Download - Module 1 of Elec 342 - UBC
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ELEC 342, F-15, M-1
ELEC 342Electromechanical Energy
Conversion and Transmission
Fall 2015
Instructor: Dr. Juri JatskevichMy Webpage: www.ece.ubc.ca/~jurij
Class Webpage:http://courses.ece.ubc.ca/elec342/
Credit: 3-lecture-hour/week + 1-tutorial/week + 5 labs
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ELEC 342, F-15, M-1
Electric Energy GridGeneration, Transmission/Distribution, UtilizationModern Electric Grid – A very complex system
Industrial Loads Motor Drives
Control Centre
Energy Storage
HydroPV Solar Wind
Energy
HVDC
Residential & Commercial loads
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Electric Power System• Transmission & Distribution
– Transmission ~ 138 to 765 kV
– Sub-transmission ~ 34 to 138 kV
– Distribution ~ 4 to 34 kV
– Service / Customer level ~ 240, 208, 120.
• Components– Wires, cables – transmission of power
– Tower – support structures
– Transformers – converting voltage levels
– Circuit breakers, relays – protective devices
– Control Centers – ensure reliable operation & power flow
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BC Transmission System
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Electromechanical Energy Conversion• Generation of Electricity – Big Scale
Thermal Power Plant
Hydro Power Plant
Wind Power
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Electrical Energy Generation– Almost all electricity produced in BC (10
~12GW) is produced by Synchronous Generators
Electrical Energy Utilization– About 65% of all electricity is consumed by
motors: induction, synchronous, etc.– For industry it is about 85%
Electromechanical Energy Conversion Devices– Predominant way of generating and
consuming electrical energy
Electromechanical Energy Conversion
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Applications of ElectromechanicsModern Transportation => More Electric Vehicle
Diesel-Electric Hybrid
All-Electric
Toyota Hybrid, operates at 288V, reaches 30kW
Tesla Roadster, Induction Motor, reaches 200 kW
Liebherr T282B earth-hauling truck 2.7MW AC Propulsion
Canada Line (Richmond-Airport-Vancouver Line) SNC-Lavalin & Rotem Company
All-Electric => Zero Emission Transportation
Vancouver TransLinkTrolley BusNew Flyer Industries
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Electromechanics Applications
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Electromechanics DevicesManufacturingAutomotiveAircraftShipsComputersOfficeHousehold…
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Electromechanical Energy Conversion
InputElectrical Energy
ConversionDevice
OutputMechanicalEnergyElectrical
System(generator,source, etc.)
MechanicalSystem(machine tool,plant, etc.)
InputMechanicalEnergy
ConversionDevice
OutputElectricalEnergyMechanical
System(Prime Mover,Turbine, etc.)
ElectricalSystem(transmission,distribution,load, etc.)
Is the energy conversion process reversible?
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Electromechanical Energy Conversion
• Transformation of Electrical Energy
InputLevel X
ConversionDevice
OutputLevel Y
ElectricalSystem(generator,source, etc.)
ElectricalSystem(load)
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ELEC 342, F-15, M-1
Electromechanical Energy Conversion• Electrical Machines
– Stationary• Transformers
– Rotating• Motors, generators
– Linear Devices• Solenoids, linear motors, other actuators
– Devices may operate with DC or AC
• Power Electronics (Switched Mode , SMPSs, Motor & Actuator Drivers, …)– Rectifiers
• AC to DC– Converters
• DC to DC– Inverters
• DC to ACVery broad & interesting area, requires its own course!
ConversionDevice
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ELEC 342Electromechanical Energy Conversion and
Transmission
Module 1, Part 1: Review of AC Circuits & Phasors
(Read Appendix B)
Objectives & Most Important Concepts• Concept of phasors & notations • RMS value • Phasor diagrams for basic RLC circuits• Balanced 3-phase system, source, load, Y / D connection,
line-to-line and phase voltages and currents, phase shifts • Real, reactive, and apparent power in 1-phase and 3-phase
systems, power factor
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ELEC 342, F-15, M-1
Review of AC Circuits• Consider linear inductive circuit
( )tVtv m ωcos)( =
dt
drieritv
λ+=+=)(
Steady-state Solution
KVL
( )em tEte ϕω += cos)(
( )im tIti ϕω += cos)(
dt
diLri +=
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( )tVtv m ωcos)( =
cvritv +=)(
Steady-state Solution
KVL
( )vmcc tVtv ϕω += cos)( ,
( )im tIti ϕω += cos)(
dt
dvC
r
vvi cc =
−=
Review of AC Circuits• Consider linear capacitive circuit
( )tvr
vrdt
dvC c
c 11=+
Note: In both cases we need to know only amplitude & phase
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( )iii tVtv ϕω += cos)(
Steady-state Solution?
