Per unit impedance of a circuit element is 0.3. if the base kV... | Electrical MCQ | Examoogle

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Per unit impedance of a circuit element is 0.3. if the base kV and base MVA are halved, then the new value of the per unit impedance of the circuit element will be

0.3

0.6

0.003

0.006

Correct Answer

⚙️ TE • Technical Direct FormulaElectricalPower System

Option B

0.6

Quick Summary:

Given: Initial per unit impedance (Z_pu_old) = 0.3, Base kV is halved ( $kV_{new}$ = 0.5 * $kV_{old}$ ), Base MVA is halved ( $MVA_{new}$ = 0.5 * $MVA_{old}$ ).

📐MAMath SolutionDirect Formula

📋 Given

Initial per unit impedance (Z_pu_old) = 0.3, Base kV is halved ( $kV_{new}$ = 0.5 * $kV_{old}$ ), Base MVA is halved ( $MVA_{new}$ = 0.5 * $MVA_{old}$ ).

🔢 Formula Used

Zpu,new=Zpu,old×(MVAnewMVAold)×(kVoldkVnew)2Z_{pu,new} = Z_{pu,old} \times \left( \frac{MVA_{new}}{MVA_{old}} \right) \times \left( \frac{kV_{old}}{kV_{new}} \right)^2Zpu,new​=Zpu,old​×(MVAold​MVAnew​​)×(kVnew​kVold​​)2

🔢 Step-by-Step Solution

Identify the per unit impedance formula

The per unit impedance $Z_{pu}$ is given by the formula $Z_{pu} = \frac{Z_{actual} \times MVA_{base}}{(kV_{base})^2}$ .

Zpu=Zactual×MVAbase(kVbase)2Z_{pu} = \frac{Z_{actual} \times MVA_{base}}{(kV_{base})^2}Zpu​=(kVbase​)2Zactual​×MVAbase​​

Relate old and new values

Given $MVA_{new} = 0.5 \times MVA_{old}$ and $kV_{new} = 0.5 \times kV_{old}$ . The actual impedance $Z_{actual}$ of the element remains constant.

Zactual=Zpu,old×(kVold)2MVAold=Zpu,new×(kVnew)2MVAnewZ_{actual} = Z_{pu,old} \times \frac{(kV_{old})^2}{MVA_{old}} = Z_{pu,new} \times \frac{(kV_{new})^2}{MVA_{new}}Zactual​=Zpu,old​×MVAold​(kVold​)2​=Zpu,new​×MVAnew​(kVnew​)2​

Calculate the new per unit impedance

Substituting the new base values into the equality: $Z_{pu,new} = Z_{pu,old} \times \frac{MVA_{new}}{MVA_{old}} \times \left(\frac{kV_{old}}{kV_{new}}\right)^2$ . Plugging in the ratios: $Z_{pu,new} = 0.3 \times (0.5) \times (1/0.5)^2$ .

Zpu,new=0.3×0.5×4=0.6Z_{pu,new} = 0.3 \times 0.5 \times 4 = 0.6Zpu,new​=0.3×0.5×4=0.6

✅

B is correct because the new per unit impedance is calculated to be 0.6 when the MVA base is halved and the kV base is squared in the denominator.

Core Concepts Used

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Per Unit System Power System Impedance Base Value Normalization

💡 EXAM TIP

This concept is vital in power system analysis, particularly for fault studies and load flow calculations where multiple voltage levels exist in a single system.

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