Ned Mohan, 2001

Teaching of Switch-Mode Power Electronics Using A Building-Block Approach, Assisted by

PSpice™ Modeling

Department of ECEUniversity of Minnesota

Minneapolis, MN 55455 USA

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Please click on the Audio button, making sure that speakers are turned on.

Ned MohanEmail: mohan@ece.umn.edu

William P. RobbinsEmail: robbins@ece.umn.edu

Audio

Ned Mohan, 2001

References

1a

1. NSF-Sponsored Faculty Workshop on Teaching of Power Electronics and Electric Drives, University of Minnesota, to be held in Tempe, Arizona January 3-6, 2002. For details, contact mohan@ece.umn.edu.

2. NSF-Sponsored Faculty Workshops on Teaching of Power Electronics and Electric Drives, held at the University of Minnesota, 1991, 1994, 1997 and 1998.

Ned Mohan, 2001

Power Processing Unit (PPU)o Efficient conversion of power from line frequency AC to

appropriate form required by the load

o Rectifier: Line frequency AC to DCo Switch-Mode Converter: DC to form required by the Load

Rectifier switch - modeconverter

Load

controller

utility

−+

dV

Audio

[3]

2

Ned Mohan, 2001

• For Practicing Engineers

- Review material very quickly

- Learn new topics in a very short time

• For a First Course in Power Electronics

- Consistent Systematic Analysis of all converter topologies

- Clearly shows Switch-Mode Synthesis using PWM

- Extremely Simple Average Model Speeds up Simulations of Large Disturbances by a factor of 100 or more

- Same Average Model Allows Small-Signal Response (Bode Plots) to be obtained using PSpice™ in CCM and DCM Modes for Feedback Controller Designs

- Allows practical topics to be covered in a single-semester course

Benefits of Building-Block Approach

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Ned Mohan, 2001

References

3a

4. N. Mohan, Tutorials on A Building-Block Approach to Switch-Mode Power Electronics at IEEE-APEC, IEEE-PESC and PCIM conferences.

5. N. Mohan, Learn a True Building-Block Approach to Power Electronics and Using this Unifying Analysis (Assisted by PSpice™ Modeling) to Design Feedback Controllers in Switch-Mode dc Power Supplies, Power-Factor-Correction Circuits and Motor Drives, 4-1/2 hour video course, http://www.mnpere.com.

Ned Mohan, 2001

Buck+

-

+

--

Boost

inV

Li

oV

qA

+

-

-

+

inV

oV

Li

qA

+

-

+

-

oV

inV

Li

qA

oi

Buck/Boost

Single-Quadrant Converters for Switch-Mode DC Power Supplies

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4

Click here for Transformer-Isolated Topologies

Ned Mohan, 2001

N3

vA

-

+

iL

N1 N2

q(t)

iin

Vo

+

-Vin

inV

T1 T

3

T2T

4

D1

D2

iL+

-

VO

+

-

v1

N 1

N 2

N 2

Vo

io

Vin

iin

q(t)

+

-

+

-

4a

Audio

Single-Quadrant Transformer-Isolated DC-DC Topologies

Flyback Forward

Full-Bridge

Ned Mohan, 2001

Four-Quadrant Converters for dc- and ac-motor drives

A

B

A

B

C

MMVd

+

−Vd

+

−

ia ia

For DC Drives For AC Drives

[6]

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Ned Mohan, 2001

6. N. Mohan, Electric Drives: An Integrative Approach, year 2001 edition, http://www.mnpere.com. A review of this book appears in the IEEE Industrial Electronics Newsletter, Vol. 47, No. 3, September 2000, http://sant.bradley.edu/ienews/00_3/edrives.html.

Reference

5a

Ned Mohan, 2001

Implementation of a Bi-Positional Switch

Audio

6

Boost

triv

,c Av qAq+

( )Aq t

Ai negative=

Buck

dV

−

+

rampvrampv

,c Av

Aq−q

Ai

Buck Boost

dV

−

+

q

triv

,c AvA

q−Aq+

( )Aq t

Ai

Buck Boost

dV

−

+

0

switching power loss for a very short time

CEVonV

Ci

ON

OFF

approx switching trajectory

Ned Mohan, 2001

o Pole as a Building Block: Synthesis by PWM

PWM-IC

( )triv t, ( )control Av t

+

−

( )ANv t

( )Ai t

currentport

voltageport

dV

+

−

dAi

( )A

q t 0 or 1=( ) ( )

( ) ( ) ( )A

A

AN d

AdA

t t

t t t

v q Vi q i

= ⋅= ⋅

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Ned Mohan, 2001

TimeV(PWR_SWITCH1:out) 140

SEL>>

V(PWM_TRI1.Vtri:+) V(V2:+) 0.0

Time-I(V1) 7.35

SEL>>

I(L1) 10.5

dA A Ai d i=

Ai

AN A dv d V=

sT

,control Av

A sd T

dV

0

0

0

0

Ai

triv

,1 12 2 ˆ

control AA

tri

vd

V= +

Syn

thes

is b

y P

WM

( ) ( ) ( )A AdAi t d t i t= ⋅( ) ( ) dAN Av Vt d t= ⋅

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8

dAi

Ned Mohan, 2001

+

−

dV

+

−

( )Ad t

tri

12V

)

