### Formulas

The synchronous rotational speed **n _{s}** and synchronous angular speed

**w**of a machine with

_{s}**p**pole pairs running on a supply of frequency

**f**are:

_{s}**n**

_{s}= 60f_{s}/ p**w**

_{s}= 2pf_{s}/ pThe output power **P _{m}** for a load torque

**T**is:

_{m}**P**

_{m}= w_{s}T_{m}The rated load torque **T _{M}** for a rated output power

**P**is:

_{M}**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**and synchronous impedance

_{s}**Z**, the terminal voltage

_{s}**V**is:

**V = E**

_{s}– I_{s}Z_{s}= E_{s}– I_{s}(R_{s}+ jX_{s})where

**R**is the stator resistance and

_{s}**X**is the synchronous reactance

_{s}*Synchronous Motor*

For a synchronous motor with stator induced voltage **E _{s}**, stator current

**I**and synchronous impedance

_{s}**Z**, the terminal voltage

_{s}**V**is:

**V = E**

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

**R**is the stator resistance and

_{s}**X**is the synchronous reactance

_{s}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. | ||||||

BE 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] | SsTVXYZdFfhqw | 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] |

akash

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.

puppala

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

Upendra

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