Understanding Reactive Power (kVAR)

In alternating current (AC) circuits, power is not just a single value. It is composed of different components. We usually talk about three types of power:

• Apparent Power (kVA): This is the total power supplied to a circuit, measured in kilovolt-amperes (kVA). It is the product of the RMS voltage and the RMS current.
• Active Power (kW): This is the power that does useful work (like running a motor or lighting a bulb), measured in kilowatts (kW). It is the real power consumed by the resistance in the circuit.
• Reactive Power (kVAR): This power is associated with the magnetic fields in inductors and electric fields in capacitors. It doesn't do useful work but is necessary for the operation of devices like motors and transformers. It is measured in kilovolt-ampere reactive (kVAR).

The Power Triangle and kVAR Formula

The relationship between these three types of power can be visualized using the power triangle. This is a right-angled triangle where:

• The hypotenuse represents Apparent Power (kVA).
• The adjacent side (usually horizontal) represents Active Power (kW).
• The opposite side (usually vertical) represents Reactive Power (kVAR).
• The angle between the Active Power and Apparent Power is the power factor angle, often denoted by ∅ (theta).

Using trigonometry on the power triangle, we can find expressions for Reactive Power (kVAR).

Let S be Apparent Power (kVA), P be Active Power (kW), and Q be Reactive Power (kVAR). The power triangle gives us:

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

\(\cos \theta = \frac{P}{S}\)

\(\sin \theta = \frac{Q}{S}\)

\(\tan \theta = \frac{Q}{P}\)

Deriving kVAR Formulae

From the trigonometric relationships, we can derive formulas for Reactive Power (Q or kVAR):

1. Using Sine:

   From \(\sin \theta = \frac{Q}{S}\), we can rearrange to solve for Q:

   \(Q = S \sin \theta\)

   In terms of units, this is:

   \(\text{kVAR} = \text{kVA} \sin \theta\)

2. Using Tangent:

   From \(\tan \theta = \frac{Q}{P}\), we can rearrange to solve for Q:

   \(Q = P \tan \theta\)

   In terms of units, this is:

   \(\text{kVAR} = \text{kW} \tan \theta\)

Conclusion on kVAR Calculation

Both formulas, \(\text{kVA} \sin \theta\) and \(\text{kW} \tan \theta\), are valid ways to calculate Reactive Power (kVAR) depending on whether you know the apparent power (kVA) or the active power (kW) along with the power factor angle ∅.

Therefore, the reactive power component kVAR is equal to both kW tan∅ and kVA sin∅.