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Electric Machinery and Apparatus 2 AE1M14SP2
Miroslav Chomát chomat@fel.cvut.cz
room B3-248
Course Overview
• Introduction • Review of basic principles • Transformers • Rotating electric machines
– Induction machines – Synchronous machines – DC machines – Switched reluctance machines
• Variable-speed drives (introduction)
Objectives
This course should help you • understand principles behind electric machinery • know construction of electrical machinery • know basic material properties used in electric
machinery • describe electric machinery using mathematical tools • know properties and characteristics of individual types
of electric machinery • choose proper type of machine for particular
application
Organization • Lectures
– once a week – slides online – discussion
• Laboratories – measurements on electrical machines – individual preparation – reports
• Individual work – reading – modelling (MATLAB/Simulink)
Literature • S. J. Chapman, Electric Machinery Fundamentals. McGraw-
Hill, Inc. 2011 • D. W. Novotny, T. A. Lipo, and T. M. Jahns, Introduction to
Electric Machines and Drives. Madison, USA: WisPERC, 2009.
• A. E. Fitzgerald, C. Kingsley jr., and S. D. Umans, Electric Machinery. New York, USA: McGraw-Hill, 2003.
• P. C. Krause, O. Wasynczuk, and S. D. Sudhoff, Analysis of Electric Machinery. New York, USA: IEEE Press, 1994.
• W. Leonhard, Control of Electrical Drives. Berlin, Germany: Springer, 1996.
• D. W. Novotny and T. A. Lipo, Vector Control and Dynamics of AC Drives. Oxford, UK: Clarendon Press, 1996.
Motivation
• Applications – industry – transportation – generation – homes – automobiles
• Performance – 10-6 – 109 W – 10-9 – 107 Nm – 10 – 105 rpm
Electrical Machinery
• Electromechanical energy conversion – based on electromagnetic induction
• Types – Motors – Generators – Transformers
Electromagnetic Energy Conversion
Energy Efficiency
Output powerInput power
η =
Mechanical Loads Characteristics • constant
– lift – crane – friction in bearing
• linear – viscous friction
• non-linear – pump – fan – vehicle
Normally – combination of two or all of them!
Equation of Motion
loadem TTdtdJ −=ω
Maxwell Equations
• Ampère’s Law: 𝑟𝑟𝑟𝑟𝑟𝑟 𝐇𝐇 = 𝐉𝐉 + ∂𝜕𝜕𝜕𝜕𝐃𝐃
• Faraday’s Law of induction: 𝑟𝑟𝑟𝑟𝑟𝑟 𝐄𝐄 = − ∂𝜕𝜕𝜕𝜕𝐁𝐁
• Gauss’s Law for magnetism: 𝑑𝑑𝑑𝑑𝑑𝑑 𝐁𝐁 = 0 • Gauss’s Law for electricity: 𝑑𝑑𝑑𝑑𝑑𝑑 𝐃𝐃 = 𝜌𝜌 • 𝐁𝐁 = 𝜇𝜇𝐇𝐇 • 𝐃𝐃 = 𝜀𝜀𝐄𝐄 • 𝐉𝐉 = 𝛾𝛾𝐄𝐄
Maxwell Equations
• H: magnetic field density [A·m-1] • J: current density [A·m-2] • D: electric displacement field [C·m-2] • E: electric field intensity [V·m-1] • B: magnetic flux density [T] • 𝜌𝜌: free electric charge density [C·m-3] • μ: permeability [H·m-1] • ε: permittivity [F·m-1] • γ: conductivity [Ω-1·m-1]
Maxwell Equations
• Ampère’s Law:
• Faraday’s Law of induction:
• Gauss’s Law for magnetism:
• Gauss’s Law for electricity:
dSJdlHSC
⋅=⋅ ∫∫∫
dStBdlE
SC
⋅∂∂
−=⋅ ∫∫
∫∫ =⋅vS
dvdSD ρ
0=⋅∫S
dSB
Magnetic Circuit
s
ml
H dl I F⋅ = =∑∫
INlHF sm ==
Φ⋅=Φ SB
ΦΦ ⋅⋅=⋅
SlSHlH s
s µµ
mm RF ⋅Φ=
For H = const.:
For B = const.:
For H, B = const., μFe >> μ0:
Hopkinson’s Law
Ampère’s Law
Magnetic circuit with air gap
( ) δδδ HlHRRF FeFemmFem +=+Φ=
lFe
δ
Analogy – Magnetic x Electric
Electromagnetic Induction
iuedt
ddlE −==−=⋅∫ψ
dxx
dtt
d∂∂
+∂∂
=ψψψ
∂∂
+∂∂
−=−= vxtdt
de ψψψ
ψ = 2 Wb · 4 + 1 Wb · 3 + 1 Wb · 1 = 12 Wb
Faraday’s Law of induction
Lorentz Force
dxdifmΨ
⋅−=
liBfm ⋅⋅=−
( )F i l B= ×
Electromagnetic Induction
vlBue i ⋅⋅==−
Magnetization curve
Permanent Magnets
Permanent Magnets
Rotating Magnetic Field
My questions
• What is your name? • Where are you from? • What is your current knowledge on EMs? • What made you take this course? • What would you like to know about EMs?
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