Per-Unit System Calculator

In power systems engineering, the per-unit system normalizes electrical quantities — voltage, current, impedance, and power — against chosen base values, making complex multi-voltage network analysis much easier. Enter your Base Power (MVA) and Base Voltage (kV) alongside your Actual Impedance and select a Calculation Type (Per-Unit Impedance, Base Quantities, or Change of Base) to get your Per-Unit Impedance. Secondary outputs include Base Impedance, Base Current, and single-phase base impedance.

MVA

Three-phase base power in mega volt-amperes

kV

Line-to-line base voltage in kilovolts

Ω

Actual impedance value in ohms

kV

Actual voltage level (if different from base)

MVA

Actual power rating (if different from base)

Results

Per-Unit Impedance

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Base Impedance

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Base Current

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Base Impedance (1φ)

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Results Table

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Frequently Asked Questions

What is the per-unit system in power system analysis?

The per-unit system is a normalization method that expresses electrical quantities as fractions of chosen base values. It simplifies calculations by eliminating the need to consider voltage levels and makes system analysis more intuitive.

How do I calculate base impedance?

Base impedance is calculated using the formula: Z_base = (kV_base)² / MVA_base. For example, with 138 kV base voltage and 100 MVA base power, the base impedance would be 190.44 ohms.

What is the advantage of using per-unit values?

Per-unit values eliminate the complexity of different voltage levels, provide dimensionless quantities that are easier to compare, and simplify transformer calculations by removing turns ratio considerations.

How do I change base values in per-unit calculations?

To change base values, use the formula: Z_pu_new = Z_pu_old × (MVA_new/MVA_old) × (kV_old/kV_new)². This maintains the actual impedance value while expressing it on a new base.

What are typical per-unit impedance values for power system equipment?

Typical values include: generators (0.1-0.3 p.u.), transformers (0.05-0.15 p.u.), transmission lines (0.01-0.05 p.u. per mile), and motors (0.15-0.25 p.u. subtransient reactance).

Can I use per-unit values for single-phase calculations?

Yes, per-unit calculations work for both single-phase and three-phase systems. The key difference is in the base power definition - use single-phase base power for single-phase calculations.

How accurate are per-unit calculations compared to actual values?

Per-unit calculations are mathematically equivalent to actual value calculations when done correctly. They provide the same accuracy while offering computational advantages in complex power system studies.