Question

A 100 MVA, 11 kV generator has a reactance of 0.2 pu. What is the reactance in ohms?

• A. $0.242 \ \Omega$
• B. $2.42 \ \Omega$
• C. $24.2 \ \Omega$
• D. $1.21 \ \Omega$

Hint:

Double check units when using the base formula:
\[ Z_{\text{base}} = \frac{(kV_{\text{base}})^2}{MVA_{\text{base}}} \] Voltage must be in \(\text{kV}\) and power must be in \(\text{MVA}\) for the formula to yield the base impedance directly in \(\Omega\). This is a useful shortcut in exams.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks to convert the reactance of a synchronous generator from per-unit (pu) values to actual physical ohmic (\(\Omega\)) values, given the machine's rated power and rated voltage.

Step 2: Key Formula or Approach:
The relationship between actual reactance (\(X_{\Omega}\)), base impedance (\(Z_{\text{base}}\)), and per-unit reactance (\(X_{\text{pu}}\)) is:
\[ X_{\Omega} = X_{\text{pu}} \times Z_{\text{base}} \] The base impedance for a three-phase system can be directly calculated from the base voltage in kilovolts (\(kV_{\text{base}}\)) and the base power in megavolt-amperes (\(MVA_{\text{base}}\)) using the formula:
\[ Z_{\text{base}} = \frac{(kV_{\text{base}})^2}{MVA_{\text{base}}} \]

Step 3: Detailed Explanation:

• Identify the base parameters from the generator ratings:
- Base Voltage, \(kV_{\text{base}} = 11\text{ kV}\).
- Base Power, \(MVA_{\text{base}} = 100\text{ MVA}\).
- Per-unit reactance, \(X_{\text{pu}} = 0.2\text{ pu}\).

• Calculate the base impedance \(Z_{\text{base}}\):
\[ Z_{\text{base}} = \frac{(11)^2}{100} = \frac{121}{100} = 1.21\ \Omega \]
• Calculate the actual reactance in ohms:
\[ X_{\Omega} = X_{\text{pu}} \times Z_{\text{base}} \] \[ X_{\Omega} = 0.2 \times 1.21 = 0.242\ \Omega \]

Step 4: Final Answer:
The reactance in ohms is \(0.242\ \Omega\).