240 th ECS Meeting I01A-1016 1 / 19 240 th ECS Meeting (Orlando, Oct.10-14, 2021), I01A-1016 S. Hasegawa a,b , M. Kimata b , Y. Ikogi b , M. Kageyama a , S. Kim c , and M. Kawase a a Department of Chemical Engineering, Kyoto University b Commercial ZEV Product Development Division, Toyota Motor Corporation c Department of Applied Physics and Chemical Engineering, Tokyo University of Agriculture and Technology [email protected]Modeling of Fuel Cell Stack for High-Speed Computation and Implementation to Integrated Fuel Cell System Model
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Virtual engine-control unit Virtual fuel cell system
Fuel cell models
Pow
er
Time
System net-power target
Pow
er
Time
System net-power response
<Features>・Entire fuel cell system hardware & controllers are integrated as an working simulation package ・Dynamic & multi-scale model : Vehicle specifications (~ m-scale) - FC Material Properties (nm-scale ~)・High-speed computation (x50 than real-time) → Applicable to life-long dynamic simulation in allowable simulation time・High-accuracy → validation and verification by the database collected with 2nd-generation Mirai FCEV system
(1) (2)
(1) Hasegawa, et al. ‘Model-Based Development of Fuel Cell Stack and System Controllers’, The 14th International Symposium on Process Systems Engineering (PSE 2021), submitted(2) Hasegawa, et al. ‘Development of Multi-Purpose Dynamic Physical Model of Fuel Cell’, The 14th International Symposium on Process Systems Engineering (PSE 2021), submitted
Sub-sustem models
Input Output
FC-currentsetpoint
FC-statesetpoints
Actuatorsetpoints
FC-powerresponse
Input
Output
240th ECS MeetingI01A-1016
7 / 19
Function-block description : 1D-physical model & state variables (Flowrate, pressure, temperature, composition) encapsulated- System model : boundary conditions for fuel cell model (pressure, flowrate, temperature, and gas compositions)- Fuel cell model : generation and consumption rate to system model & polarization (voltage, resistance) for system models
2. Fuel cell integrated system simulator - Configurations -
- Simple catalyst utilization-ratio model with 2 empirical parameters- Direct calculation of activation overpotential without iterative computation for convergence of distributions
……
……
(k)
(k+1) ∅ion(k+1)
∅ion(k)
∅C(k+1)
∅C(k)
Ionomer-phase Carbon-phaseThickness
Pt
Physical : 1D-potential distribution model
MPL
CL
PEM
H+
e-
H+
e-
Wet region = Active
Dry-out region= Inactive ×
Empirical : Catalyst utilization-ratio model
𝑖 = 𝑖0eff
CO2
Pt
𝐶ref
𝛾
𝑒𝑥𝑝 +𝛼𝑐1𝐹
𝑅𝑇∆Φ − 𝑒𝑥𝑝 −
𝛼𝑐2𝐹
𝑅𝑇∆Φ
≈ 𝑖0eff
CO2
Pt
𝐶ref
𝛾
𝑒𝑥𝑝 +𝛼𝑐1𝐹
𝑅𝑇∆Φ
↔ ∆Φ =𝑅𝑇
𝛼𝑐1𝐹𝑙𝑛
𝑖
𝑖0eff
− 𝛾𝑅𝑇
𝛼𝑐1𝐹𝑙𝑛
CO2
Pt
𝐶ref
Activation overpotential for ORR
Activation overpotential
Concentrationoverpotential
Effective exchange current density for ORR
𝑖0eff = 𝑖0
ref × 𝑓1 𝑎H2O
ion × 𝑒𝑥𝑝 −𝐸a𝑅
1
𝑇−
1
𝑇refReferenceexchange
current density(Material-unique)
Catalyst utilization ratio
function
Temperature-dependent termexpressed with activation energy
- Simple mass-transfer resistance model & limiting-current density model with 3 empirical parameters- Direct calculation of concentration overpotential without iterative computation for convergence of distributions
Mass-transferResistance of CL
Pt
𝑓 2𝑎H2O
pore
[-]
0
240th ECS MeetingI01A-1016
11 / 19
𝜆(𝑡) = 𝜆(𝑡−∆𝑡)𝑒𝑥𝑝 −∆𝑡
𝜏
≈ 𝛼𝜆 𝑡 + 1 − 𝛼 𝜆 𝑡−∆𝑡 , 𝛼 =∆𝑡
𝜏,
3. Fuel cell models – B : Pseudo-dynamic model -
Physical : Dynamic water balance model
Empirical : Psudo-dynamic water balance model
- Simple time-constant-based pseudo-dynamic water balance model with 2 parameter - Direct calculation of 𝜆 explicitly without iterative computation for convergence of 𝜆 in each time-step
𝑑𝜆
𝑑𝑡Adsorption
DesorptionDiffusion
Drug
Generation
Adsorption
DesorptionDiffusionDiffusion
𝜆(𝑡−∆𝑡)
Time-constantGeneration
DiffusionDiffusion DiffusionDrug
cMPLcCLPEMaCLaMPL
𝜆(𝑡) =𝜆aPEM(𝑡)
+ 𝜆cPEM(𝑡)
2
Updated water-uptake in PEM
aPEM cPEM
𝑡
Scaling of water-uptake transitional delay by adsorption & desorption dynamics
𝜆(𝑡) ≥ 𝜆(𝑡−∆𝑡)(Adsorption) : 𝜏 = 𝜏𝑎𝑑𝑠
𝜆(𝑡) < 𝜆(𝑡−∆𝑡)(Desorption) : 𝜏 = 𝜏𝑑𝑒𝑠
Time-constant
Transfer-function of discrete first-order lag system
