Power electronics
Slobodan Cuk came to Caltech in 1974 and obtained his PhD degree in Power Electronics in
1976. From 1977 until December, 1999 he was at the California Institute of Technology where
he conducted research and taught courses in Power Electronics and Fundamentals of Energy
Processing. During his 23 years at Caltech, more than 35 students obtained Ph.D. degree in
Power Electronics under his guidance. From 2000 until present, Dr. Cuk continued his research
contributions through TESLAco, the company he founded. Dr. Cuk is Fellow of IEEE and is the
inventor of numerous switching converter circuits such as the Cuk converter, the
TESLAconverter and many others.
Dr. Cuk is also the originator of the State-Space Averaging Method and more recently new
switching methods: Hybrid Switching and Storageless Switching methods, which resulted in a
number of ultra efficient, very compact and low cost switching converters for solar inverters,
AC-DC battery chargers, data center power supplies and many other Power Electronics
applications.
USC Power Research
Workshop:
Power Electronics
Dr. Slobodan Ćuk
November 18, 2011
1
What
What is
is in
in the
the name:
name:
PCSC
PCSC ’70
’70 and
and PCSC’71
PCSC’71
Power
Power Conditioning
Conditioning Specialists
Specialists
PPESC’72
PPESC’72
Power
Power Processing
Processing and
and Electronics
Electronics
PESC’73
PESC’73
Power
Power Electronics
Electronics Specialists
Specialists
2
Electrical
Electrical Engineering
Engineering at
at Caltech
Caltech
Sept.
Sept. 2010:
2010: celebration
celebration of
of 100
100 years
years of
of Electrical
Electrical
Engineering
Engineering at
at Caltech
Caltech
1910-1956:
1910-1956: High
High Voltage
Voltage Laboratory
Laboratory of
of Prof.
Prof.
Sorensen
Sorensen
19701970- 1999
1999 Power
Power Electronics
Electronics Laboratory
Laboratory (Profs.
(Profs.
Middlebrook
Middlebrook and
and Cuk)
Cuk)
3
Power
Power Electronics
Electronics at
at Caltech
Caltech ::
Started
Started in
in 1970
1970 by
by Prof.
Prof. Middlebrook
Middlebrook
as
as second
second in
in nation
nation after
after Duke
Duke 1968
1968
Both
Both academic
academic courses
courses and
and research
research
program
program on
on aa PhD
PhD level
level
PCSC’71
PCSC’71 at
at Jet
Jet Propulsion
Propulsion Laboratory
Laboratory
PESC’73
PESC’73 at
at Caltech
Caltech
4
Power
Power Electronics
Electronics Group
Group (( PEG)
PEG)
From
From 1970
1970 –– 1999
1999
36
36 PhD
PhD students
students
1998:
1998: 11
11 PhD
PhD in
in Electrical
Electrical Engineering
Engineering out
out of
of
which
which 55 in
in Power
Power Electronics
Electronics
Prof.
Prof. Middlebrook
Middlebrook retired
retired in
in 1998
1998
Prof.
Prof. Cuk
Cuk semi-retired
semi-retired in
in 1999
1999
5
First
First Sponsors
Sponsors 1974
1974 and
and on
on
NASA
NASA (( subcontract
subcontract from
from TRW)
TRW)
NOSC
NOSC (( Naval
Naval Ocean
Ocean System
System Center
Center
(San
(San Diego
Diego ))
ONRONR- Office
Office of
of Naval
Naval Research
Research
IBM
IBM
Other
Other companies
companies
6
Boost Converter
S
Vg
V g/(1-D)
CR
L
C
+
-
R
S
TON
TOFF
TS
t
1973: Prof. Middlebrook sent me an
article with boost converter
7
Power
PowerElectronics-Emerging
Electronics-Emergingfrom
fromLimbo
Limbo
1973
1973keynote
keynoteby
byW.E.