( )dAi t

( )ANv t

1

+

/1 2

, ( )control Av t

( )Ai t

Σ+

Average Representation of a Pole as An Ideal Transformer

PWM-IC

pole-A

( )triv t

A

N

+

−

( )ANv t

( ) or1

Aq t 0==

( )Ai t

currentport

voltageport

dV

+

−

( )dAi t

( ) ( )

( ) ( ) ( )AN A d

dA A A

v t d t V

i t d t i t

= ⋅

= ⋅

, ( )control Av t

( ) ( )

( ) ( ) ( )AN A d

dA A A

v t q t V

i t q t i t

= ⋅

= ⋅

,1 12 2 ˆ

control AA

tri

vd

V= +

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Ned Mohan, 2001

Buck/Boost

-

+

-

+

+-

-

+

-

+

-

+

-

+

Buck

+

-

+

--

inV

Li

oV

qA

Boost

+

-

-

+

inV

oV

Li

qA

Average Representation of 1-Quadrant Converters

inV inV

inV

oV oVoV

controlv controlv controlv

ˆ1/ rVˆ1/ rV

ˆ1/ rV

1 1 1

( )d t ( )d t1 ( )d t−

1

( )ˆ

control

r

vd t

V=

Audio

10

-

+

-

+

io

inVoV

Li

t

rVcontrolv

rv

sdT0

1Aq q= −

Ned Mohan, 2001

dV

+

−Ci

Bi

Ai

IC

PWM

A

B

C

n

, ( )c Av t

, ( )c Bv t

, ( )c Cv t

( )Aq t

( )Bq t

( )Cq t

triv

1f

cV

Application of Building Block – Three Phase Inverter

/1 2

( )Cd t

t r i

1

2V

( )Ai t

( )Bi t

( )Ci t

AB

Cn

( )Av t

Σ

( )Bv t ( )Cv t

( )dAi t ( )d Bi t ( )d Ci t

( )Bd t( )Ad t1

, ( )c Cv t

, ( )c Bv t

, ( )c Av t

dV

( )Ce t

( )Be t

( )Ae t

−

+

−

+

−

+

−

+

ˆt r i

12 V

ˆt r i

12 V

+

+

Σ+

+

Σ+

+

1 1

N

Switching Converter Average representation

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T i m e

0 s 4 m s 8 m s 1 2 m s 1 6 m s 2 0 m sV ( V 1 3 : + ) V ( V C _ B ) V ( V C _ C ) V ( P W M _ T R I 1 . V t r i : + ) 0 . 0

- 1 . 0

0

1 . 0

0

1−

1tr iv ,c o n t r o l Av ,c o n t r o l Bv ,c o n t r o l Cv

Time

0s 4ms 8ms 12ms 16ms 20msV(TWO_PORT1:Ncp) V(TWO_PORT2:Ncp) V(TWO_PORT3:Ncp) 0.5

0

0.5

1.0

0

0 . 5

1Ad Bd Cd

Ned Mohan, 2001

Discontinuous-Conduction Mode in DC-DC Converters

0dTs TsÄ1Ts Ä2Ts

L,DCMiL,criti

L,CCMi

0Ä1Ts Ä2Ts

Av

Li

+

-

q(t)

+

-

+

-

inV

oVAv

Li

,ACCMv,ADCMv

controlvˆ1/ rV

( )ˆ

control

r

vd t

V=

kv

kicpv 2Lv

+++

− − −

vpv

cpi

1N 2N

vpi

and are both zero in CCM.kv ik

1 2: 1: Buck, Buck/Boost

1:(1 ) Boost

N N dd

== −

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12

Ned Mohan, 2001

0

R3

8.0

R28.0

0

R1

10m

V2

0.75V

V18.5V

U1

TCLOSE = 1.5ms

12

Nvp=1

TWO_PORT1

VP1 CP1

com

mo

n

Ncp

L1

10uHIC =

C1100uF

IC =

Simulation of Large Disturbances Using the Average Model

4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8

x 1 0-3

-1

0

1

2

3

4

5

6

7

8

T ime (secs )

In

du

cto

r C

urre

nt (A

) Inductor current

swi tch ing waveform

Cycle-by-cyc le

average of the

switching waveform

Inductor current obta ined

f r o m a v e r a g e m o d e l

Fig. 6b. Inductor current profile for a load change

[5, 7, 8]

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[7]

Ned Mohan, 2001

References13a

5. N. Mohan, Learn a True Building-Block Approach to Power Electronics and Using this Unifying Analysis (Assisted by PSpice™ Modeling) to Design Feedback Controllers in Switch-Mode dc Power Supplies, Power-Factor-Correction Circuits and Motor Drives, 4-1/2 hour video course, http://www.mnpere.com.

