# Performance Analysis and Optimization of a High-Temperature PEMFC Vehicle Based on Particle Swarm Optimization Algorithm

^{*}

## Abstract

**:**

## 1. Introduction

## 2. HT-PEMFC Model

#### 2.1. Reversible Output Voltage

#### 2.2. Irreversible Overpotential

^{2}) [44].

#### 2.3. Power Density and Efficiency of HT-PEMFC

^{2}; ${P}_{f}=P{A}_{0}$ is output power; and $\Delta h\left(T\right)$ is the molar enthalpy change of the electrochemical reaction. Since the efficiency value is always less than 1, which is too small compared to the power density value, the dimensionless power ${P}^{*}=P/10$ is used for analysis in this paper for clearer comparison and optimization [50].

#### 2.4. Model Verification

## 3. Parametric Studies and Optimization

#### 3.1. Effect of Operating Parameters

#### 3.2. Effect of Design Parameters

#### 3.3. Finite Time Thermodynamic Optimization

#### 3.3.1. Multi-Objective Optimization Model

- Initialize the population: the particle swarm size is 500 and the maximum number of iterations is 500. The maximum flight speed of the particle is 10% of the optimization variables. Initialize the random position and velocity of each particle.
- Calculate the fitness value: the fitness value of each particle is evaluated by the objective function $f\left(x\right)$.
- Update the particle best value ($Pbest$) and global best value ($Gbest$): the particle velocity and position update equation are as shown in Equation (17), where ${V}_{id}^{k}$ and ${X}_{id}^{k}$ are the velocity and position of the ${i}^{th}$ particle after the $k$ iteration, respectively. ${r}_{1}$ and ${r}_{2}$ are random numbers between [0,1]. The learning factor ${c}_{1}={c}_{2}=2$ and the inertia weight $\omega =0.8$.$$\{\begin{array}{c}{V}_{id}^{k+1}=\omega {V}_{id}^{k}+{c}_{1}{r}_{1}\left(Pbes{t}_{id}^{k}-{X}_{id}^{k+1}\right)+{c}_{2}{r}_{2}\left(Gbes{t}_{id}^{k}-{X}_{id}^{k+1}\right)\\ {X}_{id}^{k+1}={X}_{id}^{k}+{V}_{id}^{k}\end{array}$$
- Judgment: the termination condition selects the maximum number of iterations. If the condition is satisfied, the optimal solution will be output.

#### 3.3.2. Optimization of Operating and Design Parameters

^{2}. When the power density of the optimized HT-PEMFC single cell is 0.5453 kW/m

^{2}, the corresponding maximum output efficiency is 64.58%.

## 4. FCV Powertrain Design

#### 4.1. Configuration

#### 4.2. Motor Parameters

#### 4.2.1. Maximum Power and Rated Power

#### 4.2.2. Maximum Speed and Rated Speed

#### 4.2.3. Maximum Torque and Rated Torque

#### 4.3. Fuel Cell Parameters

#### 4.4. Battery Parameters

## 5. Results and Discussions

## 6. Conclusions

- The reliability of the model was verified by comparing the HT-PEMFC model with the experimental data. By the parametric studies, the appropriate increase in $T$, ${p}_{{H}_{2}}$, ${p}_{{O}_{2}}$, and $RH$ is beneficial to the HT-PEMFC output performance improvement. With increasing the doping level $DL$, the output performance increases and then decreases. With the decrease in proton film thickness ${l}_{m}$, the output performance is improved;
- The PSO algorithm can optimize the power density and efficiency of the HT-PEMFC single cell based on finite-time thermodynamic theory. The simulation results show that the performance of the optimized HT-PEMFC single cell is improved, the power density can be obtained up to 6.848 kW/m
^{2}, and the efficiency can reach up to 64.58%; - Three different powertrain solutions are available for FCVs based on the different power density and efficiency curves of the LT-PEMFC, HT-PEMFC, and optimized HT-PEMFC outputs. The simulation comparison shows that the optimized HT-PEMFC stack has the lowest number of single cells, which is conducive to the vehicle’s structural arrangement and light weight. Moreover, the FCV that applied the optimized HT-PEMFC has the highest average efficiency, the lowest energy loss, and the lowest 100 km hydrogen consumption.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Comparisons of the HT-PEMFC output voltage between the modeling results and the experimental data.

