Active, Reactive and Apparent Power
Active, Reactive and Apparent Power
Many practical circuits involve a mixture of resistive, inductive and capacitive materials. These elements induce the phase change between electrical supply parameters, such as voltage and current. Due to the behavior of voltage and currents, especially when subjected to these components, power quantity comes in different forms.
Apparent Power
The result of the root mean square ( RMS) voltage and current value is known as the apparent power. This is calculated in kVA or MVA.
It has been stated that strength is absorbed only by opposition. The pure inductor and the pure capacitor do not absorb any power because, in a half-cycle, whatever power is obtained from the source by these elements, the same power is returned to the source. This power, which returns and flows in both directions to the circuit, is called the reactive power. This reactive power does not perform any useful work in the circuit.
In a strictly resistive circuit , the current is in phase with the applied voltage, while in a fully inductive and capacitive circuit , the current is 90 degrees out of phase , i.e. if the inductive load is connected by 90 degrees to the current lags voltage in the circuit, and if the capacitive load is connected, the current leads the voltage by 90 degrees.
Therefore,
- True power = Voltage x Current in phase with the voltage
- Reactive power = Voltage x Current out of phase with the voltage
The phasor diagram for an inductive circuit is shown below:
Taking voltage V as reference, the current I lags behind the voltage V by an angle ϕ. The current I is divided into two components:
- I Cos ϕ in phase with the voltage V
- I Sin ϕ which is 90 degrees out of phase with the voltage V
Therefore, the following expression shown below gives the active, reactive and apparent power respectively.
Active Power Formula
Active power P = V x I cosϕ = V I cosϕ
Reactive Power Formula
Reactive power Pr or Q = V x I sinϕ = V I sinϕ
Apparent Power Formula
Apparent power Pa or S = V x I = VI
Active Component of the Current
The current component, which is in phase with the circuit voltage and contributes to the active or true power of the circuit, is called an active component or watt-full component or in-phase component of the current.
Reactive Component of the Current
The current component, which is in quadrature or 90 degrees out of phase to the circuit voltage and contributes to the reactive power of the circuit, is called a reactive component of the current.
Reactive Power
The force that flows back and forth, which means that it travels in every direction of the circuit or responds on itself, is called the reactive force. Reactive strength is calculated by kilo volt-ampere reactive (kVAR) or MVAR.
Active Power
Power that is directly utilised or used in an AC circuit is called true power or active power or real power. It is measured in kilowatts ( kW) or MW. The direct output of the electrical device are the electrical connexions or the load.
Power Triangle
The relationship between active, reactive and apparent force can be represented by expressing quantities as vectors, often referred to as the force triangle approach as shown below. The voltage of this phasor diagram is assumed to be the reference vector. The voltage and current phasor diagram is the basis for the creation of the power triangle.
current lags the applied voltage by angle ϕ. The horizontal component of the current is I cos ϕ and the vertical component of the current is I sin ϕ. If each of the current phasor is multiplied by the voltage V, the power triangle is obtained as shown in the figure
The active power is contributed by the component I cos ϕ in phase with voltage while reactive power is produced by the quadrature component.
Therefore, the apparent power or the hypotenuse of the triangle is obtained by combining real and reactive power vectorially.
Using Pythagoras’s theorem, the sum of squares of the two adjacent sides (active power and reactive power) is equal to the square of the diagonal (apparent power). i.e.,
(Apparent power)2= (Real Power)2
S2 = P2+ Q2
S = √((Q2 + P2))
Where
S = apparent power measured in kilovolt amps, kVA
Q = reactive power measured in kilovolt amps reactive, kVAR
P = active power measured in kilowatts, kW
In terms of resistive, inductive and impedance elements, the power forms can be expressed as
Active power = P = I2R
Reactive power = Q = I2X
Apparent power = S = I2Z
Where
X is inductance
Z is impedance.