closed-loop control of a pemfc: the impact and...

Illinois Institute of TechnologyDepartment of Chemical and Biological Engineering

Closed-Loop Control Of A PEMFC: The

Impact and Control Of Vehicle Loads

Syed K. Ahmed Donald J. Chmielewski

Department of Chemical and Biological Engineering

Illinois Institute of Technology

Presented at the Annual Meeting of the AIChE: November 2007



Outline

Motivation

Motor/Vehicle Load Model

Controller Analysis



Dynamic Model of PEMFC

Cooling

Air In

Jacket

Exhaust

MEA

Anode

In

(H2, H

2O)

Ecell

H2

Cathode

Air in

Cathode

Exhaust

O2

H2O

N2

Solid Material Current Collector

H+

H+

H+

H+

H+

H+

H+

H+

Insulator

Anode

Exhaust

H2O

Parameters based

on 1 kW scale.

Humidified

hydrogen feed

Air cooling is

assumed.



Dynamic Model of PEMFC

2

2 2 2

2

2 2 2

2 2

2

2 2 2

2

2 2

,

( )

( ) ( ) ( )

,

( )

,

( )

( ) (

,

( )

H in

an an H in an H H mem

an

H O in an an an

an an H O in an H O H O mem

in an

an an H H O mem

O in

ca ca O in ca O O mem

ca

H O in ca ca

ca ca H O in ca H O

dCV F C F C r A

dt

dCV F C F C J A

dt

F C F C r J A

dCV F C F C r A

dt

dCV F C F C

dt

2

2 2

) ( )

( )

ca

H O mem

in ca

ca ca O H O mem

J A

F C F C r J A

( )

( )

( )

( )

in inca

ca ca ca ca ca sol ca

p ca

in inan

an an an an an sol an

p an

jac in in

jac jac jac jac jac sol jac

p jac

sol

p sol ca solcasol

dT UAV F T F T T T

dt C

dT UAV F T F T T T

dt C

dT UAV F T F T T T

dt C

dTC V UA T T

dt

( ) ( )jac sol an sol gen memjac anUA T T UA T T Q A

Material Balances Energy Balances



Electrochemical Model

mtohmactnercell EEEEE

OH

OHsoloner

P

PP

F

RTEE

2

22

2/1

ln2

osol

act jjF

RTE /ln

2

1

)/(22

)( o

O

ca

O

o

oo CCjj

mem

ohm

tjIRE

jjj

F

RTE

L

Lsolmt ln

2

11

)(

22 ca

OmtL CKFj

GDL

ca

GDLmt tDK )(



Hydration Model for MEA

MEA

Anode

In

(H2, H

2O) H

2

Cathode

Air in

Cathode

Exhaust

O2

H2O

N2

Solid Material Current Collector

H+

H+

H+

H+

H+

H+

H+

H+

Anode

Exhaust

H2O

2

2

( )

( )

mem

H Omem

H O diff drag

C jJ J J D

z F

Boundary Conditions

2

)(2)(

22

z

CD

t

C mem

OH

e

mem

OH

mOH

ca

OH

mem

OH

e

an

OH

mem

OH

e

zrJF

j

z

CD

zJF

j

z

CD

at0

0at0

22

2

2

2

)(

)(

)(

)(



Water Content Profiles

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014

Length Across PEM (cm)

λ=H

2O

/S

O3

-

0.4 A/cm2

0.6 A/cm2

0.2 A/cm2

memt

ohmz

dzjE

0)(

Ohmic Loss:

mtohmactnercell EEEEE

Ionic Conductivity:

( ( )) = 0.005193 (z)-0.00326z



Power/Temperature/Oxygen Control

Transportation Applications

PEMFC

Fjac Tsol

+-

PITsol

(sp)

Current

Controller

j(sp) Ecell

j

Feed-forward

ControllerFin,ca

Fin,an




Flooding



Most Frequent Question

Transportation Applications

PEMFC

Fjac Tsol

+-

PITsol

(sp)

Current

Controller

j(sp) Ecell

j

Feed-forward

ControllerFin,ca

Fin,an



Common Load Types

Resistive Load (passive).

Constant/Manipulated Current Load (active)

Constant/Manipulated Voltage Load (active)

Vehicle/DC-Motor Load (active and complex)



