These non-sinusoidal waveforms are expressed in terms of Fourier transforms which are the sum of series of sinusoidal waveforms.Now let us understand the effect of harmonic components on the synchronous generator.
So flux density at an angle θ from the interpolar axis is given by,
B = Bm1 sin θ + Bm3 sin 3θ +……….. + Bmx sin xθ
where x = Order of the harmonic component which is odd
Bm1 = Amplitude of fundamental component of flux density
Bm3 = Amplitude of 3rd harmonic component of flux density
Bmx = Amplitude of Xth (odd) harmonic component of flux density
The EMF generated in a conductor on the armature of a rotating machine is given by
ec = B.l.v
ec = [Bm1 sin θ + Bm3 sin 3θ +……….. + Bmx sin xθ].l.v
l = Active length of conductor in metre
d = Diameter of the armature at the air gap
v = Linear velocity = π d ns
where ns = Synchronous speed in r.p.s.
Now NS = 120f/P
ns = 120f/60P = 2f/P
v = π d 2f/P
ec = [Bm1 sin θ + Bm3 sin 3θ +……….. + Bmx sin xθ].l.(2πdf/P)
A1 = πdl/P
ec = [Bm1 A1 2f sin θ + Bm3 A1 2f sin 3θ +……….. + Bmx A1 2f sin xθ]
This is because there are xP poles for the xth order harmonic.
ec = 2f [Bm1 A1 sin θ + Bm3 3A3 sin 3θ +……….. + Bmx xAx sin xθ]
Bm1 A1 = Φ1m = Maximum value of fundamental flux per pole
Similarly, the average value of xth harmonic flux per pole can be obtained as,
Φx = (2/π)Ax Bmx
- Effect of Harmonic Components on EMF of Synchronous Generator
Substituting the values of flux in ec we get the expression for e.m.f. induced per conductor as
Instantaneous value of fundamental frequency EMF generated in a conductor is,
ec1 = πfΦ1 sin θ V
Hence RMS value of xth harmonic frequency emf generated in a conductor is,
It can be observed that the magnitude of harmonic e.m.f.s is directly proportional to their corresponding flux densities.
Effect of Harmonic Components on Pitch Factor in Synchronous Generator:
3α = For 3rd harmonic component
5α = For 5th harmonic component
Hence the pitch factor is expressed as,
Effect of Harmonic Components on Distribution Factor in Alternators:
Similar to the pitch factor, the distribution factor is also different for various halt components.
The general expression to obtain distribution factor is,
Total EMF Generated due to Harmonics in synchronous Generator:
E1ph = 4.44 Kc1 Kd1 Φ1 f Tph V
where Tph = Turns per phase series
Φ1 = Fundamental flux component
While the phase e.m.f. of Xth order harmonic component of frequency is given by,
The total phase EMF is given by,
