modeling, design and control of fuel cell...

Department of Chemical and Environmental Engineering

Illinois Institute of Technology

Modeling, Design and Control of

Fuel Cell Systems

Professor Donald J. Chmielewski Department of Chemical and Environmental Engineering


ChEE Department Seminar

September 21st, 2005



Outline

Update on Other Research

Fuel Cell Research

SOFC Design

PEMFC Control

Fuel Processor Design and Control

Future Efforts



Predictive Control

0

1

0,

:State InitialKnown

0

0:sConstraint Process

:Model Process..

min

x

kdDu

kcCx

BuAxxts

RuuQxx

k

k

kkk

N

k

k

T

kk

T

kux kk

+

+

+



0

1

0,

:State InitialKnown

0


:Model Process..

min

x

kdDu

kcCx

BuAxxts

RuuQxx

k

k

kkk

N

k

k

T

kk

T

kux kk

+

+

+

Predictive Control



0

1

0,

:State InitialKnown

0


:Model Process..

min

x

kdDu

kcCx

BuAxxts

RuuQxx

k

k

kkk

k

k

T

kk

T

kux kk

+

+

+

Infinite Horizon Predictive Control



0

1

0,

:State InitialKnown

0


:Model Process..

min

x

kdDu

kcCx

BuAxxts

RuuQxx

k

k

kkk

k

k

T

kk

T

kux kk

+

+

+

Tuning Predictive Controllers



0

1

0,

:State InitialKnown

0


:Model Process..

min

x

kdDu

kcCx

GdBuAxxts

RuuQxx

k

k

kkkk

k

k

T

kk

T

kux kk

++

+

+

Tuning Predictive Controllers



Expected Dynamic Operating Region

Expected Dynamic

Operating Region

(EDOR)

*

1x

2x

1x

2x



Closed-Loop Operating Region

Closed-Loop EDORs of

different controllers

*

x

u

xRQLu ),( 11

xRQLu ),( 22



MV' s

Optimal

Steady-State

Operating

PointBaked-off

Operating

Points

Expected

Dynamic

Operating

Regions

CV' s Constraint

PolytopeGoal: Bring the Backed-

off Point as close as

possible to the Optimal

Steady-State.

Constraint: Do not

allow the EDOR outside

the Constraint Polytope.

Profit Based Tuning



Sensor Selection

Extensions of the Capital Cost Formulation

Actuator Selection

Simultaneous Sensor and Actuator Selection

Distributed Parameter Systems

Fault Recoverability

Combined with Profit Based Tuning



Coal Fired Power Plants

Coal In

Air In

Flue Gas:

CO2 H2O

Heavy Metals

and NOx’s

Combustion

Chamber Boiler

Pollution

Control



Oxy-Combustion

Coal In

Air In

Flue Gas:

CO2 H2O

Heavy Metals

and NOx’s

Combustion

Chamber Boiler

Pollution

Control

O2



Oxy-Combustion

Coal In

Air In

Flue Gas:

CO2 H2O

Heavy Metals

and NOx’s

Combustion

Chamber Boiler

Pollution

Control

O2

Cryogenics

Plant

N2

Air



Heat and Power Integration

Coal In

Air In

Flue Gas:

CO2 H2O

Heavy Metals

and NOx’s

Combustion

Chamber Boiler

Pollution

Control

O2

Cryogenics

Plant

N2

Air



Boiler Dynamics and Control

Coal In

Air In

Flue Gas:

CO2 H2O

Heavy Metals

and NOx’s

Combustion

Chamber Boiler

Pollution

Control

O2

Cryogenics

Plant

N2

Air



Boiler Dynamics and Control



Outline


Fuel Cell Research

SOFC Design

PEMFC Control


Future Efforts



What is a Fuel Cell?