Outline

Motivation


Controller Analysis



DC Motor Model

Va

iaRa

La

Kv ωo

a

a a a v o a

o

o o t a L

diL R i K V

dt

dJ K i T

dt

ωo – Motor speed

TL – Load torque

Kv, Kv – Electro-force constants

Mt – Gear Ratio

β0 – Damping Ratio

J0 – Moment of Inertia



Vehicle Mass, Wheels and Gears

R

Fw

ω1

ω0

ωo – Motor Speed

ω1 – Wheel Speed

n – Vehicle Speed

R – Wheel Radius

M – Mass Car

A – Frontal Area

f – Friction Factor

1

21

2

w drag

drag air

v R

dvM F F

dt

F f v A



Combined Motor/Vehicle/Clutch Model

10

3 3 2

1 101

2 2

1

1

1

1

1

1

2

aa a v o a

a

oo o t a

o

o t t o

t

clutch o t

diR i K V

dt L

dK i T

dt J

T M f AR Md

dt J R M M

K M

R

10T

v

ωo - Motor Speed

ω1 - Wheel Speed

ia- Arm Current

n - Vehicle Speed

R - Wheel Radius

Mt - Gear Ratio

Ra- Arm Resistance

Kv- Motor Constant

Va-Arm Voltage



The Fuel Cell and its DC-DC Converter

FC kfc Va

iafcifc

Vfc

DC-DC converter relations:

Fuel cell V-I relation (polarization curve):

Combined V-I relation:

fcfcafcfcfca kiiVkV /

)( fcfc ifV

)( afcfcfca ikfkV

fcfcfcafcafcfcfcfcfc RkkVEiRiEV / then ,iscurveonpolarizati If



The Battery and its DC-DC converter

kb Va

iabib

Vb

Rb

Eb

a b bV k V

If kb increases, then iab increases

iab can become negative - charging

DC-DC converter relations:

/ab b bi i k

( / ) /ab b a b b bi E V k k R



Power Source Connections

FC kfc

iafcifc

Vfc

iab

ib

Vb

Rb

Eb

ia

Ra

La

Vakb



Outline

Motivation


Controller Analysis



The Open-Loop Process

Vehicle

kbatvveh

kfc



Open-Loop Simulation

0 2 4 6 8 100

0.005

0.01

0.015

0.02

0.025

0.03DC-DC Converter Manipulated Variables

time, sec

kbat

kfc



Open-Loop Simulation

0 2 4 6 8 100

0.005

0.01

0.015

0.02

0.025

0.03DC-DC Converter Manipulated Variables

time, sec

kbat

kfc

0 2 4 6 8 10-4

-3

-2

-1

0

1

2x 10

4 Power Profles

time, sec

Pload

(sp) [watts]

Fuel Cell Power

Battery Power

Armature Power



Power Source Connections

FC kfc

iafcifc

Vfc

iab

ib

Vb

Rb

Eb

ia

Ra

La

Vakb



Fuel Cell Voltage Control

Vehicle

kbatvveh

kfc+

-Vfc

(sp)

x

Vfc

min

max

Vfc(sp)

PI



Fuel Cell Voltage Control Simulation

0 200 400 600 800 10000

0.2

0.4

0.6

0.8

1

1.2

1.4

Current Density (mA/cm2)

Cel

l V

olt

age

(V)

0 200 400 600 800 10000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Po

wer

Den

sity

(w

atts

/cm

2)

E

eP

cell

Vehicle

kbatvveh

kfc+

-Vfc

(sp)

x

Vfc

min

max

Vfc(sp)

PI

5 10 15

-3000

-2000

-1000

0

1000

2000

3000

4000

Power Profles

time, sec

5 10 15 20

30

40

50

60

70

80

90

100

110

120

130

time, sec

Voltage

Fuel Cell

Battery

5 10 15

100

200

300

400

500

600

700

800

900

1000



Battery, Fuel Cell Voltage,

Vehicle Speed Control

Vehicle

kbatvveh

PI

kfc+

-Vfc

(sp)x

Vfc

min

max

Vfc(sp)

PI

+-

vveh(sp)



Battery, Fuel Cell Voltage,

Vehicle Speed Control Simulation

2 4 6 8 10 12 14

0

2000

4000

6000

8000

10000

12000

Power Profles

time, sec

2 4 6 8 10 12 14

30

40

50

60

70

80

90

100

110

120

130

Voltage

time, sec

Armature

Fuel Cell

Battery

Battery

Fuel Cell

0 5 10 150

200

400

600Motor Speed

0 5 10 150

5

10

15

20Vehicle Speed

time, sec

motor

[rad/s]

Vspeed

[mph]

V(sp)



Vehicle

kbatvveh

PI

kfc+

-Vfc

(sp)

x

Vfc

min

max

Vfc(sp)

PI

+-

vveh(sp)

Vehicle

kfc+

-Vfc

(sp)

Vfc

FUEL CELL

VOLTAGE

CONTROLLER

kbatvveh

PI+-

vveh(sp)

Battery Control Erratic

Why?



