<< Chapter < Page Chapter >> Page >

Chapter 5: Synchronous Machines

This lecture note is based on the textbook # 1. Electric Machinery - A.E. Fitzgerald, Charles Kingsley, Jr., Stephen D. Umans- 6th edition- Mc Graw Hill series in Electrical Engineering. Power and Energy

  • Main features of synchronous machines:
  • A synchronous machine is an ac machine whose speed under steady-state conditions is proportional to the frequency of the current in its armature.
  • The rotor, along with the magnetic field created by the dc field current on the rotor, rotates at the same speed as, or in synchronism with, the rotating magnetic field produced by the armature currents, and a steady torque results.

Figure 5.1 Schematic views of three-phase generators: (a) two-pole, (b) four-pole, and

(c) Y connection of the windings.

§5.1 Introduction to Polyphase Synchronous Machines

  • Synchronous machines:
  • Armature winding: on the stator, alternating current.
  • Field winding: on the rotor, dc power supplied by the excitation system.
    • Cylindrical rotor: for two- and four-pole turbine generators.
    • Salient-pole rotor: for multipolar, slow-speed, hydroelectric generators and for most synchronous motors.
  • Acting as a voltage source:
    • Frequency determined by the speed of its mechanical drive (or prime mover).
    • The amplitude of the generated voltage is proportional to the frequency and the field current.

λ a = k w N ph Φ p cos ( ( poles 2 ) ω m t ) = k w N ph Φ p cos ω me t alignl { stack { size 12{λ rSub { size 8{a} } =k rSub { size 8{w} } N rSub { size 8{ ital "ph"} } Φ rSub { size 8{p} } "cos" \( \( { { ital "poles"} over {2} } \) ω rSub { size 8{m} } t \) } {} #" "=k rSub { size 8{w} } N rSub { size 8{ ital "ph"} } Φ rSub { size 8{p} } "cos"ω rSub { size 8{ ital "me"} } t {} } } {} (5.1)

ω me = ( poles 2 ) ω m size 12{ω rSub { size 8{ ital "me"} } = \( { { ital "poles"} over {2} } \) ω rSub { size 8{m} } } {} (5.2)

e a = a dt = k w N ph p dt cos ω me t ω me k w N ph Φ p sin ω me t size 12{e rSub { size 8{a} } = { {dλ rSub { size 8{a} } } over { ital "dt"} } =k rSub { size 8{w} } N rSub { size 8{ ital "ph"} } { {dΦ rSub { size 8{p} } } over { ital "dt"} } "cos"ω rSub { size 8{ ital "me"} } t - ω rSub { size 8{ ital "me"} } k rSub { size 8{w} } N rSub { size 8{ ital "ph"} } Φ rSub { size 8{p} } "sin"ω rSub { size 8{ ital "me"} } t} {} (5.3)

e a = ω me k w N ph Φ p sin ω me t size 12{e rSub { size 8{a} } = - ω rSub { size 8{ ital "me"} } k rSub { size 8{w} } N rSub { size 8{ ital "ph"} } Φ rSub { size 8{p} } "sin"ω rSub { size 8{ ital "me"} } t} {} (5.4)

E max = ω me k w N ph Φ p = 2πf me k w N ph Φ p size 12{E rSub { size 8{"max"} } =ω rSub { size 8{ ital "me"} } k rSub { size 8{w} } N rSub { size 8{ ital "ph"} } Φ rSub { size 8{p} } =2πf rSub { size 8{ ital "me"} } k rSub { size 8{w} } N rSub { size 8{ ital "ph"} } Φ rSub { size 8{p} } } {} (5.5)

E rms = 2 f me k w N ph Φ p = 2 πf me k w N ph Φ p size 12{E rSub { size 8{ ital "rms"} } = { {2π} over { sqrt {2} } } f rSub { size 8{ ital "me"} } k rSub { size 8{w} } N rSub { size 8{ ital "ph"} } Φ rSub { size 8{p} } = sqrt {2} πf rSub { size 8{ ital "me"} } k rSub { size 8{w} } N rSub { size 8{ ital "ph"} } Φ rSub { size 8{p} } } {} (5.6)

  • Synchronous generators can be readily operated in parallel: interconnected power systems.
  • When a synchronous generator is connected to a large interconnected system containing many other synchronous generators, the voltage and frequency at its armature terminals are substantially fixed by the system.
    • It is often useful, when studying the behavior of an individual generator or group of generators, to represent the remainder of the system as a constant-frequency, constant-voltage source, commonly referred to as an infinite bus.
    • Analysis of a synchronous machine connected to an infinite bus.
  • Torque equation:

T == π 2 ( poles 2 ) 2 Φ R F f sin δ RF size 12{T"==" { {π} over {2} } \( { { ital "poles"} over {2} } \) rSup { size 8{2} } Φ rSub { size 8{R} } F rSub { size 8{f} } "sin"δ rSub { size 8{ ital "RF"} } } {} (5.7)

where

Φ R = size 12{Φ rSub { size 8{R} } ={}} {} resultant air-gap flux per pole

F f = size 12{F rSub { size 8{f} } ={}} {} mmf of the dc field winding

δ RF = size 12{δ rSub { size 8{ ital "RF"} } ={}} {} electric phase angle between magnetic axes of Φ R size 12{Φ rSub { size 8{R} } } {} and F f size 12{F rSub { size 8{f} } } {}

  • The minus sign indicates that the electromechanical torque acts in the direction to bring the interacting fields into alignment.
  • In a generator, the prime-mover torque acts in the direction of rotation of the rotor, and the electromechanical torque opposes rotation. The rotor mmf wave leads the resultant air-gap flux.
  • In a motor, the electromechanical torque is in the direction of rotation, in opposition to the retarding torque of the mechanical load on the shaft.
  • Torque-angle curve: Fig. 5.2.

Figure 5.2 Torque-angle characteristics.

  • An increase in prime-mover torque will result in a corresponding increase in the torque angle.
  • T = T max size 12{T=T rSub { size 8{"max"} } } {} : pull-out torque at δ = 90 size 12{δ="90"} {} .Any further increase in prime-mover torque cannot be balanced by a corresponding increase in synchronous electromechanical torque, with the result that synchronism will no longer be maintained and the rotor will speed up. size 12{ drarrow } {} loss of synchronism, pulling out of step.

Questions & Answers

do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Berger describes sociologists as concerned with
Mueller Reply
Got questions? Join the online conversation and get instant answers!
QuizOver.com Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Electrical machines. OpenStax CNX. Jul 29, 2009 Download for free at http://cnx.org/content/col10767/1.1
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Electrical machines' conversation and receive update notifications?

Ask