Winding Factor

Winding Factor is defined as the product of Distribution factor (Kd) and the coil span factor (Kc). It is denoted by Kw. The distribution Factor and the coil span factor has been already discussed earlier.

The EMF equation is given below.

Winding-factor-eq-1

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.

Winding-factor-eq-2

The third harmonic, EMF per phase will be

Winding-factor-eq-3

The nth harmonic, EMF per phase will be

Winding-factor-eq-4

Here subscript 1,3 and n denote fundamental, third and nth harmonics respectively.

Therefore,

Winding-factor-eq-5

Where,

  • ϕ1 is the total fundamental flux per pole.
  • ϕ1 = average flux density x area under one pole

Winding-factor-eq-6

Where,

  • Bm1 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 nth harmonic

Winding-factor-eq-7

Where,

Bmn is the peak value of the nth harmonic flux density

Winding Factor for nth Harmonic

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

Winding-factor-eq-8

Where Kcn and Kdn is 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.

Winding-factor-eq-9

Where,

Winding-factor-eq-10

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.

Winding-factor-eq-11

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

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