A fault occuring at the terminals of an unloaded synchronous generator operating at its rated voltage has resulted in the following values of currents and voltages:Ia0 = j2.37 p.u.Ia1 = – j3.05 p.u.Ia2 = j0.68 p.u.Va0 = Va1 = Va2 = 0.237 p.u.Which one of the following faults has occurred?

Correct Answer: B - L - L - G fault

Quick Concept Explanation

For a double-line-to-ground fault on phases b and c, the unfaulted phase current Ia is zero and the fault-point sequence voltages satisfy the appropriate equal-voltage relation. Three independent signatures agree: zero sequence present → ground fault; Ia=0 → phase a healthy; negative sequence present → unbalanced two-phase involvement.

Exam focus: Fault ID shortcut: zero-sequence present means the ground path participates. Common trap: Selecting a 3-phase fault despite nonzero I0 and I2.

Technical Verification

Given V0=V1=V2=0.237 p.u. This equality is compatible with the boundary condition for a double-line-to-ground fault on the other two phases. Ia = I0+I1+I2 = j(2.37−3.05+0.68)=0, so phase a carries no current and is the healthy phase. Nonzero zero-sequence current proves that ground is involved; therefore a pure L-L fault is excluded. Nonzero negative- and zero-sequence components exclude a balanced three-phase fault.

Core Concept

Symmetrical components turn an unbalanced fault into coupled positive-, negative- and zero-sequence networks. Ground involvement is recognized by zero-sequence current. For a double-line-to-ground fault on phases b and c, the unfaulted phase current Ia is zero and the fault-point sequence voltages satisfy the appropriate equal-voltage relation.

Formula / Key Relationship

Ia=I0+I1+I2. Here Ia=0. Phase transformation: [Va Vb Vc]^T = A[V0 V1 V2]^T.

Step-by-Step Check

Three independent signatures agree: zero sequence present → ground fault; Ia=0 → phase a healthy; negative sequence present → unbalanced two-phase involvement. Therefore L-L-G, option B.

Why the Other Options Are Wrong

A (L-L) has no zero-sequence current; C (L-G) has a different sequence-network condition; D (L-L-L) is balanced and would not have nonzero negative/zero sequence components. The given sequence relations identify L-L-G.

Answer-Key Verification Note

The uploaded provisional key marks D . After independent technical verification, the defensible answer is B . This discrepancy is stated explicitly rather than silently copying the provisional key.

Exam Shortcut / Approach

Fault ID shortcut: zero-sequence present means the ground path participates.

Common Mistake

Selecting a 3-phase fault despite nonzero I0 and I2.

Quick Revision

Identification of Double-Line-to-Ground Fault is linked with Symmetrical Components, Fault Analysis and Power Systems. Fault ID shortcut: zero-sequence present means the ground path participates.