# The Multi-Objective Optimization of Powertrain Design and Energy Management Strategy for Fuel Cell–Battery Electric Vehicle

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## Abstract

**:**

## 1. Introduction

#### 1.1. The Need for a Hybrid System

#### 1.2. Review of EMS Development for FC EV

## 2. Optimization of FC–Battery Powertrain Configurations

#### 2.1. Structure and Specifications

#### 2.2. Electric Machine

_{d}, $\mathsf{\delta}$, M, A

_{f}, φ

_{max}, and η

_{T}are gravitational acceleration, rolling resistance coefficient, aerodynamic drag coefficient, the equivalent mass of rotating parts, vehicle mass and frontal area, maximum climbing angle, energy efficiency from the electric machine to wheels, respectively; P

_{spd}, P

_{φ}, and P

_{acc}are required power for cruising at top speed v

_{top}, climbing maximum grade with speed

**v**and accelerate the vehicle to v

_{i}_{a}in t

_{a}. The rest of the performance concept design, e.g., maximum and rated torque, maximum speed, will be determined by top speed, acceleration, and gradeability, as well as being crossed checked subsequently. The electric machine specification is presented in Table 2.

#### 2.3. Fuel Cell Model

_{Cycle}represents the FC degradation coefficient in one start–stop cycle; N

_{Cycle}is the number of cycles; δ

_{0}and α are empirical coefficients of FC operating-power degradation; P

_{FC_rate}is the rated power of the FC. All parameters of FC are summarized in Table 3.

_{f}is the hydrogen lower heating value 120 MJ/kg; η

_{FC}is FC efficiency.

#### 2.4. Battery Model

_{0}, internal resistance R

_{BAT}and battery power P

_{BAT}:

_{BAT}:

_{Rate}, respectively; E

_{a}and R stand for the activation energy and constant gas values, which equal 78.06 (J) and 8.314 J/mol/K

^{−1}, respectively; T

_{bat}represents the absolute temperature in Kelvin; the accumulative current going through the battery is represented by ${\mathrm{Ah}}_{\mathrm{through}}$, which is a time-related exponential factor. Then, the model was evaluated in a field testing of Li-ion battery and achieved the following experimental calibration [33]:

#### 2.5. System Configurations

_{fc,Max}and P

_{bat,Max}are the maximum power of the FC and battery. If DoH is relatively low, most of the required power will be fed by the battery, leading to a long electric range compared to that, which FC takes the primary responsibility for in propelling. If DoH is relatively high, FC is responsible for driving the vehicle most of the time, while the battery provides power when FC is underpowered or required to alleviate the power fluctuation in FC to prolong its service time.

_{EtoH}:

_{H2-Electricity}is the equivalent energy from electricity to hydrogen consumption of electricity, η

_{dis,}and η

_{chg}are the efficiency of discharging and charging, respectively.

## 3. Optimum Design of Hybrid Powertrain

#### 3.1. Method

_{ij}

^{N}and X

_{ij}

^{N}are the velocity and position of the ith particle with jth dimension in Nth iteration; N stands for the iteration number; ϖ represents the inertial weight of velocity; c

_{1}and c

_{2}are learning factors; r

_{1}and r

_{2}are random numbers between 0 and 1.

_{1}, a

_{2}, a

_{3}, to achieve a specific goal. Thus, specifications of the hybrid powertrain with DoH = 0.5 are selected at the very beginning. In addition, 1.2 kg/100 km hydrogen consumption and 0.0377/100 km capacity degradation of battery are adopted based on state-of-the-art situation.

_{H}

_{2}is the hydrogen consumption, including the energy used to generate electricity; Cost

_{FC}is the cost of FC in terms of power; Cost

_{Bat}is the cost of the battery in terms of energy capacity; are the power bank cost; Q

_{loss}is the battery degradation; weighting factors a

_{1}, a

_{2}and a

_{3}are adopted to set the real optimization goal that reflects the preference of the designer. In this study, each group of weighing factors for the balanced energy consumption/cost/performance/degradation preferred is investigated.

_{min}, v

_{max}], specifically, [−0.05, 0.05] in this study; Pos_

_{DoH}stands for the position of each particle, which is DoH in this study.

^{®}:

_{DoH}for each particle.

_{DoH}of each particle (p_best) and the best Pos_

_{DoH}of all particles (g_best).

_{H2_Total}:

^{®}and described in Algorithm 1.

