Per Unit Impedance Calculator

Per Unit Impedance Formula:

\[ Z_{pu} = \frac{Z_{actual}}{Z_{base}} \]

Per Unit Impedance (Z_pu):

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1. What is Per Unit Impedance?

Per unit impedance is a normalized value used in power system analysis to simplify calculations and comparisons across different voltage levels and system sizes. It represents the ratio of actual impedance to a chosen base impedance.

2. How Does the Calculator Work?

The calculator uses the per unit impedance formula:

\[ Z_{pu} = \frac{Z_{actual}}{Z_{base}} \]

Where:

\( Z_{pu} \) — Per unit impedance (dimensionless)
\( Z_{actual} \) — Actual impedance in ohms (Ω)
\( Z_{base} \) — Base impedance in ohms (Ω)

Explanation: The per unit system normalizes electrical quantities to a common base, making it easier to analyze power systems with multiple voltage levels and transformer connections.

3. Importance of Per Unit System

Details: The per unit system simplifies power system analysis by eliminating the need for voltage transformation calculations and allowing direct comparison of impedances across different parts of the system.

4. Using the Calculator

Tips: Enter actual impedance and base impedance in ohms. Both values must be positive, with base impedance greater than zero for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is base impedance?
A: Base impedance is calculated as \( Z_{base} = \frac{V_{base}^2}{S_{base}} \), where V_base is base voltage and S_base is base power.

Q2: Why use per unit system?
A: It simplifies calculations, eliminates ideal transformer ratios, and allows direct comparison of equipment parameters regardless of voltage level.

Q3: What are typical per unit impedance values?
A: Typical values range from 0.05 to 0.15 pu for transformers, 0.1 to 0.3 pu for generators, and 0.01 to 0.1 pu for transmission lines.

Q4: How is base impedance selected?
A: Base impedance is typically chosen based on system voltage and power ratings, often using system nominal voltage and a convenient power base (e.g., 100 MVA).

Q5: Can per unit values be converted between different bases?
A: Yes, using the formula: \( Z_{pu(new)} = Z_{pu(old)} \times \frac{S_{base(new)}}{S_{base(old)}} \times \frac{V_{base(old)}^2}{V_{base(new)}^2} \)