Lesson 5 of 8

The Per-Unit System

8 min read

A real transmission network might have equipment rated at 11 kV, 138 kV and 400 kV all in the same diagram, connected through transformers. Comparing those numbers directly is awkward and error-prone. The per-unit system fixes this by expressing every quantity as a fraction of a chosen reference — and, as a side effect, makes transformers almost disappear from your calculations.

Why not just use actual values?

Two problems show up constantly when working with real voltage and current values. First, the numbers span huge ranges — amps in the thousands on one side of a transformer, volts in the hundreds of thousands on the other — which makes mental checks and hand calculations painful. Second, an ideal transformer changes voltage and current by its turns ratio at every boundary, so the same physical impedance looks like a different number of ohms depending which side you measure it from. Per-unit quantities solve both: they're dimensionless, usually close to 1.0 for healthy equipment, and — chosen correctly — the same on both sides of a transformer.

Choosing base quantities

You start by picking two independent base values for each voltage zone in the system: a system-wide apparent power base S_base (often 100 MVA), and a voltage base V_base matching the nominal voltage of that zone. Every other base quantity follows from those two:

I_base = S_base√3 · V_base

Base current (three-phase)

Z_base = V_base²S_base

Base impedance

S_base is usually kept the same across the whole network, while V_base changes at every transformer to match the nominal voltage on each side — this is exactly what makes the transformer's turns ratio vanish from the per-unit model.

Converting to per-unit

Once the bases are set, converting any actual value to per-unit is just division:

Value_pu = Value_actualValue_base

General per-unit conversion

A generator rated exactly at the system bases, running at nominal voltage, simply reads 1.0 p.u. — which is why per-unit values are also an instant sanity check: a bus voltage of 1.04 p.u. is obviously fine, while 0.7 p.u. is obviously a problem, without needing to know whether that bus is a 11 kV or 400 kV part of the network.

Changing base

Equipment nameplates give impedance in per-unit (or percent) on the manufacturer's own rated base, which is rarely the same as your system base. Before combining it with anything else, you have to convert it:

Z_pu,new = Z_pu,old · S_base,newS_base,old · V_base,old²V_base,new²

Converting per-unit impedance to a new base

Why this matters for transformers

If you assign V_base on each side of a transformer equal to its own rated voltage ratio, the transformer's ideal turns-ratio effect cancels out exactly in per-unit — the transformer reduces to nothing more than its leakage impedance. That's the single biggest reason the whole industry standardized on per-unit: multi-voltage-level networks become one flat, unit-less system to solve.

Key takeaways

Per-unit expresses every quantity as actual value ÷ base value — dimensionless and usually near 1.0.
Pick S_base and V_base per zone; I_base and Z_base follow from them.
V_base changes at each transformer to match nominal voltage, which makes the transformer's turns ratio disappear from the model.
Nameplate impedances are given on equipment base and must be converted to system base before use.