Control of a Boost Inverter Using Z-source for Fuel Cell ... · Control of a Boost Inverter Using Z-source for Fuel Cell Systems Jin-Woo Jung, Ph. D. Student Advisor: Prof. Ali Keyhani

Mechatronics Lab./33

Control of a Boost Inverter Using Z-source for Fuel Cell Systems

Jin-Woo Jung, Ph. D. Student

Advisor: Prof. Ali Keyhani

Sep. 26, 2003 (IAB’ 03)

Mechatronics LaboratoryDepartment of Electrical Engineering

The Ohio State University

1


ORGANIZATION

I. Introduction

II. Circuit Analysis/System ModelingA. Circuit analysis of Z-source InverterB. System ModelingC. Modified Space Vector PWM

III. Control System DesignA. Discrete Sliding Mode Current ControllerB. Discrete Optimal Voltage ControllerC. Discrete PI DC-link Voltage Controller

IV. Simulation Results

V. Conclusion

2


I. INTRODUCTION

Why are fuel cell systems increasingly used in industry?

• Renewable power generation technologiesWind turbines and photovoltaic cells⇒ Full-grown technologies⇒ Climate constraintsFuel cells⇒ Regardless of climate conditions⇒ Hydrogen and oxygen⇒ Products: electricity, heat, and water⇒ Efficiency: electricity (40%), co-generation (80%)

Fig. 1 Fuel cell generation systems.

StacksChemical energy

toElectrical energy

Hydrogen

Oxygen

Natural gasPropane

MethanolGasoline

Reformer

Air

Power ConverterDC power

3


I. INTRODUCTION

Features of fuel cell systems

• Types of fuel cells Proton-Exchange-Membrane (PEM), Phosphoric Acid (PA), Molten Carbonate (MC)Solid Oxide (SO), Alkaline, Zinc-Air (ZA) fuel cells, etc.

• Applications of fuel cellsStationary (buildings, hospitals, etc), Residential (domestic utility), Transportation (Fuel cell vehicle), Portable power (laptop, cell phone), Distributed power for remote location, etc.

• Characteristics of fuel cellsSlow dynamic responseEnvironmental-friendly (no emission)Modular electric generationHigh efficiency (co-generation)

4


I. INTRODUCTION

What are the research focuses?

• Research Focuses

Control of Power Electronic Interface System⇒ Inexpensive, reliable, small size, and light weight⇒ Good performance:

− Nearly zero steady-state voltage (RMS) error − Low Total Harmonic Distortion (THD) − Fast/no-overshoot current response − Good voltage regulation

Power distribution applications (three-phase AC 120V (L-N) /60 Hz)

⇒ Conventional: a DC-DC boost converter and a DC/AC inverter

⇒ Z-source: ♦ Impedance source (L-C) and a DC/AC inverter♦ Boosted by shoot-though zero vectors (both switches turned-on)

5


II. Circuit Analysis/System Modeling

Equivalent Circuit of the Fuel Cell

• Equivalent Circuit Model (Fig. 2 (a))Modeling of reformer and stacks by R-C circuitSlow transient response: ⇒ Initial startup to a steady state: 90 seconds⇒ Varying electrical loads to a new steady state: 60 seconds

• Simplified Equivalent Model (Fig. 2 (b))To reduce total simulation time

Vin

+

−

Rr Rs

CsCr

+

−

Vfuel Vin

+

−

reformer stacks

(a) Equivalent circuit with the time constant (b) Simplified equivalent model

Fig. 2 Equivalent circuit of the fuel cell.6



Z-source Inverter Configuration

• Z-source Inverter:a DC source, a diode, L-C impedance, a DC/AC inverter, L/C filter, and a loadDiode: to prevent a reverse current that can damage the fuel cell

FuelCell(Vin)

S1 S3 S5

S4 S6 S2

3-phaseload

L1

L2

C2C1

Cf

Lf

D

Z-source

Fig. 3 Total system configuration with Z-source inverter.

7



A. Circuit analysis of Z-source Inverter

• Two Operation Modes:Non-shoot-through switching mode: basic space vectors (V0, V1, V2, V3, V4, V5, V6, V7)Shoot-through switching mode: both switches in a leg are simultaneously turned-on

(a) In the shoot-through zero vectors (b) In the non-shoot-through switching vectors.

