## What is the power factor and its importance

In electrical systems, the Power factor is a very common word, and maintaining the power factor helps a lot in savings of energy. Since power factor improvement helps in saving energy, hence cost is also saved so it is necessary that everyone must know about the power factor. In this blog, we will help you understand what is the power factor and its importance and how we can improve it to take maximum benefits and that in simpler terms.

## What is the Power factor?

The power factor is the term used in AC (alternating current) electrical power systems.

In simpler language power factor is the ratio of power in Kilowatts (KW) to the power in Kilovolt Ampere (KVA). Power measured under KW is called real power and power measured under KVA is called apparent power. This can be explained as flowing in the circuit.

There are three types of power in the circuit

1. Real Power (KW)
2. Apparent power (KVA)
3. Reactive  Power (KVAR)

### Power factor analogy

Looking at this analogy of a cold coffee cup, one can simply understand these terms.

Imagine you went to a restaurant and you ordered a cup of cold coffee. The waiter gives a cup full of cold coffee and when you start drinking cold coffee,  you will realize that some portion of the cold coffee will not quench your thirst. The thirst-quenching part of your cold coffee cup is represented by Real Power (kW). Unfortunately, along with your actual coffee, there comes a little bit of foam and that foam doesn’t quench your thirst. This part is represented as Reactive Power (kVAR). The total quantity of cold coffee in your cup is represented as apparent power (KVA) which is the sum of Actual power kW (the Cold coffee part) and kVAR (the foam part).

As we know the ratio between Real Power and Apparent Power is called power factor. When the power factor is 1, then all the power supplied will be used for productive work and will be the perfect situation.

So, for a given power supply which is represented in kilo Volt Ampere (kVA):

Take a case 1 when the foam you are having is less this means you will have a lower percentage of kVAR, this will result in your higher ratio of kW ( coffee ) to kVA ( Coffee plus foam ).

Take a case 2 when there is more foam you have then there will be a higher percentage of kVAR this will result in lowering the ratio of kW (Coffee) to kVA (Coffee plus foam).

In case -1 you will be having a higher power factor and this is value for money.

In case -2 you will be having a lower power factor and this will be a waste of money.

## What is the unit of power factor?

Since it is a ratio Power factor, it is unitless.

The range of power factor varies from -1 to 1.

## Power factor formula

### Power factor symbol

The Power factor is represented as  Cos θ,

It is the cosine of phase angle (θ ) between voltage and current.

As mentioned above power factor is the ratio of real power (KW) and apparent power (KVA).

Power factor  (PF) =  Real power (KW) /  Apparent power ( KVA)

### Power factor formula three phase

The Power (P) = V I Cos θ, power factor ( Cos θ ) will be = ( V I )  / P

P = Power in Watts

V = Voltages in Volts

I = Current in Amperes

W = Real Power in Watts

VA = Apparent Power in Volt-Amperes

Cos θ = Power factor

## Power factor calculation

In order to calculate the power factor, you need to take Real energy  (KWh) /  Apparent energy ( KVAh) readings after some defined interval.

Let’s take an example to calculate the power factor during the whole month

Reading on the first day of Jan as under:

12400 KWh and 13800 KVAh

And readings on the first day of February

14500 KWh and 16100 KVAh

Then consumption need to be calculated

KWh consumptions as = ( 14500 – 12400 ) = 2100

KVAh consumption as = ( 16100 – 13800 )  = 2300

Power factor will be = 2100 / 2300 = 0.913

## Lagging, Leading and Unity power factors

Lagging and leading are determined with the position of current to the voltage.

### When the power factor is lagging

When the phase angle of the current ( I ) is lagging behind the voltage ( V ) then the power factor ( Cos θ ) is called a lagging power factor.

The lagging power factor occurs when the load is inductive.  This is the most common phenomenon in the industries nowadays as the load is major because of induction motors.

So in a lagging power factor situation, the load will “consume” reactive power, and the reactive component is positive. The reactive power travels in the circuit and is consumed by the load which is inductive in nature.

### When the power factor is leading

When the phase angle of the current ( I ) is leading the voltage ( V ) then the power factor ( Cos θ ) is called a leading power factor.

This occurs when the load is capacitive, and the reactive component is negative.

The reactive power is being supplied to the circuit and the load supplies reactive power.

### Unity power factor

And in the case of a purely resistive circuit, the power factor is 1 (unity) due to zero phase angle θ difference between current and voltage.

## Power factor not more than one (unity)

Since we know the Power factor is the cosine of the phase angle between current and voltage.  Cosine can never be greater than one (unity).

