Output voltage of a Synchronous Generator cannot contain even harmonics. For understanding the reason, carefully observe the figure below.
As shown in the figure, one full pitched coil a and a’ are placed. The fundamental component of field flux wave induce maximum emf in coil sides a and a’ as these are cutting the maximum filed flux Øm1. If the rms value of emf in each coil be E1 then the resultant emf of fundamental frequency across the coil ends A and B = 2E1.
Now, the second harmonics component of field flux wave also induces emf in coil sides a and a’. The induced emf because of second harmonics in coil sides a and a’ are maximum as because these are cutting the maximum field flux Øm2. But here it shall be noted that in both the coil sides the emf induced will oppose each other as both coil sides are cutting maximum positive filed flux wave of second harmonic component. Therefore the net / resultant emf because of second harmonic component across the coil sides A and B = 0
This shows that second / even though even / second harmonic is present in the field flux wave, second harmonic cannot be there in the output voltage of an Alternator.
It shall however be noted that field flux waveform of an Alternator is symmetrical and hence it do not have any even harmonics and hence there will not be any even harmonics in the generated voltage of an Alternator.