Electric Machinery and Apparatus 2
AE1M14SP2
Miroslav Chomát
chomat@fel.cvut.cz
room B3-248
Course Overview
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Introduction
Review of basic principles
Transformers
Rotating electric machines
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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. McGrawHill, 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
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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 power
η=
Input power
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
dω
J
= Tem − Tload
dt
Maxwell Equations
• Ampère’s Law:
• Faraday’s Law of induction:
• Gauss’s Law for magnetism:
• Gauss’s Law for electricity:
• 𝐁𝐁 = 𝜇𝜇𝐇𝐇
• 𝐃𝐃 = 𝜀𝜀𝐄𝐄
• 𝐉𝐉 = 𝛾𝛾𝐄𝐄
𝑟𝑟𝑟𝑟𝑟𝑟 𝐇𝐇 = 𝐉𝐉 +
𝑟𝑟𝑟𝑟𝑟𝑟 𝐄𝐄 = −
𝑑𝑑𝑑𝑑𝑑𝑑 𝐁𝐁 = 0
𝑑𝑑𝑑𝑑𝑑𝑑 𝐃𝐃 = 𝜌𝜌
∂
𝜕𝜕𝜕𝜕
∂
𝜕𝜕𝜕𝜕
𝐁𝐁
𝐃𝐃
Maxwell Equations
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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:
∫ H ⋅ dl = ∫∫ J ⋅ dS
C
S
• Faraday’s Law of induction:
∂B
∫C E ⋅ dl = −∫S ∂t ⋅ dS
• Gauss’s Law for magnetism:
∫ B ⋅ dS = 0
S
• Gauss’s Law for electricity:
∫ D ⋅ dS = ∫ ρ dv
S
v
Magnetic Circuit
Ampère’s Law
∫ H ⋅ dl= ∑ I=
Fm
ls
For H = const.:
Fm = H l s = N I
For B = const.:
Φ = B ⋅ SΦ
ls
H ⋅ l s = H ⋅ µS Φ ⋅
µS Φ
Hopkinson’s Law
For H, B = const., μFe >> μ0:
Fm = Φ ⋅ Rm
Magnetic circuit with air gap
lFe
δ
Fm = Φ(RmFe + Rmδ ) = H Fe l Fe + H δ δ
Analogy – Magnetic x Electric
Electromagnetic Induction
Faraday’s Law of induction
dψ
∫ E ⋅ dl = − dt = e = −ui
ψ = 2 Wb · 4 + 1 Wb · 3 + 1 Wb · 1 = 12 Wb
∂ψ
∂ψ
dt +
dx
dψ =
∂t
∂x
e=−
dψ
 ∂ψ ∂ψ 
= −
+
v
dt
∂x 
 ∂t
Lorentz Force
fm = −i ⋅
dΨ
dx
− fm = B ⋅ i ⋅ l
 

=
F i l ×B
(
)
Electromagnetic Induction
− e = ui = B ⋅ l ⋅ v
Magnetization curve
Permanent Magnets
Permanent Magnets
Rotating Magnetic Field
My questions
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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?