Power, in general physics, is energy per unit time. Energy in turn is force multiplied through a distance. The standard, or SI, unit for power is watts (W), while the SI unit for energy is joules (J). Time is normally expressed in seconds.
In electromagnetic physics, the principles stand but the units shift. Instead of determining power as W = J ÷ s, power is expressed as the product of potential difference in volts (V) and current in amperes (I). Thus in this scheme, W = V ⋅ I.
From these equations, it is clear that a watt is the same as a volt times an ampere, or a volt-ampere (VA). It therefore follows that a kilowatt (kW) is the same as a kilo-volt-ampere (kVA), with each side of the equation divided by 1,000.
In alternating current (AC) power systems, voltage is often delivered in phases, as this is advantageous in terms of reducing energy losses. These phases appear graphically as sine waves, with voltage rising and falling cyclically over short period of time. In a three-phase system, these sine waves overlap, but their cycles start and end at different points in time. The result is that power in these systems is not simply the product of voltage times current, but is instead (√3)( V ⋅ I).
Therefore, if you are working with a three-phase motor, the relationship between kW and kVA is:
kW = (√3)(kVA).
Assume you are given a three-phase AC power source with a voltage of 220 V supplying a current of 40 A. What is the power in kilowatts?
First, multiply the voltage and the current to obtain raw volt-amperes:
(220 V)(40 A) = 8,800 VA
Then, multiply by the normalizing factor for three-phase systems:
(√3) (880 VA) = 15,242 VA
Finally, divided by 1,000 to get the answer in kW (or kVA):
15,242 W ÷ 1,000 = 15.242 kW
