1. Pitch factor, Distribution factor and emf equation By J Binod kumar Lect. in electrical engineering Govt polytechnic malkangiri

2. Pitch factor  Pitch factor or coil span factor is the ratio of emf generated in short pitch coil to the emf generated in full pitch coil.  It is denoted by K p.  Its values lies between 0 to 1.

3. Let E 1, E 2 and E R be the emf induced in coil side lying under North Pole, South Pole and resultant of emf generated in both the active lengths of coil. As the two coil sides are separated in space by an angle of (180-ε) i.e. the coil span is (180-ε), therefore the emf induced in these coil sides will also be separated by this angle. This means, the angle between E 1 and E 2 phasor will be equal to ε as shownphasor

4. Since the magnitude of emf generated in both the coil sides are equal, therefore E 1 = E 2 = E (say). As the resultant emf E R is the phasor sum of E 1 and E 2, therefore emf generated in a full pitch coil = 2E

5. pitch factor or coil span factor K p = Cos(ε/2 ). For a full pitch coil, the value of pitch factor is unity The pitch factor or coil span factor n th harmonics is given asharmonics K p = Cos (nε/2)

6. Distribution factor  The ratio of the phasor sum of the EMFs induced in all the coils distributed in a number of slots under one pole to the arithmetic sum of the EMFs induced is known as breadth factor or distribution factor.coils distributed  It is denoted by K d.  Its value is always less than unity.

8. Let n be the number of slots per pole. m be the number of slots per pole per phase. E c be the induced emf in each coil side. Angular displacement between the slots The EMFs induced in different coils of one phase under one pole are represented by side AC, CD, DE, EF,… which are equal in magnitude but differ in phase.[Say the magnitude be E and phase difference be 180 degrees]

9. If bisectors are drawn on AC, CD, DE, EF, they would meet at a common point. This point would be the center of the circle having AC, CD, DE, EF as the chords. They represent the EMFs induced in the coils in different slots.

11.  Vector sum of emf induced Thus the distribution factor can be obtained as

12. Winding factor(K w )  winding factor defined as the product of pitch or coil span factor and distribution factor.  It is denoted by Kw  It value is less than 1.  K w = K p K d

13. Harmonics  The flux distribution along the air gaps of alternators usually is non sinusoidal so that the emf in the individual armature conductor is also non-sinusoidal.  The sources of harmonics in the output voltage waveform are the non sinusoidal waveform of the field flux.  Fourier showed that any periodic wave may be expressed as the sum of a d-c component (zero frequency) and sine (or cosine) waves having fundamental and multiple or higher frequencies, the higher frequencies being called harmonics.

15. Effect of harmonics on pitch factor and distribution factor  For a nth order harmonic  Pitch factor K pn = cos(nε/2)  Distribution factor K dn = sin(nmβ/2) ̸ msin(nβ/2)  Example if n = 3 Kp3 = cos(3ε/2), K d3 = sin(3mβ/2) ̸ msin(3β/2)  If n = 5 Kp5 = cos(5ε/2) K d5 = sin(5mβ/2) ̸ msin(5β/2)

16. Emf with harmonics

17.  All the odd harmonics (third, fifth, seventh, ninth, etc.) are present in the phase voltage to some extent and need to be dealt with in the design of ac machines.  Because the resulting voltage waveform is symmetric about the center of the rotor flux, no even harmonics are present in the phase voltage.  In Y- connected, the third-harmonic voltage between any two terminals will be zero. This result applies not only to third-harmonic components but also to any multiple of a third-harmonic component (such as the ninth harmonic). Such special harmonic frequencies are called triplen harmonics.

18. Elimination of harmonics  Small air gap at the pole centre and large air gap towards the pole ends  Skewing: skew the pole faces if possible  Distribution: distribution of the armature winding along the air-gap periphery  Chording: with coil-span less than pole pitch  Fractional slot winding  Alternator connections: star or delta connections of alternators suppress triplen harmonics from appearing across the lines

19. Emf equation of alternator  Φ = Flux per pole, in Wb  P = Number of poles  N = Synchronous speed in r.p.m  f = Frequency of induced emf in Hz  Z = Conductors per phase connected in series/phase =2T  K p = pitch factor  K d = distribution factor  K f = form factor = 1.11

20.  In one revolution of the rotor each stator conductor is cut by a flux of ɸ p webers.  d ɸ = ɸ p and dt=60/N second  average e.m.f induced per conductor = ɸ = ɸ p ̸ 60/ = ɸ NP ̸̸ 60  Now, we know that f=PN/120 or N=120f/p

21.  Substituting this values of N above, we get  Average e.m.f per conductor = ɸ P/ 60 * 120/ =2f ɸ volt  If there are z conductors in series/phase, then average e.m.f/phase =2f ɸ z volt =4f ɸ T volt  R.M.S value of e.m.f/phase = 1.11*4f ɸ T = 4.44f ɸ T volt  Actually available voltage/phase = 4.44K P K d ɸ fT volt