Per-Unit Impedance from Physical Parameters

• fundamentalsper-unitimpedanceanalysis

Purpose and Scope

This article focuses on converting physical electrical parameters—resistance, inductance, and capacitance—into per-unit values. It builds directly on the base quantities defined in Per-Unit System: Base Quantities and Their Relationships, which should be reviewed first if base impedance and admittance derivations are unfamiliar.

The emphasis is on practical implementation in RMS and EMT studies, with attention to how physical parameters are interpreted in different modelling contexts.

Physical Parameters and Their Electrical Meaning

Network components are usually specified in physical units: resistance in ohms, inductance in henries, and capacitance in farads. Simulation tools, however, require these parameters to be expressed in a consistent electrical form, typically as impedance or admittance.

The per-unit system provides a systematic way to normalise these quantities using base impedance or base admittance.

Series Resistance in Per-Unit

A physical resistance RR is converted to per-unit using the base impedance:

Rpu=RZbaseR_{pu} = \frac{R}{Z_{base}}

This conversion is independent of frequency and applies directly in both RMS and EMT studies.

Series Inductance and Reactance in Per-Unit

Inductance must first be converted to reactance at the study frequency:

X=ωL=2πfLX = \omega L = 2 \pi f L

The per-unit reactance is then:

Xpu=XZbaseX_{pu} = \frac{X}{Z_{base}}

The per-unit value therefore depends implicitly on frequency, which must be stated explicitly.

Shunt Capacitance and Susceptance in Per-Unit

Capacitance is usually represented as shunt susceptance rather than impedance. The physical susceptance is:

B=ωC=2πfCB = \omega C = 2 \pi f C

The corresponding per-unit susceptance is:

Bpu=BYbaseB_{pu} = \frac{B}{Y_{base}}

This distinction between series impedance and shunt admittance is essential when interpreting line charging and reactive power behaviour.

Worked Example: Series Impedance Conversion

Consider a line section with:

  • Resistance R=5 ΩR = 5 \, \Omega
  • Inductance L=15 mHL = 15 \, \text{mH}
  • Frequency f=50 Hzf = 50 \, \text{Hz}

Assume base quantities:

  • Sbase=100 MVAS_{base} = 100 \, \text{MVA}
  • Vbase=132 kVV_{base} = 132 \, \text{kV}

From the base quantity relationships:

Zbase=(132×103)2100×106≈174.2 ΩZ_{base} = \frac{(132 \times 10^3)^2}{100 \times 10^6} \approx 174.2 \, \Omega

Reactance:

X=2π×50×0.015≈4.71 ΩX = 2 \pi \times 50 \times 0.015 \approx 4.71 \, \Omega

Per-unit values:

Rpu=5174.2≈0.0287R_{pu} = \frac{5}{174.2} \approx 0.0287 Xpu=4.71174.2≈0.0270X_{pu} = \frac{4.71}{174.2} \approx 0.0270

Practical Considerations in EMT and RMS Studies

In RMS studies, per-unit impedance is typically locked to nominal system frequency. In EMT studies, the same per-unit parameters may be used, but the physical interpretation must account for wideband behaviour.

Common issues include inconsistent base quantities, incorrect treatment of shunt elements, and unstated frequency assumptions.

Calculator Reference

Use the Physical-to-Per-Unit Impedance Calculator to automate these conversions and enforce consistent base usage.

Next in Series

This article covered converting physical parameters to per-unit. The next step addresses changing between different bases:

→ Per-Unit System: Changing Base Across Transformers and Networks

The series concludes with common mistakes to avoid:

→ Per-Unit System: Common Mistakes in EMT and RMS Studies

Reflective Questions

  1. Are physical parameters in your models traceable to documented base quantities?
  2. Have discrepancies between EMT and RMS studies been traced back to impedance scaling?
  3. Would automated impedance conversion reduce rework in your workflow?