**Figure 2.**The effect of operating parameters on power density and efficiency ($T=448$ K; ${p}_{{H}_{2}}=1$ atm; ${p}_{{O}_{2}}=1$ atm; $RH=0.038$; ${l}_{m}=0.005$ cm; $DL=10$ ): (

**a**) different $T$; (

**b**) different ${p}_{{H}_{2}}$; (

**c**) different ${p}_{{O}_{2}}$; (

**d**) different $RH$.

**Figure 3.**The effect of design parameters on power density and efficiency ($T=448$ K; ${p}_{{H}_{2}}=1$ atm; ${p}_{{O}_{2}}=1$ atm; $RH=0.038$; ${l}_{m}=0.005$ cm; $DL=10$ ): (

**a**) different $DL$; (

**b**) different ${l}_{m}$.

**Figure 6.**Comparison of ${P}^{*}$ and $\eta $ curves of the LT-PEMFC, HT-PEMFC, and optimized HT-PEMFC.

**Figure 8.**Comparison of fuel cell system efficiency and energy loss: (

**a**) Efficiency; (

**b**) Energy loss.

**Figure 9.**Comparison of cumulative hydrogen consumption under different driving cycles: (

**a**) CCDC; (

**b**) NEDC; (

**c**) UDDS; (

**d**) HWFET.

Vehicle Parameters | Value | Design Requirements | Value |
---|---|---|---|

Mass $m$ (kg) | 1850 | Maximum speed ${u}_{max}$ (km/h) | 150 |

Rolling resistance coefficient $f$ | 0.012 | 0–100 km/h acceleration time ${t}_{e}$ (s) | 10 |

Air resistance coefficient ${C}_{D}$ | 0.32 | Maximum climb at 30 km/h ${i}_{max}$ (%) | 30 |

Windward area $A$(m^{2}) | 2.4 | ||

Wheel rolling radius $r$(m) | 0.33 |

Powertrain Components | Parameters | Values |
---|---|---|

Motor | ${P}_{e}\left({P}_{emax}\right)$ (kW) | 55 (100) |

${n}_{e}$ (${n}_{max}$) (r/min) | 4000 (1000) | |

${T}_{e}$(${T}_{max}$) (Nm) | 132 (360) | |

Fuel cell | ${P}_{fc}$ (kW) | 75 |

Type | LT-PEMFC; HT-PEMFC; Optimized HT-PEMFC | |

Battery | ${P}_{b}$/kW | 55 |

Type | Lithium-ion |

Driving Cycles | LT-PEMFC | HT-PEMFC | Optimized HT-PEMFC |
---|---|---|---|

CCDC | 1178.19 | 1047.78 | 980.65 |

NEDC | 1259.08 | 1141.45 | 1073.99 |

UDDS | 1351.05 | 1216.25 | 1144.13 |

HWFET | 908.91 | 832.23 | 787.53 |

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**MDPI and ACS Style**

Li, Y.; Ma, Z.; Zheng, M.; Li, D.; Lu, Z.; Xu, B.
Performance Analysis and Optimization of a High-Temperature PEMFC Vehicle Based on Particle Swarm Optimization Algorithm. *Membranes* **2021**, *11*, 691.
https://doi.org/10.3390/membranes11090691

**AMA Style**

Li Y, Ma Z, Zheng M, Li D, Lu Z, Xu B.
Performance Analysis and Optimization of a High-Temperature PEMFC Vehicle Based on Particle Swarm Optimization Algorithm. *Membranes*. 2021; 11(9):691.
https://doi.org/10.3390/membranes11090691

**Chicago/Turabian Style**

Li, Yanju, Zheshu Ma, Meng Zheng, Dongxu Li, Zhanghao Lu, and Bing Xu.
2021. "Performance Analysis and Optimization of a High-Temperature PEMFC Vehicle Based on Particle Swarm Optimization Algorithm" *Membranes* 11, no. 9: 691.
https://doi.org/10.3390/membranes11090691