( )jjj tJtj ϕω += cos)(
Review of AC Circuits• Consider arbitrary network
– with voltage and current sources
( )kvkk tVtv θω += cos)(
For all circuit branches the currents & voltages are sinusoidal
( )kikk tIti θω += cos)(
Note: For SS analysis we need to know only amplitudes & phases
kk VJ ,kv
ki θθ ,
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( ) ( )tVjtVtv mm ωω sincos)( ⋅+=
( ) ( )φωφω −⋅+−= tIjtIti mm sincos)(
Review of Phasors• Complex Plane
Euler’s Identity
( ) ( )tjte tj ωωω sincos +=tj
meVtv ω=)()()( φω −= tj
meIti
Note:
1. All vectors rotate at the same speed ω ! 2. Only the amplitudes and their phase
differences are important
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Phasor Notations
ωπ /2=T
Time Domain
( )θω ±tAcoso90−±∠ θA
θ±∠A
( )θω ±tAsin
Phasor Representation
0)( ∠≡= mtj
m VeVtv ω
φφω −∠≡= −m
tjm IeIti )()(
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Review of Phasors
C
L
ωπ /2=T
Linear Passive Elements
zmivm
m
im
vm ZI
V
I
V
I
VZ θθθ
θθ
∠=−∠=∠∠
==
R
o9011
−∠⎟⎠⎞
⎜⎝⎛==
CCjZ
ωω
( ) o90∠== LLjZ ωω
RZ =
Complex Impedance
⎟⎠⎞
⎜⎝⎛=+=+=
R
XXRZjXRZ zm arctan , , 22 θ
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Root-Mean-Square (RMS) Value
( )∫=T
rms dttvT
V0
2)(
1
* Value equivalent to the DC voltage (current) that when applied to a resistor dissipates the same average power as the given AC value
Given sinusoidal voltage (current), RMS values are often used with Phasors
( )vrms tVtv ϕω +⋅= cos2)(
( )irms tIti ϕω +⋅= cos2)(
vrmsVV ϕ∠=~
irmsII ϕ∠=~
21)( v
rr
vvvitP === ∫∫ ⋅==
TT
ave dttvTr
dttPT
P0
2
0)(
11)(
1
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Qualitative Phasor Diagrams
Consider RLC Circuit
Use phasors (vectors) to represent voltage and/or current equations (relationship)
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Qualitative Phasor Diagrams
Consider RLC Circuit
Use phasors (vectors) to represent voltage and/or current equations (relationship)
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Power in AC Circuits
( ) ( )ϕωϕ ++= tVIVI 2coscos
( )ϕsinVIQ =
Given inductive load
Average (real) power over one cycle
( )tVtv ωcos2)( ⋅= ( )ϕω +⋅= tIti cos2)(
( ) ( ) ( )ϕωω +== ttVIvitp coscos2
( )ϕcosVIP =
Reactive power
Apparent power 22 QPVIS +== [ ] [ ] [ ]MVAkVAVA ,,
[ ] [ ] [ ]MVARkVARVAR ,,
[ ] [ ] [ ]MWkWW ,,
( )VI
P=ϕcosPower Factor (pf)
Instantiations power is always this
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Single vs. Three-Phase Systems
Just as easy to produce !
( )tVtv ma ωcos)( =
( )o120cos)( −= tVtv mb ω
( )o120cos)( += tVtv mc ω
( )tVtv m ωcos)( =
Easy to produce !
