NOTES 01 INTRODUCTION TO POWER ELECTRONICS.ppt [Read-Only]

Notes 01 Introduction to Power Electronics Marc T. Thompson, Ph.D. Thompson Consulting, Inc. 9 Jacob Gates Road Harvard, MA 01451 Phone: (978) 456-7722 Fax: (240) 414-2655 Email: [email protected] marctt@thompsonrd com Web: http://www.thompsonrd.com

© Marc Thompson, 2005-2007 Power Electronics

Introduction to Power Electronics

1

Introduction to Power Electronics • Power electronics relates to the control and flow of electrical energy • Control is done using electronic switches, capacitors, magnetics, and control systems • Scope S off power electronics: l t i milliWatts illiW tt ⇒ gigaWatts i W tt • Power electronics is a growing field due to the improvement in switching technologies and the need for more and more efficient switching circuits

Power Electronics


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Summary • • • •

History/scope of power electronics Some interesting PE-related PE related projects Circuit concepts important to power electronics Some tools for approximate analysis of power electronics l t i systems t • DC/DC converters --- first-cut analysis • Key design challenges in DC/DC converter design • Basic system concepts

Power Electronics


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Scope of Power Electronics Power Level (Watts) System 0.1-10 • Battery-operated equipment • Flashes/strobes 10-100 • Satellite power systems • Typical offline flyback supply 100 – 1kW • Computer power supply • Blender 1 – 10 kW • Hot tub 10 – 100 kW • Electric car • Eddy current braking 100 kW –1 MW • Bus • micro-SMES 1 MW – 10 MW • SMES 10 MW – 100 MW • Magnetic aircraft launch • Big locomotives 100 MW – 1 GW • Power plant > 1 GW • Sandy S d P Pond d substation b t ti (2.2 (2 2 GW) Power Electronics


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Scope of Power Electronics

Power Electronics


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Areas of Application of Power Electronics • High frequency power conversion – DC/DC, inverters • Low frequency power conversion – Line rectifiers • Distributed p power systems • Power devices

Power Electronics

• Power Transmission – HVDC – HVAC • Power quality – Power factor correction – Harmonic reduction • Passive P i filt filtering i • Active filtering


6

Some Applications • • •

Heating and lighting control Induction heating Fluorescent lamp ballasts – Passive – Active

• • •

• • •

– Electronic ignitions – Alternators

Motor drives Battery chargers Electric vehicles

•

Switching power supplies Spacecraft power systems – Battery powered – Flywheel powered

Power Electronics

Energy storage – Flywheels y – Capacitors – SMES

– Motors – Regenerative braking

• •

Uninterruptible power supplies (UPS) Electric power transmission Automotive electronics

•

Power conditioning for alternative power sources – Solar cells – Fuel cells – Wind turbines


7

Some Power Electronics-Related Projects Worked on at TCI (Harvard Labs) • • • • • • • • • •

High speed lens actuator Laser diode pulsers Levitated flywheel Maglev Permanent magnet brakes Switching power supplies Magnetic analysis Laser driver pulsers 50 kW inverter switch Transcutaneous (through-skin) non-contact power supply

Power Electronics


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Lens Actuator z r

Iron Coil Back iron

Lens

Permanent Nd-Fe-Bo g Magnet

Air gap

Power Electronics


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High Power Laser Diode Driver Based on gy Power Converter Technology Overdrive duration set

OVERDRIVE Switching Array

Array Driver

Laser Diode

Iod

THRESH. current set

O.D. current set -12V

Drive TTL INPUT

Array Driver

Drive*

Ith

PEAK Switching Array

-12

Is PEAK current set

Rsense

Diff. Amp.

Vsense

Power Converter

-12

D PWM P.W.M.

Vc

Loop Filter

See: 1. B. Santarelli and M. Thompson, U.S. Patent #5,123,023, "Laser Driver with Plural Feedback Loops," issued June 16, 1992 2. M. Thompson, U.S. Patent #5,444,728, "Laser Driver Circuit," issued August 22, 1995 3. W. T. Plummer, M. Thompson, D. S. Goodman and P. P. Clark, U.S. Patent #6,061,372, “Two-Level Semiconductor Laser Driver,” issued May 9, 2000 4. Marc T. Thompson and Martin F. Schlecht, “Laser Diode Driver Based on Power Converter Technology,” IEEE Transactions on Power Electronics, vol. 12, no. 1, Jan. 1997, pp. 46-52 Power Electronics Introduction to Power Electronics 10

Magnetically-Levitated Magnetically Levitated Flywheel Energy Storage • For NASA; P = 100W, energy storage = 100 W-hrs Guidance and Suspension

