# Number of slots per pole per phase

*The number of slots per pole per phase determines how the winding layout is arranged. It is also disclosing information about the winding factor and its harmonics.*

If the number of slots/pole/phase is an integer, the winding is called integer-slot winding.

If the number of slots/pole/phase is fractional and superior to 1, the winding is called fractional-slot winding.

If the number of slots/pole/phase is fractional and inferior to 1, the winding is called concentrated winding.

Windings with the **same number of slots/pole/phase** $q$ have the same winding factor. Their winding layouts consist of the same basic sequence repeated by the number of winding symmetries (or machine periodicity).

**Example:**

10-pole 12-slot single-layer 3-phase winding: $q=\frac{12}{10\cdot 3}=\frac{2}{5}$, fundamental winding factor: 0.966, one winding symmetry.

20-pole 24-slot single-layer 3-phase winding: $q=\frac{24}{20\cdot 3}=\frac{2}{5}$, fundamental winding factor: 0.966, two winding symmetries.

The number of slots/pole/phase is also an indicator about what winding factor and winding-factor harmnoics one can expect.

**Example 1:**

The harmonic spectrum of the winding factor of 4-pole 3-phase integer-slot windings in Fig. 1 shows that an increasing number of slots/pole/phase (from $q=1$ for the 12-slot winding to $q=5$ for the 60-slot winding) leads to a steady decrease of the fundamental winding factor. However, since the coils are distributed over several slots per pole per phase, the back-EMF gets more sinusoidal. This fact is reflected in significantly reduced winding factor harmonics of order three and higher, cf. Fig. 1.

**Fig. 1 **Winding factor harmonics for 4-pole 3-phase integer-slot windings with different number of slots/pole/phase.

**Example 2:**

For concentrated windings, the fundamental winding factor increases and decreases as a function of the number of slots/pole/phase as shown in Fig. 2. The highest fundamental winding factors are found when the number of slots is closest to the number of poles, ie. $qpprox 1/3$.

**Fig. 2 **Fundamental winding factor for concentrated windings as a function of the number of slots/pole/phase [1].

**References:**

[1] Florence Meier, *Permanent-Magnet Synchronous Machines with Non-Overlapping Concentrated Windings for Low-Speed Direct-Drive Applications*, Phd Thesis, Royal Institute of Technology (KTH), July 2008

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