Fuel Cell

H2

Electric Power

Air

H2O

Answer:

An electrochemical

device that converts

a fuel directly to

electrical power



Solid Oxide Fuel Cell (SOFC)

N2

N2

N2

H2

H2

H2

H2

H2

H2

O2

O2

O2

e- e-

Anode

Electrolyte

Cathode

O2 N2

N2

O2

O2

O2-

O2-

O2-

O2-




N2

N2

N2

H2

H2

H2

H2

H2

H2

O2

O2

O2

e- e-

Anode

Electrolyte

Cathode

O2 N2

N2

O2

O2

O2-

O2-

O2-

O2-

)( cellnercell TjREE

+

OH

OHcelloner

P

PP

F

RTEE

2

22

21

log2

F

jArH

22




N2

N2

N2

H2

H2

H2

H2

H2

H2

O2

O2

O2

e- e-

Anode

Electrolyte

Cathode

O2 N2

N2

O2

O2

O2-

O2-

O2-

O2-

)( cellnercell TjREE

+

OH

OHcelloner

P

PP

F

RTEE

2

22

21

log2

F

jArH

22

+

OH

H

cellcellHP

PTTr

2

2

2log )()(



Resistance in the SOFC

Zirconia Electrolyte Cathode (~30 μm)

Electrolyte (10-200 μm)

Anode ( up to 1 mm)

Rint= r (T ) * ( thickness / Area )



Cross Flow SOFC Stack

Fuel

Flow

Air

Flow

Current

Flow



From Selimovic, (2002).

Thermal Stresses

Peters et al., state:

“ Large temperature gradients in

either direction can cause

damage to one or of the

components or interfaces due to

thermal stresses”

Yakabe et al., state:

“ … the internal stress would

cause cracks or destruction of the

electrolytes”



Exothermic Reactions in SOFC

Fuel

Flow

Air

Flow



Plug Flow Reactor Analogy

Feed Exhaust

Reaction

Rate

H2 H2O



Internal Reforming SOFC

CH4

Air Flow

H2OCO

2H2 H

2O

O=

Fuel Flow

O2



Impact of Internal Reforming

From Selimovic, (2002).



Plug Flow Reactor Analogy (Internal Reforming)

ReformingReaction Rate

Reforming HeatGeneration

ElectrochemicalReaction Rate

ElectrochemicalHeat Generation

Combined HeatGeneration



Exhaust

Feed

Feed

Distributed Feed SOFC

Continuous Feed Configuration

Exhaust

Feed L1

L2

L3

L4

F1

F2

F3

F4

F5

A

Discrete Injection Configuration



Isothermal Model

22

2

22

2

ˆ)(

ˆ)(

HOHs

OH

HHs

H

s

rCfdV

FCd

rCfdV

FCd

fdV

dF

+

General Model:

channel. cell fuel in the rate flow Volumetric :

feed. ddistribute in the species ofion Concentrat :ˆ

).sec( lumereactor voper flow feed dDistribute : 313

F

iC

mmf

i

s

++

+

)()(

ln)()(

2

2

2

2

2

ii

H

OH

H

H

ljGHn

jQ

nhrj

C

CTTr

F

F

Rate Equations:



Achieving Uniform Heat Generation

+

OH

H

H

OH

H

C

CTTrQ

C

C

2

2

2

2

2 log )()( since Constant Constant




+

OH

H

H

OH

H

C

CTTrQ

C

C

2

2

2

2


)(

)()( Define

2

2

zC

zCz

OH

Hr 0set Then

dz

dr




+

OH

H

H

OH

H

C

CTTrQ

C

C

2

2

2

2


)(

)()( Define

2

2

zC

zCz

OH

Hr 0set Then

dz

dr

)ˆˆ(

)]ln()[1(

22

*

spOHH

spsp

ssCC

ffr

rr

++

sprr )0( where



Energy Model

)(

)ˆ(ˆˆ)(

)()(2

2

cschc

ccc

aaaasaha

aa

asahcschs

s

TTwhddz

dTCpCF

TTCpCFTTwhddz

dTCpFC

TThdTThdQwdz

Tdak

+

Interconnect

Ta(z)