W.E.Newell,
Newell,Westinghouse
Westinghouse
8
35
35 Years
Years Anniversary
Anniversary
State-space
State-space Averaging
Averaging
*Slobodan Ćuk; “MODELING, ANALYSIS, AND
DESIGN OF SWITCHING CONVERTERS”
Ph.D. Thesis, Caltech, November 1976
*R.D.Middlebrook and Slobodan Ćuk; “A general
Unified Approach to Modeling SwitchingConverter Power Stages, IEEE PESC, 1976
9
35
35 Years
Years Anniversary
Anniversary
State-space
State-space Averaging
Averaging
*Slobodan Ćuk; “MODELING, ANALYSIS, AND
DESIGN OF SWITCHING CONVERTERS”
Ph.D. Thesis, Caltech, November 1976
*R.D.Middlebrook and Slobodan Ćuk; “A general
Unified Approach to Modeling SwitchingConverter Power Stages, IEEE PESC, 1976
10
The State-space Averaging Uses Different Criteria
1.
2.
Flux Balance on All Inductors
Charge Balance on All Capacitors
iC(t)
C: Charge Balance
L1: Flux Balance
vL1(t)
vL2(t)
+
+
0
t
0
L2: Flux Balance
+
t
t
0
−
−
−
DTS
(1-D)TS
DTS
L1
Vg
+
D
S
DTS
(1-D)TS
C
L2
−
(1-D)TS
V/Vg=D/(1-D)
−
1-D
CR
+
R
Ćuk Converter*
*US
*USPatents:
Patents:4,184,197;
4,184,197;4,257,087;
4,257,087;4,274,133
4,274,133
11
vL1(t)
Vg
0
+
t
Flux
FluxBalance
Balanceon
onLL11
vvL1L1==DV
DVgg++(1-D)(V
(1-D)(Vgg-V
-VCC))
−
Vg-VC
DTS
iC(t)
(1-D)TS
I1
+
Charge
ChargeBalance
Balanceon
onCCrr
t
0
−
I2
DTS
(1-D)TS
vL2(t)
VC-V
0
Flux
FluxBalance
Balanceon
onLL22
+
t
−
V
DTS
iCiC==D(-I
D(-I22))++(1-D)(I
(1-D)(I11))
(1-D)TS
vvL2L2==D(V
D(VCC-V)
-V) ++(1-D)(-V)
(1-D)(-V)
DC
DCSolution:
Solution:VVL1L1==0;
0; ICIC==0;
0; VVL2L2==00 12
State-space Formulation of Flux and Charge Balances
ON-time Interval:
L1
+
+
−
C
−
OFF-time Interval:
L1
L2
−
+
+
−
+
C
−
L2
−
−
C
Vg
+
D×
{
vL1 = Vg
iC = -I2
vL2 = VC-V
+
−
R
C
Vg
+
(1-D) ×
{
R
vL1 = Vg-VC
iC = I1
vL2 = -V
State-space Averaging DC Model:
1.
1.
2.
2.
3.
3.
Multiply
Multiplyequations
equationsfor
forON-time
ON-timeby
byDD
Multiply
Multiplyequations
equationsfor
forOFF-time
OFF-timeby
by(1-D)
(1-D)
Add
Addtogether
togetherand
andset
setVVL1L1=0,
=0,ICIC=0,
=0,VVL2L2=0
=0
13
Steady-State
AX + bVg = 0
A = DA 1 + D' A 2
b = Db 1 + D' b 2
Dynamic (Small Signal AC) Response
vg = Vg + v$g ; x = X + x$
d = D + d$ ; d ' = D'−d$
x&$ = Ax$ + bv$ +  A − A X +  b − b V d$
g  1 2 
 1 2  g 
14
SCAMP
Switching
Switching
Converter
Converter
Analysis
Analysis and
and
Measurement
Measurement
Program
Program
15
Coupled-Inductor Isolated Ćuk Converter
16
Manu Driven Graphics on First IBM-PC
From Paper at APEC Conference
17
Frequency Response – Loop Gain
18
Power
PowerElectronics
ElectronicsGroup
Group exhibit
exhibit at
at1983
1983
conference
conferencein
inSan
SanDiego
Diego
19
Question
Question asked:
asked:
Can
Can your
your SCAMP
SCAMP program
program do
do this:
this:
Enter
Enter desired
desired frequency
frequency plot
plot then
then
Draw
Draw the
the converter
converter topology?
topology?