In other terms, the power factor is the ratio of true power (KW) to the apparent power (KVA). So the apparent power will always be greater than true power and true power can neither exceed apparent power.  So power factor cannot come more than unity.

## Importance of power factor

Power factor is important as less power factor is a type of energy loss. When the power factor is unity the real power and apparent power are equal then there will be a minimum loss.

The power supply company charge bills based upon apparent power consumptions (KVAh). If the power factor is less than unity. The apparent power consumption will be more than real power consumption hence more units of energy will be charged. So there is a great importance of power factor to keep it at the higher side as it helps in saving energy hence reduction of power bills and reduction of cost.

## Power factor improvement

As we know the power factor is having great importance and keeping it at the higher side will save energy. By following ways we can improve the power factor:

• using static capacitor bank
• By using the synchronous condenser
• Or by using Phase advancers

1. ### Static capacitor bank:

This is a simple way to improve the power factor. This is done by adding a static capacitor bank in the power circuit.

In inductive load the current lags behind voltage and in capacitive load the current leads the voltage. In industry, due to the high inductive load, the power factor is lagging. A combination of both Inductive and capacitive load results in the correction of the power factor.

The capacitors are connected parallel with the load. This method of improving the power factor by using a static capacitor is used generally in industries.  Generally equivalent to inductive load, the capacitive load is added in the system.

• Easy to install
• Less loss.
• The maintenance required is also less.
• Not having any rotating part.

• Having less life which is around  5-6 years.
• Not easy to repair only  replacement

1. ### Using synchronous condenser

When the synchronous motor is overexcited it behaves like a capacitor. This factor is used to improve the power factor.

Technically When a synchronous motor is running at no-load and at over-excited condition then it is called a synchronous condenser.

When the synchronous motor power factor is unity, then the DC excitation is said to be normal.  When it is over-excitation this causes the motor to operate at a leading power factor.  It the excitation is Under normal then it operates at a lagging power factor. In the overexcitation stage, it behaves like a capacitor and under such conditions, the synchronous motor is called synchronous capacitor.

So in order to improve the factor for any load then the synchronous machine is used as a synchronous condenser is a connected parallel.

• There is High thermal stability of synchronous motor winding.
• It is easy to identify and remove the fault.

• There are losses in the motor.
• Since it is having rotating parts so it is having High maintenance cost.
• Since the motor is running hence Noise is produced.

There is another method to improve the power factor this is done by adding Phase advancers.

This helps in improving the power factor of the induction motor.  In normal conditions when the induction motor is running, it creates lagging in the power factor because of induction caused by its stator winding.  The current lags to the supply voltage.

If the exciting ampere-turns is provided from another alternating current ( A-C) source, then the stator winding will get rid of the exciting current and the power factor of that induction motor can be improved.

This is possible by adding a phase advancer circuit which is not a complicated thing but a simple AC exciter. The phase advance is mounted on the same shaft of the induction motor as the main motor and is connected to the rotor circuit of the induction motor.

This phase advancer circuit provides exciting ampere turns to the rotor circuit of the motor at slip frequency. This helps in improving the position of current to voltage and hence the power factor is improved and this step-up will be acting as the over-excited synchronous motor.

• Since the exciting ampere-turns are supplied at slip frequency, this helps in the reduction of lagging kVAR drawn by the induction motor.
• These phase advancers can be suitably used where the use of synchronous motors is not possible.

• phase advancer’s major disadvantage is that they are  costlier for motor below  200 H.P

## How to calculate savings for power factor improvement

Consider our example of power factor calculation:

We came to know that our power factor is =  0.913

Target of power factor is = 0.990

Savings of power factor = 0.990 – 0.913 = 0.077

Savings of units per month = 0.077 X  2100 (monthly KW consumption)

= 161.7 KVA

Savings of cost per month = 161.7 X (Unit rate )

## Summary – What is the power factor and its importance

We hope that in this post what is the power factor and its importance, you must have got good information about the power factor.

Let us now try to know the essence.

• The power factor is the ratio of the power of the kilowatt (KW) to the power of the kilovolt ampere (KVA).
• Since the power factor is a Ratio it is unitless.
• Power Factor (PF) = real power Actual power (KW) / Apparent power Apparent power (KVA).
• Power factor can be lagging or leading.
• There is a great importance of the power factor and keeping that on the higher side helps in saving energy.
• There are three ways in which we can increase the power factor.
• using static capacitor bank
• using synchronous condenser