<< 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)


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

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
Got questions? Join the online conversation and get instant answers!
Jobilize.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?

Yacoub Jayoghli
Start Quiz
Candice Butts
Start Quiz
Keyaira Braxton
Start Exam