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The base impedance of power system is given as

$Base kV 2 Base MVA$

$Base kV Base MVA$

$Base MVA Base kV 2$

$Base MVA 2 Base kV$

Correct Answer

⚙️ TE • Technical Concept & PrincipleElectricalPower System

Option A

$Base kV 2 Base MVA$

Quick Summary:

The base impedance ( $Z_{base}$ ) is a fundamental parameter in the Per-Unit (PU) system used for power system analysis · It is derived from the base power (MVA) and base voltage (kV) ratings to normalize the system components.

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$Z_{base} = \frac{(kV_{base})^2}{MVA_{base}}$ — Calculation of base impedance in ohms

$Z_{pu} = \frac{Z_{actual}}{Z_{base}}$ — Conversion of actual impedance to per-unit

⚙️ Working Principle

Given the relationship between power ( $S = \frac{V^2}{Z}$ ), where $S$ is in MVA and $V$ is in kV, we isolate $Z_{base}$ . Thus, $Z_{base} = \frac{(kV_{base})^2}{MVA_{base}}$ . This normalization simplifies complex network calculations by eliminating transformer turns ratios in the equivalent circuit.

📌 Key Points

▸
Per-unit system eliminates the need for scaling when crossing transformer stages.
▸
Base values are chosen for voltage and power; base current and impedance are then derived.
▸
The base impedance is measured in Ohms ( $Omega$ ).

✅ Advantages

▸
Simplifies power system calculations by removing transformer turns ratios.
▸
Allows direct comparison of equipment with different ratings.
▸
Expressing values in PU makes them independent of system voltage levels.

❌ Disadvantages / Limitations

▸
Requires careful keeping track of base changes when crossing transformers.
▸
Can hide actual values if one only looks at PU data without knowing the base.

🛠️ Applications / Uses

▸
Short circuit studies (Symmetrical Fault Analysis)
▸
Load flow studies in power grids
▸
Stability analysis of multi-machine power systems

📄 Additional Information

▸
Base current is given by $I_{base} = \frac{MVA_{base}}{\sqrt{3} \times kV_{base}}$ .
▸
Option B represents the ratio of voltage to power, which does not result in units of impedance.
▸
Option C represents the reciprocal of base impedance, which is base admittance.

📊 Diagram / Illustration

✅

A is correct — The base impedance is defined as the square of the base line-to-line voltage in kV divided by the base power in MVA.

Core Concepts Used

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Per-Unit System Power System Normalization Base Quantities

💡 EXAM TIP

Always ensure the MVA base is the same for the entire circuit part being studied; if not, you must perform a base change using the formula $Z_{pu(new)} = Z_{pu(old)} \times \frac{MVA_{base(new)}}{MVA_{base(old)}} \times (\frac{kV_{base(old)}}{kV_{base(new)}})^2$ .

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