Which of the following results in a symmetrical fault?

Question

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Option C: All the three phase to earth

Explanation & Concepts:
A symmetrical fault, also known as a balanced fault, is a fault in a power system where all three phases of the system are affected equally, maintaining the symmetry of the phases. This results in balanced fault currents that are identical in magnitude and displaced by $120^\circ$ electrical degrees.

Working Principle: In a three-phase system, a fault involving all three phases (either with or without a connection to the ground) disrupts the system symmetry minimally because the impedance paths for each phase remain identical. Consequently, the fault currents calculated using the per-phase equivalent circuit are balanced, satisfying the condition for a symmetrical fault analysis.

Key Formulas: $I_{f} = \frac{V_{ph}}{Z_1}$ — Current for a balanced three-phase fault where $Z_1$ is the positive sequence impedance.; $Z_{eq} = Z_1$ — For symmetrical faults, only the positive sequence network is considered.

Key Points: Symmetrical faults are rare (only about 2-5% of total faults) but are the most severe.; The fault current is calculated using only the positive sequence network.; The power system remains balanced during and after the occurrence of the fault.; Three-phase to earth (LLL-G) and Three-phase (LLL) are both symmetrical faults.

Advantages: Simplifies power system analysis using single-phase equivalent circuits.; Provides the worst-case scenario for determining circuit breaker rupturing capacity.

Disadvantages: Extremely high thermal and mechanical stresses on power equipment.; Significant voltage dips across the entire interconnected grid.

Applications: Determination of maximum fault current.; Selection and rating of switchgear and circuit breakers.

Additional Info: The vast majority of faults (approx. 80%) are Single Line-to-Ground (SLG) faults, which are asymmetrical.. Options A, B, and D describe asymmetrical faults because they cause unequal impedance paths and phase imbalance in the system.

Answer: C is correct — All three phases to earth (LLL-G) is a symmetrical fault because it affects all three phases equally, maintaining phase balance.

Exam Tip: Always remember that for symmetrical faults, the neutral current is zero ($I_n = 0$) because the three-phase currents sum to zero at the neutral point.

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Option A: Single phase to earth

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Option B: Phase to phase

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Option D: Two phase to earth

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