Question

The per unit value of a \(2\text{ }\Omega\) resistor at \(100\text{ MVA}\) base and \(10\text{ kV}\) base voltage is

• A. \(2\)
• B. \(4\)
• C. \(0.5\)
• D. \(0.2\)

Hint:

A useful shortcut formula to directly compute per-unit impedance is: \[ Z_{pu} = Z_{\Omega} \times \frac{MVA_{\text{base}}}{(kV_{\text{base}})^2} \] Substituting values directly: $2 \times \frac{100}{10^2} = 2\text{ pu}$.

Answer 1

The Correct Option is A

Concept: Per-unit normalization expresses system parameters as dimensionless fractions of defined base values. The per-unit value of any impedance is calculated using the formula: \[ Z_{pu} = \frac{Z_{\text{actual}}(\Omega)}{Z_{\text{base}}(\Omega)} \] The base impedance ($Z_{\text{base}}$) can be derived from the base power ($MVA_{\text{base}}$) and base line-to-line voltage ($kV_{\text{base}}$) using the standard power-voltage relationship: \[ Z_{\text{base}} = \frac{(kV_{\text{base}})^2}{MVA_{\text{base}}} \]

Step 1: Extract the given parameters from the text.
* Actual resistance value (\(Z_{\text{actual}}\)) = \(2\text{ }\Omega\) * Base Power (\(MVA_{\text{base}}\)) = \(100\text{ MVA}\) * Base Voltage (\(kV_{\text{base}}\)) = \(10\text{ kV}\)

Step 2: Calculate the base impedance (\(Z_{\text{base}}\)).
Using the formula for base impedance: \[ Z_{\text{base}} = \frac{(10\text{ kV})^2}{100\text{ MVA}} \] \[ Z_{\text{base}} = \frac{100}{100} = 1\text{ }\Omega \]

Step 3: Calculate the per-unit value (\(Z_{pu}\)).
Now, divide the actual resistance value by the calculated base impedance: \[ Z_{pu} = \frac{2\text{ }\Omega}{1\text{ }\Omega} = 2\text{ pu} \] The calculated per-unit value is exactly 2, which corresponds to Option (A).