comprehensive modeling and system interactions in planar ... · cera matec vt comprehensive...

Jan 27, 2005Jan 27, 2005 FloridaFlorida

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VTVT

Comprehensive Modeling and System Interactions in Planar SOFC

Power-Conditioning System

Sudip K. Mazumder (PI) and Sanjaya Pradhan(University of Illinois)

Joseph Joseph HartvigsenHartvigsen,, S. Elangovan and Michele Hollist(Ceramatec Inc.)

Michael von Spakovsky, Diego Rancruel and Doug Nelson (Virginia Tech)Comas Haynes(Georgia Tech.)

SECA Core Technology Program Review Meeting


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Pre-Analysis EffortsComprehensive Planar SOFC (PSOFC) 1D and 2D Modeling Model ValidationPower-Electronics ModelingFully-controlled BOPS Modeling Comprehensive System Modeling

Interaction Results and AnalysisLoad Power FactorLoad Transients

ConclusionFuture Works


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VTVT Modeling


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1D PSOFC Model

InputsFeed temperatureCurrentMolar flows andcompositions(Fuel, air)Cell geometryStack size

OutputsTemperatureOperating VoltageMolar flows and compositions(Fuel, air)Power Output

1 nn-1 n+1 steps. . . . . .

∆x

Variables calculated for n = 1…steps at each time include: temperature and stream flows.

Fuel cell model run in Simulink via an embedded Matlab function. Finite difference method used to approximate transient parameters.Model returns position dependent variable values as well as outflow values.

Interfaces with BOPS model in Simulink to form complete system.Radiation boundary applied to exit boundary.Co-flow setup between fuel and air streams.


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Model Characteristics

Shift Equilibrium Calculation

Equilibrium Composition

)()()()(

2

22

xpxpxpxp

KOHCO

HCOp −⋅−

+⋅+=

RTdG

p

o

eK−

= )(TfdGo =

xpp

xpp

COCO

HH

+=

+=

22

22

xppxpp

OHOH

COCO

−=−=

22

Inlet fuel stream is a reformed methane stream.Each step (control volume) along the fuel cell is treated as having homogenous properties throughout.Shift equilibrium is applied to each control volume along the fuel cell.


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1D Model Results

0.68

0.69

0.7

0.71

0.72

0.73

0.74

Time (0-30 minutes)

Ope

ratin

g V

olta

ge0

510

1520

0

10

20

301000

1010

1020

1030

1040

Time (0-20 minutes)Position along

cell length (0-8cm)

Tem

pera

ture

(K)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

H2

CO2

H2O

CH4

COA

node

Com

posi

tion

(out

let)

Time (0-1 minute)

Inlet ConditionsAir Flow(mol/s)

Fuel Flow(mol/s)

Air Comp(O2, N2)

Fuel Comp(CH4, H2O, CO, CO2, H2)

Feed temp(K)

8.87e-4 7.76e-4 (.21, .79) (.05, .45, .2, .2, .1) 1000


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2D SOFC Model

Electrolyte region

Air flow

FuelflowSame input and output variables

as 1D model. Model returns variable values at outputs as well as across entire fuel cell surface.Radiation boundary applied to each exit stream boundary.Cross-flow setup between fuel and air streams.Includes an inactive seal area around active electrolyte region.


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0

10

20

30

0

10

20

30990

995

1000

1005

1010

t = 30 seconds

0

10

20

30

0

10

20

30990

1000

1010

1020

1030

1040

t = 3 minutes0

10

20

30

0

10

20

301000

1010

1020

1030

1040

1050

1060

t = 5 minutes

2D Model Results

010

20

30

0

10

20

30995

995.5

996

996.5t = 1 second

FUEL FLOWAIR FLOW

Tem

pera

ture

(K)

Tracking transient temperature behavior


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1D vs. 2D Model ComparisonInlet Conditions

Air Flow per cell(mol/s)

Fuel Flow per cell(mol/s)

Air Comp(H2O, O2, N2)

Fuel Comp(CH4, H2O, CO, CO2, H2)

Current per stack(A/stack)

Feed temp(K)

3.7e-4 1.81e-4 (.069, .196, .74) (0.006, .31, .07, .08, .54) 15 996

Temperature (1D Model)Temperature (K) as a function of time (s) and position

0

20

40

60

05

1015

2025

990

1000

1010

1020

1030

1040

1050

Time (t = 1 to 250s)

position

tem

pera

ture

Temperature (2D Model)Temperature (K) as a function of position (t = 250s)

0 5 10 15 20 25 30

0

10

20

30990

1000

1010

1020

1030

1040

1050

FUEL FLOWAIR FLOW

tem

pera

ture


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1D vs. 2D Model ComparisonAnode Comp Out (1D Model)