S N

N S

Flywheel (Rotating)

N S

S N

S N

N S

Stator Winding

N S

S N

N S

S N

z N S

S N r

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Electromagnetic Suspension --- Maglev

Power Electronics


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Maglev - German Transrapid

Power Electronics


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Maglev - Japanese EDS

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Japanese EDS Guideway

Power Electronics


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MIT Maglev Suspension Magnet

Reference: M. T. Thompson, R. D. Thornton and A. Kondoleon, “Flux-canceling electrodynamic maglev suspension: Part I. I Test fixture design and modeling modeling,” IEEE Transactions on Magnetics, Magnetics vol. vol 35 35, no no. 3 3, May 1999 pp. 1956-1963 Power Electronics


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MIT Maglev Test Fixture

M. T. Thompson, R. D. Thornton and A. Kondoleon, “Flux Flux-canceling canceling electrodynamic maglev suspension: Part I. Test fixture design and modeling,” IEEE Transactions on Magnetics, vol. 35, no. 3, May 1999 pp. 1956-1963

Power Electronics


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MIT Maglev Test Fixture • 2 meter diameter test wheel • Max. speed 1000 RPM (84 m/s) • For F testing t ti “flux “fl canceling” HTSC Maglev • Sidewall levitation

“ electrodynamic maglev suspension: Part I. Test fixture f M. T. Thompson, R. D. Thornton and A. Kondoleon, “Flux-canceling design and modeling,” IEEE Transactions on Magnetics, vol. 35, no. 3, May 1999 pp. 1956-1963 Power Electronics


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Permanent Magnet Brakes • For roller coasters 10,000 000 • Braking force > 10 Newtons per meter of brake

Reference: http://www.magnetarcorp.com Power Electronics


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Halbach Permanent Magnet Array • Special PM arrangement allows strong side (bottom) and weak side (top) fields • Applicable to magnetic suspensions (Maglev), linear motors, and induction brakes

Power Electronics


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Halbach Permanent Magnet Array

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Linear Motor Design and Analysis

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Variac Failure Analysis

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Photovoltaics

Reference: S. Druyea, S. Islam and W. Lawrance, “A battery management system for stand-alone photovoltaic energy systems,” IEEE Industry Applications Magazine, vol. 7, no. 3, May-June 2001, pp. 67-72 Power Electronics


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Offline Flyback Power Supply

Reference: P P. Maige Maige, “A A universal power supply integrated circuit for TV and monitor applications applications,” IEEE Transactions on Consumer Electronics, vol. 36, no. 1, Feb. 1990, pp. 10-17 Power Electronics


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Transcutaneous Energy gy Transmission

Reference: H H. Matsuki Matsuki, Y Y. Yamakata Yamakata, N N. Chubachi Chubachi, S S.-I. -I Nitta and H. H Hashimoto, Hashimoto “Transcutaneous Transcutaneous DC-DC converter for totally implantable artificial heart using synchronous rectifier,” IEEE Transactions on Magnetics, vol. 32 , no. 5, Sept. 1996, pp. 5118 - 5120 Power Electronics


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50 KW Inverter Switch

Power Electronics


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Non Contact Battery Charger Non-Contact

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High Voltage RF Supply

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60 Hz Transformer Shielding Study

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“Intuitive Analog Circuit Design”

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“Power Quality in Electrical Systems”

Power Electronics


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Some Other Interesting Power-Electronics Related Systems

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Conventional vs. vs Electric Car

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High Voltage DC (HVDC) Transmission

Power Electronics


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Mass Spectrometer

Reference: http://www.cameca.fr/doc_en_pdf/oral_sims14_schuhmacher_ims1270improvements.pdf Power Electronics


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Some Disciplines Encompassed in the Field of Power Electronics •

Analog circuits – High speed (MOSFET switching, etc.) – High power – PC b board d llayoutt – Filters • EMI

• •

Machines/motors Simulation – SPICE, Matlab, etc.

•

Device physics – How to make a better MOSFET, IGBT, etc.

