Circuit Analysis II with MATLAB Computing and Simulink/SimPowerSystems Modeling

Appendix G: Per Unit System

This chapter introduces the per unit system. This system allows us to work with normalized power, voltage current, impedance, and admittance values known as per unit (pu) values. The relationship between units in a per-unit system depends on whether the system is single-phase or three-phase. Three-phase systems are discussed in Chapters 11 and 12.

G.1 Per Unit Defined

By definition,


A per unit (pu) system defines per unit values for volt-ampere (VA) power, voltage, current, impedance, and admittance, and of these only two of these are independent. It is customary to choose VA (or KVA) power and nominal voltage as the independent base values, and others are specified as multiples of selected base values.

For single-phase systems, the pu values are based on rated VA (or KVA) rated power and on the nominal voltage of the equipment, e.g., single-phase transformer, single-phase motor.

Example G.1

A single-phase transformer is rated 10 KVA and the nominal voltage on the primary winding is 480 V RMS. Compute its pu impedance.

Solution:


and assuming that the actual primary winding voltage, current, and impedance are 436 Volts RMS, 15 A RMS, and 5 ?, respectively, the per unit values are computed as follows:


The base impedance in (G.2) is also expressed as


Thus, the pu impedance can also be expressed as


and using the values above we obtain


as before.

The pu values allow us to express quantities in percentages, that is,


and thus 0.22 pu=22%

The per unit values in three-phase systems are...

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