20
Related
Related question:
question:
Can
Can you
you enter
enter desired
desired DC
DC voltage
voltage
gain
gain such
such as
as V/Vg
V/Vg == D
D xx D
D and:
and:
DRAW
DRAW ALL
ALL SUCH
SUCH CONVERTERS:
CONVERTERS:
Both
Both known
known converters
converters and
and
NEW
NEW (!!!)
(!!!) converter
converter topologies?
topologies?
21
CONFIDENTIAL
CONFIDENTIAL
Computer
Computer Generated
Generated Converters*
Converters*
Vg
L1
S1
S2
S'1
S'2
If Solution to:
C2
L2
C1
2 Inductors
1 Capacitor
2 States: ON&OFF
}
AX + bVg = 0
R
1 million
possibilities
exists, than:
Valid DC-DC Converters:
Only
Only30
30Working
Working
(Ćuk
(Ćukconverter
converter
was
wasthere
theretoo
too!)!)
*Dragan
*DraganMaksimovic,
Maksimovic,“Synthesis
“Synthesisof
ofPWM
PWMand
andQuasi-resonant
Quasi-resonant
DC-to-DC
DC-to-DCPower
PowerConverters”,
Converters”,Ph.D.
Ph.D.Thesis,
Thesis,January
January12,
12,1989,
1989,
Caltech,
Caltech,Pasadena
Pasadena
22
Enumeration via Incidence Matrices
AN EXAMPLE: (243, 146.2)
L
2
3
3
C2
L2
L1
1
1
2
L1
C1
Vg
C2
C1
Vg
R
R
0
Vg C1 C 2
2
0
L1
L2
0 −1
0
0  −1 −1
0 −1
1  1
0 −1
0 +1 
1
0
2  0


0
1
1
0
3  0
↑
↑
T1
E
1444
244431
H1
Vg C1 C 2
L1
L2
0
0  − 1 −1 −1 − 1
0 
0
0
0
1  1
1
0
0
1
2  0


1 −1 
3  0
0
1
↑
↑
T2
E
1444
244432
H2
23
NEW CONVERTER
One Transistor, Three Diodes
L
2
T
D1
D3
C1
C2
D2
L
1
M (D) = D
2
( 243, 146.2 )
24
Dr.
Dr. Ćuk’s
Ćuk’sPower
PowerTechnics
Technics1988
1988 cover
cover
1988
fs=500kHz
Ploss=20.5W
η=83%
β=20.5%
25
Power
PowerElectronics
Electronics 117
117class
classof
of 1998:
1998:
TESLA
TESLAtemple
templeprank
prank
26
TESLAco
TESLAco years:
years: 19991999- present
present
TESLAconverter
TESLAconverter
NCT
NCT converter
converter
Hybrid
Hybrid Switching
Switching Method
Method
Storageless
Storageless Switching
Switching Method
Method
Bridgeless
Bridgeless PFC
PFC converters
converters
Single-stage
Single-stage converters
converters
Solar
Solar inverters
inverters
27
Isolated Full-bridge Buck Converter
Two magnetic components
L
S1
S2
D1
DVg
D2
1:1
+
Vg
C
−
S3
S4
R
T
D3
D4
Total of 8 Switches
28
Square-wave Switching:
No 3 switches allowed
Eight needed for isolation
No capacitors
Hybrid-Switching Method:
3 switches only
Resonant capacitor
Resonant inductor
29
What about converters with
3 switches
1. Three Switches
2. A Resonant Capacitor
