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If a 3 phase fault occurs the direct axis sub-transient reactance is sufficient to calculate the fault current. But in case of an unbalanced fault it is not.

Taking the example of Line to Ground fault, where generator neutral is ground and a fault occurs on one of the terminals the circuit becomes,

enter image description here

Looking at the circuit it apparently looks fault current should be Ea/(Zs+Zn) but actually it is not. Can somebody please explain me why is it so?

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Every non-symmetrical short-circuit produces a non-symmetrical three-phase-system. Therefore symmetrical component analysis is necessary.

The problem with your figure is, that it appears that the phases B and C are open loop. Then your calculation would be right. But usually this is not the case.

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