Per-unit quantities

Per-unit system is the expression of system quantities as fractions of a defined base unit quantity.
Calculations are simplified because quantities expressed as per-unit do not change when they are referred from one side of transformer to the other.  

 The per unit value of  any quantity is defined as

Generally base values of power and voltage are chosen as base quantities.

This is the three-phase apparent power (Volt-Ampere) base that is common to the entire circuit.Expressed in MVA.

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. Expressed in KV.

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

 

Note: For single phase system is not there.The above is for three phase system.

 

Changing of base:

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

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

  Per unit (pu) system advantages:

• Circuits simplified
• Voltages have same range in per unit in all parts of the system from EHV system to distribution and utilization
• In the per unit system, apparatus parameters usually fall in narrow range.Errorneous data can be easily identified.
• The per unit values of impedance,voltage and current of a transformer are same regardless of whether they are referred to primary or secondary.
• convenient for computer analysis and simulation
•   factor in the three phase circuit calculations is eliminated