•

Control theory Magnetics – Inductor design – Transformer design

•

• •

Thermal/cooling – How to design a heat sink – Thermal interfaces – Thermal modeling

Power systems – Transmission lines – Line filtering

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Selected History of Power Switching Devices • 1831 --- Transformer action demonstrated by Michael Faraday • 1880s: modern transformer invented

Reference: f J. W. Coltman, C ““The Transformer f (historical ( overview,”” IEEE Industry Applications Magazine, vol. 8, no. 1, Jan.-Feb. 2002, pp. 8-15 Power Electronics


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Selected History y of Power Switching g Devices • Early 1900s: vacuum tube – Lee DeForest --- triode, 1906 • 1920-1940: 1920 1940 mercury arc ttubes b tto convert 50Hz, 2000V to 3000VDC for railway

Reference: M. C. Duffy, “The mercury-arc rectifier and supply to electric railways,” IEEE Engineering Science and Education Journal, vol. 4, no. 4, August 1995, pp. 183-192 Power Electronics


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Selected History of Power Switching Devices • 1930s: selenium rectifiers • 1948 - Silicon Transistor (BJT) introduced (Bell Labs) • 1950s - semiconductor power diodes begin replacing vacuum tubes • 1956 - GE introduces SiliconControlled Rectifier (SCR)

f N. Holonyak, Jr., “The “ Silicon S p-n-p-n Switch S and Controlled C Rectifier f (Thyristor),” ( ) ” IEEE Transactions on Reference: Power Electronics, vol. 16, no. 1, January 2001, pp. 8-16 Power Electronics


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Selected History of Power Switching Devices • 1960s - switching speed of BJTs allow DC/DC converters possible in 10-20 kHz range • 1960 - Metal Oxide Semiconductor Field-Effect Field Effect Transistor (MOSFET) for integrated circuits • 1976 - power MOSFET becomes commercially available, allows > 100 kHz operation

Reference: B. J. Baliga, “Trends in Power Semiconductor Devices,” IEEE Transactions on Electron Devices, vol. 43, no. 10, October 1996, pp. 1717-1731 Power Electronics


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Selected History of Power Switching Devices • 1982 - Insulated Gate Bipolar Transistor (IGBT) introduced

Reference: B. J. Baliga, “Trends in Power Semiconductor Devices,” IEEE Transactions on Electron Devices, vol. 43, no. 10, October 1996, pp. 1717-1731 Power Electronics


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Review of Basic Circuit Concepts • Some background in circuits • Laplace notation • First-order and secondorder systems • Resonant circuits, damping p g ratio,, Q • Reference for this material: M. T. Thompson, Intuitive Analog Circuit Design Design, Elsevier, Elsevier 2006 (course book for ECE529) and Power Quality in Electrical Systems, McGraw-Hill, 2007 by A. Kusko and M. Thompson

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Laplace p Notation • Basic idea: Laplace transform converts differential equation to algebraic equation • Generally, G ll method th d iis used d iin sinusoidal i id l steady t d state t t after all startup transients have died out Circuit domain Resistance, R Inductance L C Capacitance i C

R1 vi

+ -

R1

+ R2 C

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Laplace (s) domain R Ls 1 Cs

vo -

vi (s)

+ -


R2 1/(Cs)

+ vo(s) -

44

System Function • Find “transfer function” H(s) by solving Laplace transformed circuit R1 vi

+ -

R2 C

H ( s) =

Power Electronics

R1

+ vo

vi (s)

-

R2 +

+ -

R2 1/(Cs)

+ vo(s) -

1 Cs

R2Cs + 1 vo ( s ) = = ( R1 + R2 )Cs + 1 vi ( s ) R + R + 1 1 2 Cs Introduction to Power Electronics

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First-Order Systems −t

vo (t ) = V (1 − e τ ) −t

V τ ir (t ) = e R τ = RC Time constant

τ R = 2.2τ ωh =

Risetime

1

τ ωh fh = 2π

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Bandwidth

0.35 τR = fh


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First-Order Step p and Frequency q y Response p Step Response 1

Amplitud de

0.8 0.6 0.4 0.2 0 0

1

2

3

4

5

6

Time (sec.)

Ph hase (deg); Magnitude e (dB)

Bode Diagrams 0 -10 -20 -20 -40 -60 -80 -1

10

Power Electronics

0

10 Frequency (rad/sec)


1

10

47

Review of Second-Order Second Order Systems R

L +

vi

+ -

C

vo -

1 Cs

ω n2 vo ( s ) 1 1 = = = 2 = 2 H ( s) = 2 2ζs LCs + RCs + 1 s s + 2ζω n s + ω n2 vi ( s ) R + Ls + 1 + +1 2 Cs ωn ωn 1 LC ω RC 1 R 1 R ς= n = = 2 2 L 2 Zo C

Natural frequency q y ωn = Damping ratio

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Second-Order System Frequency Response H ( jω ) =