Mole fraction vs. time (s)

0 50 100 150 200 2500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

CH4

CO

CO2

H2

H2O

Anode Comp Out (2D Model)Mole fraction vs. time (s)

0 50 100 150 200 2500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

CH4

COCO2

H2

H2O

H2 flow rate (1D Model)Flow rate (mol/s) as a function of time (s) and position

0

10

20

30

40

50

60

0

510

1520

250

0.5

1

x 10-4

Time (t = 1 to 250s)

position

H2

Flow

Rat

e

H2 flow rate (2D Model)Flow rate (mol/s) as a function of position (t=250s)

05

1015

2025

30

0

10

20

300

1

2

3

4

x 10-6

FUEL FLOW

AIR FLOW

H2

Flow

Rat

e


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1D vs. 2D Model ComparisonH2O flow rate (1D Model)

Flow rate (mol/s) as a function of time (s) and position

0

20

40

60

0

10

20

304

6

8

10

12

14

x 10-5

H2O

Flo

w R

ate

Time (t = 1 to 250s)position

H2O flow rate (2D Model)Flow rate (mol/s) as a function of position (t=250s)

010

2030

0

10

20

300

1

2

3

4

5

6

x 10-6

H2O

Flo

w R

ate

FUEL FLOWAIR FLOW

Current Flux (1D Model)ji (A/m^2) as a function of time (s) and position

0

10

20

30

40

50

60

05

1015

20250

1000

2000

3000

Time (t

= 1 to 250

s)

position

Cur

rent

flux

Current Flux (2D Model)ji (A/m^2) as a function of position (t=250s)

0

10

20

30

05

1015

2025

300

1000

2000

3000

AIR FLOW FUEL FLOW

Shi

ft R

ate


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0 100 200 300 400 500 600 700995

1000

1005

1010

1015

1020

1025

1030

Time (sec)

Tem

pera

ture

(K

)

2 D1 D

1D vs. 2D Model Comparisonwith Load-Transient

600 seconds of system simulation needs

~ 3.5 hrs for the 2 D Model~ 3.5 hrs for the 2 D Model

~ 1.5 hrs for the 1D model~ 1.5 hrs for the 1D model

2D2D

1D1D


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Adjusting Model Configurations

y = 0.0136e3931.5x

R2 = 0.9531

0

0.5

1

1.5

2

6.0E-04 7.0E-04 8.0E-04 9.0E-04 1.0E-03 1.1E-03 1.2E-031/temp (K)

ASR

(ohm

-cm

^2)

ASR fit to PNNL Data

ASR (Scandia stabilized Zirconia)

0.65

0.7

0.75

0.8

0.85

0 20 40 60 80 100 120 140time (seconds)

Vop

0

0.05

0.1

0.15

0.2

0.25

0 20 40 60 80 100 120 140time (seconds)

fuel

util

izat

ion

Modified SOFC 2D fuel cell model for operating configurations provided by PNNL:

Isothermal operating conditionsUser inputs for stream flow rates, compositions, and temperatures providedSingle cell set-up

ASR fit to material data from PNNL model.

Comparable results demonstrated between PNNL model and modified SOFC model.


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PES Switching Model

Issues with the modelSwitching discontinuityStiff system with nonlinearities

DC-DC Boost DC/AC Filter

Vin

Load

DC-DC Boost DC/AC Filter

Vin

Load


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PES Average Model

NeedSimpler ConfigurationFaster Computation and guaranteed convergence with fairly larger time-steps

Cons of the modeling approachPrediction of nonlinearity and chaos

Comparison and significance1.5 sec of system simulationusing

Average Model Average Model 5 sec5 secSwitching Model Switching Model 540 sec540 sec

Significant decrease in simulation time with appreciably high accuracy

0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5290

300

310

320

330

340

350

360

370

380

390

Time (sec)

Bus

Vol

tage

(V

)

Average ModelSwitching Model

Response comparison during Response comparison during load transientload transient

Average ModelAverage Model

Switching ModelSwitching Model


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Comprehensive System Model

Modeling Issues

Bulky BOPS model in gPROMS needs an gO:Simulink interface for data transfer between Matlab/Simulink and gPROMS.

Integrity of data exchange between individual subsystems running at their individual pace on their own platforms

Need of order reduction of modelsPSOFC : 1D vs 2D and 2D vs 3D modelPES : Switching to Average modelBOPS : Lookup table model


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Simulation Issues

Problems with ConvergenceIn the PSOFC model, which behaves similar to a current-controlled voltage source, the current information is unavailable at the start of the simulation (t = 0)

Infinite sampling timeThe PSOFC model by default assumes a infinite sample time and hence needs to be triggered at a particular rate to proceed with the simulation

Simulation Time1 sec of complete system simulation takes 1 million CPU (parallel processor-based Intel Xeon) seconds.