3. A Resonant Inductor
S1
CR
S2
Cr
Lr
30
“Birth
“Birth ”” of
of Hybrid-Switching
Hybrid-Switching Method
Method
and
and Related
Related Converter
Converter Topologies
Topologies
#1
#2
#3
#4
#5
#7
#6
#9
#8
31
AC-DC
Converter Comparison
32
Conventional
ConventionalThree
ThreePower
PowerProcessing
ProcessingStage
StageApproach
Approach
LB
DB1
L
DB 400V
S1
DB2
S2
Lf
vac
D1
48V
D2
n:1
SB
Cf
+
−
+
CB
S3
DB3
DB4
C
−
R
S4
D3
D4
33
Polarity Inverting
DC-DC Converter
34
Boost Converter
S
Vg
V g/(1-D)
CR
L
C
+
-
R
S
TON
TOFF
TS
t
Problem
How to make a polarity inverting boost
converter
35
Polarity Inverting 3 Switch Boost Converter*
L
S
Vg
L
Vg
Lr CR1
Cr IC
+ Vr
IL
CR2
S
V
R
V=Vg/(1-D)
Boost Converter
CR2
Cr I
C
+ Vr
S
+
C
Cr IC
+ Vr
IL
I
Resonant
Discharge
Vr=Vg/(1-D)
Lr CR1
C
I
+
V=Vr
R
*US Patent No. 7,778,046
OFF-time
Interval (1-D)TS
36
Positive
Positiveand
andNegative
NegativeHalf-cycle
Half-cycleof
ofInput
InputVoltage
Voltage
L
+
IL A Cr Ir
+ +
iS
VCr
D
Vg
-
S
-
CR2
Lr
I
V
D'
D
CR1
C
+
-
R
VCr=0
G
L
Vg
+
IL A
i
S
D
S
+
G
Cr
- +
VCr
Ir
Lr
CR2
I
V
V=Vg/(1-D)
D
D'
CR1
C
+
-
R
VCr=V
Source
SourcePolarity
PolarityControls
ControlsConduction
ConductionInterval
Intervalof
ofTwo
TwoDiodes:
Diodes:
Full-Bridge
Full-Bridge Eliminated
Eliminated
37
True Bridgeless
PFC Converter
38
True
TrueBridgeless
BridgelessPFC
PFCConverter*
Converter*
iAC
L
iS
vAC
D
S
+
Cr Ir
- +
VCr
Lr
CR2
CR1
I
C
+
-
V
R
Input Voltage
110V
THD=1.7%
PF=0.999
*US
*USand
andforeign
foreignpatents
patentspending
pending
39
One
OneImplementation
Implementationof
ofthe
theControlling
ControllingSwitch
Switch
ION
S1
I
D
VOFF
S2
III
L
vAC
IL A
D
S1
S2
Cr Ir
+ VCr
Lr
CR2
CR1
I
C
+
-
V
R
40
Input
Input Current
Current Modulation
Modulationfor
forEach
EachPhase
Phase
at
at High
HighSwitching
SwitchingFrequency
Frequency
S
TON
TOFF
t
TS
vi, ii
vi
ii
Index "i" =1, 2, 3
t
41
Voltage

Voltageand
andCurrent
CurrentWaveforms
Waveformsin
inĆuk-rectifier
Ćuk-rectifier

with
withIntegrated
IntegratedMagnetics
MagneticsImplemented
Implemented
Input Voltage
110V
THD=1.7%
PF=0.999
Input Voltage
220V
THD=2.0%
PF=0.991
42
Efficiency

Efficiencyand
andPower
PowerLoss
Lossof
ofĆuk-rectifier
Ćuk-rectifier

99%
98%
97%
95%
94%
93%
92%
91%
90%
80
100
120
140
160
180
200
220
240
Input Voltage [V]
12.0
10.0
8.0
Power Loss
