Per-unit System

Formulas

For each system parameter, per-unit value is equal to the actual value divided by a base value:

E_pu = E / E_base

I_pu = I / I_base

Z_pu = Z / Z_base

Select rated values as base values, usually rated power in MVA and rated phase voltage in kV:

S_base = S_rated = Ö3E_lineI_line

E_base = E_phase = E_line/ Ö3

The base values for line current in kA and per-phase star impedance in ohms/phase are:

I_base = S_base / 3E_base ( = S_base / Ö3E_line)

Z_base = E_base / I_base = 3E_base² / S_base ( = E_line² / S_base)

Note that selecting the base values for any two of S_base, E_base, I_base or Z_base fixes the base values of all four. Note also that Ohm’s Law is satisfied by each of the sets of actual, base and per-unit values for voltage, current and impedance.

Transformers

The primary and secondary MVA ratings of a transformer are equal, but the voltages and currents in the primary (subscript ₁) and the secondary (subscript ₂) are usually different:

Ö3E_1lineI_1line = S = Ö3E_2lineI_2line

Converting to base (per-phase star) values:

3E_1baseI_1base = S_base = 3E_2baseI_2base

E_1base / E_2base = I_2base / I_1base

Z_1base / Z_2base = (E_1base / E_2base)²

The impedance Z_21pu referred to the primary side, equivalent to an impedance Z_2pu on the secondary side, is:

Z_21pu = Z_2pu(E_1base / E_2base)²

The impedance Z_12pu referred to the secondary side, equivalent to an impedance Z_1pu on the primary side, is:

Z_12pu = Z_1pu(E_2base / E_1base)²

Note that per-unit and percentage values are related by:

Z_pu = Z_% / 100