Real-Time Estimation of PEMFC Parameters Using a Continuous-Discrete Extended Kalman Filter Derived from a Pseudo Two-Dimensional Model
Abstract
:1. Introduction
1.1. Background
1.2. Literature Review
1.3. Study Aim
1.4. Nomenclature and Constants
2. Physical Two-Dimensional Model
2.1. Geometry and Assumptions
- Oxygen transport in the cathode catalyst layer (CCL) is fast;
- The oxygen transport in the GDL is purely 1D in the x-direction;
- The oxygen transport in the channel is assumed to be a plug-flow with an averaged velocity and the choice of plug flow in fuel cell microchannels is justified by the small dimensions of the channels. It was shown in previous studies [29,30] that the laminar velocity profile in rectangular microchannels is flat at the center. Thus, at the first order and given the high mass diffusivity of air in the cathode channel, one can assume that the average velocity of a plug flow is able to give a good description of the mass transfer in the fuel cell microchannels;
- The model is isothermal;
- The CL is supposed to be infinitely small;
- The voltage potential is equal along the CL in the y-dimension;
- All channels of the cell are supposed to be operated in the same condition such as temperature, humidity, etc.; and
- The concentrations in the canal and the GDL are supposed to be equal (concentration on the channel inlet) before any current is applied to the FC.
2.2. General Equations
2.3. Normalized Adimensional Equations
3. Finite-Difference Discretization
4. Description of the Experimental Test Bench and Considered Fuel Cell
5. Experimental Validation of PEMFC Model
5.1. Current Profile with Step-Up
5.2. Current Profile with Forward/Backward Sweeps
6. Estimating the PEMFC Parameters Using an Extended Kalman Filter
7. Results of the EKF Observer and Discussion
7.1. Current Profile with Forward/Backward Sweeps
7.2. Current Profile with Step-Up/Down
7.3. Modified PEMFC Cell with Step-Up/Down Profile
8. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
Appendix B
Appendix C
References
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Geometry and Model Parameters | |||||
---|---|---|---|---|---|
Parameter | Unit | Signification | m/s | Constant | |
V | Tafel slope | M | Spatial coordinate | ||
mol/m3 | Oxygen concentration in the channel | M | Spatial coordinate | ||
mol/m3 | Oxygen concentration in the GDL | - | Normalized spatial coordinates | ||
mol/m3 | Reference concentration on the channel inlet | V | Cathode potential | ||
- | Normalized oxygen concentrations | - | Normalized potential | ||
F/m2 | Double-layer capacity | Discretization parameters | |||
m2/s | Effective diffusivity of the GDL | - | |||
V | Cell voltage | - | Number of grid points in the x-axis | ||
V | Fuel cell potential reference | - | |||
C/mol | Faraday constant | - | Number of grid points in the y-axis | ||
m | Channel depth | n | - | Number of state variables | |
m | GDL thickness | Observer parameters | |||
A/m2 | Exchange current density | - | Constant | ||
A | Fuel cell current | - | Observation matrix | ||
A/m2 | Local current density | - | Kalman gain | ||
- | Normalized Local current density | - | Dynamic matrix | ||
m | Channel length | - | Time index | ||
m | Channel width | - | White noise covariance | ||
A/m2 | Limiting current density | - | Covariance matrix | ||
Ω m2 | Ohmic resistance | s | Sampling period | ||
s | Temporal coordinate | - | Measurement noise covariance | ||
°C | Temperature | - | Process noise | ||
m/s | Air velocity | - | State variables |
Parameter | Value | Parameter | Value |
---|---|---|---|
V | m | ||
F/m2 | m | ||
mol/m3 | A/m2 | ||
m2/s | Ωm2 | ||
V | °C | ||
96,487 C/mol | m/s |
Period of Real-Time Measurement (s) | Number of Samples | Period of Simulation Time (s) | |
---|---|---|---|
3979 | 23,471 | 0.1695 | 2340 |
6000 | 81,455 | 0.073 | 5188 |
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Diab, Y.; Auger, F.; Schaeffer, E.; Chevalier, S.; Allahham, A. Real-Time Estimation of PEMFC Parameters Using a Continuous-Discrete Extended Kalman Filter Derived from a Pseudo Two-Dimensional Model. Energies 2022, 15, 2337. https://doi.org/10.3390/en15072337
Diab Y, Auger F, Schaeffer E, Chevalier S, Allahham A. Real-Time Estimation of PEMFC Parameters Using a Continuous-Discrete Extended Kalman Filter Derived from a Pseudo Two-Dimensional Model. Energies. 2022; 15(7):2337. https://doi.org/10.3390/en15072337
Chicago/Turabian StyleDiab, Yasser, Francois Auger, Emmanuel Schaeffer, Stéphane Chevalier, and Adib Allahham. 2022. "Real-Time Estimation of PEMFC Parameters Using a Continuous-Discrete Extended Kalman Filter Derived from a Pseudo Two-Dimensional Model" Energies 15, no. 7: 2337. https://doi.org/10.3390/en15072337