Pitch Factor or Coil Span Factor and Winding Factor

Pitch Factor or Coil Span Factor

Pitch Factor or Coil Span Factor is definite as the ratio of emf generated in short pitch coil to the emf generated in full pitch coil. It is denoted by K_p and its value is always less than unity. This factor basically represents the effect of short pitch winding on generated emf across the winding terminals of electrical machine.

As per the definition, the formula for pitch factor is given as below.

 

Calculation of Pitch Factor or Coil Span Factor

To calculate the value of pitch factor, first of all we need to calculate the value of emf generated in short pitch coil and that in full pitch coil. Let us now calculate the emf generated in a short pitch coil. Figure below shows a short pitch coil.

Let E₁, E₂ and E_R be the emf induced in coil side lying under North Pole, South Pole and resultant of emf generated in both the active lengths of coil.  As the two coil sides are separated in space by an angle of (180-ε) i.e. the coil span is (180-ε), therefore the emf induced in these coil sides will also be separated by this angle. This means, the angle between E₁ and E₂ phasor will be equal to ε as shown in figure below.

Since the magnitude of emf generated in both the coil sides are equal, therefore E₁ = E₂ = E (say). As the resultant emf E_R is the phasor sum of E₁ and E₂, therefore

Above expression gives the emf induced in a single turn short pitch coil with chording angle ε. Since the chording angle for full pitch coil is 0 degree, therefore from the above expression (2),

emf generated in a full pitch coil = 2E

Thus from (1),

Hence, pitch factor or coil span factor K_p = Cos(ε/2).

For a full pitch coil, the value of pitch factor is unity whereas for its value is also unity for concentrated coils.

The pitch factor or coil span factor n^th harmonics is given as

K_p = Cos (nε/2)

Winding Factor

Winding factor is defined as the ratio of emf generated in short pitch distributed coil to the emf generated in a concentrated coil. It is denoted by K_w.

The emf induced in a coil having N turns is given as

E = √2πK_pK_dfNØ ……………..(3)

where K_p and k_d are pitch and distribution factor respectively.

In electrical machine, the winding are generally short pitch coils distributed along the periphery of stator slots. Therefore, to account for short pitch coil and its distribution in the stator slots, two factors K_p and k_d are introduced in the expression of generated emf in (3). There are various advantages of short pitch coils. You are suggested to read “Advantage and Disadvantage of Short Pitch Winding” to understand the need for short pitch winding in electrical machine.

The emf generated in a concentrated coil having N number of turn is given as

E’ = √2πfNØ ……………..(4)

Thus from the definition of winding factor and (3) & (4),

K_w = K_pK_d

Thus winding factor can also be defined as the product of pitch or coil span factor and distribution factor. It value is less than 1.

Winding factor for n^th harmonics is given as the product of pitch factor and distribution factor for n^th harmonics. Therefore, winding factor for nth harmonics K_wn is give as below:

K_wn = K_pnK_dn

A short video to quickly understand the pitch factor and winding factor.

https://www.youtube.com/watch?v=-gIIrGLdT2w&t=8s