Switched Mode One-Quadrant Power Converters...Switched Mode One-Quadrant Power Converters - R....

Switched ModeOne-Quadrant Power Converters

R. Petrocelli

Switched Mode One-Quadrant Power Converters - R. Petrocelli - 2014 2

Summary

● Power Electronics. Basics definitions and rules

● Basic DC-DC Power Converters

● Control of DC-DC Power Converters

● Derived Topologies

● Other Issues


Power converter Definition

ElectricalEnergySource

ElectricalLoad

PowerConverter


Clasification of Power converters

DC

AC

Source Load

DC/DC

Rectifier

DC

Inverter

ACCycloconverterMatrix converter


One-Quadrant Definition

ElectricalEnergySource

ElectricalLoad

PowerConverter

Energy flow

Vo

Io


One-Quadrant Power Converter in Particle Accelerators

IL

C

F

C

B

BFB

LB

L

B

G G


Power ElectronicsBasic Definition and Rules

● Sources Definition

● Basic Rules

● Interconnection Rules


Type of Sources

Voltage Source• A voltage source is able to impose a voltage

regardless of the current flowing through it. VV

C

• In a more open sense, if the voltage across and element can not have discontinuities in time due to the current flowing through it


Source Type

Current Sources

A current are able to impose current regardless the voltage across its terminals.

Similar to the voltage sources this can be extended to elements which current can not have discontinuities.

L

I


Basic Rules

• Rule 1: A voltage source must never be short-circuited

V I


Basic Rules

• Rule 2: A current source must never be open-circuited

I V →∞


Basic Rules

• Interconection Rules

S

V 1 V 2

S must not be closed Unless V 1=V 2

SI 1 I 2

S must not be open Unless I 1=−I 2


Interconection Rules

S1

V 1 S2I 1

S1S1S1S1S1 Basic Commutation Cell

S1

S2

open open Not allowed

open closed Allowed

closed open Allowed

closed closed Not allowed


Basic DC-DC Converter

● Chopper

● Buck Converter

● Boost Converter

● Buck-Boost Converter


S1

V S RL

tT

VO

D T

S1Closed S1Open

VS

DC Chopper

• Resistive Load


DC Chopper

• Inductive Loadload

S1

V O RLV S

LL

D1

• Application: Motor control


Chopper Waveforms

V S

S1

RL

LL

D1

S1

V S D1

V S

V O

S1Closed S1OpenD T T t

I L

I L

D T T t

I S1I D1

I L=V S D

RL


Buck Converter

VS D

L

R

S

C VO

+ -VL

iL

iS

iC

iC

iO


(V S−V O)D T =V O(1−D)T

iL

iS

iC

iD

t

t

t

t

VL

t

VS-V

OV

S-V

O

-VO

VS D

L

R

S

C VO

+ -VL

iL

iS

iC

iC

iR

Faraday Law : volt-second product of the inductor voltage should be zero for steady-state operation

Buck Converter


Output-Input Voltage Ratio

V O

V S

D

M V ≡V O

V S

=D


Lb=(1−D) R

2 f

Cmin=(1−D)V O

8 V r L f 2

Inductance for boundary between CCM and DCM

Minimum capacitance for an output voltage ripple V

r


Continuous and Dis-Continuous Mode

iL

VL

t

VS-V

OV

S-V

O

-VO

iO

DT T

iL

VL

t

VS-V

OV

S-V

O

-VO

iO

DT TΔT


CCM and DCM Boundary

D

I OB

I OB MAXiOB=D T2 L

(V S−V O)=T V S

2 L(D−D2

)

I OB MAX=

T V S

8 L


iL

VL

t

VS-V

OV

S-V

O

-VO

iO

DT TΔT

(V S−V O)D T =V O Δ T

V O

V S

=D

(D+ Δ )

I O=I Lpeak

(D+Δ)T

2 T

I Lpeak=

V O Δ T

L

I O=4 I OB MAXD Δ


Output-Input Voltage Ratio in DCM

V O

V S

=D2

(D2+14

I O

I OB MAX)

D=0.90

D=0.75

D=0.50

D=0.25

D=0.10

V O

V S

I OB

I OB MAX


Buck Converter

• Widely used. Even for high power converters

● Advantages:

● Simple

● Linear output-input voltage ratio. It makes easier the control.

● Smooth output current.

● Disadvantages:

● Discontinuous input current

● No isolation.


