In many engineering situations it is useful to scale, or normalize, dimensioned quantities. This is commonly done in power system analysis. The standard method used is referred to as the per-unit system. Historically, this was done to simplify numerical calculations that were made by hand. Although this advantage is eliminated by the calculator, other advantages remain.
• Device parameters tend to fall into a relatively narrow range, making erroneous values conspicuous.
• Using this method all quantities are expressed as ratios of some base value or values.
• The per-unit equivalent impedance of any transformer is the same when referred to either the primary or the secondary side.
• The per-unit impedance of a transformer in a three-phase system is the same regardless of the type of winding connections (wye-delta, delta-wye, wye-wye, or delta-delta).
• The per-unit method is independent of voltage changes and phase shifts through transformers where the base voltages in the winding are proportional to the number of turns in the windings.
• Manufactures usually specify the impedance of equipment in per-unit or percent on the base of its nameplate rating of power (usually kVA) and voltage (V or kV). The per-unit system is simply a scaling method. The basic per-unit scaling equation is
The base value always has the same units as the actual value, forcing the per-unit value to be dimensionless. The base value is always a real number, whereas the actual value may be complex. The subscript pu will indicate a per-unit value. The subscript base will indicate a base value, and no subscript will indicate an actual value such as Amperes, Ohms, or Volts.
Per-unit quantities are similar to percent quantities. The ratio in percent is 100 times the ratio in per-unit. For example, a voltage of 70kV on a base of 100kV would be 70% of the base voltage. This is
equal to 100 times the per unit value of 0.7 derived above.