Per unit system and its advantages

In the per-unit system, every quantity (voltage, current, power, impedance) is expressed as a fraction of a chosen base value of the same unit:

$$\text{per-unit value} = \frac{\text{actual value}}{\text{base value}}$$

Usually the base MVA ($S_b$) and the base kV ($V_b$) are chosen. The other bases follow from them:

$$I_b = \frac{S_b}{\sqrt3 V_b},\qquad Z_b = \frac{V_b^2}{S_b}$$

For example, at 100 MVA and 132 kV, $Z_b = 174.24\ \Omega$, so a 50 Ω line has $Z = 0.287$ p.u.

Advantages

1. Transformers disappear: The p.u. impedance of a transformer is the same on both sides, so the ideal transformers drop out of the equivalent circuit.
2. Compact ranges: The p.u. impedances of machines and transformers of similar type lie in a narrow range whatever their size. This makes it easy to check data and to estimate missing values.
3. Manufacturers' data: Impedances are given in % or p.u. on the equipment's own rating, so they can be used directly after a simple change of base.
4. Three-phase and single-phase are the same: In p.u. the line and phase values are equal and the factor $\sqrt3$ disappears from the calculations.
5. Easier hand and computer calculation: The numbers are of order 1, so errors are easy to spot. Load flow and fault programs use p.u. throughout.
6. Meaningful comparison: A voltage of 0.95 p.u. immediately shows a 5 % drop at any voltage level.