Relaxation coefficient
Time-series
𝑡 − ∆𝑡𝑡 − 2∆𝑡𝑡 − 3∆𝑡𝑡 − 4∆𝑡
Steady-stateslice
𝜆(𝑡)
𝛼𝜆(𝑡)
Fixed time-step (8ms)
𝛼𝛼
𝛼Transition to next time-step withRelaxation coefficientα
- Simple scaling model of 2D-distribution with 2 parameters (Currently set as constant values)- Direct calculation of 1D mass transport without iterative computation for convergence of 2D-distribution
𝑃𝑖aCH = 𝛼aCH𝑃𝑖
aCHin + 1 − 𝛼aCH 𝑃𝑖aCHout
Scaling functions
Scaling coefficients
MEA
Dry
Wet Dry
Wet
Air
H2
In-plane water transport
Through-plane water transport
Scaled 1D-boundary
conditions
Empirical : Scaled boundary condition model
<1D mass transport models>
In-plane water transport
Inlet&Outlet conditions
Scaling functions
Overall flux of O2, H2, N2 and H2O
across the cell
Concentration distribution& Polarization
Source-termin system models
<Input> <Output>
For i = O2, H2, N2 and H2OcCH
aCH
𝑃𝑖cCH = 𝛼cCH𝑃𝑖
cCHin + 1 − 𝛼cCH 𝑃𝑖cCHout
Scaling coefficients (0 ≤ 𝛼 ≤ 1)
𝛼aCH = 𝑓3aCH ሶ𝑣aCHin, 𝑇𝑎𝑣𝑒
𝛼cCH = 𝑓3cCH ሶ𝑣cCHin , 𝑇𝑎𝑣𝑒
Volumetric flowrate at channel-inlet
Average fuel cell temperature
For i = O2, H2, N2 and H2O
𝛼aCH = 𝛼cCH = 0.5
𝛼aCH = 𝛼cCH = 1.0
For i = O2, H2, N2
For i = H2O
For i = O2, H2, N2
For i = H2O
Implementation
𝑓 3aCH
ሶ𝑣aCHin,𝑇
𝑎𝑣𝑒
[-]
𝑓 3cCH
ሶ𝑣cCHin,𝑇
𝑎𝑣𝑒
[-]
(Constant)
(Constant)
ሶ𝑣 [m3/s]
240th ECS MeetingI01A-1016
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Physics in FC-stack& sub-systems
Integrated system model
All the models are implemented on MATLAB platform (toolbox : SIMULINK only) for (1) Dynamic simulation platform, and (2) Controller integration
Fuel cell & Sub-system models
3. Fuel cell models - Implementation -
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All the parameters can be determined with 1cm2-cell data (NOT cell/stack data)and microscopic measurements of material geometry (thickness, porosity, …)
System-testbeds / Test vehicles2nd-generation Mirai FCEV
Measurementby sensors
Actuating values(Pump, valve…)
FC-System models
Stack-inlet /outlet Boundary conditions- Flowrate- Pressure- Temperature- Gas compositions
Fuel cell model
(Model)Dynamic I-V performance
(Experiment)Dynamic I-V performance
Validation procedureValidation data collection
Validated by the database collected in low to high operating load and temperature with 2nd-generation Mirai(3) S. Hasegawa, et al. ‘Application of Model-Based Development to Product Fuel Cell Systems and Controller Design’, EVTeC 2021 Proceedings, in press(4) Hasegawa, et al. ‘Development of Multi-Purpose Dynamic Physical Model of Fuel Cell’, The 14th International Symposium on Process Systems Engineering (PSE 2021), submitted
(3)(4)
P Pressure
Q Flowrate
T Temperature
H2 H2 concentration
L Liquid-water level
Sensors
240th ECS MeetingI01A-1016
16 / 194. Model validation - Accuracy -
Cu
rren
t d
en
sit
y [A
/cm
2]
Coola
nt-
ou
tlet
tem
pera
ture
[℃
]
Time [s]
Time [s]
Time [s]
Cell v
olt
age [
V]
Cell v
olt
age [
V]
Current density [A/cm2]
(Input) Boundary conditions (Output) Average cell voltage in FC-stack
Good agreement including dynamic behavior with experimental data collected in wide range of operating conditions with the commercial FCEV
ー SIMー EXP
● SIM● EXP
240th ECS MeetingI01A-1016
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Summary of computational speed
> 50 timesacceleration
than real-time
Capability of year-long durability simulation in allowable computational time
240th ECS MeetingI01A-1016
18 / 19Conclusions
FC-Platform Program : Development of design-for-purpose numerical simulators for attaining long life and high performance project (FY2020 - 2022), New Energy and Industrial Technology Development Organization (NEDO), Japan
- Model-reduction methods of 1D & 2D distribution by keeping accuracy
- Parameter determination procedures based on the small-size cell database
- Validation by considerable amount of 2nd-generation Mirai FCEV database
Acknowledgement
1D fuel cell stack model for high-speed computation was developed to enable year-long simulation of an entire fuel cell system dynamics in allowable calculation time
Future study : Integration of degradation models of platinum, carbon, PEM