For a fault at the terminals of synchronous generator, the fault current is maximum for

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Option C: Single line to ground fault

Explanation & Concepts:
In a synchronous generator, the Single Line to Ground (SLG) fault is typically the most severe fault current because it involves the zero-sequence impedance of the generator, which is often significantly lower than the positive and negative sequence impedances. Consequently, the fault current path presents the least impedance, resulting in a higher magnitude compared to balanced three-phase faults.

Working Principle: During an SLG fault, the fault current is determined by $I_{f} = \frac{3E_{a}}{Z_{1} + Z_{2} + Z_{0}}$. Since the zero-sequence impedance $Z_{0}$ is generally much smaller than the positive-sequence reactance ($X_{d}''$) and negative-sequence reactance ($X_{2}$), the denominator is minimized, leading to a higher fault current than in symmetric faults where only $Z_{1}$ dominates.

Key Formulas: $I_{f(SLG)} = \frac{3E_{a}}{Z_{1} + Z_{2} + Z_{0}}$ — Total fault current for a single line-to-ground fault; $I_{f(3\Phi)} = \frac{E_{a}}{Z_{1}}$ — Total fault current for a balanced three-phase fault

Key Points: The zero-sequence impedance $Z_{0}$ depends on the machine grounding and is usually the smallest component.; A three-phase fault is constrained by the sub-transient reactance $X_{d}''$.; SLG fault current is the highest for machines with solid grounding at the neutral.; Synchronous machines typically exhibit $X_{d}''

Advantages: Enables conservative design of grounding systems.; Helps in sizing circuit breakers for the worst-case scenario.

Disadvantages: High fault currents cause thermal and mechanical stress on windings.; Can lead to high transient recovery voltages across circuit breaker contacts.

Applications: Protection relay coordination; Grid stability studies; Grounding system design

Additional Info: In some machines, if the grounding impedance is very high, the SLG fault current can be lower than a 3-phase fault; however, for typical direct-grounded generators, SLG is the design maximum.. Option A (Three-phase fault) is often considered the 'base' symmetrical fault but does not involve $Z_{0}$ in its calculation.

Answer: C is correct — Single line to ground fault typically yields the highest current in a grounded synchronous generator due to the dominance of the low zero-sequence impedance.

Exam Tip: Always verify the grounding condition of the generator; if the generator is isolated (ungrounded), the SLG fault current is zero.

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Option A: Three phase fault

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Option B: Three phase to ground fault

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Option D: Line to line fault

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