H ( jω ) =

1 2 jςω ⎛ ω 2 ⎞ + ⎜⎜1 − 2 ⎟⎟ ωn ⎝ ωn ⎠ 1 2

⎛ 2ςω ⎞ ⎛ ω 2 ⎞ ⎟⎟ + ⎜⎜1 − 2 ⎟⎟ ⎜⎜ ⎝ ωn ⎠ ⎝ ωn ⎠

2

⎛ 2ςω ⎞ ⎜⎜ ⎟⎟ −1 ⎝ ω n ⎠ −1 ⎛ 2ςωω n ⎞ ⎟ ∠H ( jω ) = − tan = − tan ⎜⎜ 2 2 ⎟ 2 ωn − ω ⎠ ⎛ ω ⎞ ⎝ ⎜⎜1 − 2 ⎟⎟ ⎝ ωn ⎠

Power Electronics


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Second-Order Second Order System Frequency Response • Plots show varying damping ratio Frequency response for natural frequency = 1 and various damping ratios

30 20 10

Phase (deg); Ma agnitude (dB)

0 -10 -20 -30 -40

0

-50

-100

-150

-1

10

0

10

1

10

Frequency (rad/sec)

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Second-Order System Frequency Response at Natural Frequency • Now, what happens if we excite this system exactly at the natural t l frequency, f or ω = ωn? Th The response iis:

H ( s ) ω =ω

n

1 = 2ς

∠H ( s )ω =ωn = −

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π


2

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Relationship Between Damping Ratio and “Quality Factor” Q • A second order system can also be characterized by its “Q lit F “Quality Factor” t ” or “Q”

H ( s ) ω =ω

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n

1 = =Q 2ς


52

Second-Order System Step Response • Shown for varying values of damping ratio Step Response Step response for natural frequency = 1 and various damping ratios 2 1.8 1.6 14 1.4

Amplitude

1.2 1 0.8 0.6 0.4 0.2 0 0

1

2

3

4

5

6

7

8

9

10

Time (sec.)

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Second-Order Mechanical System • Electromechanical modeling

Reference: Leo Beranek, Acoustics, Acoustical Society of America, 1954 Power Electronics


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Pole Location Variation with Damping

Very underdamped

Critically damped

Overdamped jω

jω

jω

x + jω n

σ

− ωn x

σ

x

σ

x

2 poles x − jω n

Power Electronics


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Undamped Resonant Circuit iL + vc

C

L

-

Now, we can find the resonant frequency by guessing that the voltage v(t) is sinusoidal with v(t) = Vosinωt. Putting this into the equation for capacitor voltage results in:

1 − ω sin(ωt ) = − sin(ωt ) LC 2

This means that the resonant frequency is the standard (as expected) resonance:

ω r2 = Power Electronics

1 LC


56

Energy Methods iL + vc

C

L

-

By using energy methods we can find the ratio of maximum capacitor voltage to maximum inductor current. Assuming that the capacitor it is i iinitially iti ll charged h d tto Vo volts, lt and d remembering b i th thatt 2 capacitor stored energy Ec = ½CV and inductor stored energy is EL = ½LI2, we can write the following: 1 1 2 2 CVo = LI o 2 2

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Energy Methods iL + vc

C

L

What does this mean about the magnitude of the inductor current ? Well, we can solve for the ratio of Vo/Io resulting in: Vo L = ≡ Zo C Io

The term “Z Zo” is defined as the characteristic impedance of a resonant circuit. Let’s assume that we have an inductor-capacitor circuit with C = 1 microFarad and L = 1 microHenry. This means that the resonant frequency is 106 radians/second (or 166.7 kHz) and that the characteristic impedance i 1 Oh is Ohm. Power Electronics


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Simulation iL + vc

C

L

-

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Typical Resonant Circuit • Model of a MOSFET gate drive circuit

1 Cs

1 1 vo ( s ) H ( s) = = = = 2 2 1 2ζs vi ( s ) R + Ls + LCs + RCs + 1 s + +1 2 Cs ωn ωn 1 LC ω RC 1 R 1 R ς= n = = 2 2 L 2 Zo C

ωn =

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Resonant Circuit --- Underdamped • With ““small” ll” resistor, i t circuit i it iis underdamped d d d

ωn =

1

= 200 Mrad / sec

LC f n 31.8 MHz

L = 5Ω Zo = C ω n RC 1 R 1 R ς= = = = 0.001 2 2 L 2 Zo C Power Electronics


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Resonant eso a C Circuit cu --- U Underdamped de da ped Results esu s • This circuit is very underdamped, so we expect step p to oscillate at around 31.8 MHz response • Expect peaky frequency response with peak near 31.8 MHz

