In the advent of computers, per unit or percent methods of calculations simplify short circuit calculations. J. Lewis Blackburn and Thomas J. Domin, in their book Protective Relaying, Principles and Applications, 3rd Edition, some of the advantages of using per unit or percent were listed as follows. Additional explanations were added where necessary.
1. Its representation results in more meaningful data when the relative magnitudes of all the similar circuit quantities can be compared
- All quantities are expressed as a percent or fraction to the base units. It is easier to compare the relationship between 80% ( or 0.80 ) to 90% ( or 0.90 ) than 105.6kV to 118.8kV.
2. The per unit equivalent impedance of any transformer is the same when referred to either the primary or the secondary side.
- Impedances of the same base unit regardless if these are connected to primary or secondary of the transformer can be added directly.
3. 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).
- Per unit impedances are independent of the transformer connections.
4. The per unit method is independent of voltage changes and phase shifts through transformers; and the base voltages in the windings are proportional to the number of turns in the windings.
- The relationship between the line quantities to phase quantities are affected by the transformer connections. In a wye connected transformer winding, the line current is equal to the phase current but line-to-line voltages are √3 x phase voltages. The opposite principle applies to delta connected transformers. In per unit or percent method of calculations, there is only one parameter to deal with.
5. Manufacturers usually specify the impedance of an equipment in per unit or percent on the base of its nameplate rating of power (kVA or MVA) and voltage (V or kV). Thus, the rated impedance can be used directly if the bases chosen are the same as the nameplate ratings.
- The proper selection of base units could significantly reduce calculation time.
6. The per unit impedance values of various ratings of equipment lie in a narrow range, whereas the actual ohmic values may vary widely. Therefore, when actual values are unknown, a good approximate value can be used. Typical values for various types of equipment are available from many sources and reference books. Also, the correctness of a specified unit can be checked, when the typical values are known.
7. There is less chance of confusion between single-phase power and three-phase power, or between line-to-line voltage and line-to-neutral voltage.
8. The per unit method is very useful for simulating the steady-state and transient behavior of power systems on computers.
9. The driving or source voltage usually can be assumed to be 1.0 pu for fault and voltage calculations.
- The pre-fault voltage of a source in normal practice is always assumed to be 1pu and the fault voltage to be zero for a bolted fault.
10. With per unit, the product of two quantities expressed in per unit is expressed in per unit itself. However, the product of two quantities expressed as percent must be divided by 100 to obtain the result in percent. Consequently, it is desirable to use per unit, rather than percent, in computations.
Protective Relaying, Principles and Applications, 3rd Edition
J. Lewis Blackburn and Thomas J. Domin