What is the Relationship between the Grid voltage and Generator voltage ? how to link up generator with grid ?

To Connect Generator to the Utility you Should Check 

- Equal Magnitude

- Equal Frequency 

- Equal Phase Shift

- Same Phase Rotation

- Same Vector group connection 

  and to check the phase Shift you should have Automatic Synchronizing  Control Unit because it cannot done manually as measuring the frequency and voltage

Follow generator synchronization 

- Equal magnitude, phase shift, phase rotation, and frequency

The relation is to equalize the both of voltages with three parameters for the sinusoidal wave (the magnitude):

1- voltage (Vmax)

2- frequency (Hz)

3- phase shift (Phi)

And regarding to the synchronization, there is synchro-check comparator to ensure that all of the3 conditions mentioned above are satisfied, then the generator circuit breaker closes immediately, and the time of closing is calibrated and calculated accurately.

the allowed error parameters for the.8 KV Hz Siemens generator is:

+-2 Volt from the Vmax (dV)

+-0. Hz from the frequency (df)

+- Deg from the phase shift (dPhi)

The magnitude of the sinusoidal voltage produced by the generator must be equal to the magnitude of the sinusoidal voltage of the grid.If the generator voltage is higher than the grid voltage and it is connected to the grid the generator will be overexcited and it will put out MVAR.If generator voltage less than the grid voltage the generator will be under-excited and it will absorb MVAR.

For synchronize with grid firs generator frequency must be little bit high than grid.Have to check phase sequence,voltage if all condition is match then it connected with grid.