What is Earth Fault?
What is relation between Earth Current and Neutral?

Earth fault refers to any current in a circuit that is flowing directly to earth potential, as opposed to a "bolted fault" or a phase-to-phase fault. In a 3 phase system, all 3 phases have a return current to another phase, even if there is a phase-to-phase fault. So when power flows out to a load, it should all return. Any current that does not return then MUST be flowing to ground (earth).

Neutral is a reference point for a power flow diagram. Neutral is often referenced to earth, but that is not absolutely necessary.

What is mathematical relation between phase(R,Y and Current and Earth current and Neutral current?

What would be the value of earth current if single or two phase or all three phases current connected to ground?

Hello VSP

It depends on the electrical configuration and loads that are connected.
Most European systems are MEN systems where the supply transformer is delta primary and star secondary with the star point connected to neutral and the neutral earthed.
If you apply a single phase load, then the neutral current will equal the phase current in magnitude but the power will be flowing in the opposite direction. If you pass the phase and neutral cables through a single CT, then the current measured would be zero due to cancellation.
If you apply a three phase three wire load, there will be no neutral current.

If you apply three equal single phase loads to the three phases, the current in each phase will be equal but displaced by 120 degrees. The neutral current will be the vector sum of these currents and will equal zero.

If you have an unbalanced three phase load comprising single phase loads only, the neutral current will be the vector sum of the three phase currents, and due to the imbalance, will not equal zero.

Best regards,