Modeling of Electrical Interactions with SOFCs

Industrial CollaboratorsD. Herbison & V. Tchkalov

Synopsys Inc.

Joseph HartvigsenCeramatech

Project InvestigatorsS.K. Mazumder

University of Illinois

M. von Spasovsky andD. Nelson

Virginia Tech.

C. Haynes Georgia Tech.

SECA Modeling & Simulation Team – Integration MeetingFebruary 19-20, 2003

Sacramento, CA

Student AcknowledgementR. Burra and K. Acharya (U of I)Diego Rancruel (VT)Robert Williams (GT)

AcknowledgementDoE SECADon Collins (NETL)Engineous SoftwareJoe Hertvigsen (Ceramatech)Jonathan Felton (PSE, UK)Lee Johnson and Ken Ruan (Synopsys Inc.)

R&D ObjectivesDevelop fully transient nonlinear, unified models for SOFC planar configurations, different PESs and application loads, and a variety of BOPS componentsDemonstrate the feasibility of integrating these models into an overall systems-analysis and optimization tool (Phase I)Develop a prototypical software package (Phase II) for industry to understand the dynamical and stead-state system interactions among of SOFC stack, power electronics, and BOPS and system optimizationConduct parametric studies (Phase I) and optimizations (Phase II) to determine control strategies and their effects on the cell reliability, efficiency, and power density; as well as system response and configuration, and component designs.

Applicability to SECAA “Unique” “Simple-to-Use” Tool for “Rapid” Prototype SOFC Power-Conditioning System Design and MarketabilityResolving the “Steady-State” and “Transient” Dynamics of the SOFC, Power-Electronics Interface, BOPS for

Stationary LoadsNon-Stationary LoadsHigher Power Distributed Power Systems

Optimization and Control EnhancementDesigning control for optimal bandwidthCost-effective design

“Multi-Disciplinary” “Industry +Academic” Expertise for SOFC Power-Conditioning System Design:

University of Illinois – PES Synopsys Inc. (SABER – 30000 models)Virginia Tech – BOPS gPROMS (PSE - Optimizer + Nonlinear Solvers)Georgia Tech – SOFC iSIGHT – (Engineous - System Integration)

TOPAZ – (Ceramatech - FEA for SOFC thermal and current-density distribution)

DoE SECA Tasks Timeline – Phase I

Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug SepPhase I

Task 1.0 Planar SOFC Model Development

Task 2.0 Model of Power-Electronic Interface

Task 3.0 Load Profile Development

Task 4.0 BOPS Model Development, Implem. & Valid.

Task 5.0 SOFCSS Model Implementation Environ.

Task 6.0 Integration of PES, SOFCSS, & BOPS Models

Task 7.0 Analysis of System Stability and Dynamics

Task 8.0 Parametric Studies of Best-Practice Ctl. Strat.

Task 9.0 Final Report and Phase II Proposal

Methodology

Power-Electronics System (PES)

Fuel Cell Power-Conditioning System

PES

V=f(i)VDC or

• Conventional Modeling Techniques– Fuel cell manufacturers typically model the FC feeding a constant impedance– Power Electronic Engineers typically model the FC as a dc voltage source or a current controlled voltage

source feeding the PES

• Our Approach

),,( LOADPESBOPSfIV

=

SOFC

IMPEDANCE

SW1, SW2 MOSFET, IGBT

SOFC

Impedence1

LOAD

SW1

SW2

SOFC

Impedence2

LOAD

SW1

SW2

Source

FuelFuel

ProcessorFuel-Cell

Stack

Water Management

Air System

Thermal Management

Power-Electronics

System

Fuel In

Wat

er

Out

Air In

Heat Out

Exha

ust

Heat Out

Exhaust Out

Stationary/

Non-stationary

Load

PESSOFC

BOPS

V,I

Proposed Simulation Platform for Fuel-Cell System

SABER (PES)

Visual Fortran (SOFC)

iSIGHT (Integration)

gPROMS (BOPS)

TOPAZ (FEA Simulation)

Power-Electronics TopologiesLine Commutated Self Commutated (PWM)

Line Commutated Transformer Assisted

• Variation in topologies effect the current and voltage ripple dynamics of the SOFC, cost, and dynamic response

