# What is Power Factor & Power Triangle With Solved Numerical

The power factor is defined as the ratio of real power to apparent power. As power is transferred along a transmission line, it does not consist purely of real power that can do work once transferred to the load, but rather consists of a combination of real and reactive power, called apparent power. The power factor describes the amount of real power transmitted along a transmission line relative to the total apparent power flowing in the line.

## Power Factor

Power factor is basically a ratio of active power consumed by the load to the to the apparent power in the circuit.

Power Factor = Cosθ

Unit of power factor is a ratio quantity, because of it does not have any units.

More Precisely, it is a cosine angle between current and the voltage.

In a simple language , power factor is the difference of angle between voltage waveform and current waveform at a particular time.

If the current waveform is leading by some angles with respect to voltage waveform then, there will be leading power factor according to the angle difference, and vice-versa in case of lagging power factor.

The ratio of KW to KVA is called the power factor, which is always less than or equal to unity. Theoretically, when electric utilities supply power, if all loads have a unity power factor, maximum power can be transferred for the same distribution system capacity. However, as the loads are inductive in nature, with power factor ranging from 0.2 to 0.9, the electrical distribution network is stressed for capacity at low factors.

Losses: To understand losses let’s take an example. If we have transmitted 66KV voltage supply to any transmission line and we are getting around 65.5 KV at the receiving end, then there will be 0.5 KV voltage loss in the transmission lines due to various effects.

### The Losses Of Poor Power Factor

• High KVA (Maximum Demand) charges in utility bills
• High distribution losses (KWH) within the plant network
• The poor voltage at motor terminals and improved performance of motors
• Penalty charges imposed when operating with a low power factor
• Investment in system facilities such as transformers, cables, switch gears, etc. for delivering load is high.

## Power Triangle

Typical inductive loads are AC motors, induction furnaces, transformers, and ballast-type lighting. Inductive loads require two kinds of power: a) active (or working) power to perform the work and b) reactive power to create and maintain electromagnetic fields.

Active power is measured in KW (Kilo Watts). Reactive power is measured in KVAr (Kilo Volt Ampere Reactive).

The vector sum of Reactive power (KVAR) and Active power (KW) is called the apparent power or KVA and it reflects actual electrical load on the distribution system.

One can relate the various components of AC power by using the power triangle in vector space. Real power extends horizontally in the î direction as it represents a purely real component of AC power. Reactive power extends in the direction of ĵ as it represents a purely imaginary component of AC power. Complex power (and its magnitude, Apparent power) represents a combination of both real and reactive power, and therefore can be calculated by using the vector sum of these two components. We can conclude that the mathematical relationship between these components is:

## Reactive Power

The part of the power which is stored in the elements of any electric circuit qualifies as reactive power. For example

• when you supply a pure inductor (i.e. which has zero resistance) it uses all the power to create a magnetic field or in other words stores the supplied energy in the form of the magnetic field. So all the power is converted into reactive power.
• Similarly, when energy is supplied to a pure capacitor (the one having zero resistance in its plates) it stores all of the energy in the form of the electric field.
• When supply is given to a transformer is uses a part of the energy supplies to set up a flux across the iron core and the rest energy is transferred to the load.

## Apparent Power

It is the total power supplied by the supply i.e. it is the sum of the active and reactive powers.
Now, that you have an idea of what active reactive and apparent powers mean the concept of power factor and its significance is easy to understand.
Power Factor = Active Power

Key Points

Power factor is (real power/apparent power)

Real power =VI cosθ

Where θ is angle between voltage and current.

Apparent power = VI

• In pure resistors voltage and current is in phase. Therefore θ = 0.
• real power = apparent power.
• ∴ in pure resistor power factor = 1
• In inductor as voltage leads the current by 90°.
• θ = 90°, hence P=0
• ∴ power factor in inductor = 0 lag.
• In a capacitor, current leads the voltage by 90°.
• θ = 90°, hence P=0.
• ∴ power factor in capacitor = 0 lead.

## Example On Power Triangle

A wound coil that has an inductance of 180mH and a resistance of 35Ω is connected to a 100V 50Hz supply. Calculate: a) the impedance of the coil, b) the current, c) the power factor, and d) the apparent power consumed. Also, draw the resulting power triangle for the above coil. Data given: R = 35Ω, L = 180mH, V = 100V and ƒ = 50Hz.

( example source:electronics-tutorials)

• Impedance (Z) of the coil

• Current (I) consumed by the coil

• The power factor and phase angle Φ

• Apparent power (S) consumed by the coil

• Power triangle for the coil