ωn =

1

= 200 Mrad / sec

LC f n 31.8 MHz

L = 5Ω C ω n RC 1 R 1 R = = = 0.001 ς= 2 2 L 2 Zo C Zo =

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Resonant eso a C Circuit cu --- U Underdamped de da ped Results, esu s, Step Response • Rings at around 31.8 MHz

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Resonant eso a C Circuit cu --- U Underdamped de da ped Results, esu s, Frequency Response • Frequency response peaks at 31.8 MHz

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Resonant eso a C Circuit cu --- C Critical ca Damping a p g • Now, let’s employ “critical damping” by increasing value of resistor to 10 Ohms • This is also a typical MOSFET gate drive damping resistor value

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Critical C ca Damping, a p g, S Step ep Response espo se • Note that response is still relatively fast (< 100 ns p time)) but with no overshoot response • If we make R larger, the risetime slows down

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Critical C ca Damping, a p g, Frequency eque cy Response espo se • No overshoot in the transient response corresponds to peaking g in the frequency q y response p no p

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Circuit Concepts • Power – Reactive power – Power quality – Power factor • Root R t Mean M S Square (RMS) • Harmonics – Harmonic distortion

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Sinewaves • A sinewave can be expressed as v(t) = Vpksin(ωt) • Vpk = peak voltage • ω = radian frequency (rad/sec) •ω=2 2πff where f is in Hz • VRMS = Vpk/sqrt(2) = 120V for sinewave with peaks at ±170V • More on RMS later

Power Electronics

120V RMS 60 Hz sinewave 200

150

100

50

0

-50

-100

-150

-200 0

0.002

0.004


0.006

0.008 0.01 Time[sec Time [sec.]]

0.012

0.014

0.016

69

0.018

Sinewave with Resistive Load • v(t) and i(t) are in phase and have the same shape; i.e. no harmonics in current - Time representation -Phasor Ph representation t ti -In this case, V and I have the same phase p

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Sinewave with Inductive Load • For an inductor, remember that v = Ldi/dt • So, i(t) lags v(t) by 90o in an inductor

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Sinewave with Inductive Load --- PSIM

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Sinewave with L/R Load • Phase shift (also called angle) between v and i is somewhere between 0o and -90o

⎛ ωL ⎞ ∠ = − tan ⎜ ⎟ ⎝ R ⎠ −1

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Sinewave with Capacitive Load • Remember that i = Cdv/dt for a capacitor • Current leads voltage by +90o

- Phasor representation

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Phasor Representation of L and C

In inductor, current lags g by y 90 degrees g voltage

Power Electronics

In capacitor, voltage lags current by 90 degrees


75

Response of L and C to pulses

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Review of Complex Numbers • In “rectangular” form, a complex number is written in terms of real and imaginary components • A = Re(A) + j×Im(A) - Angle

⎛ Im( A) ⎞ θ = tan ⎜⎜ ⎟⎟ ⎝ Re( A) ⎠ −1

- Magnitude of A

A=

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(Re(( A) )2 + (Im(( A) )2

77

Find Polar Form • Assume that current I = -3.5 3 5 + j(4 j(4.2) 2)

I = ( −3.5) 2 + ( 4.2) 2 = 5.5 A

θ = 180o − γ ⎛ 4.2 ⎞ o γ = tan ⎜ = 50 . 2 ⎟ ⎝ 3.5 ⎠ θ = 180o − 50.2 o = 129.8o −1

∴ 5.5 A∠129.8o Power Electronics


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Converting from Polar to Rectangular Form

Re{A} = A cos(θ ) Im{A} = A sin(θ ) Power Electronics


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Power • “Power” has many shapes and forms – Real power p – Reactive power • Reactive power does not do real work – Instantaneous power

p (t ) = v(t )i (t ) – Peak P k instantaneous i t t power – Average power

1 p (t ) = T Power Electronics

T

∫

v(t )i (t )dt

0


80

Power Factor • Ratio of delivered power to the product of RMS voltage and RMS current
PF = VRMS I RMS

• • • •

Power factor always <= 1 With pure sine wave and resistive load, PF = 1 With p pure sine wave and p purely y reactive load,, PF = 0 Whenever PF < 1 the circuit carries currents or voltages that do not perform useful work • The more “spikey” spikey a waveform is the worse is its PF – Diode rectifiers have poor power factor

• Power factor can be helped by “power factor correction” Power Electronics


81

Causes of Low Power Factor Factor--- L/R Load • Power angle is θ = tan-1(ωL/R) • For L = 1H 1H, R = 377 Ohms Ohms, θ = 45o and PF = cos(45o) = 0.707