Fuel-Cell Transients With Variations in Input Filter

340

380

420

460

500

0.065 0.075 0.085 0.095 0.105

Input Filter -- 1mHInput Filter -- 0.5mHInput Filter -- 0.2mH

Time (s)

Vol

tage

(V)

0

50

100

150

200

250

0.065 0.075 0.085 0.095 0.105

Input Filter -- 1mHInput Filter -- 0.5mHInput Filter -- 0.2mH

Time (s)

Cur

rent

(A)

Ove

rsho

ot

Steady State Ripple

0.065 0.075 0.085 0.095 0.105

Input Filter -- 1mH

Input Filter -- 0.5mH

Input Filter -- 0.2mH

0

20

40

60

80

Time (s)

Pow

er (k

W)

60

66

72

78

84

90

0 0.2 0.4 0.6 0.8 10

2

4

6

8

10

Input Filter Inductor (mH)

Cur

rent

Ove

rsho

ot D

urin

gLo

ad T

rans

ient

(A)

Stea

dy S

tate

Cur

rent

Rip

ple

(A)

• Steady state ripple decreases with increase in input filter size, but load transient overshoot increases• Transient and steady state power ripple could subject the fuel cell to thermal cycles• Therefore, an optimum value of input filter should be chosen to reduce the degrading effect on the SOFC

Project Status at UIC

PES

SOFC loadtransient response

SOFC steady state response

Parametricvariations

Topological Variations

Energy Storage Distri--bution & Optimization

Nonlinear Behavior•Circuit parameters•Load

Control Strategies•Local/global•Modulation Schemes

α

β

u*

Modulation

SVM

Tasks Accomplished

Tasks to beAccomplished

IllustrationsNonlinear Behavior of a DC-DC Converter

Multi-Objective Control and

Optimization for Hybrid IPNs

DoE SECA +NSF CAREER

• By simply varying “only one” parameter (load in this case), the voltage and current ripples of the converter change drastically. In reality, more than one parameter can vary simultaneously.

VR

CR

VR

CR

VR

CR

VR

Idea Behind A New Fast Hybrid Control For Protecting the SOFC during Load Traneints

Hybrid StrategyControl the dynamics of

unsaturated and

saturatedregions separately

σ1 = 0

σ 2=

0

Integrating TOPAZ

Co-flow SOFC Symmetry Section Mesh

Co-flow SOFC Symmetry Section Mesh

Model Temperature Distribution

Selected Nodes on Electrode MeshVoltage

Current Response to Imposed Voltage

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.000 0.010 0.020 0.030 0.040 0.050 0.060

Time (sec)

Interior Nodal Voltage Response

0.5

0.6

0.7

0.8

0.9

1.0

0.00 0.01 0.02 0.03 0.04 0.05 0.06

Time (sec)

Negligible Thermal Response in 60 msec

1140

1145

1150

1155

1160

1165

1170

1175

0.00 0.01 0.02 0.03 0.04 0.05 0.06

Time (sec)

Typical Step Load Thermal Response

1070

1080

1090

1100

1110

1120

1130

1140

1150

1160

1170

0 60 120 180 240 300 360 420 480 540 600

Time (sec)

Cross-Flow Temperature Distribution

Internal reformingExternal radiation boundaries

1086.8 K Tmax973.0 K Tmin

Solid-Oxide Fuel Cell Modeling

Transient SOFC Response to Electrical Stimulus: Modeling Approach

Reactants’ inlet flow rates and properties are invariant during relatively short transient episode

Quasi-steady state electrochemistry

Lagrangian extension of validated steady state model to track fuel parcels that travel over electroactive area

Fuel Cell

11

Fuel Stream

Oxidant Stream

x

t + ∆t t

x+ ∆x

t t + ∆t v1

v2

ηelement(t+∆t) =ηfield(x+∆x, t +∆t)

SOFC Example: SWPC TSOFC “Bundle”

3 (parallel) x 8 (series) stack producing single-digit kilowatts

Field tested

Complementary simulation to the “flat planar” designs under SECA support

Design with experimental data available limited extent

Steady-State Validation

100

200

300

400

500 C

urre

nt (A

mps

)

