## What is Power Factor?

In electrical engineering, the power factor (PF) of an AC electrical power system is defined as the ratio of working power (measured in kilowatts, kW) absorbed by the load to the apparent power (measured in kilovolt amperes, kVA) flowing through the circuit. Power factor is a dimensionless number in the closed interval of −1 to 1.

The “ideal” power factor is one (also referred to as “unity”). This is when there is no reactive power through the circuit, and hence apparent power (kVA) is equal to real power (kW). A load with a power factor of 1 is the most efficient loading of the supply.

That said this is not realistic, and the power factor will in practice be less than 1. Various power factor correction techniques are used to help increase the power factor to this ideal state.

To help explain this better, let’s take a step back and talk about what power is.

Power is the capacity to do work. In the electrical domain, electrical power is the amount of electrical energy that can be transferred to some other form (heat, light, etc) per unit of time.

Mathematically power factor is the product of voltage drop across the element and current flowing through it.

Considering first the DC circuits, having only DC voltage sources, the inductors and capacitors behave as short circuit and open circuit respectively in steady-state.

Hence the entire circuit behaves as resistive circuit and the entire electrical power is dissipated in the form of heat. Here the voltage and current are in same phase and the total electrical power is given by:

Now coming to AC circuit, here both inductor and capacitor offer a certain amount of impedance given by:

The inductor stores electrical energy in the form of magnetic energy and capacitor stores electrical energy in the form of electrostatic energy. Neither of them dissipates it. Further, there is a phase shift between voltage and current.

Hence when we consider the entire circuit consisting of a resistor, inductor, and capacitor, there exists some phase difference between the source voltage and current.

The cosine of this phase difference is called **electrical power factor**. This factor (-1 < cosφ < 1 ) represents the fraction of the total power that is used to do the useful work. The other fraction of electrical power is stored in the form of magnetic energy or electrostatic energy in the inductor and capacitor respectively.

The total power in this case is:

This is called apparent power and its unit is VA (Volt Amp) and denoted by ‘S’. A fraction of this total electrical power which does our useful work is called active power. We denote it as ‘P’.

P = Active power = Total electrical power.cosφ and its unit is watt.

The other fraction of power is called reactive power. Reactive power does no useful work, but it is required for the active work to be done. We denote it with ‘Q’ and mathematically is given by:

Q = Reactive power = Total electrical power.sinφ and its unit is VAR (Volt Amp Reactive). This reactive power oscillates between source and load. To help understand this better all these power are represented in the form of a triangle.

Mathematically, S^{2} = P^{2} + Q^{2} and **electrical power factor** is active power / apparent power.

## Power Factor Improvement

The term power factor comes into the picture in AC circuits only. Mathematically it is the cosine of the phase difference between the source voltage and current. It refers to the fraction of total power (apparent power) which is utilized to do the useful work called active power.

Need for Power Factor Improvement

- Real power is given by P = VIcosφ. The electrical current is inversely proportional to cosφ for transferring a given amount of power at a certain voltage. Hence higher the pf lower will be the current flowing. A small current flow requires a less cross-sectional area of conductors, and thus it saves conductors and money.
- From the above relation, we see having poor power factor increases the current flowing in a conductor and thus copper loss increases. A large voltage drop occurs in the alternator, electrical transformer and transmission and distribution lines – which gives very poor voltage regulation.
- The KVA rating of machines is also reduced by having higher power factor, as per the formula:

Hence, the size and cost of the machine is also reduced.

This is why electrical power factor should be maintained close to unity – it is significantly cheaper.

### Methods of Power Factor Improvement

There are three main ways to improve power factor:

- Capacitor Banks
- Synchronous Condensers
- Phase Advancers

### Capacitor Banks

Improving power factor means reducing the phase difference between voltage and current. Since the majority of loads are of inductive nature, they require some amount of reactive power for them to function.

A capacitor or bank of capacitors installed parallel to the load provides this reactive power. They act as a source of local reactive power, and thus less reactive power flows through the line.

Capacitor banks reduce the phase difference between the voltage and current.

### Synchronous Condensers

Synchronous condensers are 3 phase synchronous motor with no load attached to its shaft.

The synchronous motor has the characteristics of operating under any power factor leading, lagging or unity depending upon the excitation. For inductive loads, a synchronous condenser is connected towards load side and is overexcited.

Synchronous condensers make it behave like a capacitor. It draws the lagging current from the supply or supplies the reactive power.

### Phase Advancers

This is an AC exciter mainly used to improve the PF of an induction motor.

They are mounted on the shaft of the motor and are connected to the rotor circuit of the motor. It improves the power factor by providing the exciting ampere turns to produce the required flux at the given slip frequency.

Further, if ampere-turns increase, it can be made to operate at leading power factor.

## Power Factor Calculation

In **power factor calculation**, we measure the source voltage and current drawn using a voltmeter and ammeter respectively. A wattmeter is used to get the active power.

Now, we know P = VIcosφ watt

Hence, we can get the electrical power factor.

Now we can calculate the reactive power Q = VIsinφ VAR

This reactive power can now be supplied from the capacitor installed in parallel with the load in local. The reactive power of a capacitor can be calculated using the following formula:

IMPORTANT: In **power factor improvement**, the reactive power requirement by the load does not change. It is just supplied by other devices, thus reducing the burden on the source to provide the required reactive power.