Calculating cable size required for UPS installation.

For many prospective power engineers especially involved in the business of alternative power generation primarily involving inverters, UPS and related technologies, solutions design is usually one of the major challenges. Often times they have an inverter that is adequately rated to take care of a particular load (in terms of rating) however, due to wrong cable section, the entire installation is a mess within the shortest possible period you can think of. A simple and safe approximation method of obtaining the right cable size is illustrated below:

Case Study:
Consider an installation that involves a Powerware 40kVA 9355(3-phase) UPS rated at 432VDC. Calculate the cable sizes required to install the UPS assuming the UPS will be operating at full load for a backup time of 12 hours.

Solution:
UPS rating; 40,000VA
UPS DC rating; 432V - 36 batteries

Battery cable Selection:
Maximum DC current(current drawn from battery) will be as calculated below:

Recall,

Power = Current x Voltage'

Then, Current = Power / Voltage

Therefore, Battery Current = UPS Power Rating / UPS DC Voltage rating

Battery Current = 40000VA / 432V = 92.59A

Battery cable size selector guide(safe assumption)

1mm sq => 4A

From the above assumption, the cable size that can accomodate 92.59A will be

92.59 / 4 = 23.15mm.

The minimum cable size that can be used for such an application( from battery to UPS should be 25mm sq. However, to be on a safer side, 35mm sq. can be used.

UPS Output Cable selection:
Since the output of the UPS is rated at 40kVA, and the output will be available as three
phase, then the power per phase will be

Power per phase = 40000VA / 3 = 13333.333VA

Phase voltage = 230V

Therefore, phase current = 13333.333VA / 230V = 57.97A

At 1mm sq. => 4A,

Minimum cable size to accommodate 57.97 A will be

57.97 / 4 = 14.49mm sq.

16mm sq. will be the reccommended minimum size

UPS input cable selection:
Recall, UPS output rating is 40kVA. However, the input power will usually be greater than
the output power. This is because charging power and overloads have to be considered. A
safe assumption is 30% extra on the output power.

To this end, the input power will be about

Input power = 130% of 40kVA = 52kVA

Therefore, input phase power will be

52kVA / 3 = 17333.333VA

Input phase current will be

17333.333VA / 230V = 75.36A

At 4A per mm sq., cable size will be

75.36 / 4 = 18.84mm sq.

That is, minimum cable size required will be 18.84mm sq(25mm sq. will be ideal)

Hence, cables required are:

Input cable - 25mm sq.
Output cable - 16mm sq.
Battery cable - 25 - 35mm sq.

For single phase UPS systems, the only difference is that you don't need to divide the power by 3.