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# Power factor and its importance

Updated: Aug 9

What is power factor?

Power factor (PF) is defined as the ratio of real power to apparent power. Real power is measured in kW and apparent power is measured in kVA. Apparent power is also known as Demand. The power factor is a measure of how efficiently you are using electricity.

### The beer analogy

To understand the concept of the power factor, let's see the beer analogy. As you can see, in the beer mug above some of the bear is getting wasted due to foam spill.

Liquid beer - This represents the active power or real power or working power which is measured in kW.

Foam - This represents the reactive power that is measured in kVAR.

Mug - Mug as the whole represents the apparent power that is measured in kVA.

If a circuit is 100 % efficient, demand would be equal to the real power available. A strain will be placed on the utility system when demand is greater than the power available. Demand is calculated by taking the average load during a certain time interval. The lower the power factor, higher the current and hence the operating cost.

Power factor calculation

Power factor is the cosine of the angle between voltage and current.

S = P + jQ ;

where

S - Demand / Apparent power

P - Real power

Q - Reactive power

Power factor - (P/S) * 100

In the case of DC circuits, both inductive and capacitive reactance is zero because of zero frequency. Thus the power factor of DC circuits is always unity.

In the case of AC circuits, power factors exist since the frequency is not zero.

P = VI ( In DC circuits)

P = VI COSØ ( In AC circuits)

PF = COSØ

For pure resistive circuits,

Q = 0

S = P

S/P = 1

Thus unity power factor.

Phasor diagram of R - Load Power factor phasor diagram of R-load

Ø = 0 ; PF = COSØ = 1

Inductive load: In the case of Inductive loads (motors, generators, transformers - any load that has windings has inductance), the inductance of the windings does not allow the sudden change in current, so the current will lag behind the applied voltage and the power factor in such circuits is lagging power factor. Power factor phasor diagram of L-load

P = VI Cos (90) = 0

PF = Cos (90) = 0

Thus power factor of the pure inductive circuit is zero.

Capacitive load: In the case of capacitive loads, the capacitance does not allow the sudden change in voltage. Thus, the current leads the capacitor voltage. The power factor in such circuits is the leading power factor.

Phasor diagram of C - Load Power factor phasor diagram of C-load

P = VI Cos(-90) = 0

PF = Cos(-90) = 0

Thus power factor of the pure capacitive circuit is zero.

Similarly power factor can be calculated for different types of loads viz., RL, RC, LC, RLC.

### Importance of power factor:

Power factor is very crucial for economic operation and quality transmission of the power system. The current required to deliver the same power increases with a decrease in power factor. For example, Pure resistive load (unity PF) of 50A becomes 100A for a power factor of 0.5 (for same load and voltage).

Poor factor indicates the inefficient usage of available power

• Low power factor results in increased cross-section and thus the equipment size.

• Reduction in the amount of available useful power.

• Lower power factor causes heat damage to insulation and other equipment.

Hence greater the power factor, the higher the efficiency, the lower the losses, and the lower the operating cost. Every utility aims for a higher power factor since higher efficiency indicates better utilization of generating and transmission systems.

Greater power factor also indicates lower current -> lesser cross-section -> lesser resistance -> lesser I^2R losses and thus indicates long-lasting equipment with low operating cost and high efficiency.

### Power factor correction:

To overcome all the above-mentioned issues, it is very important to correct the power factor (i.e., making sure that the power factor is closer to unity, usually greater than 0.95).

Linear loads such as induction motors and transformers with low power factors can make use of passive components such as capacitors or inductors.

Non-linear loads such as arc furnaces and rectifiers distort the current drawn from the system. In such cases, active or passive power factor correction can be used to counteract the distortion and raise the power factor.

A higher power factor is often desirable since it improves the voltage regulation at the load. The apparent power can be reduced by installing reactive elements which supply or absorb reactive power near the load. For example, the inductive effect of motors can be diluted by installing capacitor banks and vice versa.

Benefits of power factor correction:

• Voltage regulation is improved.

• I^2R losses are reduced. which will increase the life span of insulation and other components.

• Electricity charges are reduced.

• Rating of the cables is reduced.

• Voltage dip problems are minimized.

• Reactive power penalties paid by industries for operating with lower power factors will be reduced.