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