Limited Time Offer: Save 15% on Pro Plan with discount coupon: MX15. Study specialized LV/MV/HV technical articles and studies.

# Synchronous Machines

### Formulas

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

 NOTATION The symbol font is used for some notation and formulae. If the Greek symbols for alpha beta delta do not appear here [ a b d ] the symbol font needs to be installed for correct display of notation and formulae. B E f G I j k m N n P p R susceptance induced voltage frequency conductance current j-operator coefficient number of phases number of turns rotational speed power pole pairs resistance [siemens, S] [volts, V] [hertz, Hz] [siemens, S] [amps, A] [1Ð90°] [number] [number] [number] [revs/min] [watts, W] [number] [ohms, W] S s T V X Y Z d F f h q w voltamperes slip torque terminal voltage reactance admittance impedance loss angle magnetic flux phase angle efficiency temperature angular speed [volt-amps, VA] [per-unit] [newton-metres, Nm] [volts, V] [ohms, W] [siemens, S] [ohms, W] [degrees, °] [webers, Wb] [degrees, °] [per-unit] [centigrade, °C] [radians/sec]

50% Discount 💥 - Save 50% on all 90+ video courses with Enterprise Membership plan.

1. akash
Aug 11, 2014

i think there is an error in this article. a synchronous motor in under-excited mode has lagging power factor and during over-excited mode has leading power factor. they mentioned it in reverse.

2. puppala
Apr 06, 2013

why the alternators rated power factor is 0.8 lag only.
why we are not producing 0.99 pf lag or unity induction motors.
if possible give a technical article over the above said.
The data u are giving is most useful to the EE.
thanks and regards
Ganesh

3. Upendra
Feb 17, 2013

How is the generation voltage of generators like 0.4, 6.6, 11, 13.2 kv are selected for design?