Electric Machinery and Apparatus 1 AE1M14SP1

Miroslav Chomát chomat@fel.cvut.cz

room B3-248

Course Overview • Introduction • Review of basic principles • Transformers • Electric drives • Rotating electric machines

– Induction machines (three-phase, single-phase) – Synchronous machines – DC machines

• Operation of electric machines – starting – braking

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 – assignments

Literature

• S. J. Chapman, Electric Machinery Fundamentals. McGraw-Hill, Inc. 2011

• A. E. Fitzgerald, C. Kingsley jr., and S. D. Umans, Electric Machinery. New York, USA: McGraw-Hill, 2003.

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

• 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

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]

Magnetic Field in Conductor

image source: wikipedia.org

Lorentz Force

image source: wikipedia.org

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?