Tc(z)

ha

Q(z), Ts(z)

hc

d z

Anode

Cathode

Electrolyte

Adiabatic Wall

Fuel

z

Air



Simulations with a Hydrogen Feed

Hydrogen to Steam Ratio



Simulations with a Hydrogen Feed

Solid Temperature Profile



Fuel Utilization Hydrogen Case

inH

outHinH

C

CCU

,

,,

2

22



Methane Fed Design Equations

22

2

24

2242

2

2242

2

44

4

4

ˆ)(

ˆ)(

ˆ)(

3ˆ)(

ˆ)(

2

COCOs

CO

COCHCOsCO

HCOCHOHs

OH

HCOCHHs

H

CHCHs

CH

CHs

rCfdV

FCd

rrCfdV

FCd

rrrCfdV

FCd

rrrCfdV

FCd

rCfdV

FCd

rC

fdV

dF

+

++

+

+

+

General Model:

++

+

)(

)(

ln)()(

2

,

2

2

22

22

44

2

2

2

iiHelecii

H

eq

COHCOOHfshiftCO

CHrefCH

OH

HH

ljrGrHQ

nhrj

K

CCCCkr

Ckr

C

CTTr

F

Rate Equations:



Methane Fed Design Scheme

Again define:

And set

This is achieved if

0dz

dr

)ˆˆ)(1()ˆˆ)((

)432()]ln()[1)((

222

*

4

2

*

spCOCOeqspspOHHeqsp

CHeqspeqspspspspeqsp

sCCKCCK

rKKKf

rrrr

rrrrrr

++

++++++

sprr )0(

sp rr)(

)()(

2

2

zC

zCz

OH

H and = the desired HSR



Internal Reforming Case



Carbon Deposition

OHCHCO

OHCHCO

COCCO

HCCH

222

22

2

24

22

2

2

++

++

+

+



Carbon Deposition

OHCHCO

OHCHCO

COCCO

HCCH

222

22

2

24

22

2

2

++

++

+

+

Steam to Carbon Ratio (SCR)

inCHinOH CC ,, 42

:



Indicator of Carbon Deposition

OH

CHCO

C

CCCMMSR

2

4+

If CMMSR > 1: Carbon deposition risk

CMMSR < 1: No risk of carbon deposition



Internal Reforming Case



Conventional Efficiency

LHV

Pe1



Measures of Efficiency



Modified Stack Efficiency

pre

e

HLHV

P

+2



System Efficiency

LHV

HHP preposte )(45.03

+



Polymer Electrolyte Membrane

Fuel Cell (PEMFC)

N2

N2

N2

H2

H2

H2

H2

H2

H2

O2

O2

O2

H+

e- e-

Anode

Electrolyte

Cathode

O2 N2

N2

O2

O2

H+

H+

H+



Polymer Electrolyte Membrane

Fuel Cell (PEMFC)

N2

N2

N2

H2

H2

H2

H2

H2

H2

O2

O2

O2

H+

e- e-

Anode

Electrolyte

Cathode

O2 N2

N2

O2

O2

H+

H+

H+

Transportation Applications



Electrochemistry

),(),(22 cellohmOHHnercell TjEPPEE

F

jArH

22

SOFC:



Electrochemistry

),(),(22 cellohmOHHnercell TjEPPEE

F

jArH

22

SOFC:

PEMFC:

))(,(),,(

)(),(22

RHKjERHTjE

jEPPEE

mtmtcellohm

actOHOnercell

F

jAr OH

22



0 2000

PEMFC Polarization Curve



Ohmic Resistance

humidity with increases

, ty,conductivi Ionic



Ohmic Resistance

)(TP

PxRH

satw

xw = 0.35





Mass Transfer Resistance

)(

2

s

OC

OH

s

OOmt rxxK222 2

1)( )(

j

2OC



Mass Transfer Resistance

)(

2

s

OC

OH

s

OOmt rxxK222 2

1)( )(

j

2OC

0 2000



Efficient Operation

)(TP

PxRH

satw

xw = 0.35





0 20 40 60 80 1000

0.5

1

1.5

2x 10

-3

Relative Humidity (%)

