The per-unit system
The key idea
A per-unit value is the actual value divided by a chosen base value. 1.00 pu means "exactly nominal". 0.97 pu means "3% low" — at 33 kV, at 11 kV and at 400 V alike. One scale works across the whole network.
The idea
A real network spans several voltage levels. Is 31,900 V a problem? You cannot say until you work out which level it belongs to and do the division: on a 33 kV feeder it is 3.3% low — worth attention.
The per-unit system does that division once, up front. Choose a base for each quantity — the nominal voltage of each level, and one power base (the base MVA) for the entire project. Then express every value as a fraction of its base:
per-unit value = actual value ÷ base value
Now 0.967 pu is the answer. No level to look up, no division to do. A bus at 0.967 pu is 3.3% low wherever it sits in the network.
Try it
One slider, three voltage levels. The per-unit number is the same statement at all three.
| Where | Nominal | 0.97 pu means |
|---|---|---|
| 33 kV feeder | 33 kV | 32.0 kV |
| 11 kV feeder | 11 kV | 10.67 kV |
| 400 V circuit | 400 V | 388 V |
Inside the normal band. All three levels are equally healthy — that is the point of per unit.
Why it matters
- Results become readable at a glance. A voltage profile in pu can be scanned for anything outside 0.95–1.05. The same profile in volts needs a lookup at every bus.
- Transformers almost vanish. Choose the voltage bases to match the transformer ratios, and a transformer's ideal ratio becomes 1:1 in per unit — only its impedance remains. The network solves as if it were one flat circuit.
- Equipment data arrives in per unit already. A transformer nameplate says "Z = 6%": that is 0.06 pu on the transformer's own rating. To use it in a study, it must be converted to the project base — Phasor does this on entry.
One base, everywhere
Per-unit values only compare if they share a base. The classic error is typing an impedance that is in percent on the equipment rating as if it were on the project base. Nothing downstream can detect it — the number is simply wrong. State the base; convert once; convert on entry.
The math, if you want it
Choose base power Sb (one for the project) and base voltage Vb (one per voltage level). The remaining bases follow: Ib = Sb/(√3 Vb) and Zb = Vb²/Sb. Converting an impedance from an equipment base to the project base: Znew = Zold · (Sb,new/Sb,old) · (Vb,old/Vb,new)². The V² term is why using the wrong voltage base is such an expensive mistake.
See it in Phasor
A new Phasor project asks for two things before anything else: the system frequency and the base MVA. Every study result — bus voltages, impedances, losses — is then reported in per unit alongside physical units.