automatically perform the same workflow, there is a voltage drop calculator tool to reduce time spending and prevent error.