Mass

Tra

nsf

er

Co

eff

icie

nt

Flooding Resistance via the MTC

( ))1(

, 1

)(

RH

omt

mt

eK

RHK

coef.porosity

theis where



PEMFC Operating Window

%100%80 RH

CTC cat

00 100 60

Membrane

Dried Out

Membrane

Flooded



Dynamic Model of PEMFC

Cooling

Air In

Jacket

Exhaust

MEA

Anode

H2 In

Ecell

H2

Cathode

Air in

Cathode

Exhaust

O2

H2O

N2

Solid Material Current Collector

H+

H+

H+

H+

H+

H+

H+

H+

Insulator Material and energy

balances combined

with PEMFC

electrochemistry.

Parameters based on a

50 kW scale.

Air cooling is assumed.



Power Set-Point Tracking

Transportation Applications

PEMFCPower

Controller

Pe(sp) MV

Pe



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

Selecting the Power Output



Selecting the Power Output

0 200 400 600 800 10000

0.2

0.4

0.6

0.8

1

1.2

1.4


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



Power Controller

PEMFCE

cell

j

+- PI

j(sp)

Pe

PI

+

-

Pe(sp)



Power Controller

PEMFCE

cell

j

+- PI

j(sp)

Pe

PI

+

-

Pe(sp)

0 200 400 600 800 10000

0.2

0.4

0.6

0.8

1

1.2

1.4


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



Power Controller

0 5 10 15 20 25

0.18

0.19

0.2

0.21

0.22

Time (seconds)

Pow

er D

ensi

ty (

wat

ts/c

m2)

P e (sp) P e



Power Controller Failure

0 200 400 600 800 10000

0.2

0.4

0.6

0.8

1

1.2

1.4


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




0 5 10 15 20 25200

300

400

Time (seconds)

Cu

rren

t D

ensi

ty (

mA

/cm

2)

0 5 10 15 20 250.5

0.6

0.7

0.8

Cel

l V

olt

age

(V)

j

cell E




0 5 10 15 20 2570

80

90

100

Time (seconds)

Tem

per

atu

re (

Cel

siu

s)

0 5 10 15 20 2570

80

90

100

Rel

ativ

e H

um

idit

y (

%)

cat T

RH



Temperature / RH Controller

PEMFC

Fjac

Tcat

+-

PIT

cat(sp)

Power

Controller

Pe(sp)

Ecell

Pe, j

RH

RH(sp)

+-

PI



PEMFC

Fjac

Tcat

+-

PIT

cat(sp)

Power

Controller

Pe(sp)

Ecell

Pe, j

RH

RH(sp)

+-

PI





0 20 40 60 800.18

0.2

0.22

0.24

0.26

0.28

0.3P

ow

er D

ensi

ty (

wat

ts/c

m2)

e P (sp)

e P

Time (seconds)




0 20 40 60 8065

70

75

80

85

Time (seconds)

Tem

per

atu

re (

Cel

siu

s)

0 20 40 60 8080

85

90

95

100

Rel

ativ

e H

um

idit

y (

%)

cat T

(sp)

cat T

RH



Oxygen Controller

PEMFC

Fjac

Tcat

RH(sp)

Power

Controller

Pe(sp)

Ecell

Pe, j

RH

ControllerRH,

+-

PIF

cat

xO2

xO2

(sp)



Available Power and Efficiency

0.17 0.18 0.19 0.2 0.21 0.22

55

60

65

70

75

Power Density (watts/cm2)

Eff

icie

ncy

(%

)

