The maximum short circuit current occurs in the case of

Question

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Option A: Three phase fault

Explanation & Concepts:
A three-phase fault, being a symmetrical fault, involves all three phases and results in the lowest possible impedance path to ground or between phases. Because the positive sequence impedance ($Z_1$) is typically the smallest impedance in the network compared to negative ($Z_2$) or zero-sequence ($Z_0$) impedances, the short circuit current in a balanced three-phase fault is higher than in any unbalanced fault condition.

Working Principle: In a three-phase short circuit, the fault current is governed solely by the sub-transient reactance ($X''d$) of the generator, as the sequence network reduces to only the positive sequence network. For asymmetrical faults, additional impedances such as $Z_2$ and $Z_0$ are added in series or parallel, increasing the total fault impedance and consequently reducing the magnitude of the fault current according to $I_f = \frac{V}{Z_{eq}}$.

Key Formulas: $I_{f(3\phi)} = \frac{V_{ph}}{Z_1}$ — Three-phase fault current formula; $I_{f(LG)} = \frac{3V_{ph}}{Z_1 + Z_2 + Z_0}$ — Single line to ground fault current formula

Key Points: Three-phase faults are symmetrical and are the most severe in terms of current magnitude.; The sub-transient current is the peak current occurring immediately after the fault.; Positive sequence impedance ($Z_1$) is the primary limiting factor for balanced faults.; Single line-to-ground faults occur most frequently, but three-phase faults represent the worst-case design load.

Advantages: Provides worst-case scenario for circuit breaker sizing; Simplifies relay coordination calculations

Disadvantages: Causes high thermal stress on equipment; Leads to severe voltage dips across the system

Applications: Switchgear rating selection; Protection system relay setting

Additional Info: In most power systems, the sequence impedances satisfy $Z_1 \approx Z_2. Option D (Single line to ground fault) is the most frequent type of fault, occurring about 70-80% of the time, but it is not the most severe.

Answer: A is correct — The three-phase fault results in the maximum short circuit current because the system impedance is limited only by the positive sequence reactance.

Exam Tip: Always remember that in fault analysis, 'symmetrical' does not mean 'smaller'; three-phase faults are symmetrical yet provide the maximum current values for system protection design.

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Option B: Double line to ground fault

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Option C: Line to line fault

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Option D: Single line to ground fault

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