Question

A symmetrical 3-phase fault occurs at a bus. If the pre-fault voltage is 1.0pu and the Thevenin impedance is j0.2pu, the fault current in per-unit is:

• A. 0.2pu
• B. 2.0pu
• C. 5.0pu
• D. 10.0pu

Hint:

For any symmetrical fault, the fault current is inversely proportional to the Thevenin impedance.
If \(Z_{\text{th}} = jX\), the magnitude of the fault current is simply \(1/X\) (for \(V_{\text{th}} = 1.0\)).
Here, \(1 / 0.2 = 5.0\text{ pu}\). This calculation can be performed mentally in seconds.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks for the per-unit (pu) magnitude of the short-circuit fault current during a symmetrical three-phase fault at a busbar, given the pre-fault voltage and the Thevenin impedance at that bus.

Step 2: Key Formula or Approach:
Using the Thevenin equivalent circuit at the fault location, the fault current (\(I_f\)) in per-unit is given by:
\[ I_f = \frac{V_{\text{th}}}{Z_{\text{th}}} \] where:
- \(V_{\text{th}}\) is the pre-fault Thevenin voltage at the bus (usually \(1.0\text{ pu}\)).
- \(Z_{\text{th}}\) is the equivalent Thevenin impedance of the network seen from the faulted bus.

Step 3: Detailed Explanation:

• Identify the given parameters:
- Pre-fault voltage, \(V_{\text{th}} = 1.0\text{ pu}\).
- Thevenin impedance, \(Z_{\text{th}} = j0.2\text{ pu}\).

• Substitute these values into the fault current formula:
\[ I_f = \frac{1.0}{j0.2} \]
• Simplify the expression:
\[ I_f = -j \left(\frac{1.0}{0.2}\right) = -j5.0\text{ pu} \]
• Calculate the magnitude of the fault current:
\[ |I_f| = 5.0\text{ pu} \]

Step 4: Final Answer:
The fault current in per-unit is 5.0pu.