Modeling of Fuel Cell Stack for High-Speed Computation and ...

240th ECS MeetingI01A-1016

1 / 19

240th 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 Universityb 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


2 / 19Outlines

1. Objective 3. Fuel Cell Models

2. Integrated Fuel Cell System Simulator 4. Model validation


3 / 191. Objective - V-flow of FC-system development -

Vehicle planning

System Design

Component Design

Control Design ECU Prototype

Component Prototype

Vehicle Prototype

Design Phase Evaluation Phase

System Prototype

CHALLENGE : Application of FC-system to wider range of commercial mobility

LEAD TIME

…

…



Vehicle planning

System Design

Control Design ECU Prototype


Iterative loop of controller calibration

System Prototype

LEAD TIME

Controller calibration can be started only after system prototype is ready

ISSUES : System complexity → Cost & lead time of iterative prototyping and calibration

Vehicle Prototype

…

…

Component Design Component Prototype



ECU Prototype

Vehicle Prototype


System Prototype

Virtual FC-systemVehicle planning

System Design

Control Design

TARGET : Virtual platform of FC-system hardware & software development for reduction of cost and lead time of prototyping

LEAD TIME

Hardware ＆ Control software, with prospective goal achievements, BEFORE prototyping, DURING design phase

Virtual unit & control development platformwith lower-cost of prototypes

for iterative design-change

…

…

Component Design Component Prototype


6 / 192. Fuel cell integrated system simulator - Overview -

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


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 -

Fuel cell & H2 sub-system

H2


8 / 193. Fuel cell models - Overview -

Category Component Physics Modeling method Novelty

Mass-transport

Cell In-plane distribution Empirical weighting-function model of in-plane distribution 〇

GDL/MPL Mass transport in through-plane direction Maxwell-Stefan equation

Gas diffusivity Chapman–Enskog equation, Knudsen diffusion equation

CL Mass transport from pore to catalyst surface Mass transfer resistance model 〇

Humidity effect on mass transport Empirical mass transport resistance function, Limiting current density model 〇

PEM Mass transport at polymer-gas boundary Empirical discrete-first-order-lag model 〇

Water diffusion Fick’s law

Water uptake Empirical water uptake function

Water diffusivity Empirical water diffusivity function

Electro-osmotic drag Empirical drag coefficient function, Water flux by electro-osmotic drag 〇

Gas diffusion Fick’s law

Gas diffusivity Empirical gas diffusivity functions 〇

Polari-zation

Cell Short-circuit current Short circuit current model 〇

CL Open circuit voltage Empirical standard electrode potential, Nernst equation

Activation overpotential Butler-Volmer equation

Concentration overpotential Butler-Volmer equation

Catalyst utilization by H+ limitation Empirical catalyst utilization function 〇

Direct combustion reaction Empirical direct-combustion reaction model 〇

PEM Proton conductivity Empirical proton conductivity function

GDL/MPL Ohmic overpotential Empirical electric resistance & Ohmic law

(A)

(B)

(C)

A : 1D (Physical model) → 0D (Empirical model) B : Dynamic → Pseudo-dynamicC : 2D (Through-plane + In-plane) → 1D (Through-plane only)

3 Model-reduction methods for high-speed computation

(A)


9 / 193. Fuel cell models – A : Empirical catalyst layer models (1/2) -

- 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


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

Water activity at ionomer : 𝑎H2Oion [-]

1.0

Wet condition

Dry-outcondition

𝑓 1𝑎H2O

ion

[-]

1.0

00


10 / 19

∆Φ = −𝛾𝑅𝑇


𝐶O2

Pt

𝐶ref

= −𝛾𝑅𝑇


𝐶O2

pore

𝐶ref1 −

𝑖

𝑖lim,

𝜏agg

3. Fuel cell models – A : Empirical catalyst layer models (1/2) -M

ola

r C

on

cen

trati

on

[mol/

m3]

Mola

r C

on

cen

trati

on

[mol/

m3]

Length [m]

Length [m]

Physical : Agglomerate model

Empirical : Mass-transfer resistance model

𝑖

4𝐹× 𝑅O

2

eff = 𝐶O2

pore− 𝐶O

2

Pt

Mass transfer resistance

𝐶O2

pore

𝐶O2

Pt

𝐶O2

pore

𝐶O2

Pt Limiting current density

𝑖lim,

4𝐹× 𝑅O

2

eff = 𝐶O2

pore− 0 ↔ 𝑖lim, =

4𝐹𝐶O2

pore

𝑅O2

eff

𝑅O2

eff = 𝑓2 𝑎H2O

pore× 𝑅O

2

ref

Concentration overpotential

𝐶O2

Pt = 𝐶O2

pore1 −

𝑖

𝑖lim,

𝜏agg

Water activity at pore : 𝑎H2Opore

[-]

1.0

Dry condition

Floodingcondition

1.0

𝑖lim,

𝐶O2

𝑝𝑜𝑟𝑒

𝐶O2

Pt

[mol/

m3]

0

0

Current density: 𝑖 [A/m2]

𝜏agg= 1

0 < 𝜏agg << 1

𝜏agg>> 1

Flooding function

Reference Mass-transfer

resistance

Agglomerate coefficient

- 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


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


12 / 193. Fuel cell models – C : 2D→1D reduction -

Physical : 2D water transport model

- 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]


13 / 19

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 -


14 / 19

All the parameters can be determined with 1cm2-cell data (NOT cell/stack data)and microscopic measurements of material geometry (thickness, porosity, …)

1cm2-cell

- 5 Relative humidity (100, 80, 60, 40, 20%)- 5 O2 concentration (21, 10, 6, 3, 1%)- 3 Cell temperature (80 + 40, 60 ℃)+ dry/wet step-response test

DatabaseTestbed

PLOT : expLINE : sim

3. Fuel cell models – Parameter determination-

Boundary conditions

Current density [A/m2]

Cell v

olt

age [

V]


15 / 194. Model validation - Overview -

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


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


17 / 194. Model validation - Computational speed -

Summary of computational speed

> 50 timesacceleration

than real-time

Capability of year-long durability simulation in allowable computational time


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


19 / 19240th 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 Universityb 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 System Model

Modeling of Fuel Cell Stack for High-Speed Computation and ...

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