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Synchronous machine

 

The synchronous rotational speed ns and synchronous angular speed ws of a machine with  pole pairs running on a supply of frequency fs are:
ns = 60fs / p
ws = 2p
fs / p

The output power Pm for a load torque Tm is:
Pm =
wsTm

The rated load torque TM for a rated output power PM is:
TM = PM /
ws = PMp / 2pfs = 60PM / 2pns

Synchronous Generator
For a synchronous generator with stator induced voltage Es, stator current Is and synchronous impedance Zs, the terminal voltage V is:
V = Es - IsZs = Es - Is(Rs + jXs)
where Rs is the stator resistance and Xs is the synchronous reactance

Synchronous Motor
For a synchronous motor with stator induced voltage Es, stator current Is and synchronous impedance Zs, the terminal voltage V is:
V = Es + IsZs = Es + Is(Rs + jXs)
where Rs is the stator resistance and Xs is the synchronous reactance

Note that the field excitation of a parallelled synchronous machine determines its power factor:
- an under-excited machine operates with a leading power factor,
- an over-excited machine operates with a lagging power factor.
The field excitation of an isolated synchronous generator determines its output voltage.