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Electrical Engineering DISCUSSION
The nameplate of our workshop transformer says 100 kVA, the biggest motor says 75 kW, and a small UPS is marked 1000 VA / 600 W. I understand that volts times amps gives power, so I do not see why three devices need two different units.
In practical terms: can a 100 kVA transformer supply loads that add up to 90 kW, and why does the UPS carry both a VA and a W figure?
kW is real power, the part that is converted to heat or mechanical work. kVA is apparent power, simply RMS voltage times RMS current. They are linked by the power factor: kW = kVA × pf. With inductive loads part of the current is reactive; it is 90° out of phase with the voltage and transfers no net energy, but it is still current in the wires. The three quantities form a right triangle: kVA² = kW² + kvar².
So the answer for your transformer depends on power factor. 90 kW at pf 0.8 is 90 / 0.8 = 112.5 kVA, which overloads it. 90 kW at pf 0.95 is 94.7 kVA, which fits.
A transformer is rated in kVA because its heating does not depend on power factor. Copper loss is I²R, set by the current, and core loss is set by the voltage. The manufacturer cannot know what load you will connect, so the limit is given as voltage times current.
For a 100 kVA, 400 V three-phase unit the full-load current is S / (√3 × V) = 100,000 / (1.732 × 400) = 144 A per line. That 144 A is the limit whether it delivers 100 kW to heaters at unity power factor or 80 kW to motors at 0.8.
A motor is rated by what it delivers, which is mechanical power at the shaft, so kW (or hp) is the natural unit. The electrical input is larger on two counts. Take the 75 kW motor with 94 percent efficiency and a power factor of 0.86: input power is 75 / 0.94 = 79.8 kW, apparent power is 79.8 / 0.86 = 92.8 kVA, and line current at 400 V is 92,800 / (1.732 × 400) = 134 A.
That single motor uses 93 percent of the 100 kVA transformer at full load, before its starting current is considered. Always convert motor kW to kVA with the efficiency and power factor on the nameplate before adding up loads.
The UPS has two limits because two different parts set them. The VA figure is the inverter's current limit. The W figure is the real power the battery and power stage can deliver. 1000 VA / 600 W means the designer assumed loads with a power factor of 0.6. Both limits must be respected: a 700 W load at unity power factor is only 700 VA but still overloads it on watts.
Modern computer power supplies have active power factor correction and draw close to unity power factor, so with those the watt rating is normally the one you reach first.
One addition: power factor is not only the phase angle. Rectifier loads such as LED drivers, variable-speed drives and older switch-mode supplies draw current in distorted pulses. The harmonic currents add to the RMS current, and therefore to the kVA, without delivering real power, even when the fundamental current is in phase with the voltage. A power analyser reports this as true power factor (kW / kVA) as opposed to displacement power factor (cos φ). When sizing a transformer or generator for mostly electronic loads, use the true figure.
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