The per unit impedance of a circuit element is 0.15. If the ba... | Electrical MCQ | Examoogle

Examoogle • User • info@examoogle.com • EE-2024-8821

Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked

ElectricalPower System

The per unit impedance of a circuit element is 0.15. If the base kV and base MVA are halved, then the new value of the per unit impedance of the circuit element will be

075

Correct Answer

⚙️ TE • Technical Concept & PrincipleElectricalPower System

Option C

Quick Summary:

The per-unit (pu) impedance of a circuit element is inversely proportional to the square of the base voltage and directly proportional to the base MVA. Mathematically, the relation is given by $Z_{pu(new)} = Z_{pu(old)} \times \left(\frac{MVA_{new}}{MVA_{old}}\right) \times \left(\frac{kV_{old}}{kV_{new}}\right)^2$ .

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$Z_{pu} = Z_{\Omega} \times \frac{MVA_{base}}{(kV_{base})^2}$ — Definition of per-unit impedance

$Z_{new} = Z_{old} \times \frac{MVA_{new}}{MVA_{old}} \times (\frac{kV_{old}}{kV_{new}})^2$ — Change of base formula

⚙️ Working Principle

Given that the new MVA ( $MVA_{new}$ ) is $\frac{1}{2}$ of the old MVA ( $MVA_{old}$ ) and the new kV ( $kV_{new}$ ) is $\frac{1}{2}$ of the old kV ( $kV_{old}$ ), we substitute these into the change-of-base formula. Since the square of the voltage ratio cancels the MVA ratio (i.e., $\frac{0.5}{(0.5)^2} = \frac{0.5}{0.25} = 2$ ), the impedance value doubles.

📌 Key Points

▸
Per unit impedance is a dimensionless quantity used to normalize circuit values.
▸
The change in base values does not affect the actual ohmic impedance of the element.
▸
Doubling the impedance value results from the specific ratio change applied to MVA and kV.

✅ Advantages

▸
Simplifies power system calculations by eliminating transformer turns ratios.
▸
Allows direct comparison of machines of different ratings.

❌ Disadvantages / Limitations

▸
Requires careful keeping track of base changes during complex calculations.
▸
Can be confusing if system base MVA is not defined globally.

🛠️ Applications / Uses

▸
Short circuit studies
▸
Power flow analysis
▸
Relay coordination studies

📄 Additional Information

▸
Calculated value: $0.15 \times (0.5) \times (1/0.5)^2 = 0.15 \times 0.5 \times 4 = 0.30$ .
▸
Option A (0.075) is the result if the squared factor was ignored; Option B (1.5) is incorrect scaling.

📊 Diagram / Illustration

✅

C is correct — The new per unit impedance is 0.30 because scaling MVA by 0.5 and kV by 0.5 results in a net multiplication factor of 2.

Core Concepts Used

Click any tag to open in AI Tutor

Per Unit System Base Impedance Change of Base Calculation

💡 EXAM TIP

Always remember the base impedance definition $Z_b = (kV_b)^2 / MVA_b$ ; because kV is squared, changes to voltage base have a much larger impact on the final pu impedance than changes to MVA base.

Discussion (0)

Loading discussion...

Prev Next

Correct Answer

Related Questions

Discussion (0)