Boost Converter

VS

DL

RS C VO

+ -

iL

iS

iC

iD

iO

VL


Boost Converter

V S D T=(V O−V S )(1−D)T

M V ≡V O

V S

=1

(1−D)

iL

iS

iC

t

t

t

VL

t

VS

VS-V

O

iD

t

Lb=(1−D)

2 D R2 f

Cmin=D V O

V r R f

VS

DL

RS C VO

+ -

iL

iS

iC

iD

iO

VL

Faraday Law :


Boost Converter: Output-Input Voltage Ratio

V O

V S

D

M V ≡V O

V S

=1

(1−D)


Boost Converter

• Output voltage higher than input voltage

● Advantages:

● Simple

● Smooth input current.

● Disadvantages:

● Discontinuous output current. Stress the output capacitor

● No isolation.


Buck-Boost Power Converter

VO

iO

VS

D

L RC

+

-

iL

iS

iC

iD

VL


iL

iS

iC

t

t

t

VL

t

VS

VO

iD

t

V S T D=−V O (1−D)T

M V ≡V O

V S

=−D

(1−D)

Lb=(1−D)2 D R

2 f

VO

iO

VS

D

L RC

+

-

iL

iS

iC

iD

VL


Buck-Boost Converter: Output-Input Voltage Ratio

−V O

V S

D

M V ≡V O

V S

=−D

(1−D)


Buck-Boost Converter

Reverse voltage polarity

● Advantages:

● Simple

● Step-down and step-up

● Disadvantages:

● Discontinuous input and output current.

● No isolation.


Control of DC-DC Power Converters

● Regulation

● Pulse-Width Modulation. (PWM)

● Current Mode

● Variable Structure Control


Control of Switched Mode DC-DC Power Converter

s(t )={1 when the switch is on0 whenthe switch is off }

Switching function.

Definition:

The switching function, S(t), has a value of 1 when the corresponding physical

switch is on and 0 when it is off.

Switching functions are discrete-valued functions of time, and control of

switching devices can be represented with them.


Power Converter Block Diagram


Regulation – Feedback

● Close loop, the output voltage is sensed and the feedback controller acts to get the wished value.

● Stability issues


Regulation – Feed-Forward

● It is very fast. Perturbations do not have to reach the output in order to be compensated.

● It need a good model of the converter in order to design the controller.

● Usually is used together with a feedback loop.


Constant Frequency PWM

v D

c(t )

S (t )

t

t

tT

S (t )

v D

c(t )


Variable Frequency PWM

constant off-time, variable on-time

t on1

t

t

S (t )

v D

c(t )

t off t on2 t off t offt on3

constant off-time, variable on-time

constant on-time, variable off-time


Current Mode Control (CMC)

t

t

v D iL(t )

t

TS (t )

T

VS D

L

R

S

C

iL

S

RQ

s( t)

v D

latch


Current Mode Control

The CMC controls the inductor current. An outer control loop is needed

for output voltage regulation.

Advantages:

● Simple

● Low cost

● Easy input voltage feed-forward

Disadvantages

● Sub-harmonic oscillation for D>0.5 . An slope compensation solves

this problem.


Variable Structure Control

It is a nonlinear control which generates the switching function according

to the state-space variables of the system.

Advantages:

● Low sensitivity to plant parameter uncertainty

● Robustness

Disadvantages

● Chattering

● Variable frequency


Variable Structure Control

Hysteresis control

t

VS D

L

R

S

C

iL

s(t)

v D

t

v DV R

S (t )


Derived Topologies

● Half Bridge Converter

● Push-Pull Converter

● Full Bridge Converter

● Forward Converter

● Flyback Converter

● Ćuk Converter


Derived Topologies

L

RC VO

+-

VL

iC

iR

VS

D1

-

n1

n2

D2

V S

2

V S

2

S1

S2

+

-

iL

VP

+

-

Half Bridge Converter


VP

t

V S

2

−V S

2 T2

TD T

Transformer Input Waveform

● Volt-second product over a period must be zero to avoid transformer saturation


Push-Pull Converter

L

RC VO

+-

VL

iC

iR

VS

D1

-

n1

n2

D2

S2

+

-

iL

-

S2

S1

M V ≡V O

V S

=2 Dn2

n1

Derived Topologies


Full Bridge Converter

L

RC VO

+-

VL

iC

iR

VS

D1

-

n1

n2

D2

S2

S4

+

-

iL

VP

+

-

S1

S3

M V ≡V O

V S

=2 Dn2

n1

Derived Topologies


Forward Converter

S L

RC VO

+ -VL

iC

iR

VS

D1

D2

D2

D3

n1

n2

n3

M V ≡V O

V S

=Dn2

n1

n1 D≤n3(1−D)

Derived Topologies


Flyback Converter

S

RC VO

iC

iR

VS

D

n1

n2

M V ≡V O

V S

=n2

n1

D1−D

Derived Topologies


Derived TopologiesĆuk Converter

VS

D

L1

RS VO

iS

iC

iR

i L1i L2

L2

C1

C2

I L2D T =I L1

(1−D)T

P IN =V S I L1=−V O I L2

=POUT

M V ≡V O

V S

=D

(1−D)


Derived TopologiesĆuk Converter

There is also an isolated version.

