Transformer Calculations Practice

Because what limits a transformer is how much current its windings can carry without overheating, and that current is set by volt-amperes regardless of the load's power factor. A 100 kVA transformer delivers 100 kW into a unity power factor load but only 80 kW at 0.8 power factor — and the winding current, and therefore the heating, is identical in both cases.

Divide the volt-amperes by the winding voltage for single phase, or by 1.732 times the voltage for three phase. A 75 kVA three-phase transformer with a 480-volt primary draws 75,000 ÷ (1.732 × 480) = 90.2 amperes on the primary, and with a 208-volt secondary delivers 75,000 ÷ (1.732 × 208) = 208.2 amperes. The kVA is the same on both sides; only the voltage and current differ.

Inversely to voltage, because volt-amperes in equals volt-amperes out apart from small losses. A transformer with a 480-volt primary and a 240-volt secondary delivering 100 amperes draws 50 amperes on the primary. Checking that the volt-amperes balance on both sides, 24,000 in that example, is the fastest way to catch an inverted ratio.

In a wye winding, line-to-line voltage is 1.732 times the line-to-neutral voltage, and line current equals winding current. In a delta winding it is the reverse: line voltage equals winding voltage, but line current is 1.732 times winding current. A delta primary with a wye secondary at 120 volts to neutral gives 208 volts line-to-line, which is where the 208Y/120 designation comes from.

An autotransformer has a single winding tapped to give the output voltage, rather than separate primary and secondary windings. That makes it smaller and cheaper for a given capacity, but because the windings share a conductive path there is no galvanic isolation. The common application is a buck-boost transformer, field-connected to add or subtract a modest voltage — useful for feeding 240-volt equipment from a 208-volt supply, because the unit only handles the difference rather than the whole load.

Because with separate windings the secondary has no electrical connection to the supply conductors, so it has no reference to ground until one is deliberately established. A system bonding jumper and a grounding electrode conductor create that reference and give secondary-side faults a low-impedance path back to the secondary source. An autotransformer, sharing a winding, does not create a separately derived system.

Core losses — hysteresis from repeatedly remagnetising the steel, and eddy currents circulating within it — plus the magnetizing current needed to establish the flux. These are roughly constant whenever the transformer is energized. Copper losses, by contrast, vary with the square of load current and are nearly zero at no load.