How to calculate Reactive Power ?

Reactive Power

We know that reactive loads such as inductors and capacitors dissipate zero power, yet the fact that they drop voltage and draw current gives the deceptive impression that they actually do dissipate power.

This “phantom power” is called reactive power, and it is measured in a unit called Volt-Amps-Reactive (VAR), rather than watts.

The mathematical symbol for reactive power is (unfortunately) the capital letter Q.

True Power

The actual amount of power being used, or dissipated, in a circuit is called true power, and it is measured in watts (symbolized by the capital letter P, as always).

Apparent Power

The combination of reactive power and true power is called apparent power, and it is the product of a circuit’s voltage and current, without reference to phase angle.

Apparent power is measured in the unit of Volt-Amps (VA) and is symbolized by the capital letter S.

Calculating for Reactive, True, or Apparent Power

As a rule, true power is a function of a circuit’s dissipative elements, usually resistances (R). Reactive power is a function of a circuit’s reactance (X).

Apparent power is a function of a circuit’s total impedance (Z). Since we’re dealing with scalar quantities for power calculation, any complex starting quantities such as voltage, current, and impedance must be represented by their polar magnitudes, not by real or imaginary rectangular components.

For instance, if I’m calculating true power from current and resistance, I must use the polar magnitude for current, and not merely the “real” or “imaginary” portion of the current.

If I’m calculating apparent power from voltage and impedance, both of these formerly complex quantities must be reduced to their polar magnitudes for the scalar arithmetic.

Equations Using Scalar Quantities

There are several power equations relating the three types of power to resistance, reactance, and impedance (all using scalar quantities):

How to Calculate Reactive Power(kVAr)

JUL 22,2021

An example of how to calculate the capacity of reactive power (kVAr)?

An Motor is supplying a load of 700 kW at a P.F (Power factor) of 0.65. What size of Capacitor in kVAr is required to raise the P.F (Power Factor) to unity (1)?

And how many more kW can the motor supply for the same kVA loading when P.F improved.

Supplying kW = 700 kW

Original P.F = Cosθ1 = 0.65

Final P.F = Cosθ2 = 1

θ1 = Cos-1 = (0.65) = 49°.45;

Tan θ1 = Tan (41°.24) = 1.169

θ2 = Cos-1 = (1) = 0°;

Tan θ2 = Tan (0°) = 0

Required Capacitor kVAr to improve P.F from 0.65 to 1

Required Capacitor kVAr = P (Tan θ1 – Tan θ2)

= 700kW (1.169– 0)

= 818.3 kVAr