0.5 0.55 0.6 0.65 0.7 0.75 0.8 Voltage (J/C)

Experiment Model

Comparison of Model and ExperimentF.U.=85%; NOS=6; 89%H2, 11%H2O

Pressure=3 atm

Accuracy to within 3-5%

Steady-State Validation: Cont.’d

100

200

300

400

500 C

urre

nt (A

mps

)

0.55 0.6 0.65 0.7 0.75 0.8 0.85 Voltage (Volts)

Experiment Model

Comparison of Model and ExperimentF.U.=85%; NOS=6; 89% H2, 11% H2O

Pressure=15 atm

Accuracy to within 3-5%

Impact of Electrical Stimulus:Potentiostatic Control (Power Increase)

360

400

440

480

520

84%

87%

90%

93%

96%

0 0.2 0.4 0.6 0.8 1 t*=t/T

Current, Fuel Utilization TransientsDependence on Dimensionless Time

Fuel utilization

Current (Amps)

Current spikes up, yet the fuel supply remains invariant due to the decoupling of the cellFuel utilization thus increases; this causes current (and power) to decrease from t*=0+

values, until a new steady state “match” occurs at the new voltage (t*=1)Attainment of steady state at the time constant {T=Lcell/vfuel}

Impact of Electrical Stimulus:Potentiostatic Control (Cont.’d)

Fuel Cell

1234

Fuel Stream

Oxidant Stream

t = 0+

Reactants’ inlet flow properties are the same

The fuel elements’ exit properties depend upon their locations at t*=0+

Steady state is regained when element 3 exits (t*=1), because every successive element will then pass along the cell “seeing” only the new operating potential

Impact of Electrical Stimulus:Galvanostatic Control (Power Increase)

4.74.84.9

55.15.25.35.45.55.65.75.8

0.000 1.000 2.000 3.000 4.000 5.000

τ (s)

Bun

dle

Volta

ge (V

)

FU - 0.500FU - 0.625FU - 0.750

*τ equals fuel celllength divided bythe fuel velocity.

Initial Current: 1000AStep Change to: 1200A

Multiple voltage reductions are “seen” by the reactant streams

Transient is thus longer by multiples of the time constant

Larger initial fuel utilizations prolong the relative transient due to enhanced fuel depletion effects

Illustration of Respective Fuel Utilization Trends {20% Increases}

00.10.20.30.40.50.60.70.80.9

1

0.000 1.000 2.000 3.000 4.000 5.000

τ (s)

Fuel

Util

izat

ion

Initial Current: 1000AStep Change to: 1200A

Dual Mode Potential Loss: Polarization Curve Effect & Reactant Depletion

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Dimensionless Current,I*

Volta

ge

12

3

Low Fuel Utilization High Fuel Utilization

“Polarization Curve Effect” Less Dominant at Higher Initial Fuel Utilizations

0.68

0.7

0.72

0.74

0.76

0.78

0.8

0.82

0.84

0.86

0.45 0.5 0.55 0.6 0.65 0.7 0.75

Fuel Utilization

V L

VL= Fraction of Voltage Drop due to Polarization Curve Effect

Variations in Current Density Distribution via Load Fluctuation

0

0.5

1

1.5

2

2.5

3

Dimensionless Distance

Slic

e C

urre

nt (A

)

1100 Amps

1000 Amps

Balance-of-Plant System (BOPS)

SOFC Based APU: Steam Methane Reformer ComponentSMR Dynamic Response

0.81

0.82

0.83

0.84

0 10 20 30Time (Min)

CH4

Conv

ersi

on (%

)

5% Step 2% Step

MODEL DESCRITIONAssumptions

Axial dispersion and radial gradient are negligible

Reforming and combustion gases behave ideally in all sections of the reactor

Gas flow pattern through the channels is plug flow

Demethanation and water gas shift reactions are kinetically controlled

Reaction kinetics are adequately described by a pseudo-first-order rate equation

Bed pressure drops are neglectedUniform Temperature through each

catalyst particle

The mass balance on a control volume

MODEL PHYSICS AND DYNAMICS

222 COHOHCO +→+SMR reaction: COHOHCH +→+ 224 3

∫=

= −=

4

4

,4

0

CHi

XX

X CHo

smrCH

rdX

D

nL

π4 4expSMR SMR

CH o CHSMR

avg

EAr k P

RT− = −

( )tCer

zvC

BCH ∂∂=−

∂−∂

4

( ) ( ) ( ) ( ) ( )tTCdTTdAhTTdh

zXHF

zTFC

pi

ci

cci

wip

∂∂=−+−+

∂∂∆−+

∂∂

∑=

ρπππ44

222

11

2

SMR kinetics:

