Winding Factor | Pitch Factor | Distribution Factor

The winding factor accounts for the reduction in fundamental emf caused by short pitching and distributing a winding. It is the product of the pitch factor and distribution factor.
Using K_w for winding factor, K_p for pitch factor and K_d for distribution factor gives

The following sections explain the pitch factor and distribution factor.

Pitch Factor

A full-pitch coil spans 180 electrical degrees. Its two coil-side emfs add in the series connection to give twice the emf of one side. A short-pitch coil spans less than 180 electrical degrees, so its connected coil-side emfs add as phasors.
Pitch factor compares the magnitude of the short-pitch coil emf with the emf of an otherwise identical full-pitch coil. Its magnitude cannot exceed one.

Pitch factor is therefore the ratio of the phasor sum of the coil-side emfs to their arithmetic sum.
Suppose a coil is short pitched by the chording angle α in electrical degrees. If the emf induced in each coil side is E, the full-pitch coil would produce a terminal voltage of 2E.
For the short-pitch coil, the phasor diagram gives the resultant emf shown below.

From the definition of pitched factor, the fundamental pitch factor is Kp = cos(α/2).

This expression gives the pitch factor for the fundamental emf. A non-sinusoidal air-gap flux wave may also contain space-field harmonics, which can produce corresponding harmonics in the generated voltage waveform.

For the 3^rd space harmonic, the electrical angle changes three times as fast as it does for the fundamental.
The effective chording angle for the r^th harmonic is rα, and the pitch factor for the r^th harmonic is

The r^th harmonic pitch factor becomes zero when

The 3^rd harmonic is a zero-sequence component in a three-phase alternator. It cancels from line-to-line voltage in a balanced system, although it may remain in phase-to-neutral voltage. Designers therefore also consider the 5^th and 7^th harmonics.
For the 5^th harmonic

For the 7^th harmonic

A chording angle of α = 30^o, equivalent to a 5/6-pitch coil, reduces both components while retaining most of the fundamental emf. This is one practical design choice for the armature winding of alternator.

Distribution Factor

If all coil sides of one phase under one pole occupy one slot, the arrangement is a concentrated winding. The equal, in-phase coil emfs then add arithmetically.
In practical machines, the armature winding of alternator is often distributed among several slots under each pole to improve the emf waveform. Adjacent coil-side emfs are separated by the electrical slot angle.
The distributed-winding emf is therefore the phasor sum of the individual coil emfs. Its magnitude is lower than the arithmetic sum unless only one slot per pole per phase is used.
An equivalent concentrated winding produces the arithmetic sum.
Distribution factor compares the distributed-winding emf with that concentrated-winding emf.

Distribution factor is the ratio of the phasor sum of the emfs induced in coils spread among slots under one pole to their arithmetic sum:


Its magnitude cannot exceed one.
Let n be the number of slots per pole.
Let m be the number of slots per pole per phase.
Let E_c be the induced emf per coil side.
The electrical angle between adjacent slots is

In the phasor diagram, AC, CD, DE and EF represent equal coil emfs separated by the slot angle β.
The perpendicular bisectors of AC, CD, DE and EF meet at the common point O.
The emf induced in each coil side is

Because there are m slots per pole per phase, the arithmetic sum of the coil-side emfs is

The chord AB in the diagram represents the resultant emf.
Therefore, the resultant emf is

The angle mβ is the phase spread in electrical degrees.
This equation for K_d applies to the fundamental emf.
If the flux distribution contains the r^th space harmonic, its effective slot angle is rβ. The distribution factor for the r^th harmonic is