Efficiency
96%
6.0
4.0
2.0
0.0
80
100
120
140
160
180
Input Voltage [V]
200
220
240
43
Demo #1:
400W Bridgeless
PFC converter
44
45
46
True Isolated
Bridgeless
PFC Converter
47
True
TrueBridgeless
BridgelessPFC
PFCConverter
Converter with
withIsolation*
Isolation*
iAC
IM Cr2
L
vAC
S
Cr1
NP
NS
CR2
Lr
CR1
C
V
+
−
R
PFC IC Controler
S
TON
TOFF
TS
vAC, iAC
t
vAC
iAC
t
*US
*USand
andforeign
foreignpatents
patentspending
pending
48
True
TrueAC
ACTransformer
Transformer
+BS
BS
2BS
-BS
H
No Air-gap
No Energy Storage
Automatic Reset
Scalable to High Power
49
Comparison
Comparison
Power Processing
Single-stage
Three-stage
Type of Converter
Isolated Bridgeless PFC
Switching Method
HYBRID
Bridge-Boost PFC-Fullbridge
Square-wave
3
14
Switch-voltage Stress
Low
High
Lossless-switching
YES
NO
Simple
Complex
1
4
3%
10%
Efficiency
>97%
88% to 90%
Size
Small
Big
Weight
Light
Heavy
Cost
Low
High
Number of switches
Control
Magnetics pieces
Power Losses
50
Three-Phase
AC-DC
Converter Comparison
51
Present
Present Approach:
Approach:Two
TwoStages
Stages
First
First Stage:
Stage: Rectification
Rectification and
and PFC
PFC
Efficiency
Efficiency == 98%
98%
i0
v0
v240
L1
Q1
Q2
Q3
L2
L3
+VH
C
Q4
Q5
Q6
Three-phase properties prematurely
lost after rectification and PFC control
52
Second
SecondStage:
Stage: Isolated
IsolatedDC-to-DC
DC-to-DCconverter
converter
Second
Second Stage:
Stage: DC
DC Isolation
Isolation
Efficiency
Efficiency == 95%
95%
+VH
L
S1
S2 D1
V
D2
n:1
+
C
C
S3
S4
D3
−
R
D4
Power processed sequentially in Two stages so
Low Total Efficiency of 92%
53
New Single-stage
Three-phase Rectifier
54
55
56
New
New Direct
Direct Three-Phase
Three-Phaseto
toDC
DCConversion
Conversionwith
with
PFC
PFCand
andIsolation
Isolationin
inaaSingle
SingleStage
Stage
i01
i1
98%
v1
n
v3
Isolated Bridgeless PFC
Phase 1
v2 i
2
98%
i02
Isolated Bridgeless PFC
Phase 2
+V
C
R
i03
i3
98%
i0
Isolated Bridgeless PFC
Phase 3
Power processed in parallel and not in series
Each
EachPhase
PhaseEfficiency
Efficiency98%;
98%; TOTAL
TOTALEfficiency
Efficiency98%
98%
57
AC-DC
AC-DCConverter
Converter for
for Each
EachPhase
Phasewith
withPFC
PFCand
andIsolation*
Isolation*
ii
L
vi
S
Cr1
NP
Cr2
Lr
NS
CR1
CR2
C
V
+
−
R
Islolated
Bridgeless PFC IC
Three
ThreeSwitches
SwitchesOnly
Only
*US
*USPatent
PatentNo.
