Understanding kVAR and Power Factor in Electric Circuits

The power in an AC electric circuit can be divided into three components:

• Active Power (P): Measured in Watts (W) or kilowatts (kW), this is the useful power that does work, like running a motor or lighting a bulb.
• Reactive Power (Q): Measured in Volt-Ampere Reactive (VAR) or kilo-Volt-Ampere Reactive (kVAR), this power is required by reactive components like inductors and capacitors to establish magnetic and electric fields. It doesn't do useful work but is necessary for the operation of many AC devices.
• Apparent Power (S): Measured in Volt-Ampere (VA) or kilo-Volt-Ampere (kVA), this is the total power supplied to the circuit. It is the vector sum of active and reactive power.

Relationship between Power Components and Power Factor

These power components are related by the power triangle, which follows the Pythagorean theorem:

\(S^2 = P^2 + Q^2\)

The power factor (PF) is the ratio of active power to apparent power. It indicates how effectively the apparent power is converted into active power.

\(PF = \frac{P}{S}\)

Power factor can also be expressed as the cosine of the angle (\(\phi\)) between the voltage and current waveforms:

\(PF = \cos(\phi)\)

In the power triangle, the angle \(\phi\) is the angle between the apparent power (S) and the active power (P). We also know that \(Q = S \sin(\phi)\).

Operating Power Factor when kVAR is Zero

The question states that the kVAR (reactive power, Q) of the electric circuit is equal to 'ZERO'. Let's see how this affects the power factor.

Given: \(Q = 0\)

Using the relationship \(S^2 = P^2 + Q^2\), if \(Q = 0\), the equation becomes:

\(S^2 = P^2 + 0^2\)

\(S^2 = P^2\)

Taking the square root of both sides (and considering positive power values):

\(S = P\)

Now, let's use the power factor formula: \(PF = \frac{P}{S}\).

Since we found that \(P = S\) when \(Q = 0\), we can substitute P with S (or S with P) in the power factor formula:

\(PF = \frac{P}{P} = 1\)

or

\(PF = \frac{S}{S} = 1\)

Alternatively, using the trigonometric relationship \(Q = S \sin(\phi)\):

If \(Q = 0\) and \(S\) is typically non-zero for an operating circuit, then \(\sin(\phi)\) must be 0.

\(S \sin(\phi) = 0 \implies \sin(\phi) = 0\)

The angle \(\phi\) for which \(\sin(\phi) = 0\) is \(0^\circ\) (assuming the fundamental angle). The power factor is \(PF = \cos(\phi)\).

\(PF = \cos(0^\circ)\)

\(PF = 1\)

A power factor of 1 is known as unity power factor. This condition occurs when the circuit behaves purely resistively, meaning there is no net reactive power being consumed or supplied by the circuit.

Conclusion

If the kVAR of an electric circuit is equal to zero, the active power (kW) is equal to the apparent power (kVA). This results in the operating power factor being equal to 1.