What is Winding Factor?

Definition: Winding Factor is the product of the Distribution factor (Kd) and the coil span factor (Kc). The main purpose of  the winding factor is to improve the rms generated voltage in a three-phase AC machine.

Now question arises why we need to keep winding factor.The answer is the winding factor makes the output voltage almost sinusoidal free from harmonics. As a result, the improved voltage makes the electrical machines generate constant torque. As we all know, the torque is proportional to the square of the RMS AC voltage.In addition to this, it reduces the harmonics in the system, lower the losses and improves the machine efficiency.

The resultant voltage depends on the distributed winding and the coil span. The distribution of the winding and coil span factor decides the winding factor. The winding factor is denoted by the Kw. 

The EMF equation is given below:

emf equation of alternator-winding factor

The induced voltage in the winding is non- sinusoidal because of non-sinusoidal flux density distribution. For individual harmonics order, the coil span factor, distribution factor, and winding factor will be different. EMF per phase is given below.

winding factor equation

EMF per phase for 3 rd order harmonic is ;

EMF per phase for 3 rd order harmonic- winding factor equation

The ratio of the n th harmonic order phase voltage to fundamental phase voltage is given below.


ratio of harmonic generated voltage to fundamental


  • ϕis the total fundamental flux per pole.
  • ϕ1 = average flux density x area under one pole
winding factor equation


  • Bm1 is the peak value of the fundamental component of the flux density wave
  • D is the mean diameter of the armature 
  • L is the armature axial length 

Similarly for the nth harmonic

Rtaio of total voltage to fundamental voltage in alternator- winding factor equations


Bmn is the peak value of the nth harmonic flux density

Winding Factor for nth order Harmonic

The winding factor corresponding to the nth harmonic voltage is given as:

winding factor formula

Where Kcn and Kdn are the coil span factor and distribution factor for the nth harmonic.

Therefore, the nth order harmonic induced EMF per phase is given by the equation shown below:

voltage generated per phase in alternator with n order harmonics

The induced voltage in the winding contain  harmonics because of non-sinusoidal flux distribution. If we analyze the induced voltage waveform, it has odd harmonics. The even harmonic order is absent because voltage waveform is symmetrical about x- axis. Thus, the phase voltage has 3rd, 5th, and 7th harmonics.

The star connected synchronous generator does not have 3rd harmonics because all three phase voltage are in the same phase and have the same magnitude. Thus the 3rd order harmonic and multiples of 3rd order harmonic is absent in star connected alternator.

The magnitude of current of lower order harmonic is more compared to the higher order harmonic. The magnitude of harmonic order voltage reduces with an increase of harmonic order. Therefore,5th and 7 th harmonic order is predominant and proper care of its reduction at design stage is must. The 5 th and 7 th order harmonics are known as Belt Harmonics.

The RMS valve of line voltage of the star connected alternator  can be expressed by below-given equation.

line volatge and phasevolatge

Where, subscripts 1, 5, 7, 11  denote fundamental,5th order,7th order,11th order harmonic voltage.

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