Power Control




0 0.05 0.1 0.15 0.2 0.25 0.3

55

60

65

70

75


Eff

icie

ncy

(%

)

Power Control

Power & Humidity Control




0 0.1 0.2 0.3 0.4 0.5 0.6

55

60

65

70

75


Eff

icie

ncy

(%

)

Power Control

Power & Humidity Control

Power, Humidity & Oxygen Control



Outline


Fuel Cell Research

SOFC Design

PEMFC Control


Future Efforts



Fuel Cell System

Fuel

Processor Fuel Cell

Stack

Spent-Fuel

Burner

Thermal & Water Management

Air

Air

Fuel

H2

Exhaust

H2O CO2

Electric Power

Conditioner



Hydrogen Storage vs. On-Board Reforming

Transportation

Applications

PEMFCReformerLiquid Fuel

Storage Tank

Cm

Hn

H2

CO

H2O

CO2

PEMFCHydrogen

Storage Tank

H2



PEMFC and CO Poisoning



Fuel Processing Reactors

PEMFCPreferential

Oxidation

(PrOx)

Water-

Gas

Shift

(WGS)

Reformer

Hydrocarbon Feed

Large Hydrocarbons Cracked:

Low H2 to CO ratio Most CO converted to CO2: ~ 1% CO remaining

CO levels down to ~ 10 ppm



Preferential Oxidation

222

1COOCO + OHOH 222

2

1+

Desired Reaction: Parasitic Reaction:



Preferential Oxidation

222

1COOCO +

PrOx

Reactor

OHOH 2222

1+

Reformate

Air ppm 10CO

2%-1~COto PEMFC

Desired Reaction: Parasitic Reaction:



PrOx Design Challenge

Achieve an exit CO concentration

less than 10 ppm

Minimize the oxidation of H2

Inlet concentration of CO is known



PrOx Modeling

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Stoichiometry

Exit C

O C

on

ce

ntr

atio

n,

%

0.2% CO

1.3% CO

2.5% CO

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2 2.5

l X1/4

CO

Se

lectivity

GHSV = 36,000/h

2.6% CO

1.3% CO

0.2% CO



Optimal PrOx Design

0.0

0.5

1.0

1.5

2.0

2.5

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Inlet CO Concentration (%)

Sto

ichio

metr

y

0.0

0.2

0.4

0.6

0.8

1.0

CO

Sele

ctivity

S

l



Multistage PrOx Reactors

Reformate

Air

100oC 100oC

Intercooler Intercooler

Prox

Stage 1

Prox

Stage 2

Prox

Stage 3

Air Air



Optimal Multistage PrOx Designs

0

0.5

1

1.5

2

2.5

0 0.5 1 1.5 2 2.5 3 3.5


Hyd

rog

en

Co

nve

rete

d (

%)

1-Stage3-Stage

2-Stage



Optimal Air Flow Rates for

the 3 Stage System

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.5 1 1.5 2 2.5 3 3.5


Op

tim

al O

xyg

en

Flo

w (

mo

l/s)

Overall

Stage 3

Stage 1

Stage 2



Fuel Processing Reactors

PEMFCPreferential

Oxidation

(PrOx)

Water-

Gas

Shift

(WGS)

Reformer

Hydrocarbon Feed

Large Hydrocarbons Cracked:

Low H2 to CO ratio Most CO converted to CO2: ~ 1% CO remaining

CO levels down to ~ 10 ppm



Partial Oxidation

Hydrocarbon Fuel

Air (at a sub-

stoichiometric rate)

PO

Reactor

Total Oxidation: OHnmCOOnmHC nm 222 2/)2/( +++

Steam Reforming: 22 )2/( HnmmCOOmHHC nm +++

Water Gas Shift: 222 HCOOHCO ++

22

2

COOH

COH



Partial Oxidation

Hydrocarbon Fuel

Air (at a sub-


PO

Reactor

Oxidation: OHnmCOOnmHC nm 222 2/)2/( +++



22

2

COOH

COH



Water Gas Shift Reaction

At High temperatures equilibrium favors:

