Single Phase To Ground Fault In Star-Star Transformer

If there is a phase-to-ground fault then a protection device will operate, disconnecting the fault.

You are likely to experience over excitation and saturation of the metal core and possible overheating of the transformer due to increased currents in the unshorted phases. This can cause the windings to burn out or even a fire if the transformer is oil immersed. Although you are probably already seeing 3rd harmonics, you may also experience more induced harmonics in the secondary due to the unbalanced primary. These will cause a distortion of the secondary waveform.

You don't say if the primary star is connected to the generator star or simply earthed at the transformer, results can vary with these differences.

The primary and secondary stars are simply earthed. The primary star is not connected to the generator star .

I want to know whether the zero sequence current will also flow in secondary windings or only there will be distortion of the secondary waveform caused by third harmonics.

Here's a bit of reading that may help

definetly there s a provision for the flow of zero sequence component of currents in the system since the fault is associated ground.. these zero sequence currents may not flow if ur windings are connnected in delta.