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.
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| 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] | |
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Synchronous Motor Construction | EEP
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