beginner Power Systems

Per-Unit System

Master the per-unit (pu) system used throughout power engineering. Convert voltages, currents, impedances, and power between physical SI units and per-unit values on a chosen base.

QuantityPhase

S_base

MVA

V_base

Z_base174.240 Ω= 132² / 100I_base (3φ)0.4374 kA= 100 / (√3 × 132)I_base (1φ)0.7576 kA= 100 / 132S_base100 MVA

Physical (kV)

⇔Per-unit (pu)

Change of Base: Z_pu_new = Z_pu_old × (S_new/S_old) × (V_old/V_new)²

Z_pu (old base)

Old S_base

MVA

Old V_base

Z_pu (new base: 100 MVA, 132 kV)0.000694 pu

The per-unit system normalises all electrical quantities to a common base. Choose a system base: S_base (MVA) and V_base (kV). From these two, derive Z_base = V_base² / S_base and I_base = S_base / (√3 · V_base).

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100 MVA and 132 kV are common system bases in UK transmission networks.
Select 'Impedance' as the quantity and enter a physical resistance of 15 Ω. Set V_base = 132 kV and S_base = 100 MVA. The calculator will show the per-unit value. Verify: Z_base = 132² / 100 = 174.24 Ω, so Z_pu = 15 / 174.24 ≈ 0.0861 pu.

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Z_base depends only on the voltage and MVA base — it has nothing to do with the actual impedance being converted.
Now convert a voltage of 138 kV (line-to-line) on the same 132 kV base. The per-unit value should be 138 / 132 ≈ 1.045 pu. This is a typical generator terminal voltage in the IEEE 14-bus system.

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A voltage above 1.0 pu means the physical voltage is above nominal — common at generator buses.
Switch to 'Change of base'. Enter an impedance of 0.1 pu on a 100 MVA, 11 kV base and convert it to a 100 MVA, 132 kV base. The new value = 0.1 × (100/100) × (11/132)² ≈ 0.000694 pu — much smaller on the higher voltage base.

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Transformers change voltage base. Impedances on the secondary must be converted to the system base before adding to the Y-bus.
Try a three-phase power of 50 MW + j25 MVAr on a 100 MVA base. P = 50/100 = 0.5 pu, Q = 0.25 pu. The per-unit system makes power balance equations scale-invariant — the same solver works for a 10 MVA distribution network and a 10 GW transmission grid.

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All power flow solvers — Newton-Raphson, Gauss-Seidel — operate entirely in per-unit.