Winding factor

In power engineering, winding factor${\displaystyle k_{w}}$ provides a way to compare of the effectiveness of different designs of stators for alternators. Winding factor is the ratio of electromotive force (EMF) produced by a stator having a short-pitch, distributed, or skewed winding, with a stator having full-pitch, concentrated, and non-skewed, windings.

For most alternators, the stator acts as the armature. Winding factor also applies to other electric machines, but this article focuses on winding factor as it applies to alternators.

Practical alternators have a short-pitched and distributed windings to reduce harmonics and maintain constant torque. Also, either the stator or rotor may be slightly skewed from the rotor's axis to reduce cogging torque. The armature winding of each phase may be distributed in a number of pole slots. Since the EMF induced in different slots are not in phase, their phasor sum is less than their numerical sum. ^[1] This reduction factor is called distribution factor ${\displaystyle k_{d}}$. The other factors that can reduce the winding factor are pitch factor ${\displaystyle k_{p}}$ and skew factor ${\displaystyle k_{s}}$.

Pitch

In alternator design, pitch means angle. The shaft makes a complete rotation in 360 degrees, and is called mechanical degrees. However, the current in a conductors makes a complete cycle in 360 electrical degrees. Electrical degrees and mechanical degrees are related as follows:

${\displaystyle {\text{electrical degrees}}={\frac {P}{2}}\cdot {\text{mechanical degrees}}}$

where P is the number of poles. ^[2]

No matter how many poles, each pole always spans exactly 180 electrical degrees, and it is called pole pitch. Coil pitch is the number of electrical degrees spanned by the coil. ^[1]

Short pitch factor

A full-pitched coil is 180 electrical degrees, meaning it spans the entire pole. A short-pitched coil is less than 180 electrical degrees, meaning it does not spans the entire pole. The amount the coil is short-pitched is given by the variable ${\displaystyle a}$ in electrical degrees:

${\displaystyle a={\text{pole pitch}}-{\text{coil pitch}}}$, and the pitch factor is:

${\displaystyle k_{p}=\cos({\frac {a}{2}})}$.

A short pitched coil is also called chorded, in reference to the chord of a circle. ^[1]

Calculating winding factor

The winding factor can be calculated as
${\displaystyle k_{w}=k_{d}k_{p}k_{s}}$ ^[3]

where
${\displaystyle k_{d}}$ is the distribution factor.
${\displaystyle k_{p}}$ is the pole factor.
${\displaystyle k_{s}}$ is the skew factor resulting from the winding being skewed from the axis of the rotor.

Example

For a 3-phase 6 slot 4 pole non-overlapping winding alternator:
${\displaystyle {\text{coil pitch}}={\frac {2\pi }{6}}={\frac {\pi }{3}}({\text{mech}})={\frac {2\pi }{3}}({\text{elec}})}$
${\displaystyle {\text{pole pitch}}={\frac {2\pi }{4}}={\frac {\pi }{2}}({\text{mech}})=\pi ({\text{elec}})}$

Most of 3-phase motors have winding factor values between 0.85 and 0.95.

The winding factor (along with some other factors like winding skew) can help to improve the harmonic content in the generated EMF of the machine.

References

1. Suad Ibrahim Shahl. "Introduction to AC Machines" (PDF). p. 7. Retrieved August 3, 2022.
2. "Armature Winding". Circuit Globe. 5 January 2016. Retrieved July 29, 2022.
3. Mustafa Al-Refai (2018). "Synchronous generator" (PDF). Electrical and Communications Consulting Office (ECCO). p. 20. Retrieved August 6, 2022.

• Saadat, Hadi. 2004. Power Systems Analysis. 2nd Ed. McGraw Hill. International Edition.
• Rakesh Kumar Jha1; Arvind S. Pande2; Harpreet Singh3 (October 2013). "Design and Analysis of Synchronous Alternator for Reduction in Harmonics and Temperature by Short Pitch Winding". International Journal of Emerging Technology and Advanced Engineering. 3 (10). CiteSeerX   10.1.1.641.1708 . Archived from the original on August 11, 2022. Retrieved November 25, 2022.
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