Fig. 4 Equivalent circuit of Z-source inverter.

8




Assumption: L1 = L2, C1 = C2

VC1 = VC2 and vL1 = vL2

Case 1: one of shoot-through zero vectors (Fig. 4 (a)) vL1 = VC1, vf = 2VC1, and vi = 0.

Case 2: one of non-shoot-through switching vectors (Fig. 4 (b)) loop 1: vL1 = Vin – VC1 and loop 2: vi = VC1 - vL1 = 2VC1 - Vin,

where Vin is the output voltage of the fuel cell.

( )in

z

a

z

a

inab

bC

T

z

CinbCaLLL V

TT

TT

VTT

TV

TVVTVT

dtvvVz

⋅−

−=

−=⇒=

−⋅+⋅=== ∫

21

10 1

0

11111

Average voltage of the inductors

where Tz = Ta + Tb, Tz: switching period, Ta: total duration of shoot-through zero vectorsand Tb: total duration of non-shoot-through switching vectors

9




Average DC-link voltage:

( )1

1

0

20Cin

ab

b

z

inCbaTiii VV

TTT

TVVTT

dtvvVz

=−

=−⋅+⋅

=== ∫

Peak DC-link voltage:

ininab

zinCDCp VKV

TTT

VVV ⋅=−

=−= 1_ 2

z

aab

z

TTTT

TK

⋅−=

−=

21

1where K is called a boost factor,

Peak phase voltage of inverter output

22_

_inDCp

paV

KMV

MV ⋅⋅=⋅=

where, M denotes the modulation index

10



B. System modeling

S1 S3 S5

S4 S6 S2

Vdc

+

−

AB

C

3-phaseloadCf

Lf

ViAB

ViBC

iiA

iiB

iiC

+−+−

VLAB

VLBC VLCA

iLA

iLB

iLC

Fig. 5 Simplified system circuit model of Z-source inverter.

11



B. System modeling

Current/voltage equations from the L-C filter

−−=

−−=

−−=

)(3

13

)(3

13

)(3

13

LALCff

iCALCA

LCLBff

iBCLBC

LBLAff

iABLAB

iiCC

idt

dV

iiCC

idt

dV

iiCC

idt

dV

−−

−=

101110

011, iTLi

fi

f

L

CCdtd

ITIV

31

31

−=

−=

−=

−=

LCAf

iCAf

iCA

LBCf

iBCf

iBC

LABf

iABf

iAB

VL

VLdt

di

VL

VLdt

di

VL

VLdt

di

11

11

11

Lf

if

i

LLdtd

VVI 11

−=

where, state variables: VL (= [VLAB VLBC VLCA]T ) and Ii (= [iiAB iiBC iiCA]T = [iiA-iiB iiB-iiC iiC-iiA]T ), control input (u): Vi (= [ViAB ViBC ViCA]T ), disturbance (d): IL (= [iLA iLB iLC]T )

12



B. System modeling

abcsqd fKf =0

where fqd0=[fq fd f0]T, fabc=[fa fb fc]T, and f denotes either a voltage or a current variable.

−

−−=

2/12/12/1232302/12/11

32

sK

Fig. 6 Relationship between abc reference frame and stationary qd reference frame.

13



B. System modeling

State equations in the stationary qd reference frame

−

123

231

23

Lqdiqdf

iqdf

Lqd

CCdtd

ITIV

31

31

−=

Lqdf

iqdf

iqd

LLdtd

VVI 11

−=

, Tiqd = [KsTiKs-1]row and column, 1,2 =

Continuous-time state space equation of the given plant model

)()()()( tttt EdBuAXX ++=&

14×

=

iqd

Lqd

IV

X

44

2222

2222

013

10

×

××

××

−=

IL

IC

f

fA

242203

1

××

−= iqd

fCT

E 12][ ×= LqdId

24

22

2210

×

×

×

= I

L f

Bwhere,12][ ×= iqdVu

14



C. Modified Space Vector PWM

Conventional Space Vector PWM:

q axis

d axis

V1(100)

V2(110)

V3(010)

V4(011)

V5(001)

V6(101)

V0(000)

V7(111)

)0,3/2(

)3/1,3/1()3/1,3/1(−

)0,3/2(−

)3/1,3/1( −− )3/1,3/1( −

T1

T2Vref

1

2

3

4

5

6

α

)()3/sin(

)sin()3/sin(

)3/sin(

210

2

1

TTTT

aTT

aTT

z

z

z

+−=

⋅⋅=

−⋅⋅=

παπ

απ

=

dc

ref

V

Vawhere

32

,

Fig. 7 Basic space vectors and switching patterns.

