perunit

The per-unit system, often abbreviated as pu, is a method used in electrical power engineering to express electrical quantities as fractions of chosen base values. By normalizing quantities, the analysis of power systems becomes largely independent of equipment ratings, and quantities from different devices can be compared on a common scale.

Bases and normalization: A typical setup selects a single apparent-power base S_base for the system and a voltage base V_base for each node. Then I_base = S_base / V_base and Z_base = V_base^2 / S_base. Voltages, currents, powers, and impedances are converted as V_pu = V / V_base, I_pu = I / I_base, P_pu = P / S_base, Q_pu = Q / S_base, and Z_pu = Z / Z_base.

Why use pu: The pu representation reduces the range of numerical values in calculations, makes line impedances and transformer ratings appear on a similar scale, and simplifies the formulation of power-flow and short-circuit analyses.

Practice and considerations: The base values are chosen to reflect the system being modeled, frequently with a common S_base (for example 100 MVA) and voltage bases aligned with nominal voltages. All components must be converted to the same base before analysis. When a transformer or a change of base is involved, the corresponding z-pu is adjusted by the base-change rules.

Limitations: The method requires consistent base selection; mixing bases or misapplying conversions can lead to errors. It is most advantageous for steady-state analysis and is less helpful for highly nonlinear or time-domain simulations unless bases are handled carefully.

Example: If a component has an actual impedance of 0.5 ohm and Z_base is 1 ohm, Z_pu = 0.5 pu.