Subject : Electrical Machines II (AC Machines)
Unit : Alternators
Pitch factor of alternator
Pitch factor:
- Full-pitched coils i.e. coils having span which is equal to one pole-pitch i.e. spanning over 180° (electrical). As shown in Fig. 1, if the coil sides are placed in slots 1 and 7, then it is full-pitched.
- If the coil sides are placed in slots 1 and 6, then it is short-pitched or fractional-pitched because coil span is equal to 5/6 of a pole-pitch. It falls short by 1/6 pole-pitch or by 180°/6 = 30°. Short-pitched coils are deliberately used because of the following advantages:
1. They save copper of end connections.
2. They improve the wave-form of the generated e.m.f. i.e. the generated e.m.f. can be made to approximate to a sine wave more easily and the distorting harmonics can be reduced or totally eliminated.
3. Due to elimination of high frequency harmonics, eddy current and hysteresis losses are reduced thereby increasing the efficiency.
- But the disadvantage of using short-pitched coils is that the total voltage around the coils is somewhat reduced. Because the voltages induced in the two sides of the short-pitched coil are slightly out of phase, their resultant vectorial sum is less than their arithmetical sum.
It is always less than unity.
- Let E_{S} be the induced e.m.f. in each side of the coil. If the coil were full-pitched i.e. if its two sides were one pole-pitch apart, then total induced e.m.f. in the coil would have been = 2E_{S} [Fig. 2 (a). If it is short-pitched by 30° (elect.) then as shown in Fig. 2 (b), their resultant is E which is the vector sum of two voltage 30° (electrical) apart.
- In general, if the coil span falls short of full-pitch by an angle α (electrical), this angle α is known as chording angle and the winding employing short-pitched coils is called chorded winding
Then,
k_{c} = cos α/2.
- Similarly, for a coil having a span of 2/3 pole-pitch, k_{c} = cos 60°/2 = cos 30° = 0.866. It is lesser than the value in the first case. The value of α will usually be given in the question, if not, then assume k_{c} = 1.