Thermal Management of Fuel Cells Based on Diploid Genetic Algorithm and Fuzzy PID
Abstract
:1. Development Status and Research Content of Fuel Cell
1.1. Prospect of Fuel Cell
1.2. The Importance of Thermal Management Systems
1.3. Advances in Fuel Cell Research
1.4. Research Content of This Paper
2. Modeling of Fuel Cell Systems
2.1. Fuel Cell Single Cell Modeling
2.1.1. End-Plate Temperature Model
2.1.2. Bipolar Plate Temperature Model
2.1.3. MEA Temperature Model
2.2. Tank Model and Radiator Model
- The temperature of the condensate at the outlet of the unit is the same as that at the inlet of the next unit;
- Heat from condensed water entering the tank from the fuel cell spreads rapidly through the tank;
- In the radiator, air and condensed water exchange heat, and the air temperature is always room temperature.
- The conservation equation of the water tank energy is:
3. Design of Thermal Management Control Strategy for Fuel Cells
3.1. Design of Fuzzy PID Control Strategy
3.2. Parameter Optimization of Diploid Genetic Algorithm
3.2.1. Genetic Coding and Trait Expression
3.2.2. Calculation of Fitness
3.2.3. Selection Operator
3.2.4. Crossover Operator
- Gene crossover. The same position of the 7-bit binary code of two “gene fragments” will be exchanged under a certain probability;
- Fragment crossover. All the genetic information carried by the two “gene segments” is exchanged together with a certain probability, including the “traits” of the parameters.
3.2.5. Mutation Operator
4. Simulation Results
5. Discussion
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
PEMFC | Proton exchange membrane fuel cell |
MEA | Membrane electrode assembly |
GA | Genetic algorithm |
HGA | Haploid genetic algorithm |
DGA | Diploid genetic algorithm |
GDL | Gas diffusion layer |
FEA | Finite element analysis |
CFD | Computational fluid dynamics |
LSA | Lightning search algorithm |
FTT | Finite time thermodynamic |
HT-PEMFC | High temperature proton exchange membrane fuel cell |
PID | Proportional integral differential |
LQR | Linear quadratic regulator |
MPL | Micro-porous layer |
ITAE | Integral of Time and Absolute Error |
NEDC | New European Driving Cycle |
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Parameter | Name | Value |
---|---|---|
The end plate density | 1300 kg/m3 | |
The end plate area | 0.0064 m2 | |
The end plate thickness | 0.01 m | |
Specific heat capacity of the end plate | 1200 J/(kg·K) | |
Heat transfer coefficient (L1, air) | 16.44 W/m2·K | |
Heat transfer coefficient (L1, L2) | 481.18 W/m2·K | |
Specific heat capacity of mixing (air, liq) | 1395 J/(kg·K) | |
Density of the bipolar plate | 8000 kg/m3 | |
Area of the bipolar plate | 0.0049 m2 | |
Thickness of the bipolar plate | 0.005 m | |
Specific heat capacity of the bipolar plate | 500 J/(kg·K) | |
The MEA layer density | 1300 kg/m3 | |
The MEA layer area | 0.0036 m2 | |
The MEA layer thickness | 0.0015 m | |
Specific heat capacity of the bipolar plate | 864 J/(kg·K) | |
Specific heat capacity (water) | 4200 J/(kg·K) | |
Length of gas passage | 1768.8 mm | |
Gas passage section perimeter | 5.69 mm | |
Gas passage section area | 2.00 mm2 | |
Gas density (air) | 1.24 kg/m3 | |
Aerodynamic viscosity (air) | 1.71 × 10−5 Pa·s | |
Prandtl constant (air) | 0.708 | |
Conductivity coefficient (air) | 0.0263 W/m2·K | |
Length of liquid runner | 381 mm | |
Liquid runner section perimeter | 7.62 mm | |
Section area of liquid runner | 3.23 mm2 | |
