## Synchronous machine

The
synchronous rotational speed n_{s} and synchronous angular speed
w_{s}
of a machine with pole pairs running on a supply of frequency f_{s}
are:

n_{s} = 60f_{s} / p

w_{s}
= 2pf_{s} / p

**
The output power P _{m} for a
load torque T_{m} is:**

P_{m} = w_{s}T_{m}

**
The rated load torque T _{M}
for a rated output power P_{M} is:**

T_{M} = P_{M} / w_{s} = P_{M}p / 2pf_{s} = 60P_{M} / 2pn_{s}

Synchronous Generator

For a synchronous generator with stator induced voltage E_{s},
stator current I_{s} and synchronous impedance Z_{s}, the
terminal voltage V is:

V = E_{s} - I_{s}Z_{s} = E_{s} - I_{s}(R_{s}
+ jX_{s})

where R_{s} is the stator resistance and X_{s} is the
synchronous reactance

Synchronous Motor

For a synchronous motor with stator induced voltage E_{s}, stator
current I_{s} and synchronous impedance Z_{s}, the terminal
voltage V is:

V = E_{s} + I_{s}Z_{s} = E_{s} + I_{s}(R_{s}
+ jX_{s})

where R_{s} is the stator resistance and X_{s} 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.