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Resolution of Simulation Issues

SOFC Model Changes to resolve convergence at the PSOFC and PES interface at t = 0

Multiple sampling ratesFor PES-BOPS interface to enhance simulation speed

Rate transition blocksEnsure data integrity at multiple sampling rates

Solver algorithmOde23tb

Solving crude error tolerances to solve stiff differential equations with algebraic loops.

BOPS reduced-order polynomial fit model

BOPS comprehensive lookup table model (in progress)


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VTVT BOPS Optimization


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BOPS Optimum Configuration

C E

HX IV

R

AirTank

Mixer

HX III

Motor

Anode

CathodeH2Tank

Mixer

MethaneTank

Mixer

HX I

HX II

Burner

PES LOAD

BBMotor

BoilerPump

WaterTank

Note: This optimal configuration was synthesized from a super-configurationinitially developed based on maximum

efficiency followed by parametric studies and the dynamic minimization of life cycle costs to arrive at the subset seen in this

schematic; this synthesis/design was carried out optimally taking into account the dynamic operational control of the

system.

Note: This configuration has been optimally synthesized/designed to respond in the shortest time possible to all transients.


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Residential Load Profiles

0

1

2

3

4

5

6

0 2 4 6 8 10 12 14 16 18 20 22 24

time (h)

Pow

er (k

W)

Summer Profile:Approximated load profile.

Cooling Day in Atlanta, Georgia Occurs on 07/11

012345678

24 26 28 30 32 34 36 38 40 42 44 46 48

time (h)

Pow

er (k

W)

Winter Profile:Approximated load profile.

Heating Day in Atlanta, Georgia Occurs on 01/12

Note: The system is optimally synthesized/designed using these two profiles back to back; the synthesis/design

accounts for optimal dynamic operation and control.


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Optimum Transient Response over Entire Load Profile

0.88

0.89

0.9

0.91

0.92

0.93

0.94

0.95

0.96

0.97

0 50000 100000 150000 200000

Time (sec)

Met

hane

Con

vers

ion

0.88

0.92

0.96

1

85000 87000 89000 91000

24 hrs


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994

998

1002

1006

1010

0 50000 100000 150000 200000

Time (sec)

Tem

pera

ture

(K)

Anode Inlet Temperature Cathode Inlet Temperature

996

998

1000

1002

85000 87000 89000 91000

24 hrs


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250

300

350

400

450

500

550

0 50000 100000 150000 200000

Time (sec)

Pres

sure

(kPa

)

Pressure Reference Tank Pressure

250

350

450

550

85000 86000 87000 88000

Time (sec)

Pres

sure

(kPa

)

Hydrogen tank pressure dynamic response.

250

300

350

400

450

500

550

0 50000 100000 150000 200000

Time (sec)

Pres

sure

(kPa

)

Pressure Reference Tank Pressure

250

350

450

550

85000 87000 89000 91000

Time (sec)

Pres

sure

(kPa

)

Air tank pressure dynamic response.

24 hrs


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1045

1052

1059

1066

0 50000 100000 150000 200000

Time (sec)

Tem

pera

ture

(K)

Temperature Reference Temperature

1050

1056

1062

1068

85000 87000 89000 91000 93000

Optimum steam-methane reformer reformat exit

temperature (state variable) dynamic response.

900

1000

1100

1200

1300

0 50000 100000 150000 200000

Time (sec)

Tem

pera

ture

(K)

1000

1100

1200

1300

85000 87000 89000

Optimum steam-methane reformer hot gases inlet

temperature (control variable) dynamic

response.

24 hrs


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VTVT Interaction Analysis


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Effect of Load Power Factor

Effect of Load Power Factor on Hydrogen utilization

0.47

0.49

0.51

0.53

0.55

0.57

0.59

0.15 0.16 0.17 0.18 0.19 0.2

Time (sec)

Hyd

roge

n Util

izat

ion

H2 util 0.8H2util 0.9H2util 0.95H2util 1

SOFC Current variation with Load Power Factor

21

22

23

24

25

26

27

28

29

0.15 0.16 0.17 0.18 0.19 0.2Time (sec)

SOFC

Cur

rent

(A)

Current PF=1Current PF=0.95Current PF=0.9Current PF=0.8

0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.2523.5

23.75

24

24.25

24.5

24.75

25

25.5

T ime (sec)

