# Understanding the Power Factor

Energy is needed and utilized everywhere in the world. From the point of view of convenience, efficiency and economy, it is best that we generate, transmit and distribute it in electrical form before it is converted into the required one by suitable equipments. For the same reasons of economy and efficiency, we use AC rather than DC. Practically, we generate, transmit and distribute energy in AC form almost exclusively. DC is used either in DC applications (DC machines and electronic circuits) or in HVDC transmission links.

Wherever AC power is utilized, the question of power factor arises itself.

## Power Factor

• Defined as 'the cosine of the angle between the voltage and current'.
• In AC circuit, the voltage and current are ideally in phase.
• But practically, there exists a phase difference between them.
• The cosine of this phase difference is termed as power factor.
• It can be defined and mathematically represented as follows:

From the fig. (a) above, it can be clearly noted that there is a phase difference of angle ɸ between the voltage phasor and the current phasor.
Power Factor = cosɸ

The fig. (b) is called as Power Triangle
Here, VI sinɸ = Reactive power (in VAR)
VI cosɸ = Active power (in Watts)
VI = Apparent power (in VA)
PF = cosɸ = Active Power (W) / Apparent Power (VA)

The fig. (c) is called as Impedance Triangle
Here, R = Resistance, X = Reactance, Z = Impedance
Z2 = R2 + X2
PF = cosɸ = R/Z

The Power Factor can be lagging, leading or unity.

### Lagging Power Factor

• When current lags behind the voltage, the power factor of the circuit is called 'Lagging'
• When the circuit is inductive, the pf is lagging.
• The loads such as induction motors, coils, lamps, etc are inductive and have Lagging pf.

### Leading Power Factor

• When current leads the voltage (or voltage lags behind the current), the power factor of the circuit is called 'Leading'.
• When the circuit is capacitive, the pf is leading.
• Capacitive loads such as Synchronous condensers, capacitor banks etc draw leading current. Such circuits have leading power factor.

### Unity Power Factor

• Power factor is unity (i.e. 1) for ideal circuits.
• When current and voltage are in phase, PF = 1
• Power factor cannot be more than unity.
• Practically, it should be as close to unity as possible.
If power factor is low, following problems are encountered:

## Effects of low power factor

Power in an AC circuit can be given as: P = VI cosɸ
Therefore, cosɸ = P / VI
I ∝ 1 / cosɸ
Similar relationship can be derived for 3 phase circuit too. We can see that current is inversely proportional to pf.

For example, consider that we want to transfer 10 kVA power at 100 V
If PF = 1,
I = P / (V cosɸ) = 10000 / (100 x 1) = 100 A
If PF = 0.8,
I = P / (V cosɸ) = 10000 / (100 x 0.8) = 125 A
Hence, the current drawn is higher for low power factor.
2. Losses: As stated above, for low pf, the current drawn is high. Hence copper losses (I2R losses) will also be high. This decreases the efficiency of the equipment.
3. Overheating of the equipment: I2R losses produce heat (Joule's law). Hence, the temperature rise will be relatively more for low PF which will further increase the stress on the insulation.
4. Size of conductor: Low power factor causes higher load current. If the load current increases, the size of the conductor required will also increase. This will further increase the conductor cost.
5. kVA rating of the machine: Machines are not rated in kW while manufacturing because the power factor of supply is unknown. Instead, they are rated in kVA.
According to definition, Cosɸ = Active power (kW) / Apparent power (kVA)
Hence, kVA rating = 1 / cosɸ
Therefore, for low pf, equipment of larger kVA rating is needed. But larger kVA rating means larger size of the equipments. If size increases, the cost also increases.
6. Voltage Regulation: It is defined as the difference between sending and receiving end voltage per unit sending end voltage. When power is transferred from one end to another, the voltage drops due to several reasons. This voltage drop should be within permissible limits.
P = VI cosɸ , Therefore I ∝ 1 / V
For low power factor, current will be more and hence voltage drop will be increased. Hence, the voltage regulation at low power factor is poor.
7. Active and Reactive power (Power Transfer Capacity): Active and reactive power both are transferred over the line together. Active power is needed for supplying the load. Reactive power is needed to maintain the voltage of the line. But if reactive power is more, then active power transferred is decreased. For low pf, active power is low because, cosɸ = Active power (W) / Apparent power (VA). This results in uneconomic operation.
These are the results of low power factor. For optimum performance, the power factor should be as close to unity as possible. To achieve this, power factor correction equipments are used.

[Also read: Comparison of Various Power Plants]

Author: Manoj Arora is an electrical engineering student and a writer from Gujarat, India. He writes poems and short stories whenever he's not immersed in a book.
Credits for the Graphics: Kiran Daware.