222 HCOOHCO ++

At Low temperatures equilibrium favors:

222 HCOOHCO ++

More H2O in the feed will also favor the forward direction



Autothermal Reforming

Hydrocarbon Fuel Air (at a sub-


ATR

Reactor




22

2

COOH

COH

Steam



Autothermal Reforming

Hydrocarbon Fuel Air (at a sub-


ATR

Reactor




CO

H

Less

More 2

Steam 222 ,,, COOHCOH



ATR Reactor

Vaporized gasoline,

Steam

Liquid water

Heat exchangerAir (25 °C)

Hot air

Nozzle

7 m

m1

2 m

m1

2 m

m

96 mm

Catalyst bed

Heater rod

Thermocouple1 2 3 4

5 6 7

8 9 10

Metal wall

thickness=1.7 mm

High Space Velocity

(GHSV ~ 50,000/h)

Noble Metal Catalyst

(Rh on a Gd-CeO2 substrate).

Operating Temperature

~ 700 – 1000o C



Start-up the ATR Reactor

1. Partial Oxidation Mode

to achieve desired operating temperature quickly

(feed of fuel and air only)

2. ATR Mode

to achieve desired CO conversion

(feed of fuel, air and steam)



CFD Model of the ATR Reactor

0

100

200

300

400

500

600

700

800

900

1000

20 40 60 80 100 120 140 160 180 200

Time (s)

Tem

pera

ture

(°C

)

7 mm19 mm

Inlet temperature

Partial Oxidation Start-up:



ATR Reactor Model

0

100

200

300

400

500

600

700

800

900

20 40 60 80 100 120 140 160 180

Time (s)

Tem

pera

ture

(°C

)

7 mm

19 mm

Inlet temperature

Partial Oxidation Start-up: (Liquid Water Spray at 75 s)



ATR Reactor Model

0.00

0.05

0.10

0.15

0.20

0.25

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Dimensionless x-axis (x/L)

Mo

lar

frac

tio

ns w

et

(-)

H2

CO

H2O

CO2

Fuel

Partial Oxidation Steady State:



Feedback Control of the ATR Reactor

ATR

Reactor

T3 Inlet Air Flow

+ +

+ +

T4

T5

T2

T1

+

- PI

Control

T3, set point

Inlet Air Temperature

T3, measured

Sensor Noise

Temperature Fluctuations in Reactor



Feedback Control of the ATR Reactor

ATR

Reactor

T3 Inlet Air Flow

+ +

+ +

T4

T5

T2

T1

+

- PI

Control

T3, set point

Inlet Air Temperature

T3, measured

Sensor Noise

Temperature Fluctuations in Reactor

Manipulated

Variable

Control Variable

Disturbances



Step Test Modeling

0 20 40 60 80 100800

850

900

950

1000

1050

T3

T1

T2

T3

T4

T5

AT

R T

em

pera

ture

(oC

)

time (sec)

0 20 40 60 80 100650

700

750

800

850

900

950

1000

1050

time (sec)

AT

R T

emp

erat

ure

(oC

)

T1

T2

T3

T4

T5

1, +

s

eK

F

T

i

s

i

inAir

ii

1, +

s

eK

T

T

i

s

i

inAir

ii

1, +

s

eK

F

T

i

s

i

inSteam

ii



Analysis of the Feedback Controller

Regulation During Partial Oxidation:

0 200 400 600 800800

900

1000

1100

1200CV (T

3) Response: Open vs. Closed-loop

time (sec)

Tem

per

atu

re (

oC

)

Open-loop

Closed-loop

0 200 400 600 800-50

0

50

100

150MV (Air Flow) Response: Open-loop vs. Closed-loop

time (sec)

