Per Unit System

Per Unit System
The Per – Unit Value of any quantity is defined as the ratio of the quantity to its base value expressed as a decimal.

Voltage, current, kilovoltamperes and impedance are so related that the selection of the base values for any two of them determines the base values for the remaining two.
Base Current, A, = (base kVA1Φ)/base Voltage kVLN

Base Impedance, Z, = (base Voltage VLN)/base Current A
Base Impedance, Z  = ((base Voltage kVLN)2 * 1000)/Base kVA1Φ
Base Impedance, Z  = (base Voltage, kVLN)2/Base MVA1Φ

Base Power kW = base kVA1Φ
Base Power MW = base MVA1Φ

Per Unit Impedance = (Actual Impedance [Ω]) /Base Impedance [Ω]

To change from per unit impedance on a given base to Per Unit impedance on a new base the following equation applies.

Per Unit Znew  = Per-Unit Zgiven(Base kVgiven/Base kVnew)2(BasekVAnew/Base kVAgiven)

Note that this expression has nothing to do with transferring the ohmic value of impedance from one side of the transformer to the other.

Advantages of Per Unit Computations

1.    Manufacturers usually specify the impedance of a piece of apparatus in percent or per unit on the base of the nameplate rating
2.    The Per-Unit impedances of machines of the same type and widely different rating usually lie within a narrow range though the ohmic values differ materially for machines of different ratings. For this reason, when the impedance is not known definitely, it is generally possible to select from tabulated average values a per-unit impedance which will be reasonably correct. Experience in working with Per-Unit values brings familiarity with the proper values of per-unit impedance for different types of apparatus.
3.    When impedance in ohms is specified in an equivalent circuit, each impedance must be referred to the same circuit by multiplying it by the square of the ratio of the rated voltages of the two sides of the transformer connecting the reference circuit and the circuit containing the impedance.  The Per-Unit impedance once it is expressed on the base is the same referred to either side of the transformer.
4.    The way in which transformers are connected in three phase circuits does not affect the per unit impedances of the equivalent circuit although the transformer connection does determine voltage bases on the two sides of the transformer.