The generated power in a power system should be utilized without wasting. The amount of power that is generated at the station is not received at the end point because of wastage of power. This wastage of power is mainly because of the reactive power absorption. This affects the power factor (pf) of the system. To increase the reliability and life expectancy of the system this pf plays a crucial role. To utilize the maximum amount of power that is generated pf must be high. The losses result in the interruption of the maximum power to be received at the load end. In this article, we will discuss what is Power Factor? What are the factors affecting it, its importance, and methods of improving it?

## Definition of Power factor

- It is is the proportion of real power and apparent power.
- power factor = Real power / apparent power
- Apparent power is the total amount of power that is being utilized by any equipment.
- Apparent power = V.I
- Real power is the product of apparent power and some factor. This factor is considered as the power factor. Depending upon this factor the real amount of power delivered can be known.
- Real power is the amount of power that is observed after some losses. The total amount of power generated is not received at the received end due to some loss factor. This loss factor is considered as a power factor.
- The amount of power that is being lost is due to the reactive components present in any equipment. These components develop magnetic flux used for the function of the device. As this lost power is reactive in nature it is termed as Reactive power.
- So, apparent power is a combination of Real power and Reactive power. Real power is denoted by ‘P’ whereas Reactive power is denoted by ‘Q’. The Total power I,e Apparent power is denoted by ‘S’.

The angle between Real power ‘P’ and Apparent power ‘Q’ is ‘Ф’.

**Real power = apparent power * cos****Ф**

**cos****Ф = Real power / apparent power**

cosФ is the power factor

### The formula of PowerFactor

**power factor = Real power / apparent power**

**cosФ = R / Z**

**cosФ = R / √R ^{2 }+ (X_{l}– X_{c})^{2}**

**cosФ = R / √R ^{2 }+ (2πfl- 1 / (2πfc))^{2}**

From this, we can say power factor depends on resitance, inductance, and capacitance of the equipment.

power factor is maximum when **2πfl- 1 / (2πfc) = 0**

Then **cosФ = 1**

We get Unity power factor when 2πfl- 1 / (2πfc) = 0. At Unity power factor Real power and apparent Power are equal.

### Unity PowerFactor

The power factor is said to be unity if both real power and reactive power are equal.

The current ‘I’ and the voltage ‘V’ will be in phase with each other.

#### Lagging and Leading PowerFactor

- When the current ‘I’ lags the voltage ‘V’ by an angle ‘θ’ is said to be as ‘Lagging power factor’
- When the current ‘I’ leads the voltage ‘V’ by an angle ‘θ’ is said to be as ‘Leading power factor’.

The figure which depicts the Lagging and Leading power factor is shown below.

The power factor is based upon the type of load. They purely resistive, inductive, and capacitive.

### Purely Resistive

- A purely resistive load is shown in the figure below in which voltage ‘V’ and current ‘I’ are in phase. The waveform representation of a purely resistive load is shown in the figure.

### Purely Inductive

- The purely inductive load is shown in the figure below in which voltage ‘V’ leads the current ‘I’ by an angle of 90 degrees.
- The waveform representation of a purely inductive load is shown in the figure where voltage ‘V’ leads current ‘I’ by an angle of 90 degrees.

### Purely Capacitive

- The purely capacitive load is shown in the figure below in which current ‘I’ leads voltage ‘V’ by an angle of 90 degrees.
- The waveform representation of a purely capacitive load is shown in the figure where current ‘I’ leads voltage ‘V’ by an angle of 90 degrees.

### Importance of Power Factor

- A power system requires a good power factor in order to maintain good profits. Say, if the amount of power generated annually is one million MW with a 50% power factor. Then, the power system delivers only 50% of the generated power. The rest of the power generated is wasted as losses. So, in order to avoid these losses, a power system requires a better power factor.

### Improvement of PowerFactor

- The power factor can be improved by the compensation of Reactive power in the system. There are certain methods to be followed for the improvement of the power factor by generating Reactive power.

### Methods used to Improve PowerFactor

- Capacitor Banks
- Synchronous condensers
- Phase Advancers

#### Capacitor Banks

- Most of the equipment used is of the inductive type where current ‘I’ lags the voltage ‘V’. In order to compensate this, capacitor banks are connected in parallel which neutralizes the lagging current ‘I’.
- Capacitor banks are the cheapest means of generating reactive power which also requires less maintenance.

#### Synchronous Condensers

- A Synchronous condenser is similar to the synchronous motor operating at no-load and is over-excited. Under over-excited conditions, the synchronous motor delivers reactive power just like a capacitor bank. It neutralizes the lagging current ‘I’ which improves the power factor of the system.
- Synchronous condensers are used by large industries whose cost is huge.

#### Phase Advancers

- Phase advancers are used by an Inductor motor (IM) to compensate for the reactive power. As the (IM) observes the reactive power its power factor is low such that the current ‘I’ lags the voltage ‘V’. In order to compensate this, a phase advance is used by an IM which compensates the reactive power required which further neutralizes the lagging current ‘I’.

#### Applications of Power Factor

- Based on the power factor itself electrical appliances are named as 5 stars rated, 3 starred and 2 starred. The basic difference between these ratings is the amount of power consumption.
- For example, a 1000W output is needed for an appliance that has a unity power factor. Then it requires 1000W of input as energy consumption. Similarly, for a 1000W output with 0.8 power factor requires 1250W of input and for a 1000W output with a 0.5 power factor requires 2000W of input.
- Therefore, the power factor is decreasing the amount of power consumption is also increasing. This is how the appliances are rated as 5 stars, 3 stars, and 2 stars. The 5-star appliances consume less power compared to 2-star appliances.

Therefore, we can conclude that a power supply system requires an efficient power factor in order to reduce the losses. In this article, we had an overview of what is Power factor, Its importance, methods to improve it, and its applications. Here is a question for the readers, What is the power factor formula for 3 phase?

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