15




Modified Space Vector PWM Implementation (1)

(a) Sector 1 (b) Sector 2

Fig. 8 Modified SVPWM implementation for Z-source inverter.*shoot-through zero vectors (T = Ta/3)

16





(c) Sector 3 (d) Sector 4


17





(e) Sector 5 (f) Sector 6


18




19


III. Control System Design

Entire Control-loop Structure

Fig. 9 Total control system block diagram.

where, DSMC is the discrete-time sliding mode controller, PI is the discrete-time proportional-integral controller, SVPWM is a three-phase space vector pulse width modulation, Icmd,,qd is the current command signal, I*

iqd is the limited current command, V*

iqd is the voltage command, and Vi is the true inverter output voltage.

20



A. Discrete Sliding Mode Current Controller

Block diagram of Current Controller

Fig. 10 Discrete-time current controller using DSMC.

21




Continuous-time state space equation

−==

++=

)()()()()(

)()()()(

1

ttttt

tttt

refyyeXCy

EdBuAXX&

=

iqd

Lqd

IV

−=

××

××

2222

2222

013

0

IL

IC

f

fA

=

×

×

22

2210

IL f

B

−=

×2203

1iqd

fCT

E

=

10000100

1C

=

id

iq

VV

u

=

Ld

Lq

ii

d

−

=1

23

231

23

iqdT

1

=

id

iq

II

yXwhere,

Discrete-time state space equation

−==

++=+

)()()()()(

)()()()1(

1

***

kkkkk

kkkk

refyyeXCy

dEuBXAX

∫ −= zz

T T de0

)(* ττ EE A∫ −= zz

T T de0

)(* ττ BB Awhere, zTeAA =*

22




Sliding-mode manifold

)()()()()( 1 kkkkk refref yXCyys −=−=

Equivalent control law

0)1()()()()1()1()1( *1

*1

*1 =+−++=+−+=+ kkkkkkk refref ydECuBCXACyys

( ) ( ))()()()( *1

*1

*1*1 kkkk iqdeq dECXACIBCu −−=∴

−

Control limit

>

≤=

00

0

)(for )()(

)(for )()( ukk

ku

ukkk

eqeqeq

eqeq

uuu

uuu

0)( uk ≤u

23



B. Discrete Optimal Voltage Controller

Block diagram of Voltage Controller

Fig. 11 Discrete-time Optimal voltage controller

24




Discrete-time state space equation

)()()()1( *** kkkk dEuBXAX ++=+

Augmented system model including DSMC

=++=+

)()()()()()1( *

1

kkkkkk

d

dd

XCydEuBXAX

( ) ( )12*

11*

11*

1** CECACBCBAA −−=

−

dwhere,

=

××

××

2222

222211 0

0I

IC( ) 1*

1* −

= BCBB d [ ]222212 0 ××= IC

[ ]2222 0 ××= IdC )()( kk LqdVy =)()( ,1 kk iqdcmdIu =

25




Continuous time servo-compensator

LqdLqdvqdvqdcc VVeeBηAη −=+= *,&

where,

16164444444

4432244

4444244

000000000000

××××

×××

×××

×××

=

c

c

cc

AA

AA

A

2164

3

2

1

×

=

c

c

c

c

c

BBBB

B442222

22222

00

×××

××

⋅−

=I

I

ici ω

A2422

220

××

×

=

IciB

4444441c

(Ac is the given tracking/disturbance poles)

Discrete time servo-compensator

)()()1( ** kkk vqdcc eBηAη +=+

∫ −= zzc

T

cT

c de0

)(* ττ BB Awhere, zcTc eAA =*

26




Augmented system combining both the plant and the servo-compensator

)(ˆ)(ˆ)(ˆ)(ˆˆ)1(ˆref211 kkkkk yEdEuBXAX +++=+

−

= **

0ˆcdc

d

ACBA

A

= *2

0ˆcB

E

=

0ˆ dBB

=

0ˆ

*

1E

E

)()( * kk Lqdref Vy =

=

)()(

)(ˆkk

kηX

Xwhere,

)()( ,1 kk iqdcmdIu = )()( kk LqdId =

Optimization criterion

)()()(ˆ)(ˆ0

kkkkJk

TT∑ +=∞

=uuXQX εε

where, Q is a symmetrical positive-definite matrix and ε>0 is a small number

Control input

[ ] )()()()(

)(ˆ)( 21211 kkkk

kk ηKXKηX

KKXKu +=

==

27



C. Discrete PI DC-link Voltage Controller

Fig. 12 Discrete PI controller to regulate the DC-link average voltage.

