Synchronous generators and per-unit quantities

Rotating fields, synchronous speed and consistent three-phase bases.

From rotation to electrical frequency

The rotor field rotates relative to the three-phase stator winding. With p pole pairs, one mechanical revolution produces p electrical cycles. In synchronous operation the generated EMF has the grid frequency; a temporary speed deviation changes rotor angle relative to the grid.

At 50 Hz, a two-pole machine runs at 3000 rpm and a four-pole machine at 1500 rpm. Electrical load angle is not the absolute shaft position.

Consistent bases

Choose total three-phase apparent-power base Sb and RMS line-to-line voltage base Ub. For a balanced system, the per-unit single-phase equivalent then needs no extra factor of three in its power formulas.

At 100 MVA and 10.5 kV, Ib = 5.499 kA and Zb = 1.1025 Ω. A reactance of 0.6 pu is 0.6615 Ω. Power of 0.8 pu means 80 MW here, not a power factor of 0.8.

Changing bases

Refer generator, transformer and line reactances to consistent bases before adding them. In the laboratory, X is the total reactance between internal EMF and grid bus. Changing only Sb and Ub in the form changes the physical scale while keeping per-unit parameters fixed; it represents another physical system with the same normalized dynamics.

Independent exercises

1. Find the speed of a six-pole machine at 50 Hz.

2. Transfer x = 0.2 from 50 MVA to 100 MVA at unchanged voltage base.

Practical work

Record the current base at 100 MVA and 10.5 kV. Double Sb without changing the other form fields: per-unit traces remain identical while current in kA doubles. Explain the physical scaling.

Key takeaways

Power and line-voltage bases determine current and impedance bases. Electrical angle is mechanical angle multiplied by the number of pole pairs.