# Winding Factor

The winding factor is the method of improving the rms generated voltage in a three phase AC machines so that the torque and the output voltage does not consists any harmonics which reduces the efficiency of the machine**. Winding Factor** is defined as the product of Distribution factor (K_{d}) and the coil span factor (K_{c}).The distribuition factor measured the resultant voltage of the distributed winding regards concentrate winding and the coil span is the measure of the number of armature slots between the two sides of a coil. It is denoted by **K _{w}**. The EMF equation is given below.

It is assumed that the induced voltage is sinusoidal. However, if the flux density distribution is non-sinusoidal, the induced voltage in the winding will be non-sinusoidal. The coil span factor, distribution factor and the winding factor will be different for each harmonic voltage. From the equation (1), the fundamental EMF per phase is given by the equation shown below.

The third harmonic, EMF per phase will be

The n^{th} harmonic, EMF per phase will be

Here subscript 1,3 and n denote fundamental, third and n^{th} harmonics respectively.

Therefore,

Where,

- ϕ
_{1 }is the total fundamental flux per pole. - ϕ
_{1}= average flux density x area under one pole

Where,

- B
_{m1}is the peak value of the fundamental component of the flux density wave - D is the diameter of the armature or the mean air gap diameter
- L is the axial length of armature or the active coil side length

Similarly for n^{th} harmonic

Where,

B_{mn }is the peak value of the n^{th} harmonic flux density

## Winding Factor for n^{th} Harmonic

The winding factor corresponding to the n^{th} harmonic voltage is given as

Where K_{cn} and K_{dn} is the coil span factor and distribution factor for the n^{th} harmonic.

Therefore, the n^{th} order harmonic induced EMF per phase is given by the equation shown below.

Where,

In addition, to the fundamental flux, the induced voltage in a winding will contain harmonics because of non-sinusoidal space flux density distribution. Since the positive and the negative halves of the flux density wave are identical, only odd harmonics can be present, and even harmonics are absent. Therefore, phase voltage may contain third, fifth, seventh and higher order harmonics.

Mainly the three phase alternators are star connected. The third order harmonic voltages of all the phases are equal in phase and magnitude. The phase of the star connected machine is such that the voltage across any two lines is the phasor difference in the voltages of the corresponding phases. Hence, the third harmonic or multiple of the third harmonic are absent in the line voltage of star connected synchronous machine.

Since the strength of the harmonic components of voltage decreases with the increasing frequency, only fifth and seventh harmonic are important. These are known as Belt Harmonics.

Thus, the root mean square voltage of the induced voltage across lines of a 3 phase, star connected machine is given by the equation shown below.

Where, subscripts 1, 5, 7, 11 ….. denotes fundamental fifth, seventh, eleventh harmonics respectively.