0=++ cba vvvFor balanced system we have
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Balanced Three-Phase SystemsSingle vs. Three Phases
Efficient transmission of power – just one more conductor = 3 times more power
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Three-Phase SourceWye (Y) - Connected Line Voltages
baab VVV −=
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Three-Phase SourceDelta (Δ) - Connected Line Currents
caaba III −=
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Three-Phase LoadWye (Y) - Connected Line Voltages
baab VVV −=
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Three-Phase LoadDelta (Δ) - Connected Line Currents
caaba III −=
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Power in Three-Phase Systems
ccbbaa vivivi ++=cba PPPtP ++=)(3φ
( )tVtv pha ωcos2)( =
( )o120cos2)( −= tVtv phb ω
( )o120cos2)( += tVtv phc ω
Instantaneous Power can always be calculated as
( )ϕω −= tIti pha cos2)(
( )ϕω −−= o120cos2)( tIti phb
( )ϕω −+= o120cos2)( tIti phc
For balanced system we have
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ELEC 342, F-15, M-1
Power in Balanced Three-Phase Systems
3/ , LphLph VVII ==
( )phLLIVP ϕφ cos33 =
( )phphphph IVPtP ϕφ cos33)(3 ==In terms of phase quantities (Y - connection)
( )phphphph IVQtQ ϕφ sin33)(3 ==
In terms of line-to-line quantities
LphLph VVII == ,3/
( )phLLIVQ ϕφ sin33 =
Y - connection Δ - connection
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ELEC 342, F-15, M-1
ELEC 342Electromechanical Energy Conversion and
Transmission
Module 1, Part 2: Basic Magnetic Circuits
(Read Chap. 1)
Objectives & Most Important Concepts• Fundamentals of Electromagnetics, Maxwell’s Equations • Sign & direction conventions • Basic magnetic circuits, concepts, analogies, calculations• Flux, flux linkage, inductance • Magnetic materials, saturation, hysteresis loop• Coil under ac excitation, type of core losses
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ELEC 342, F-15, M-1
Review of Basic Quantities and Units
⎥⎦⎤
⎢⎣⎡ =
2m
WbT
E – electric field intensity
B – magnetic flux density
H – magnetic field intensity
Φ – magnetic flux
⎥⎦⎤
⎢⎣⎡m
A
⎥⎦⎤
⎢⎣⎡ ==
⋅m
H
meter
Henry
A
mT
[ ]2mTWb ⋅=
B-H Relation• Current produces the H field (see Ampere’s law)• H is related to B
HHB rμμμ 0==μ – permeability (characteristic of the medium)
μ0 – permeability of vacuum
μr – relative permeability of material
⎥⎦⎤
⎢⎣⎡ =
2meter
WeberTesla
[ ]mH7104 −⋅⋅= π
000,100100L=rμmagnetic materials
⎥⎦⎤
⎢⎣⎡m
V
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ELEC 342, F-15, M-1
Fundamentals
Summarized in Maxwell’s Equations (1870s)
1) Gauss’s Law for Electric Field
Electric flux out of any closed surface is proportional to the total charge enclosed
daEq
d e
s∫∫ =Φ==⋅ θ
εcos
0
aE
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ELEC 342, F-15, M-1
FundamentalsSummarized in Maxwell’s Equations (1870s)
2) Gauss’s Law for Magnetic Field
Magnetic flux out of any closed surface is zero
There are no magnetic charges
0=Φ=⋅∫ ms
daB
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ELEC 342, F-15, M-1
FundamentalsSummarized in Maxwell’s Equations (1870s)
3) Faraday’s Law
ElectroMotive Force (emf)
The line integral of the electric field around a closed loop/contour Cis equal to the negative of the rate of change of the magnetic flux through that loop/contour
emfdt
dd
dt
dd
SC
=Φ
−=⋅−=⋅ ∫∫ aBlE
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ELEC 342, F-15, M-1
FundamentalsSummarized in Maxwell’s Equations (1870s)
4) Ampere’s Law (for static electric field)
The line integral of the magnetic field B around a closed loop Cis proportional to the net electric current flowing through thatloop/contour C
net
SC
IdaJd ∫∫ =⋅=⋅ 00 μμlB
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ConventionsRight hand rule
Right-screw ruleDot and cross notations
Magnetic field produced by coil (solenoid)
Flux Lines:• form a closed loop/path• Lines do not cut across or merge• Go from North to South magnetic poles
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ELEC 342, F-15, M-1
Magnetic Field of an Infinite Conductor
Apply Ampere’s Law
enclosed
C
I=⋅∫ dlH
θRd=dlIncremental length
IRH =⋅ π2
R
IH
π2=
R
IHB
πμμ
2==
H and dl have the samedirection
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enclosed
C
I=⋅∫ dlH
∫ ∫∫ ∫∫ ⋅+⋅+⋅+⋅=⋅d
c
a
d
b
a
c
bC
dlHdlHdlHdlH 21dlH
Apply Ampere’s Law
22 1
0
11
IdR
R
IdlH
c
b
==⋅∫ ∫−
θππ
22 2
0 22
IdR
R
IdlH
a
d
==⋅∫ ∫ θπ
π
Magnetic Field of an Infinite Conductor