Liquid density (water) | 1000 kg/m3 | |
Hydrodynamic viscosity (water) | 3.79 × 10−4 Pa·s | |
Prandtl constant (water) | 7 | |
Conductivity coefficient (water) | 0.602 W/m2·K | |
The number of electrons exchanged by chemical reactions | 2 | |
Faraday constant | 96485 C/mol | |
Coolant mass (Water tank) | 2.5 kg | |
Heat transfer coefficient (coolant, Tank wall) | 0.64 W/m2·K | |
Coolant mass (radiator) | 0.2 kg |
Working Parameter | Value Range |
---|---|
Current density | 0~0.7 A/cm2 |
Air and hydrogen flow | 1~20/min, 1~5 L/min |
Initial coolant temperature | 60 °C |
Gas pressure | 1.5 bar |
Gas humidity | 90% |
e | NB | NM | NS | ZO | PS | PM | PB | |
---|---|---|---|---|---|---|---|---|
ec | ||||||||
NB | PB | PB | PM | PM | PM | ZO | ZO | |
NM | PB | PM | PM | PM | PS | ZO | ZO | |
NS | PM | PM | PS | PS | ZO | NS | NS | |
ZO | PM | PS | PS | ZO | NS | NS | NM | |
PS | PS | ZO | ZO | NS | NM | NM | NM | |
PM | PS | NS | NS | NS | NM | NM | NB | |
PB | ZO | NS | NS | NM | NM | NB | NB |
e | NB | NM | NS | ZO | PS | PM | PB | |
---|---|---|---|---|---|---|---|---|
ec | ||||||||
NB | NB | NB | NM | NM | NS | NS | ZO | |
NM | NM | NM | NM | NS | NS | ZO | ZO | |
NS | NM | NM | NS | ZO | ZO | ZO | PS | |
ZO | NS | NS | NS | ZO | PS | PM | PM | |
PS | NS | NS | ZO | PS | PS | PM | PB | |
PM | ZO | ZO | ZO | PS | PM | PB | PB | |
PB | ZO | ZO | PS | PM | PM | PB | PB |
e | NB | NM | NS | ZO | PS | PM | PB | |
---|---|---|---|---|---|---|---|---|
ec | ||||||||
NB | NB | NB | NM | NM | NS | NS | ZO | |
NM | NM | NM | NM | NS | NS | ZO | ZO | |
NS | NM | NM | NS | ZO | ZO | ZO | PS | |
ZO | NS | NS | NS | ZO | PS | PM | PM | |
PS | NS | NS | ZO | PS | PS | PM | PB | |
PM | ZO | ZO | ZO | PS | PM | PB | PB | |
PB | ZO | ZO | PS | PM | PM | PB | PB |
Number of Iterations | GA | Excellent | Good | Bad | Max | Min |
---|---|---|---|---|---|---|
1~30 | haploid | 2 | 6 | 22 | 9.8 | 3.80 |
diploid | 2 | 14 | 14 | 10.1 | 3.37 | |
31~60 | haploid | 3 | 10 | 17 | 13.3 | 2.64 |
diploid | 9 | 17 | 4 | 8.64 | 2.54 | |
61~90 | haploid | 1 | 10 | 19 | 10.6 | 3.94 |
diploid | 11 | 18 | 1 | 9.95 | 2.72 | |
91~120 | haploid | 0 | 5 | 25 | 12.9 | 4.05 |
diploid | 5 | 16 | 9 | 10.8 | 2.94 | |
121~150 | haploid | 2 | 15 | 13 | 9.90 | 3.42 |
diploid | 24 | 3 | 3 | 9.06 | 2.13 | |
1~150 | haploid | 8 | 46 | 96 | 13.3 | 2.64 |
diploid | 51 | 68 | 31 | 10.8 | 2.13 |
Maximum Temperature Difference | Mean Temperature Difference | Variance | |
---|---|---|---|
DGA | 2.22 | 1.87 | 0.010 |
HGA | 3.03 | 2.09 | 0.046 |
FUPID | 3.17 | 2.54 | 0.020 |
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Zhao, R.; Qin, D.; Chen, B.; Wang, T.; Wu, H. Thermal Management of Fuel Cells Based on Diploid Genetic Algorithm and Fuzzy PID. Appl. Sci. 2023, 13, 520. https://doi.org/10.3390/app13010520
Zhao R, Qin D, Chen B, Wang T, Wu H. Thermal Management of Fuel Cells Based on Diploid Genetic Algorithm and Fuzzy PID. Applied Sciences. 2023; 13(1):520. https://doi.org/10.3390/app13010520
Chicago/Turabian StyleZhao, Ruikang, Dongchen Qin, Benhai Chen, Tingting Wang, and Hongxia Wu. 2023. "Thermal Management of Fuel Cells Based on Diploid Genetic Algorithm and Fuzzy PID" Applied Sciences 13, no. 1: 520. https://doi.org/10.3390/app13010520
APA StyleZhao, R., Qin, D., Chen, B., Wang, T., & Wu, H. (2023). Thermal Management of Fuel Cells Based on Diploid Genetic Algorithm and Fuzzy PID. Applied Sciences, 13(1), 520. https://doi.org/10.3390/app13010520