Cur

rent

(A)

PF = 1PF = 0.9PF = 0.8

The lower the load power factor

The higher is the SOFC stack current and current rippleThe higher is the hydrogen utilization


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Operating temperature increase ASR decreases exponentially with increase in the temperatureLesser potential dropHigher efficiency

0 100 200 300 400 500 6000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Time (sec)

Con

vers

ion

Eff

icie

ncy

FF = 0.053 mols/secFF = 0.064 mols/secFF = 0.107 mols/sec

FF = Fuel F low

0 100 200 300 400 500 600 700 800 900995

1000

1005

1010

1015

1020

1025

1030

1035

1040

1045

Time (sec)M

ax. T

empe

ratu

re (

K)

FF = 0.064 mols/secFF = 0.107 mols/secFF = 0.053 mols /sec

FF = Fuel F low rate

010 100 200 300 400 500 600

0.38

0.4

0.42

0.44

0.46

0.48

Time (sec)

Sta

ck C

onve

rsio

n E

ffic

ienc

y

980 K990 K1000 K1010 K1020 K

Fuel flow rate increaseSlight decrease in the temperatureDecrease in the efficiency

Impacts of Parametric Variations on the Impacts of Parametric Variations on the Effects of Load TransientEffects of Load Transient

Con

vers

ion

Eff

icie

ncy

Con

vers

ion

Eff

icie

ncy

Max

. Tem

pera

ture

Max

. Tem

pera

tureC

onve

rsio

n E

ffic

ienc

yC

onve

rsio

n E

ffic

ienc

y


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1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 3.75 40

0.1

0.2

0.3

0.4

0.5

0.6

Time (sec)

Fuel

Util

izat

ion

1 1.5 2 2.5 3 3.5 40

0.2

Cur

rent

Den

sity

(A

/m2 )

1 1.5 2 2.5 3 3.5 40

0.05

0.1

0.15

0.2

0.25

1 1.5 2 2.5 3 3.5 4200

240

280

320

360

400

Time (sec)

Bus

Vol

tage

(V

)

Hyd

roge

n U

tiliz

atio

nH

ydro

gen

Util

izat

ion

Cur

rent

Den

sity

(A/c

m^2

)C

urre

nt D

ensi

ty (A

/cm

^2)

DC

Bus

Vol

tage

(V)

DC

Bus

Vol

tage

(V)

Effect of step-load transient vs. single-load transient

StepStep--load Transientload Transient

SingleSingle--load Transientload Transient

Step-load transient leads toSignificant reduction in the drop of the DC bus voltageReduction in increase of the hydrogen utilization and current density during the transient

Reduction in the battery size

StepStep--load load TransientTransient

SingleSingle--load load TransientTransient


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Conclusion

1D PSOFC model appears to be a good choice to study the load tra1D PSOFC model appears to be a good choice to study the load transient nsient effects to reduce computation time without compromising accuracyeffects to reduce computation time without compromising accuracy. But, to . But, to accurately study the characteristics including thermal stress, taccurately study the characteristics including thermal stress, temperature, emperature, strength, and the reliability prediction should be based on the strength, and the reliability prediction should be based on the PSOFC 2D PSOFC 2D model;model;

On a similar note, the stateOn a similar note, the state--space averaged model of PES is better suited for space averaged model of PES is better suited for the study of loadthe study of load--transient effects from computational efficiency standpoint; transient effects from computational efficiency standpoint;

FullyFully--controlled BOPS model may accurately emulate the actual system bcontrolled BOPS model may accurately emulate the actual system but, ut, for for spatiospatio--temporal studies on a basic PC, a reducedtemporal studies on a basic PC, a reduced--order lookuporder lookup--table table model based on the comprehensive model is a more effective choicmodel based on the comprehensive model is a more effective choice;e;

StepStep--load transients as compared to single loadload transients as compared to single load--transient reduces the transient reduces the harmful effects on the SOFC and improves the performance of the harmful effects on the SOFC and improves the performance of the PES, PES, which may lead to reduction in the sizes of energywhich may lead to reduction in the sizes of energy--buffering components buffering components (e.g., battery or PHT) and hence, the cost and weight of the pow(e.g., battery or PHT) and hence, the cost and weight of the power system.er system.


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Future Works

Build a complete look-up table model for the BOPS to enhance faster and accurate simulation

Experimental validation of the obtained simulation result on a PSOFC stack

Investigate the electrical feedback effects on the material properties of the PSOFC and prediction of life of the PSOFC

Build an optimal hybrid controller for the PSOFC system to optimize the stack performance whilewhile enhancing the reliability of the PSOFC

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