Short notes

Per Unit System Short Notes

A 100 MVA, 11 kV generator connected through a 11/220 kV transformer to a 220 kV line has three different voltage levels — working in ohms simultaneously is a calculation nightmare. The per-unit system converts everything to a dimensionless scale on a common base, making the whole network a uniform impedance network.

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How it works

Choose a system base: Sbase = 100 MVA and Vbase at each voltage level following transformer turns ratios (11 kV on LV side, 220 kV on HV side). Base impedance Zbase = Vbase²/Sbase; on the HV side Zbase = 220²/100 = 484 Ω. If a transformer has 8% leakage reactance on its own rating (50 MVA, 11/220 kV), convert to system base: Znew = Zold × (Sbase_new/Sbase_old) × (Vbase_old/Vbase_new)². This formula appears in almost every per-unit numerical. The beauty is that transformer pu impedance is the same on both sides of the transformer — no need to refer to primary or secondary.

Key points to remember

Advantages of the pu system: transformer pu impedance is independent of which side it is referred to, pu values for equipment of the same type fall in a narrow range (transformer leakage reactance 0.05–0.10 pu, generator synchronous reactance 0.8–1.2 pu), and network equations become simpler. When multiple machines have different ratings, always convert all pu quantities to the common system base before adding or comparing. The actual value = pu value × base value — never forget to convert back at the end of the calculation.

Exam tip

The examiner always asks you to convert transformer impedance from its own MVA base to a new system base — write down Znew = Zold × (MVAnew/MVAold) × (kVold/kVnew)² and substitute carefully to avoid base confusion.

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