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

Purpose and Scope

This article concludes the per-unit system series by focusing on common mistakes observed in practical engineering studies, particularly in RMS (phasor-domain) and EMT (time-domain) simulations.

Rather than revisiting definitions or derivations, the emphasis here is on failure modes: how per-unit inconsistencies arise, how they manifest in results, and how they can be identified and prevented. The discussion assumes familiarity with base quantities, impedance derivation, and base changes covered in earlier articles:

Mistake 1: Inconsistent or Undocumented Base Quantities

One of the most frequent sources of error is the use of inconsistent base quantities across a model. This often occurs when data from different sources is combined without explicitly reconciling bases.

Typical symptoms include:

Unexpected voltage or current magnitudes
Per-unit impedances that appear unusually large or small
Difficulty benchmarking RMS and EMT results

Prevention: Always document $S_{base}$ and $V_{base}$ explicitly. Use the Base Quantity Calculator to derive consistent $I_{base}$ , $Z_{base}$ , and $Y_{base}$ values.

Mistake 2: Mixing Line-to-Line and Phase Quantities

Mixing line-to-line and phase quantities introduces implicit scaling errors, particularly in three-phase systems where a factor of $\sqrt{3}$ is involved.

This mistake commonly appears when:

Manual calculations are mixed with software defaults
Voltage definitions are omitted from documentation
Data sheets specify phase values while models expect line quantities

Prevention: Establish a convention (typically line-to-line for transmission studies) and verify all inputs conform before entering them into models.

Mistake 3: Incorrect Treatment of Shunt Elements

Shunt elements such as capacitance should be represented using admittance rather than impedance. Deriving susceptance using base impedance (rather than base admittance) leads to incorrect reactive power behaviour, especially in long lines and cables.

The correct approach:

B_{pu} = \frac{B}{Y_{base}} = B \times Z_{base}

This issue is often more visible in EMT simulations where time-domain behaviour exposes the error.

Prevention: Use the Physical-to-Per-Unit Impedance Calculator, which correctly treats capacitance as shunt susceptance.

Mistake 4: Unnecessary Base Changes Across Transformers

When base voltages are propagated correctly using transformer ratios, no base change is required across an ideal transformer.

Applying base-change formulas unnecessarily can result in impedance values being scaled multiple times. The general formula:

Z_{pu,new} = Z_{pu,old} \left( \frac{S_{base,new}}{S_{base,old}} \right) \left( \frac{V_{base,old}}{V_{base,new}} \right)^2

should only be applied when the voltage or power base actually changes.

Prevention: Use the Per-Unit Base-Change Calculator to verify when a base change is truly required. The calculator warns when voltage bases differ.

Mistake 5: Frequency Assumptions Hidden in Reactance and Susceptance

Per-unit quantities derived from inductance and capacitance implicitly assume a specific frequency. For inductive elements, this appears through reactance:

X = \omega L = 2 \pi f L

For capacitive elements, it appears through susceptance:

B = \omega C = 2 \pi f C

In RMS studies, this frequency is usually the nominal system frequency and is often left unstated. Problems arise when the same per-unit parameters are reused in EMT studies or across different analysis contexts without revisiting this assumption.

This issue commonly manifests when:

Per-unit line or cable parameters are reused directly in EMT models
Shunt capacitance or line charging is interpreted without reference to frequency
Frequency-dependent behaviour is analysed using parameters derived at a single frequency

While per-unit representation itself remains valid, the physical meaning of reactance and susceptance changes with frequency. Failing to document the assumed frequency can lead to discrepancies between RMS and EMT results, particularly for cable systems and long transmission lines.

Prevention: Explicitly state the frequency at which per-unit reactance and susceptance are derived. When converting physical inductance or capacitance to per-unit, always specify $f$ in the documentation.

Mistake 6: Blind Trust in Software Defaults

While software tools handle per-unit scaling automatically, default assumptions may not align with study intent. This is particularly risky when:

Importing external models with different base conventions
Modifying base quantities mid-study
Using library components with built-in assumptions

Prevention: Verify software defaults against study requirements. Perform spot-checks on critical impedances by manually calculating expected per-unit values.

Practical Mitigation Strategies

Most per-unit-related issues can be mitigated by:

Explicitly documenting base quantities at the start of every study
Validating per-unit values against expected ranges (e.g., transformer impedance typically 0.05–0.15 pu)
Using calculators to enforce consistency and provide audit trails
Cross-checking between RMS and EMT results for the same network

Role of Calculators in Error Prevention

Throughout this series, calculators have been referenced as consistency tools rather than conveniences. Used correctly, they reduce manual errors and improve traceability.

Base Quantity Calculator — derive $I_{base}$ , $Z_{base}$ , $Y_{base}$
Physical-to-Per-Unit Impedance Calculator — convert R, L, C to per-unit
Per-Unit Base-Change Calculator — convert between different bases

Reflective Questions

Which of these mistakes have you encountered most frequently?
Are per-unit assumptions explicitly documented in your workflows?
Would standardised calculators reduce review effort in your team?