What happens when the supply frequency of a transformer increases?

When the frequency of supply to a transformer increases , the following happens:

1) Transformer operates with increased core losses and hence poorer efficiency.

2) If you are maintaining the same voltage but higher frequency , flux ( ~ V/f ) in the transformer falls, the induced emf would hence remain the same and would not increase, unlike what has been stated in one of the answers. Although the rate of change of flux increases due to increased frequency but the value of flux is reduced and hence the overall effect is that voltage induced in the secondary remains same but at a higher frequency of course.

3) If you are increasing primary voltage along with increasing frequency so as to maintain constant flux, only in that case the secondary voltage will increase. Therefore you can safely conclude that secondary voltage depends only upon the primary voltage and turns ratio. Look at it in a simpler way , Vsec/Vpri = Nsec/Npri. This basic equation in a transformer doesn’t relate the secondary voltage to frequency.

There is not much scope for significant changes in frequency in our supply system, maximum possible may be about + or – 1 Hz, more so on negative side.
Still if you want to have an experimental set up in the laboratory to see the effect of increased frequency in an existing transformer, the following may be noted:
flux and flux density will reduce.

1. hysteresis loss may slightly reduce.
2. transformer will move more away from the saturation region, etc