# What is Power Factor (PF) ?

In order to understand about the term power factor and how to calculate power factor, it is important to know about some basic terms;

##### Real Power:

Real power is defined as the active or working power which is utilized by the load (equipment) to perform useful work. It is measured in KW or MW.

##### Reactive Power:

It is defined as the power which will help the equipment (load) to perform useful work. Reactive power occurs in AC circuits ( inductive & capacitive loads) when voltage and current are not in phase with each other. It is measured in KVAR.

Let’s take an example of motor↗. In order to convert mechanical energy into electrical energy, motor needs to generate magnetic field between the air gap of rotor and stator. Magnetic field is created by taking reactive power from the source. Hence, we can say that without reactive power, motor will not be able to rotate (i.e.  conversion of electrical to mechanical energy is not possible without the magnetic field which is produce by the reactive power).

##### Apparent Power:

It is simply defined as the combination of both real and reactive power. Apparent power is represented as KVA or MVA.

Now, let define the power factor by using the above basic terms ;

“Power factor is simply defined as the ratio of real power to apparent power. In other words, ratio of the real power to apparent power in AC circuits is called the power factor of load. #### Power Factor Triangle :

The relationship between Real power (KW), Apparent Power (KVA) and Reactive Power (KVAR) can also be understand by power factor triangle. In the above fig, is the phase angle difference between current and voltage waveform in AC circuit. As the value of varies power factor also varies. Hence we can also define power factor as:

“ Cosine of the phase angle difference between current and voltage in an AC circuit is known as power factor.” The power factor formula can be expressed as : OR, The value of power factor lies from 0 to 1 whereas desirable value of power factor considered as 1 or it should be nearer to 1. Moreover, the value of power factor depends on the type of load.

#### Power Factor of AC Circuit :

Electrical loads generally consist of resistive, inductive and capacitive components. Let discuss the most common type of loads (resistive, inductive, capacitance) to understand the concept of power factor in AC circuit. We will check the behavior of source voltage and current waveforms by applying a sinusoidal voltage V under steady state conditions.

##### Pure Resistive Circuit: In the above fig, blue curve represents the sinusoidal voltage waveform and red curve represents current waveform. As you can see that for resistive load, the applied voltage and current waveform is in phase with each other. In other words, phase angle difference between the current and voltage is zero in case of pure resistive load. Let see how to calculate power factor of this circuit.

Power Factor Calculation of Purely Resistive Circuit:

Since average power in single phase AC circuits is calculated as:

P= VI cos .

Here

P= Power in watts.

V= voltage in volts.

I= Current in amperes.

Cos = power factor of the circuit ( i.e. it is the phase difference between current and voltage waveform).

Putting =0 (Since phase angle difference between current and voltage waveform is 0 ),we have

Cos 0=1

Hence, the power factor of pure resistive circuit will be considered as one since cos =1. Therefore we can say that we will have a desirable value of power factor in case of pure resistive loads.

PF=1, if Load is purely resistive. Let us analyze the behavior of current and voltage waveforms in order to find the power factor of pure capacitor. By analyzing the sinusoidal waveform, we can see that there is phase difference between the current and voltage waveform. In simple words, current waveform is leading the voltage by 90 degrees in case of pure capacitive loads.( shown in the below fig). Power Factor Calculation of Pure Capacitor :

Average power in single phase AC circuits is calculated as:

P= VI cos .

Cos = power factor of the circuit (i.e. it is the phase difference between current and voltage waveform).

Putting =90 ( Since phase angle difference between current and voltage waveform is 90 ), hence we have

Cos 90=0

Since Cos 90=0,  we can say that capacitive load power factor is zero which is not desirable at all.

##### Inductive load Power Factor : In this case, we will analyze the behavior of current and voltage waveforms in case of pure inductive load. By analyzing the above diagram,  we can see that the phase difference between the current and voltage waveform is 90 degrees. In other words, load current lags the supply voltage by 90. Power Factor of Purely Inductive Circuit:

Average power in single phase AC circuits is given by :

P= VI cos .

Cos = power factor of the circuit.

Putting =90,  We have

Cos 90=0

Since Cos 90=0,  we can say that power factor of the circuit in case of pure inductive load is zero which is not desirable at all.

PF=0, if load appears as pure Inductive.

Power Factor for R-L  Circuit : Let takes both resistive and inductive loads as in the above circuit. In the above sine wave diagram, we have a phase lag of 90 degree between current and voltage waveform as in the case of pure inductive circuit. However  this phase difference lag varies in case of R-L circuit.

When the value of resistance R=0 (we have pure inductive circuit). In such a case, current waveform lag the voltage waveform by 90 and  power factor of the circuit will be zero. As the value of R increases, phase lag start to decrease and thus power factor start to increase. If the value of resistance R approaches to infinity, the value of inductor is so small that is negligible. In that case we have a phase difference of zero (i.e. pure resistive load in which phase lag is zero) and value of power factor is 1. Hence we can say that

For R-L Load, power factor varies between 0 and 1(Lagging).

The term “lagging” is used when the load current lags the applied voltage. In case of Inductive loads, current waveform lags behind the voltage. Therefore, we say that inductive loads have a lagging power factor.

Power Factor of R-C  Circuit : We will have another circuit having resistive and capacitive load. In the above sine wave diagram, there is a phase lag of between current and voltage waveform as in the case of pure capacitive circuit. However, this phase angle varies due to the addition of resistive load in the circuit. When the value of resistance R=0 (we have pure inductive circuit), current waveform lag the voltage by 90. In such a case power factor of the circuit will be zero.

As the value of R increases, phase lag start to decrease and power factor start to increase. If the value of resistance R approaches to infinity, the value of capacitance is so small that is negligible. In that case we have a phase difference of zero (i.e. pure resistive load in which phase lag is zero). In that case value of power factor is 1. Hence we can say that

#### Conclusion:

From the above discussion, we can say that

Power Factor=1, if Load is purely resistive.

PF=0, Power Factor of Pure Capacitor .

Power Factor =0, if Load is purely Inductive.

For R-L Load, power factor lies between 0and 1(Lagging Power Factor).