Unbalanced winding

An unbalanced winding has a combination of number of poles and number of slots that does not allow to arrange the coils in such a way that they produce a symmetrical system of equally time-phase displaced emf's of identical magnitude, frequency, and waveform.

In the Emetor winding calculator, black cells indicate unbalanced windings.

If a winding is feasible, i.e. balanced, depends solely on the number of slots $Q_s$ and the number of poles $p$. A winding layout will yield unsymmetrical phase coils, whenever the number of slots per phase per machine periodicity is not an integer.

Unbalanced winding: $$\frac{Q_s}{3\cdot GCD\left( Q_s, \frac{p}{2} \right)} \mbox{ is not integer}$$ Balanced winding: $$\frac{Q_s}{3\cdot GCD\left( Q_s, \frac{p}{2} \right)} \mbox{ is integer}$$

The greatest common divisor (GCD) between the number of slots and the number of pole pairs indicates the number of winding symmetries, respectively the machine periodicity.

Examples: A look at the Emetor winding calculator shows that unbalanced windings only appear when the number of pole pairs is a multiple of 3, i.e., $p=$6, 12, 18, ...
A 6-pole 9-slot winding has 3 winding symmetries and is balanced, since: $\frac{Q_s}{3\cdot GCD\left( Q_s, \frac{p}{2} \right)} = \frac{9}{3\cdot 3} = 1$.

A 6-pole 12-slot winding has also 3 winding symmetries but is unbalanced, since: $\frac{Q_s}{3\cdot GCD\left( Q_s, \frac{p}{2} \right)} = \frac{12}{3\cdot 3} = 1.33$.

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