Electric Machinery and Transformers, Third Edition

When an electric machine is designed or analyzed using the actual values of its parameters, it is not immediately obvious how its performance compares with another similar-type machine. However, if we express the parameters of a machine as a per-unit (pu) of a base (or reference) value, we will find that the per-unit values of machines of the same type but widely different ratings lie within a narrow range. This is one of the main advantages of a per-unit system.
An electric system has four quantities of interest: voltage, current, apparent power, and impedance. If we select base values of any two of them, the base values of the remaining two can be calculated. If S b is the apparent base power and V b is the base voltage, then the base current and base impedance are
The actual quantity can now be expressed as a decimal fraction of its base value by using the following equation.
Since the power rating of a transformer is the same on both sides, we can use it as one of the base quantities. However, we have to select two base voltages one for the primary side and the other for the secondary side. The two base voltages must be related by the a-ratio. That is,
where V bH and V bL are the base voltages on the high- and low-voltage sides of a transformer, respectively.
Since the base voltages have been transformed, the currents and impedances...