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ELEC 342, F-15, M-1
Some DefinitionsMagnetic Flux
∫∫Φ
−=⋅−=⋅SC dt
dd
dt
dd aBlE
Recall Faraday’s Law - Electromotive Force (emf)
- voltage induced in one turn due to the changing magnetic flux
For coil with N turnsdt
dNe
Φ⋅=
flux scaled by the number of turns
Φ⋅= Nλ [ ]tWb ⋅
dt
de
λ=Total induced emf [ ]V
Flux is always continuousc
S
c AB∫ =⋅=Φ daB
Flux Linkage
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Some DefinitionsInductance
( ) ( ) iLif ⋅⋅==λ
Need a function that relates Flux Linkage to the Current
Consider
Recall
iL
λ= ⎥⎦
⎤⎢⎣⎡ =
⋅H
A
tWb
i
N
iL
Φ⋅==
λ
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Magnetic Circuits• Consider basic magnetic circuit
net
l
c Ic
=⋅∫ dlH
Source of magnetic field is ampere-turn product
0μμ >>Assume
⇒All magnetic flux is concentrated inside the core
Recall Ampere’s Law
Magnetomotive force (mmf) NiF =
Assume uniform corecc
l
cnet lHdlHINiFc
=⋅=== ∫ [ ]turnAmpere ⋅
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ELEC 342, F-15, M-1
Magnetic Circuits• Consider basic magnetic circuit
c
cc A
l
μ=ℜ
Flux is always continuous
Assume all magnetic field is confined inside the core
Define Magnetic Flux
Consider mmf c
c
ccccc A
llBlHNiF ℜΦ=Φ====
μμDefine Reluctance (of the given magnetic path)
c
S
c AB∫ =⋅=Φ daB [ ]Wb
⎥⎦⎤
⎢⎣⎡Wb
A
Recall Inductance
cc
N
i
iNN
i
N
iL
ℜ=
ℜ⋅⋅⋅
=Φ⋅
==2λ
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Magnetic Circuits• Magnetic circuit with air gap
Assuming all magnetic flux is confined inside the core
and
Consider mmf
∫ ⋅==C
NiF dlH
ggcc lHlH +=
0μμggcc
lBlB+=
cc A
BΦ
=g
g AB
Φ=
( ) totaligcg
g
c
c
A
l
A
lF ℜΦ=ℜΦ=ℜ+ℜΦ=⎟
⎟⎠
⎞⎜⎜⎝
⎛+Φ= ∑
0μμ
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Magnetic and Electric Circuits Analogy
21 ℜ+ℜ=Φ
F
Electric Circuit
21 RR
vi
+=
Magnetic Circuit
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Magnetic Circuit
- mmf,
- Flux
- Reluctance,
- Permeance,
- Permeability,
Electric Circuit
- Voltage (emf),
- Current,
- Resistance,
- Conductance,
- Conductivity,
Magnetic and Electric Circuits Analogy
[ ]Ω= ,A
lR
σ
[ ]AmpsI ,
[ ]VoltV ,
∑= nniRv
[ ]SiemensR
G ,1
=
⎥⎦⎤
⎢⎣⎡
m
Siemens,σ
[ ]tAF ⋅,
[ ]Wb,Φ
⎥⎦⎤
⎢⎣⎡=ℜWb
A
A
l,
μ
⎥⎦⎤
⎢⎣⎡
ℜ=
A
Wb,
1ρ
∑= nnlHF
0=∑N
ni 0=Φ∑N
n
⎥⎦⎤
⎢⎣⎡
m
H,μ
For node
For loop For loop
For node
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Inductance: Example 1Consider the following electromagnetic system (device)
Equivalent Magnetic Circuit
Equivalent Electric Circuit
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Inductance: Example 2Consider the following electromagnetic system
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Magnetic Circuits: Example 3Consider the following electromagnetic system
Equivalent Magnetic Circuit
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Magnetic Materials
Magnetic moment of an atom
Magnetic Domain Structure
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Magnetic Material Domain Model
demagnetized magnetized
B External field
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Magnetic Saturation
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Hysteresis Loop
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Hysteresis Loop
Hysteresis loops for different excitation levels
Br – residual magnetismHc – coercivity force,
external field required to demagnetize the material
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Magnetic Materials
[ ]mA /1001.0~ LcHSoft mag. materials
Hard mag. materials
100>cH [ ]mA /
Permanent magnets (PM)64 1010~ LcH [ ]mA /
Types of PMs• Neodymium Iron Boron (NdFeB or NIB)• Samarium Cobalt (SmCo)• Aluminum Nickel Cobalt (Alnico)• Ceramic or Ferrite, very popular
Iron-oxide, barium, etc. compressed powder
Classes of Magnetic Materials
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Magnetic MaterialsSome common PM materialsSecond quadrant
hysteresis curve for M-5 steel
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Core Losses
( ) ∫∫ ∫ =⎟⎠⎞
⎜⎝⎛==Δ cccccc
cccycleh dBHAldBNA
N
lHidW λ,
Consider AC
excitation
Hysteresis Losses
Power loss can be approximated as
( )nchh BfKP max,⋅⋅=
hK nWhere the constants and determined experimentally
5.25.1~ Ln
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Where the constant depends on lamination thickness and is determined experimentally
Core Losses
( )2max,2
cee BfKP ⋅⋅=
Consider AC
excitation
Eddy Current Losses
Power loss can be approximated as
eK
∫∫ ⋅−=⋅SC
daBdt
ddlE
Faraday’s law
Laminated coreSolid-iron core
Equivalent circuit including core losses ?