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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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ELEC 342, F-15, M-1

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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ELEC 342, F-15, M-1

BC Transmission System

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ELEC 342, F-15, M-1

Electromechanical Energy Conversion• Generation of Electricity – Big Scale

Thermal Power Plant

Hydro Power Plant

Wind Power

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ELEC 342, F-15, M-1

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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ELEC 342, F-15, M-1

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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ELEC 342, F-15, M-1

Electromechanics Applications

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ELEC 342, F-15, M-1

Electromechanics DevicesManufacturingAutomotiveAircraftShipsComputersOfficeHousehold…

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ELEC 342, F-15, M-1

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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ELEC 342, F-15, M-1

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 342, F-15, M-1

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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ELEC 342, F-15, M-1

( )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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ELEC 342, F-15, M-1

( )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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ELEC 342, F-15, M-1

( ) ( )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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ELEC 342, F-15, M-1

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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ELEC 342, F-15, M-1

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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ELEC 342, F-15, M-1

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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ELEC 342, F-15, M-1

Qualitative Phasor Diagrams

Consider RLC Circuit

Use phasors (vectors) to represent voltage and/or current equations (relationship)

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ELEC 342, F-15, M-1

Qualitative Phasor Diagrams

Consider RLC Circuit

Use phasors (vectors) to represent voltage and/or current equations (relationship)

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ELEC 342, F-15, M-1

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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ELEC 342, F-15, M-1

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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ELEC 342, F-15, M-1

Balanced Three-Phase SystemsSingle vs. Three Phases

Efficient transmission of power – just one more conductor = 3 times more power

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ELEC 342, F-15, M-1

Three-Phase SourceWye (Y) - Connected Line Voltages

baab VVV −=

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ELEC 342, F-15, M-1

Three-Phase SourceDelta (Δ) - Connected Line Currents

caaba III −=

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ELEC 342, F-15, M-1

Three-Phase LoadWye (Y) - Connected Line Voltages

baab VVV −=

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ELEC 342, F-15, M-1

Three-Phase LoadDelta (Δ) - Connected Line Currents

caaba III −=

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ELEC 342, F-15, M-1

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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ELEC 342, F-15, M-1

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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ELEC 342, F-15, M-1

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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ELEC 342, F-15, M-1

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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ELEC 342, F-15, M-1

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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ELEC 342, F-15, M-1

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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ELEC 342, F-15, M-1

Magnetic and Electric Circuits Analogy

21 ℜ+ℜ=Φ

F

Electric Circuit

21 RR

vi

+=

Magnetic Circuit

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ELEC 342, F-15, M-1

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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ELEC 342, F-15, M-1

Inductance: Example 1Consider the following electromagnetic system (device)

Equivalent Magnetic Circuit

Equivalent Electric Circuit

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ELEC 342, F-15, M-1

Inductance: Example 2Consider the following electromagnetic system

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ELEC 342, F-15, M-1

Magnetic Circuits: Example 3Consider the following electromagnetic system

Equivalent Magnetic Circuit

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ELEC 342, F-15, M-1

Magnetic Materials

Magnetic moment of an atom

Magnetic Domain Structure

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ELEC 342, F-15, M-1

Magnetic Material Domain Model

demagnetized magnetized

B External field

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ELEC 342, F-15, M-1

Magnetic Saturation

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ELEC 342, F-15, M-1

Hysteresis Loop

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ELEC 342, F-15, M-1

Hysteresis Loop

Hysteresis loops for different excitation levels

Br – residual magnetismHc – coercivity force,

external field required to demagnetize the material

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ELEC 342, F-15, M-1

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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ELEC 342, F-15, M-1

Magnetic MaterialsSome common PM materialsSecond quadrant

hysteresis curve for M-5 steel

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ELEC 342, F-15, M-1

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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ELEC 342, F-15, M-1

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 ?