Power Factor

Definition – Power factor is defined as the cosine of angle between voltage & current in an a.c. circuit. or

It is the ratio of Active Power (output) to Apparent Power (Input). In other wordsIt the ratio of power consumed by the load to the total power given to it.

It is denoted by Cos Ø.The value of power factor depends on the types of load.

Power Factor Cos Ø = Output (Active Power) in W/ Input (Apparent Power) in VA

Power Factor (pf) plays an important role in power consumption. Value of power factor depends on the type of load. Broadly there are three types of load resistive, inductive & capacitive load. Value of pf is unity on resistive load, pf is lagging on inductive load & pf is leading on capacitive load

(Note -Power factor happens in AC circuits only not in DC circuits because in DC system voltage & current don’t vary with time.)


A -Resistive load(Ex – Incandescent Lamps & Heaters) –

When AC voltage is applied to a resistive load, current follows the same cycle of voltage with respect to time(but amplitude may not be same), hence there is no phase difference between voltage & current (Ø = 0 deg).

B -Inductive load –(Ex – Induction motors, Transformers, choke, Induction Heaters, electromechanical relays etc) –

When AC voltage is applied to an inductive load, it resists the flow of current & it builds up slowly and becomes steady. That is why current lags behind voltage which creates phase difference between voltage & current. The value of phase difference between voltage & current varies between 0 to 90 deg depending on the value of inductance.

This can be understood by the diagram given below –


C – Capacitive load –(Ex – Flash of camera, synchronous motors and capacitors) –

When AC voltage is applied to a capacitive load, the current flows to build voltage across capacitor,so current leads voltage with respect to time which creates phase difference between voltage & current. The value of phase difference between voltage & current is between 0 to 90 deg.


Power factor plays as important role in power consumption. There are three categories of power factor – 1) Unity power factor, 2) Lagging power factor & 3) Leading power factor. Let us understand one by one –

Let us say Power, P = VI CosØ. If the value of V&I is constant, power is directly proportional to the pf (Cos Ø).

  • Power on Unity Power Factor– Where Ø = 0

So,  P = VI Cos0  = VI X 1 = VI     ………. (1)

  • Power on Lagging Power Factor– Where Ø  ˃  0 & max upto 90 deg (lagging)

So,   P = VI CosØ

Where, value of CosØ varies from 0.01 to 0.99 which depends on phase angle(˃ 0deg to 90 deg) between voltage & current. Hence the value of power will be less than the value of power in equation –(1).

It’s clear that if phase difference between voltage & current (on inductive load) is more, the power factor will be less&power will be less. Now let us understand effect of power factor in electrical system –

  • P = VI CosØ or I = P / V CosØ or I ά 1/CosØ. Current is inversely proportional to the power factor. It means low power factor will draw high current & vice versa to get same power.
  • Due to above reason, for a particular load of a building, more current will be drawn by the load.
  • When more current will be drawn, higher capacity of equipment (like transformer, switchgears etc) will be used.
  • High current will cause high I’2R losses. So higher size of conductors will be used.
  • High current means higher capacity generating plants will be installed.
  • High current means higher voltage drop in the line which causes low voltage regulation.
  • It causes less efficiency of generating plants due to higher loses which happens due to high current,
  • Government keeps a watch on power factor of premises due to above reasons & has guidelines on low power factor if it goes below a certain value.

Let us understand the effect of power factor on power demand through the table given below – (let us say power demand is 2300 W in a building) –

Eample-1 –

Power Utilized ˭ Voltage X Current X Power Factor Wastage of power due to low PF(in watts)
P (in Watts) V I PF P – P1,P2,P3,..
P 2300 230 10 1 0
P1 2070 230 10 0.9 230
P2 1840 230 10 0.8 460
P3 1610 230 10 0.7 690
P4 1380 230 10 0.6 920
P5 1150 230 10 0.5 1150

Note – In other words we can say that due to low power factor, full power is not utilized & power goes waste. This wastage of power is called reactive power. The power which is actually utilized is called active power. The power which is available (includes both active & reactive power) to the building is called apparent power.

Eample-2 –Let us understand by this example that how more current is drawnto get same power in the system when power factor is low –

Power Utilized ˭ Voltage X Current X Power Factor
P (in Watts) V I PF (cosØ)
P 2300 230 10 1
P 2300 230 11.11 0.9
P 2300 230 12.50 0.8
P 2300 230 14.29 0.7
P 2300 230 16.67 0.6
P 2300 230 20 0.5



  • Most of the ac motors are of induction type(1-ph and 3-ph) which have low PF.These motors works at a PF which is extremely small on light load 0.2 to 0.3) and rises to 0.8 or o.9 at full load.
  • Arc lamps, electric discharge lamps and industrial heating furnaces operate at low PF,
  • Power on Leading Power Factor– In our industries, mostly induction equipment are used which causes low power factor in the system which is highly undesirable as it causes an increase in current resulting in losses of active power in all elements of power system from power generation to utilization. Hence it is important to have power factor as close to unity as possible.

So, in order to improve the power factor, equipment which cause leading power factor are used in parallel with load. These are –

  1. Static Capacitors,
  2. Synchronous motor (or condenser),
  3. Phase advancement. Details are given below –
  1. Static Capacitors – Banks of static capacitorsare installed in the main LT panel & connected parallel with main supply.
  2. An over excited synchronous motor can be used for pf correction as when it runs, current leads the voltage by some angle. An over excited synchronous motorrunning on no load is known as synchronous condenser. When such motor is connected in parallel with main supply, it takes leading current which partly neutralizes the lagging effect of current (or load). Thus the power factor is improved.
  3. Phase advancer is simply an a.c exciter. It is mounted on the same shaft of the induction motor & is connected with the rotor. It provides exciting ampere turns to the rotor circuit at slip frequency. By providing more ampere turns then required, the induction motor can be made to operate on leading power factor like an over excited synchronous motor.

However the main disadvantage of phase advancers is that they are not economical.