Harmonics In Synchronous Machines

What Are ? Harmonics In Synchronous Machines

Harmonics: When the uniformly sinusoidally distributed air gap flux is cut by either the stationary or rotating armature sinusoidal emf is induced in the alternator. Hence the nature of the waveform of induced emf and current is sinusoidal. But when the alternator is loaded waveform will not continue to be sinusoidal or becomes non-sinusoidal. Such non-sinusoidal wave form is called complex wave form.

By using Fourier series representation it is possible to represent complex non-sinusoidal waveform in terms of series of sinusoidal components called harmonics, whose frequencies are integral multiples of fundamental wave. The fundamental wave form is one which is having the frequency same as that of complex wave.The waveform, which is of the frequency twice that of the fundamental is called second harmonic. The one which is having the frequency three times that of the fundamental is called third harmonic and soon. These harmonic components can be represented as follows.

Fundamental: e1 = Em1 Sin ( t ± θ1)

2nd Hermonic e2 = Em2 Sin (2 t ± θ2)

3rd Harmonic e3 = Em3 Sin (3 t ± θ3)

5th Harmonic e5 = Em5 Sin (5 t ± θ5) etc.

In case of alternators as the field system and the stator coils are symmetrical the induced emf will also be symmetrical and hence the generated emf in an alternator will not contain any even harmonics.

Slot Harmonics: As the armature or stator of an alternator is slotted, some harmonics are induced into the emf which is called slot harmonics. The presence of slot in the stator makes the air gap reluctance at the surface of the stator non uniform. Since in case of alternators the poles are moving or there is a relative motion between the stator and rotor, the slots and the teeth alternately occupy any point in the air gap. Due to this the reluctance or the air gap will be continuously varying. Due to this variation of reluctance ripples will be formed in the air gap between the rotor and stator slots and teeth. This ripple formed in the air gap will induce ripple emf called slot harmonics.

Minimization Techniques of Harmonics: To minimize the harmonics in the induced waveforms following methods are employed:
1. Distribution of stator winding.
2. Short Chording
3. Fractional slot winding
4. Skewing
5. Larger air gap length.

Effect of Harmonics on induced emf:

The harmonics will affect both pitch factor and distribution factor and hence the induced emf. In a well designed alternator the air gap flux density distribution will be symmetrical and hence can be represented in Fourier series as follows.

The RMS value of the resultant voltage induced can be given as

Eph2 =  [(E1)2+ ....+ …………… (En)2]

**(A)2 Means A Square 

Effect of Harmonics of pitch and distribution Factor:

The pitch factor is given by Kp = cos /2, where is the chording angle.
For any harmonic say nth harmonic the pitch factor is given by Kpn = cos n α/2
The distribution factor is given by Kd = (sin mβ /2) / (m sin β/2)

For any harmonic say nth harmonic the distribution factor is given by 
Kdn = (sin mn β/2)/(m sin nβ/2)

This is the detailed info about Harmonics In Synchronous Machines,Minimization Methods of Harmonics.Effect of Harmonics on induced emf.