By Kevin Beck
Updated Mar 24, 2022

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Power Fundamentals

In physics, power is defined as energy per unit time. While energy is measured in joules (J) and power in watts (W), electrical engineering often uses the product of voltage (V) and current (I). Thus:

P = V * I

Because 1 W = 1 V·A, a kilowatt (kW) equals a kilovolt-ampere (kVA). This equivalence holds for single-phase circuits.

Three-Phase Power and the kVA-kW Relationship

Three-phase AC systems distribute voltage across three sinusoidal waveforms that are offset by 120°. The combined power of such a system is calculated as:

P = sqrt(3) * V * I

Consequently, for three-phase equipment:

kW = sqrt(3) * kVA

This relationship means that a motor rated at 10 kVA will draw approximately 17.3 kW of real power when operating at unity power factor.

Step-by-Step Example

Suppose a three-phase supply delivers 220 V per phase and 40 A per phase. What is the apparent power in kilowatts?

1. Compute the raw apparent power per phase: (220 V)(40 A) = 8,800 VA.
2. Apply the three-phase factor: sqrt(3) * 8,800 VA ≈ 15,242 VA.
3. Convert to kilowatts: 15,242 VA ÷ 1,000 ≈ 15.24 kW.

Thus, the three-phase circuit consumes about 15.2 kW of real power.

For a deeper dive into power factor, load balancing, and three-phase motor sizing, consult resources such as IEEE Transactions on Power Delivery or the IEC 60204 standard.