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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