The inductors can be integrated using only one magnetic core

Advantage:

● Smooth input and output current

Disadvantage:

● More components


Other Issues

● Synchronous Rectification

● Interleaved Converters

● Hard Switching, Snubbers and Soft Switching

● DC-DC Resonant Converters

● References and Further Readings


Synchronous Rectification

PD=V F I O(1−D)

η=V O I O

V O I O+ V F I O(1−D)=

V O

V O+ V F (1−D)

Conduction losses VF = diode forward voltage drop

S1

L

RC VR

VS

S2

Efficiency is low for low output voltage power converters


Power Losses in Diode and MOSFET

I O [ A]

P [W ]

Diode

MOSFET


Interleaved Converters

VS R V

O

D11

L11

S11

D12

L12

S12

D1N

L1N

S1N

2π0N

2π1N

2π(N −1)

N

CIN

COUT

iO1

iO2

iON

iO


Interleaved Converters: Output Current


Normalized Output Current Ripple

Io pk− pk

Io pk−pk [N =1]

D

N=1

N=2

N=3

N=4

N=5


Normalized Input Capacitor RMS Current

I C (RMS )

D

N=1

N=2

N=3

N=4 N=5

I O=1 A. Δ I ON=0.30 I ON .


Hard Switching

S

I SW

V SW

V SW

I SW

Switch on

Switch off

V SW

I SW

t

ESW


Snubbers

V SW

I SW

Switch on

Switch off EnergyTransfered to The snubber

V SW

I SW

t

S

I SW

V SW

R

C

snubber


Soft Switching

V SW

I SW

Switch on

Switch off

V SW

I SW

t

ESW


Soft Switching

v A

M 1D1

C1/C 2

M 2D2

C1/C 2

iL

t

t

M 1

V GS1

V GS2

V S

D1

D2

C2

C1

L

CO RO

M 2iL

M 1

v A


DC-DC Resonant Converters

Resonant Converters operates by applying a square voltage or current generated by switches to a a resonant circuit.

● Series resonant converter

LrC r

ir

R

Lr

ir

RC r● Parallel resonant converter

The converters operate at frequencies close to the resonant frequency.

The energy transferred to the load is controlled by changing the operating frequency.


LCC and LLC Resonant Converters

● LCC resonant converter

– Disadvantages: two capacitors

● LLC resonant converter

– Advantage: the two inductances can be integrates into one magnetic component

C r2

LrC r1

R

LrC r1

RLm


LLC Resonant Converters

V O

D1

D2

C2

C

LrC r

M 2ir

M 1

v A

n1

n2

+

-+

D3

D4

L

R


LLC Converter Waveforms. ZVSv A

M 1D1M 2D2

ir

t

t

M 1

V GS1

V GS2

D1

t

t


DC-DC Resonant Converters

● High Efficiency – Soft switching operation

● High operating frequency – small reactive components

● High power density

● More complex control

● Stress in semiconductors (large voltages and currents)


References and Further Reading

● MOHAN, Ned; UNDELAND, TORE M.; ROBBINS, W. P. Power electronics: converters, applications and design, 1995. 1997. ISBN: 978-0471226932

● RASHID, Muhammad H. (ed.). Power electronics handbook. Academic Pr, 2001.. ISBN: 978-0123820365

● BORDRY, F. Power converters: definitions, classification and converter topologies. CAS CERN Accelerator School and CLRC Daresbury Laboratory. 2004.

● SHEEHAN, Robert; ANATOLE, Hilton. Understanding and Applying Current-Mode Control Theory. En Power Electronics Technology Exhibition and Conference, Dallas. 2007. p. 1-26.

● HUNG, John Y.; GAO, Weibing; HUNG, James C. Variable structure control: a survey. Industrial Electronics, IEEE Transactions on, 1993, vol. 40, no 1, p. 2-22.

● MAPPUS, Steve. Synchronous rectification for Forward Converters. Fairchild Semiconductor Power Seminar 2010-2011.

● HEGARTY, T. Benefits of multi-phasing buck converters. EE Times–India, 2007, p. 1-4.

● HUANG, Hong. Designing an LLC resonant half-bridge power converter. En TI Power Supply Design Seminar SEM1900. 2010.


Thank You !

Switched Mode One-Quadrant Power Converters...Switched Mode One-Quadrant Power Converters - R....

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