28



C. Discrete PI DC-link Voltage Controller

Discrete PI DC-link voltage controller equation

( ) ( )

−+⋅⋅+−−⋅+−=

−=

)1()()1()()1()(

)()()( C2C2*

kekeTKkekeKkTkT

kkke

zip

VV

2

Duration (Tcal = Ta/3) of shoot-through zero vectors Desired capacitor voltage: VC1 = VC2 = 340 V

( )( )

( )( )

3

2500.2093

1300.3814

3

680340

221

1

**

zmin_

zmax_

1

11

a

ina

inaacal

zin

in

inC

inCain

z

az

a

inab

bC

TT

VVTT

VVTTTT

TVV

VVVVTV

TT

TT

VTT

TV

=∴

=⇐⋅=

=⇐⋅=⇒=∴

⋅−−

=−−

=⇒⋅−

−=

−=

29



System parameters for simulations

30



A. Linear load (R-L)

0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09 0.095 0.10

100

200

300

400

500Fue l ce ll output voltage (Vf ) and capacitor voltage (VC2)

Vf a

nd V

C2 [V

]VfVC2

0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09 0.095 0.1-400

-200

0

200

400Line to line load voltages [VLAB, VLBC, VLCA]

VLAB

, VLBC

, VLCA [V

]

0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09 0.095 0.1-50

0

50Load phas e currents [iLA, iLB, iLC]

Time [s ec]

i LA, i

LB, i

LC [A]

0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09 0.095 0.10

100

200

300

400


Vf a

nd V

C2 [V

]VfVC2

0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09 0.095 0.1-400

-200

0

200


VLAB

, VLBC

, VLCA [V

]

0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09 0.095 0.1-5

0

5Load phas e currents [i

LA, i

LB, i

LC]

Time [s ec]

i LA, i

LB, i

LC [A]

(a) 130V/10kW (b) 250V/700W

Fig. 13 Simulation waveforms under a linear load.

31



B. Nonlinear load (A bridge diode)

0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09 0.095 0.10

100

200

300

400

500Fuel ce ll output voltage (Vf ) and capacitor voltage (VC2)

Vf a

nd V

C2 [V

]VfVC2

0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09 0.095 0.1-400

-200

0

200


VLAB

, VLBC

, VLCA [V

]

0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09 0.095 0.1-50

0

50Load phase currents [iLA, iLB, iLC]

Time [s ec]

i LA, i

LB, i

LC [A]

0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09 0.095 0.10

100

200

300

400


Vf a

nd V

C2 [V

] VfVC2

0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09 0.095 0.1-400

-200

0

200


VLAB

, VLBC

, VLCA [V

]

0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09 0.095 0.1-5

0

5Load phas e currents [iLA, iLB, iLC]

Time [s ec]

i LA, i

LB, i

LC [A]

(a) 130V/9Ω (10kW) (b) 250V/120Ω (700W)

Fig. 14 Simulation waveforms under a nonlinear load.

32


V. Conclusion

Z-source PWM inverter⇒ L-C Impedance components instead of a boost converter⇒ Modified PWM Technique using Shoot-through zero vectors⇒ Inexpensive, reliable, small size, and light weight⇒ Good performance:

− Nearly zero steady-state voltage (RMS) error − Low Total Harmonic Distortion (THD) − Fast/no-overshoot current response − Good voltage regulation

Future Works⇒ Good performance for no-load⇒ Reduction of sensors using observers⇒ Experiment by a test-bed with DSP

33

Documents

Control of a Boost Inverter Using Z-source for Fuel Cell ... · Control of a Boost Inverter Using Z-source for Fuel Cell Systems Jin-Woo Jung, Ph. D. Student Advisor: Prof. Ali Keyhani