Per Unit Impedance in 3-Phase Systems

In a 3-phase system, if

Z_ohms = line-to-neutral impedance in ohms per phase and
VA = the 3-phase volt-ampere base and
V = the base line-to-line voltage then

[6-103]

There are cases in which transformers, generators, and transmission lines are operated at voltages somewhat different from rated value. Transformers are seldom operated at normal frequency with voltages that are substantially above rated values because of oversaturating the iron, which leads to excessive exciting current and to excessive core losses. However, transformers may operate at somewhat reduced voltages, as for example, 13.8-kv transformers operating at 13.2 kv and at normal frequency. In changing the per unit value from one base to another, the change in voltage base must be taken into account. Thus, if

is the per unit value of Z_ohms impedance for volt-ampere and voltage bases of VA₁ and V₁ then the same impedance will have a per unit value of

for volt-ampere and voltage bases of VA₂ and V₂ from which it is evident that

[6-104]

Equation 6-103a is valid for single-phase systems as well as for 3-phase systems.