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Causes of Low Power Factor --- Non-linear Load • Nonlinear loads include: • Variable-speed drives • Frequency converters • Uninterruptable power supplies (UPS) • Saturated magnetic circuits • Dimmer switches • Televisions • Fluorescent lamps • Welding sets • Arc furnaces • Semiconductors • Battery B tt chargers h Power Electronics


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Half Wave Rectifier with RC Load • In applications where cost is a major consideration, a capacitive filter may be used. • If RC >> 1/f then this operates like a peak detector and the output voltage is approximately the peak of the input voltage • Diode is only ON for a short time near the sinewave peaks

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Half Wave Rectifier with RC Load • Note poor power factor due to peaky input line current

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Unity Power Factor --- Resistive Load • Example: purely resistive load – Voltage and currents in phase v(t ) = V sin ωt V i (t ) = sin ωt R V2 sin 2 ωt p(t ) = v(t )i (t ) = R V2 < p(t ) >= 2R V VRMS = 2 V I RMS = R 2 V2 < p(t ) > 2R PF = = =1 VRMS I RMS ⎛ V ⎞⎛ V ⎞ ⎜ ⎟⎜ ⎟ ⎝ 2 ⎠⎝ R 2 ⎠ Power Electronics


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Causes of Low Power Factor --- Reactive Load • Example: purely inductive load – Voltage and currents 90o out of phase

v(t ) = V sin ωt V i (t ) = cos ωt ωL V2 p(t ) = v(t )i (t ) = sin ωt cos ωt ωL < p (t ) > >= 0

• For purely reactive load PF=0 load, PF 0

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87

Why is Power Factor Important? • Consider peak-detector full-wave rectifier

• Typical power factor kp = 0.6 • What is maximum power you can deliver to load ? – VAC x current x kp x rectifier efficiency – (120)(15)(0.6)(0.98) = 1058 Watts • Assume you replace this simple rectifier by power electronics module with 99% power factor and 93% y efficiency: – (120)(15)(0.99)(0.93) = 1657 Watts Power Electronics


88

Power Factor Correction • Typical toaster can draw 1400W from a 120VAC/15A line • Typical offline switching converter can draw <1000W because it has poor power factor • High power factor results in: – Reduced electric utility bills – Increased system capacity – Improved voltage – Reduced heat losses • Methods of power factor correction – Passive • Add capacitors across an inductive load to resonate • Add inductance in a capacitor circuit – Active Power Electronics


89

Power Factor Correction --- Passive • Switch capacitors in and out as needed as load changes

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Power Factor Correction --- Active • Fluorescent lamp ballast application

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91

Root Mean Square (RMS) • Used for description of periodic, often multi-harmonic, waveforms • Square root of the average over a cycle (mean) of the square of a waveform T I RMS =

1 2 i (t )dt ∫ T 0

• RMS current of any waveshape will dissipate the same amount of heat in a resistor as a DC current of the same value – DC waveform: Vrms = VDC – Symmetrical square wave: • IRMS = Ipk – Pure sine wave 0 0 pk • IRMS=0.707I • Example: 120 VRMS line voltage has peaks of ±169.7 V Power Electronics


92

Intuitive Description of RMS • The RMS value of a sinusoidal or other periodic waveform dissipates the same amount of power in a resistive load as does a batteryy of the same RMS value • So, 120VRMS into a resistive load dissipates as much power in the load as does a 120V battery Power Electronics


93

RMS Value of Various Waveforms • Following are a bunch of waveforms typically found in power electronics, power systems, and motors, and their corresponding RMS values • Reference: R. W. Erickson and D. Maksimovic, Fundamentals of Power Electronics, 2nd edition, Kluwer, 2001

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DC Voltage • Battery

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Sinewave • AC line

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96

Square Wave • This type of waveform can be put out by a square wave converter or full-bridge converter

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97

DC with Ripple • Buck converter inductor current (DC value + ripple)

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98

Triangular Ripple • Capacitor ripple current in some converters (no DC value)

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99

Pulsating Waveform • Buck converter input switch current (assuming small ripple)

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100

Pulsating with Ripple • i.e. buck converter switch current • We can use this result to get RMS value of buck diode current

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101

Triangular

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102

Piecewise Calculation • This works if the different components are at different frequencies

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103

Piecewise Calculation --- Example • What Wh t is i RMS value l off DC + ripple i l ((shown h b before)? f )?