Inle

t A

ir F

low

Rate

(sl

pm

)

Closed-loop

Open-loop



Analysis of the Feedback Controller

Regulation During ATR Mode:

0 200 400 600 800800

900

1000

1100

1200CV (T

3) Response: Open- vs. Closed-loop

time (sec)

Tem

per

atu

re (

oC

)

Open-loop

Closed-loop

0 200 400 600 8000

50

100

150

200MV (Air Flow) Response: Open vs. Closed-loop

time (sec)

Inle

t A

ir F

low

Rate

(sl

pm

) Open-loop

Closed-loop



Transition from PO to ATR Mode

0 50 100 150 2000

400

600

800

0 50 100 150 2000

50

100

T3 T

emp

erat

ure

(oC

)

Impact of Steam Injection

Ste

am F

low

Rat

e (g

/min

)

time (sec)

With Feedback Controller

Without Feedback Controller

Steam Flow Rate



Transition from PO to ATR Mode

0 50 100 150 200

400

600

800

0 50 100 150 2000

50

100

0 50 100 150 200

Impact of Steam Injection Rate

With Feedback Controller

Without Feedback Controller

Steam Flow Rate

time (sec)

T3 T

emper

ature

(oC

)

Ste

am F

low

Rat

e (g

/min

)



Feed-forward Control

TF w.r.t.

Air Flow

T3 Air Flow

+ + +

- PI

T3, set point

Steam Flow Rate (Measured)

+ +

TF w.r.t.

Steam

FF

-



Impact of Model Mismatch

0 20 40 60 80 100400

600

800

1000

1200

time (sec)

T3 T

em

pera

ture

(oC

)

Feedback Controller Only

Feed-forward Without

Model Mismatch

Feed-forward With Model Mismatch

Impact of Model Mismatch on Feed-forward

0 20 40 60 80 100200

400

600

800

1000

T3 T

em

pera

ture

(oC

)

Impact of Model Mismatch on Feed-forward

time (sec)

Feed-forward Without Model Mismatch

Feedback Controller Only

Feed-forward With

Model Mismatch



Outline


Fuel Cell Research

SOFC Design

PEMFC Control


Future Efforts



Computational Aspect of MPC



Reduced Order Modeling

20 40 60 80 100 120 140 160 180 2000

200

400

600

800

1000

Time, s

Tem

per

ature

,oC

@ z = 7 mm

Measured Inlet Temperature

@ z = 19 mm

Experimental Measurements - "*"

High Order CFD Simulation - Solid

Reduced Order Simulation - Dashed

Computational

Effort:

CFD: ~10 min

ROM: ~30 sec



Reduced Order Modeling

0 0.2 0.4 0.6 0.8 1-0.05

0

0.05

0.1

0.15

0.2

Dimensionless Axial Position, 1 unit =7mm

Mo

le F

ract

ion

, w

et b

asis

H2 CO

CO2 Fuel H

2O

High Order CFD Simulation - SolidReduced Order Simulation - Dashed

Computational

Effort:

CFD: ~10 min

ROM: ~30 sec



Acknowledgements

Collaborators

• @ IIT: Said Al-Hallaj J. Robert Selman Vijay Ramani Satish Parulekar Herek Clack Jai Prakash

• @ Argonne National Laboratory:

Shabbir Ahmed Dennis Papadias Rajesh Ahluwalia Qizhi Zhang

Michael Inbody (LANL)



Acknowledgements

• Students:

Ayman Al-Qattan Jui-Kun Peng

Amit Manthanwar Kevin Lauzze

Yongyou Hu Jotvinge Vaicekauskaite

Janet Ruettiger Ali Zenfour

• Funding:

Argonne National Laboratory

Illinois Clean Coal Institute

American Air Liquide

Kuwait Institute for Scientific Research

Graduate and Armour Colleges, IIT

Chemical & Environmental Engineering Department, IIT

modeling, design and control of fuel cell...

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