Chapter 1: Modelling Power System Components

Section VI: Per Unit Representation

In a power system different power equipment with different voltage and power levels are connected together through various step up or step down transformers. However the presence of various voltage and power levels causes problem in finding out the currents (or voltages) at different points in the network. To alleviate this problem, all the system quantities are converted into a uniform normalized platform. This is called the per unit system . In a per unit system each system variable or quantity is normalized with respect to its own base value. The units of these normalized values are per unit (abbreviated as pu) and not Volt, Ampere or Ohm. The base quantities chosen are:

• VA base ( Pbase ): This is the three-phase apparent power (Volt-Ampere) base that is common to the entire circuit.
• Voltage Base ( Vbase ): This is the line-to-line base voltage. This quantity is not uniform for the entire circuit but gets changed by the turns ratio of the transformer.

Fig. 1.20 Three balanced sources supplying two balanced load through balanced source impedances.

Fig. 1.21 Per phase equivalent circuit of the network of Fig. 1.20.

Based on the above two quantities the current and impedance bases can be defined as

 (1.119) (1.120)

Assume that an impedance Z is defined as Z1 per unit in a base impedance of Zbase _ old . Then we have

 (1.121)

The impedance now has to be represented in a new base value denoted as Z base_new . Therefore

 (1.122)

From (1.120) Z2 can be defined in terms of old and new values of VA base and voltage base as

 (1.123)

Example 1.2