7. G. Nirgude, R. Tirumala and N. Mohan, “A New, Large-Signal Average Model for Single-Switch DC-DC Converters operating in both CCM and DCM,” IEEE-PESC, Vancouver, Canada, June 2001.

8. N. Mohan, Power Electronics Modeling Simplified using PSpice™ (Release 9), http://www.mnpere.com.

Ned Mohan, 2001

Frequency Response for Feedback Controller Design

0

IF(( ( (V(K,0)*(-I(Eout)))/(V(VP1,VL2)*V(Ncp,0)) )<1 ) , ((1-((V(K,0)*(-I(Eout)))/(V(VP1,VL2)*V(Ncp,0))))*V(VL2,common)) , 0 )

0

CP1

-+

+-

Eout

GAIN = 1

common

VP1

V(Ncp,0) * V(VP1, common)

-V(Ncp,0)*I(Eout)

For Buck and Buck-Boost

- ++-

E1

E

IF(( ( (V(K,0)*(-I(Eout)))/(V(VP1,VL2)*V(Ncp,0)) )<1 ) , ( ( V(Ncp,0)*V(Ncp,0)*V(VP1,VL2)/V(K,0)) - (V(Ncp,0)*(-I(Eout))) ) , 0 )

VL2 KNcp

[5, 8]

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Ned Mohan, 2001

Frequency

10Hz 100Hz 1.0KHz 10KHz 100KHz 1.0MHzP(V(VOUT_AVG))

-400d

-200d

0d

SEL>>

DB(V(VOUT_AVG))-100

0

100

Frequency Response for Feedback Controller Design – cont.

CCM response

DCM response

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[5, 8]

Ned Mohan, 2001

Power-Factor-Correction (PFC) Circuito Use a boost dc-dc converter to shape the rectified current

is+

−vs

iL

+

−

Voload

vsvs

iL io

C = ∞

+

−

Vo1

Average model

1 d(t)−

V

v d t

d tV t

V

o

s

s

o

=−

∴ ( ) = −

1

1

1

( )

$ sin ωa f

vs

d(t) 1

0

oL Vi(s) =

sLd

%%

s so L L

o o

ˆ ˆV V1 1ˆ ˆi (t) = I I cos(2 t)2 V 2 V

ω−

o~ s

oL~

ˆi V1(s) =

ˆ 2 VI

Inner Current Loop:

Outer Voltage Loop:

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16

[5]

Ned Mohan, 2001

1. Consistent Systematic Analysis of switch-mode topologies

2. Clearly shows Switch-Mode Synthesis using PWM

3. Extremely Simple Average Model Speeds up Simulations of Large Disturbances by a factor of 100 or more

4. Same Average Model Allows Small-Signal Response (Bode Plots) to be obtained using PSpice™ in CCM and DCM Modes for Feedback Controller Designs

5. Allows practical topics to be covered in a single-semester course

Ideal For:

• Practicing Engineers

• For a First Course in Power Electronics

SUMMARY

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17

Ned Mohan, 2001

References

18

1. NSF-Sponsored Faculty Workshop on Teaching of Power Electronics and Electric Drives, University of Minnesota, to be held in Tempe, Arizona January 3-6, 2002. For details, contact mohan@ece.umn.edu.

2. NSF-Sponsored Faculty Workshops on Teaching of Power Electronics and Electric Drives, held at the University of Minnesota, 1991, 1994, 1997 and 1998.

3. Mohan, Undeland and Robbins, Power Electronics: Converters, Applications and Design, 2nd Edition 1995, http://www.wiley.com.

4. N. Mohan, Tutorials on A Building-Block Approach to Switch-Mode Power Electronics at IEEE-APEC, IEEE-PESC and PCIM conferences.

Continued……

Ned Mohan, 2001

5. N. Mohan, Learn a True Building-Block Approach to Power Electronics and Using this Unifying Analysis (Assisted by PSpice™ Modeling) to Design Feedback Controllers in Switch-Mode dc Power Supplies, Power-Factor-Correction Circuits and Motor Drives, 4-1/2 hour video course, http://www.mnpere.com.

6. N. Mohan, Electric Drives: An Integrative Approach, year 2001 edition, http://www.mnpere.com. A review of this book appears in the IEEE Industrial Electronics Newsletter, Vol. 47, No. 3, September 2000, http://sant.bradley.edu/ienews/00_3/edrives.html.

7. G. Nirgude, R. Tirumala and N. Mohan, “A New, Large-Signal Average Model for Single-Switch DC-DC Converters operating in both CCM and DCM,” IEEE-PESC, Vancouver, Canada, June 2001.

8. N. Mohan, Power Electronics Modeling Simplified using PSpice™ (Release 9), http://www.mnpere.com.

References (contd.)19