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Harmonics • Harmonics are created by nonlinear circuits – Rectifiers • Half-wave rectifier has first harmonic at 60 Hz • Full-wave has first harmonic at 120 Hz – Switching DC/DC converters • DC/DC operating at 100 kHz generally creates harmonics at DC, 100 kHz, 200 kHz, 300 kHz, etc. • Line Li harmonics h i can be b ttreated t d by b liline filt filters – Passive – Active

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Total Harmonic Distortion • Total harmonic distortion (THD) – Ratio of the RMS value of all the nonfundamental frequency terms to the RMS value of the 2 fundamental I 2 2 ∑ THD =

n ≠1

n , RMS

I1, RMS

=

I RMS − I1, RMS I12, RMS

• Symmetrical square wave: THD = 48.3% I RMS = 1 I1 =

4 2π 2

⎛ 4 ⎞ 1− ⎜ ⎟ 2 π ⎝ ⎠ = 0.483 THD = 2 ⎛ 4 ⎞ ⎟ ⎜ 2 π ⎠ ⎝

• Symmetrical triangle wave: THD = 12.1% Power Electronics


106

Half-Wave Rectifier, Resistive Load • Simplest, cheapest rectifier • Line current has DC component; this current appears in neutral • High harmonic content, Power factor = 0.7

P.F . =

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Pavg VRMS I RMS

107

Half Wave Rectifier with Resistive Load --- Power F t and Factor d Average A Output O t t Voltage V lt Average output voltage:

1 < v d >= 2π

∫

π

0

V pk sin( i (ωt )d (ωt ) =

V pk 2π

[− cos((ωt )]

ωt =π ωt = 0

=

V pk

π

Power factor calculation: 2

2 I pk 1 ⎛ I pk ⎞ ⎟⎟ R = < P > = ⎜⎜ R 2⎝ 2 ⎠ 4

VRMS =

V pk

I RMS =

I pk 1 2 2

2

=

RI pk 2

2 I pk

R
4 = 0.707 = PF = I I VRMS I RMS ⎛ pk ⎞⎛ pk 1 ⎞ ⎜⎜ R 2 ⎟⎟⎜⎜ 2 2 ⎟⎟ ⎝ ⎠⎝ ⎠ Power Electronics


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Half-Wave Rectifier, Resistive Load --- Spectrum off L Load dV Voltage lt

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Half Wave Rectifier with RC Load • More practical rectifier • For large RC, this behaves like a peak detector

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Half Wave Rectifier with RC Load • Note poor power factor due to peaky line current • Note DC component of line current

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Half Wave Rectifier with RC Load --S Spectrum t off Line Li Current C t

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Crest Factor • Another term sometimes used in power engineering • Ratio of peak value to RMS value • For F a sinewave, i crestt factor f t = 1.4 14 – Peak = 1; RMS = 0.707 • For a square wave, crest factor = 1 – Peak = 1; RMS = 1

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Harmonics and THD - Sinewave • THD = 0% Number of harmonics N = 1 THD = 0 % 15 1.5

1

0.5

0

-0.5

-1

-1 1.5 5

Power Electronics

0

0.01

0.02

0.03

0.04

0.05


0.06

0.07

114

Harmonics and THD - Sinewave + 3rd Harmonic

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Harmonics and THD --- Sinewave + 3rd + 5th Harmonic • THD = 38.9%

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Harmonics --- Up to N = 103 • THD = 48%

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Full Wave Rectifier (Single Phase) Full-Wave

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Full-Wave Rectifier with Capacitor Filter

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6-Pulse (3-Phase) Rectifier • Typically used for higher-power applications where 3phase power is available

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12-Pulse Rectifier • T Two paralleled ll l d 6 6-pulse l rectifiers tifi • 5th and 7th harmonics are eliminated • Onlyy harmonics are the 11th, 13th, 23rd, 25th …

Reference: R. W. Erickson and D. Maksimovic, Fundamentals of Power Electronics, 2d edition Power Electronics


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Techniques for Analysis of Power Electronics Circuits • Power electronics systems are often switching, nonlinear, li and d with ith other th ttransients. i t A variety i t off techniques have been developed to help approximately pp y analyze y these circuits – Assumed states – Small ripple assumption – Periodic steady state • After getting approximate answers, often circuit simulation is used

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Assumed States • In a circuit with diodes, etc. or other nonlinear elements, how do you figure out what is happening ? • Guess….and G d th then check h k your guess 1 10 1:10

Vout

120 VAC

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Small Ripple Assumption • In power electronic circuits, generally our interest is in the average value of voltages and current if the ripple is small compared to the nominal operating point. • In DC/DC converters, often our goal is to regulate the average value of the output voltage vo. State-space averaging is a circuit approach to analyzing the local average g behavior of circuit elements. In this method,, we make use of a running average, or: t

1 v (t ) = ∫ v(τ )dτ T t −T

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Periodic Steady State • In the periodic steady state assumption, we assume that p transients have died out and that from p periodall startup to-period the inductor currents and capacitor voltages return to the same value. • In other words words, for one part of the cycle the inductor current ripples UP; for the second part of the cycle, the inductor current ripples DOWN. • Can C calculate l l t converter t d dependence d on switching it hi b by using volt-second balance.

