Per-Unit System: Base Quantities and Their Relationships

• fundamentalsper-unitbase-quantitiesanalysis

Purpose and Scope

This article builds on the conceptual foundation of the per-unit system introduced in Per-Unit System: Concept and Why It Works. The focus here is on base quantities: how they are defined, how they relate to each other, and how they propagate through a power system model.

The intent is practical. The goal is not to memorise formulas, but to understand how a small number of base selections control all per-unit quantities in a study.

Role of Base Quantities in the Per-Unit System

Every per-unit value is defined relative to a corresponding base quantity. In power system analysis, it is customary to select base apparent power and base voltage.

Once these two are chosen, all other base quantities are derived. Maintaining this dependency is critical for consistency.

Choice of Base Apparent Power

The base apparent power, SbaseS_{base}, is typically chosen as a system-wide constant such as 100 MVA. This choice is largely a matter of convention rather than physics.

Using a common SbaseS_{base} across the network ensures that per-unit impedances and power quantities are directly comparable.

Choice of Base Voltage

The base voltage is selected at a specific bus and propagated through the network using transformer ratios.

For three-phase systems, base voltage is defined as the line-to-line RMS voltage.

Derived Base Current

For a three-phase system:

Ibase=Sbase3⋅VbaseI_{base} = \frac{S_{base}}{\sqrt{3} \cdot V_{base}}

Derived Base Impedance

Zbase=Vbase2SbaseZ_{base} = \frac{V_{base}^2}{S_{base}}

Derived Base Admittance

Ybase=1Zbase=SbaseVbase2Y_{base} = \frac{1}{Z_{base}} = \frac{S_{base}}{V_{base}^2}

Worked Example

Given:

  • SbaseS_{base} = 100 MVA
  • VbaseV_{base} = 132 kV
Ibase=100×1063×132×103≈437 AI_{base} = \frac{100 \times 10^6}{\sqrt{3} \times 132 \times 10^3} \approx 437 \text{ A} Zbase=(132×103)2100×106≈174.2 ΩZ_{base} = \frac{(132 \times 10^3)^2}{100 \times 10^6} \approx 174.2 \text{ }\Omega Ybase=1174.2≈0.00574 SY_{base} = \frac{1}{174.2} \approx 0.00574 \text{ S}

Calculator Reference

Use the Base Quantity Calculator to compute derived base quantities from your selected SbaseS_{base} and VbaseV_{base}.

Next in Series

This article establishes how to derive base quantities. The next step is converting physical parameters into per-unit values:

→ Per-Unit Impedance from Physical Parameters

After that, learn how to change between different bases:

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

Reflective Questions

  1. Are base quantities explicitly stated in your studies?
  2. Have base mismatches caused errors in your models?
  3. Would automated base-quantity derivation reduce manual calculation errors?