Lesson from Reactor Control

CSTR

Valve

position

FjacketPI+

-

Fjacket(sp)

T

PI+-

T (sp)

CA

PI

CA(sp)

+-




CSTR

Valve

position

CA

PI

CA(sp)

+-




Vehicle

kbat

vveh

PI+-

vveh(sp)



Power Load Control

Vehicle

kbatvveh

+-

kfc

x

Pfc

+-

x

Pbat

Pfc(sp)

Pbat(sp)

VfcFUEL CELL

VOLTAGE

CONTROLLER

Vfc(sp)

PI

PI



Power Load Control

Vehicle

kbatvveh

+-

kfc

x

Pfc

+-

x

Pbat

Pfc(sp)

Pbat(sp)

VfcFUEL CELL

VOLTAGE

CONTROLLER

Vfc(sp)

PI

PI

5 10 15

100

200

300

400

500

600

700

800

900

1000

20 25 30 35

100

150

200

250

300

Power Profles

time, sec

PBattery

(sp) [watts]

Fuel Cell Power

Battery Power



Power Load Control

Vehicle

kbatvveh

+-

kfc

x

Pfc

+-

x

Pbat

Pfc(sp)

Pbat(sp)

VfcFUEL CELL

VOLTAGE

CONTROLLER

Vfc(sp)

PI

PI

5 10 15

100

200

300

400

500

600

700

800

900

1000

20 25 30 35

100

150

200

250

300

Power Profles

time, sec

PFuel Cell

(sp) [watts]

Fuel Cell Power

Battery Power



Power Load Control

Vehicle

kbatvveh

+-

kfc

x

Pfc

+-

x

Pbat

Pfc(sp)

Pbat(sp)

VfcFUEL CELL

VOLTAGE

CONTROLLER

Vfc(sp)

PI

PI



Vehicle

kbatvveh

+-

kfc

x

Pfc

+-

x

Pbat

Pload(sp)

Pbat(sp)

VfcFUEL CELL

VOLTAGE

CONTROLLER

Vfc(sp)

PI

PI

Power Load Control



Power Load Control Simulation

FC Kfc

iafcifc

Vfc

iab

ib

Vb

Rb

Eb

ia

Ra

La

VaKb

Vehicle

kbatvveh

+-

kfc

x

Pfc

+-

x

Pbat

Pload(sp)

Pbat(sp)

VfcFUEL CELL

VOLTAGE

CONTROLLER

Vfc(sp)

PI

PI

5 10 15

100

200

300

400

500

600

700

800

900

1000

5 10 15 20

0

100

200

300

400

500

600

700

800

900

1000

Power Profles [W]

time, sec

Pload

(sp)

Battery

Fuel Cell

Armature



Power Load Control Simulation

FC Kfc

iafcifc

Vfc

iab

ib

Vb

Rb

Eb

ia

Ra

La

VaKb

5 10 15 20 25 30 35

-200

0

200

400

600

800

1000

Power Profles [W]

time, sec

Pload

(sp)

Battery

Fuel Cell

Armature

Vehicle

kbatvveh

+-

kfc

x

Pfc

+-

x

Pbat

Pload(sp)

Pbat(sp)

VfcFUEL CELL

VOLTAGE

CONTROLLER

Vfc(sp)

PI

PI

10 20 30

200

400

600

800

1000



Speed/Fuel Cell Power Control

Vehicle

kbatvveh

+-

kfc

x

Pfc

+-

x

Pbat

Pload(sp)

Pbat(sp)

+-

x

vveh(sp) Vfc

FUEL CELL

VOLTAGE

CONTROLLER

Vfc(sp)

PI

PI

PI



Speed Control Simulation

0 10 20-2000

0

2000

4000

6000

8000

10000

12000

14000Power Profles [W]

time, sec

0 10 200

20

40

60

80

100

120

140

time, sec

Voltage [V]

Armature

Pload

(sp)

Battery

Fuel Cell

Battery

Armature

Fuel Cell

0 5 10 15 200

200

400

600Motor Speed

0 5 10 15 200

5

10

15

20Vehicle Speed

time, sec

[rad/sec]

Vehicle Speed [mph]

Vehicle Speed Request



Speed Control Simulation

0 5 10 15 20-4000

-2000

0

2000

4000

6000

8000

10000

12000

14000Power Profles [W]

time, sec

0 5 10 15 200

20

40

60

80

100

120

140

160

180

time, sec

Voltage [V]

Armature

Fuel Cell

Battery

Pload

(sp)

Battery

Armature

Fuel Cell

0 5 10 15 200

100

200

300

400

500Motor Speed

0 5 10 15 200

5

10

15

20Vehicle Speed

time, sec

[rad/sec]

Vehicle Speed [mph]

Vehicle Speed Request



Vehicle

kbatvveh

+-

kfc

x

Pfc

+-

x

Pbat

Pfc(sp)

Pbat(sp)

VfcFUEL CELL

VOLTAGE

CONTROLLER

Vfc(sp)

PI

PI

Conclusions

PEMFC

Fjac Tsol

+-

PITsol

(sp)

Current

Controller

j(sp) Ecell

j

Feed-forward

ControllerFin,ca

Fin,an



Acknowledgements

Prof. Said Al-Hallaj, ChBE, IIT

Prof. Emadi, ECE, IIT

Kevin Lauzze

Argonne National Laboratory

Department of Chemical &

Biological Engineering, IIT

closed-loop control of a pemfc: the impact and...

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