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Motivation for DC/DC Converter: Offline Linear +5V, 50 Watt Regulator AC

Vbus

Linear Reg.

Vo

Cbus

•

Must accommodate:

•

– Variation in line voltage

IIn order d to t maintain i t i regulation:

Vbus > 5V + Vdropout

• Typically 10%

– Drop in rectifier rectifier, transformer • Rectifier 1-2V total • Transformer drop depends on load current

•

Regulator power dissipation:

•

For = 7V and Io = 10A, P = 20 Watts !

P ≈ [< Vbus > − Vo ]I o b

– Ripple in bus voltage

ΔVbus ≈

IL 120Cbus

– Dropout D t voltage lt off regulator l t • Typically 0.25-1V Power Electronics


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Offline Switching +5V +5V, 50 Watt Regulator

AC

• If switching regulator is 90% efficient, Preg = 5.6 Watts (ignoring losses in diode bridge and transformer) • Other switching topologies can do better

Vbus

Switching Reg.

Vo

Cbus

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PSIM Simulation

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PSIM Simulation

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Switcher Implementation D + Vi

vo(t)

RL

-

• Switch turns on and off with switching frequency fsw • D is “duty duty cycle, cycle ” or fraction of switching cycle that v (t) switch is closed o

Vi t DT

T

T+DT

• Average value of output = Dvi – Can provide real-time control of by varying duty cycle

• Unfortunately, output is has very high ripple at switching frequency fsw Power Electronics


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Switcher Design Issues • Lowpass filter provides effective ripple reduction in vo(t) if LC >> 1/fsw • Unfortunately, this circuit has a fatal flaw….. D

L +

Vi

C

RL

vo((t)) -

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Buck Converter • Add diode to allow continuous inductor current flow when switch is open D

L +

Vi

C

RL

vo(t) -

• This is a common circuit for voltage step-down applications • Examples E l off buck b k converter t given i llater t

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Types of Converters • Can have DC or AC inputs and outputs • AC ⇒ DC – Rectifier • DC ⇒ DC – Designed to convert one DC voltage to another DC voltage – Buck, boost, flyback, buck/boost, SEPIC, Cuk, etc. • DC ⇒ AC – Inverter • AC ⇒ AC – Light dimmers – Cycloconverters

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Ideal Power Converter • Converts voltages and currents without dissipating power p Pout Pout – Efficiency = 100% = ε= Pin Pout + Ploss • Efficiency is very important, especially at high power levels • High Hi h efficiency ffi i results lt iin smaller ll size i (d (due tto cooling li requirements) • Example: p 100 kW converter – 90% efficient dissipates 11.1 kW ⎛1 ⎞ Pdiss = Pout ⎜ − 1⎟ – 99% efficient dissipates 1010 W ⎝ε ⎠ – 99.9% 99 9% efficient dissipates 100 W Power Electronics


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Buck Converter • Also called “down converter” • Designed to convert a higher DC voltage to a lower DC voltage • Output voltage controlled by modifying switching “duty i ratio” D ratio D L

Vcc

L

Vo + R

C vc -

• We’ll figure out the details of how this works in later weeks Power Electronics


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Possible Implementations • Many companies make buck controller chips (where you supply y pp y external components) p ) as well as complete p modules

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Real World Buck Converter Issues Real-World • Real-world buck converter has losses in: – MOSFET • Conduction loss • Switching loss – Inductor I d t • ESR – Capacitor • ESR – Diode • Diode ON voltage

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Converter Loss Mechanisms • Input rectifier • Input filtering – EMI filtering – Capacitor ESR • Transformer – DC winding loss – AC winding loss • Skin effect • Proximity effect – Core loss • Hysteresis • Eddy currents • Ou Output pu filter e – Capacitor ESR Power Electronics

• Control system – Controller – Current C t sensing i d device i • Switch – MOSFET conduction loss – MOSFET switching loss – Avalanche loss – Gate driving loss – Clamp/snubber • Diode Di d – Conduction loss – Reverse recovery – Reverse current


138

NOTES 01 INTRODUCTION TO POWER ELECTRONICS.ppt [Read-Only]

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