SMR dynamic mass balance:

SMR dynamic energy balance:

A∆

ipn ,

0, =ipX

actualpn

pX

actualp

actualp dnn +

pp dXX + opX ,

actualpn 0,

L

SOFC Based APU: Heat Exchanger and Steam Generator ComponentsCOMPACT HX

Heat Exchanger Dynamic Response

425430435440445450

0 200 400 600 800 1000

Time (s)

Tem

pera

ture

(k)

Cold Output Temp Hot Output TempMODEL PHYSICS AND DYNAMICS

( ) ( ) ( ) ( ) ( ) 0=−+−=∂

∂WccWhh

WWp TThATThA

tTmC ηη

( ) ( ){ }0.22 0.7811 exp exp 1r

r

NTU C NTUC

ε = − − −

( ) ( )

11 1

o oh c

UA

Ah Ahη η

=+

min

UANTU

C=

23

ph jGC Pr−

=

( ) ( ) ( ) ( ) 0=−+∂∂+

∂∂

Wccc

ycpc

cp TThAyTLwC

tTmC η

Heat

transfer:

Energy

Balance:( ) ( ) ( ) ( ) 0=−+

∂∂−

∂∂

Whhh

yhph

hp TThAy

TLwCt

TmC η

STEAM GENERATOR

MODEL DESCRITIONCompact Heat Exchanger: Energy and mass balance are performed

Plate-fin type with a single-pass, counter-flow arrangementOne-dimensional flowWall temperature in each section is a function of time only (spatially

constant)Heat exchanger is adiabatic overallHeat transfer models based on Shah (1981) and Kays and London

(1998)Effectiveness-NTU method applied in order to relate the geometric

models to the thermodynamic ones Fluid thermal capacitance is negligible compared to the wall’s

Steam GeneratorCross-flow, shell-and-tube heat exchanger (single-pass shell and two

tube passes)Consists of an economizer, an evaporator and a superheaterTube-side heat transfer coefficient: Correlation for fully developed

laminar or turbulent flow for the economizer and superheater. Correlation of Kandlikar (1989) for the evaporator

Shell-side heat transfer coefficient: Correlation suggested by Kern (1950)

SOFC Based APU: Compressor and Turbine Components

Compressor Dynamic Response

480

495

510

525

540

0 200 400 600 800Time (s)

Tem

pera

ture

(K)

Compressor Exit TemperatureMODEL DESCRITION

Compressor/ExpanderTwo energy balances performed to determine

the input power required for a certain pressure ratio and percentage of that power recovered

Heat transfer coefficient to the environment is constant

The internal heat transfer coefficient is flow dependant and a function of the hydraulic diameter

Performance maps for the steady state condition were used

Thermal capacitance of the casing, impeller, and inlet ducts is approximated to a single thermal mode Tm Wkt is the turbine power output, Wkc is the compressor power input, Wkm is the

mechanical loss

kmkcktk WWWW −−=∆

( )( )

−

+=∆ m

pq TTT

CWhA

T2

21

2

1&

Heat transfer:

Energy

Balance:

−

=∆

−

1

1

1

21 γγ

η PPTT

cWork

Workq TTTT ∆+∆−= &12

NIW

tN k

⋅∆=

∂∂

( ) ( ) ( ) ( )ambmomm

p TThATTThAt

TmC −−

−

+=

∂∂

221

1

Air

ED

M

Electric Motor

Hot Gases

Latter Phase I/ Phase II Activities

Expansion of transient performance modelingBridge the transient simulation algorithms to prototype/ pre-prototype “flat planar” SOFC modulesSimulate “real world” load following and fluctuations via superposition of step changes in electrical variablesEnhanced integration with balance-of-plant reactants supply and power conditioning subsystems

Investigation of current ripple impact upon reliabilityElectrochemical “fatigue”/degradation due to multiple charge-discharge cycles associated with current rippleThermal “fatigue” associated with oscillations in current density distribution

SOFC Based APU: Balance of Plant Sub-System (BOPS) Summary

PHASE I : TRANSIENT MODELING OF THE SOFC BASED APU’S BOPS

TASKS ALREADY PERFORMED

Sub-system interactions definition (fuel cell stack, power conditioner, and balance of the plant).