No.7,778,046
7,778,046
58
Three-Phase
Three-Phase Ćuk-rectifier
Ćuk-rectifier with
with PFC
PFC IC
IC
Control
Control
i1
v1
n
v3
v2
Bridgeless
3-phase Isolated
PFC Converter
i2
C
R
i3
3-phase Isolated
Bridgeless PFC IC
59
Sum
Sumof
ofInstantaneous
InstantaneousOutput
OutputPowers
Powersof
of
Three
ThreePhases
Phasesis
isConstant
Constant
1.75
po1, po2, po3, P
P
1.5
1.25
po1
1
po2
po3
0.75
0.5
0.25
0
0
60
120
180
240
300
360
60
Sum
Sumof
ofInstantaneous
InstantaneousOutput
OutputCurrents
Currentsof
ofEach
Each
Phase
Phaseis
isConstant
Constant
io1,io2,io3,I
1.75
I
1.5
1.25
io1
1
io2
io3
0.75
0.5
0.25
0
0
60
120
180
240
300
360
61
Constant
Constant Output
OutputPower
Powerand
andConstant
ConstantOutput
OutputVoltage
Voltage
Lead
Leadto
toConstant
ConstantOutput
OutputCurrent
Current
v(t)
i0(t)
V
I
t
0
i01+ i02+ i03
t
0
P = constant
V = constant
I = constant
62
“Birth
“Birth ”” of
of Storageless
Storageless Switching
Switching Method
Method
and
and Related
Related Converter
Converter Topologies
Topologies
#1
#2
#3
#4
#5
#7
#6
#9
#8
63
Demo #2:
200W DC-DC converter
48V to 24V
64
CONFIDENTIAL
CONFIDENTIAL
Power
PowerStage
Stageof
of200W
200WStorageless
StoragelessConverter
Converter
65
CONFIDENTIAL
CONFIDENTIAL
Bi-directional Specifications
Switching Frequency:
50kHz
Input Voltage:
48V
Output Voltage:
24V
Output Current:
4A
Power:
200W
Volume :
0.2in3
Power Density:
1kW/in3
No Heat Sink
No Forced Air Cooling
66
CONFIDENTIAL
CONFIDENTIAL
200W,
200W, 48V/24V
48V/24VStorageless
StoragelessĆuk-buck
Ćuk-buckConverter
Converter
67
CONFIDENTIAL
CONFIDENTIAL
Efficiency
Efficiencyof
of200W
200WStorageless
Storageless Converter
Converter
Efficiency vs Output Power
100.0%
Efficiency
99.5%
99.0%
98.5%
98.0%
97.5%
97.0%
0
25
50
75
100
125
150
175
200
Output Power (W)
68
**
Power
Stage
of
750W,
48V
Prototype
Power Stage of 750W, 48V Prototype
Storageless

Storageless Buck
Buck Converter
Converter

Efficiency
Efficiency over
over 99%
99%
*US
*
USand
andforeign
foreignpatents
patentspending
pending
69
Efficiency
Efficiency of
of 750W,
750W, 100V
100V to
to 48V
48V Converter
Converter
100.0%
Efficiency
99.5%
99.0%
98.5%
98.0%
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Iout (A)
70
**
Isolated
Storageless
Converter
Isolated Storageless Converter
*US
*
USand
andforeign
foreignpatents
patentspending
pending
71
Efficiency
Efficiency of
of Isolated
Isolated Storageless
Storageless Converter
Converter
98.2% efficiency
360V to 24V Efficiency
100.00%
95.00%
Eff
90.00%
85.00%
80.00%
75.00%
0.00
50.00
100.00
150.00
200.00
250.00
300.00
350.00
Output Power (W)
360V to 24V Efficiency
72
Green
GreenDream
DreamPower
PowerTechnology™
Technology™
Efficiency
98%
i1
v1
n
v3
v2
99%
48V
i2
3-phase Isolated
Bridgeless PFC
C
97%
12V
3 switchbuck
non-isolated
1V
3 switch
POL
R
i3
3-phase Isolated
Bridgeless PFC IC
Switching
method
Hybrid
Storageless
POL
73
Applications
Applications Summary
Summary
- Computer servers
Battery chargers for electric
cars and bycycles
- Desktop computers
- AC Adapters, projectors, etc.
-Solar photovoltaic conversion
-LED lighting
VRM (12V to 1V regulators)
74
Applications
Applications Summary
Summary
-Wide range of power
-From cell hones and under a
one 1 Watt to 100kW for electric
drive for motors, etc.
75
July
July10,
10, 2010
2010:: Memorial
Memorialfor
forProfessor
Professor Middlebrook
Middlebrook
76
July
July10,
10, 2010
2010:: Power
PowerElectronics
ElectronicsGroup
GroupMembers
Members
and
andtheir
theirrelatives
relatives
77