Definition of BOPS and system configurationsDevelopment of dynamic thermodynamic, heat transfer,

and physical models for each component of the BOPSCompressor, expander, heat exchangers, steam

generator, reformer, fuel storageImplementation of models in a dynamic programming

environment using state-of-the-arte transient numerical solver

Compressor, expander, heat exchangers, reformer

PHASE II : SYSTEM CONTROL STRATEGIES

Application of large-scale optimization using decomposition

Determination of optimal control strategies based on their effects on system reliability, performance and response

TASKS TO BE PERFORMED

Implementation of models in a dynamic programming environment

Steam generator, fuel storageIntegration of BOPS component models into a

BOPS sub-system modelIntegration of the PES, SOFCSS, and BOPS modelsAnalysis of system stability and dynamicsParametric studies (trade-off analysis) of best-

practice control strategies

A: Pre-reformerB: CombustorC: Steam generatorD: Air compressorE: Gas expanderF: Water pumpFT: Fuel tank G: Water tankH: Pre-reforming mixerI: Combustor mixerM: Air-Comb gas mixerN: Methane compressorHXI: Fuel preheating HXHXII: Air preheating HX HXIII: Methane preheating HXHXIV: Steam preheating HXHXV: Air RecuperatorHXVI: District heating HX

SOFC Based APU Configuration

Air

Combustion Gases

Water

District Heating

Anode

Cathode

E

AH

C

G

D

M

F

FT

IB

Methane

Power-Electronics Subsystem

Application Load

Combustion Gases

Water

District Heating

AnodeCathode

E

AH

C

G

D

MMF

HX III

HX V

HX IV

HX I

HX II

HX VI

FT

IIBB

Electric Motor

Power-Electronics Subsystem

Power-Electronics Subsystem

Application Load

Application Load

Battery Bank

Energy storageBattery Bank

Energy storageMMF MMD MMN

DN

Summary: SOFC Based PowerSummary: SOFC Based Power--Conditioning SystemConditioning System(PES+SOFC) ANALYSES

gPROMS (BOPS)

iSIGHT (INTEGRATION)

SABER (Power-Electronics System)

VISUAL FORTRAN (SOFC)

SOFTWARE SYSTEM INTEGRATION

0

50

100

150

200

250

0.065 0.075 0.085 0.095 0.105

Input Filter -- 1mHInput Filter -- 0.5mHInput Filter -- 0.2mH

60

66

72

78

84

90

0 0.2 0.4 0.6 0.8 10

2

4

6

8

10

Steady State Parametric

PHASE I (Industrial Support: Synopsys Inc., Ceramatech, Engineous Software, PSE)(Communication: Delphi, ORNL, IFC)

CompletedModeling of PES interfaces for stationary applicationsIntegration of PES and preliminary SOFC modelsMulti-software platform integration

In Process (and carry on to Phase II)Integration of PES and SOFC models with BOPS modelModeling of PES interfaces for non-stationary applicationsLoad profilingParametric studies and bifurcation analyses related to ripple dynamicsImpact of steady-state and transient ripple dynamics “for any given PES topology” on

the current-density and thermal distribution inside a SOFC (with Ceramatech)PES and BOPS control and energy-conservation techniques to alleviate the impact of

load transients on SOFC

PHASE II

Experimental validation of theoretical predictions to determine the accuracy of models and methods and predictions of analyses and control strategies

System optimization (based on cost, durability, performance, and response): distributed control strategies, energy-conservation techniques, ripple dynamics for a given topology vs thermal and current-density distribution inside a SOFC

Optimal PES for stationary and non-stationary application loads and experimental verification

PES TOPOLOGIES

Line Commutation Line Commutation

Self Commutation (PWM) Transformer Assisted

Transient