Algorithm 1 PSO-based multi-objective DoH optimization |

1: for each particle i |

2: for each dimension j |

3: Initialize velocity V_{ij} and position X_{ij} for particle i |

4: Calculate the fitness value fit(X_{ij}) and set p_best_{ij} = X_{ij}, |

5: end for |

6: end for |

7: Choose the particle having the best fitness value as the g_best_{j} |

8: for iteration N = 2, M do |

9: for each particle i |

10: for each dimension j |

11: Updata the velocity of particle i: |

12: ${V}_{ij}^{N}=\varpi \cdot {V}_{ij}^{N-1}+{c}_{1}{r}_{1}\left(p\_bes{t}_{ij}^{N-1}-{X}_{ij}^{N-1}\right)+{c}_{2}{r}_{2}\left(g\_bes{t}_{j}^{N-1}-{X}_{ij}^{N-1}\right)$ |

13: Updata the position of particle i: |

14: ${X}_{ij}^{N}={X}_{ij}^{N-1}+{V}_{ij}^{N}$ |

15: end for |

16: if $\mathrm{fit}({X}_{ij}^{N}$$)\mathrm{fit}(p\_bes{t}_{ij}^{N-1}$) |

17: $p\_bes{t}_{ij}^{N-1}$$={X}_{ij}^{N}$ |

18: end if |

19: if $\mathrm{fit}(p\_bes{t}_{ij}^{N-1}$$)\mathrm{fit}(g\_bes{t}_{j}^{N-1}$) |

20: $g\_bes{t}_{j}^{N-1}$$=p\_bes{t}_{ij}^{N-1}$ |

21: end if |

22: end for |

23: end for |

24: print the last g_best value |

#### 3.2. Concept Design Optimization Results

_{1}= 0.34, a

_{2}= 0.33, a

_{3}= 0.33 are applied to 0 < DoH < 0.375, which indicates no preference for any item in the objective function. The corresponding optimized DoH is 0.2016 with 24.19 kW maximum fuel cell power; if the objective function prefers to extend battery lifetime by applying weighting factors a

_{1}= 0.2, a

_{2}= 0.2, a

_{3}= 0.6, the final DoH is 0.2323 with 0.6703 fitness value. The third group of weighting factors, i.e., a

_{1}= 0.2, a

_{2}= 0.6, a

_{3}= 0.2 is adopted to reduce system cost, which needs the DoH to be 0.0347 and leads to 4.16 kW maximum fuel cell power. If hydrogen consumption is preferred via applying weighting factors a

_{1}= 0.6, a

_{2}= 0.2, a

_{3}= 0.2 to the objective function, the optimum DoH is 0.3493, and the corresponding Max power of FC is 41.92 kW. The process of optimization and convergence of each preference is shown in Figure 5.

## 4. RL EMS

_{t}is the total rewards, γ is the discount factor to introduce the influence of the future on the current, and rt represents the current reward.

_{H2}is instant equivalent hydrogen consumption per 100 km; Q

_{loss}is the capacity loss of battery at t; FC

_{loss}is the performance degradation coefficient at t; ${\mathrm{a}}_{1}$, ${\mathrm{a}}_{2}$, ${\mathrm{a}}_{3}$ are weighting factors.

_{t}, a

_{t}are the state and action at time t, respectively; Q

_{ϕ}is the output function of critic network at time t, while Q

_{ϕ}, is the output function of critic network at time t + 1.

_{1}= 0.34, a

_{2}= 0.33, a

_{3}= 0.33 for hydrogen consumption, battery, and FC degradation, respectively, in the worldwide harmonized light-duty test cycle (WLTC). The total reward of each training episode converges to the highest reward in the end, which is usually taken as a successful training process for an optimal agent. The DDPG-based optimization of EMS is optimized by Matlab

^{®}as well. The agent of optimal EMS is derived from 300 training episodes with converged reward; specifically, the 200th round is selected, as shown in Figure 8.

_{1}= 0.2, a

_{2}= 0.2, and a

_{3}= 0.6, given the preference for FC performance maintenance. The training process shown in Figure 10 also illustrates the convergent total rewards, which is taken as a successful training process of the EMS agent.

_{1}= 0.34, a

_{2}= 0.33, a

_{3}= 0.33, the power distribution between the battery and FC shown in Figure 11 shows a lower threshold for battery participation; in other words, the battery takes the responsibility of taking care of FC degradation by providing power more frequently together with FC. In addition, compared to the balanced weighting factors group, the FC performance maintenance preferred weighting factors that significantly reduced the participation of FC and limited the FC power to lower than 40 kW through the cycle.

_{3}= 0.6, 39.4% improvement is recorded by reducing the FC performance degradation per cycle from 0.0071 to 0.0043, while hydrogen consumption increases 12.3% from 0.3652 kg to 0.41 kg, and a significant increase in battery capacity degradation ensues.

_{1}= 0.34, a

_{2}= 0.33, a

_{3}= 0.33 and a

_{1}= 0.2, a

_{2}= 0.2, a

_{3}= 0.6, respectively. Comparing these two figures, it is clear that EMS with FC performance maintenance weight factors successfully limit the participation of FC in large power events, while the battery takes the principal role in driving the vehicle. In addition, the power of FC charging battery is well restricted, with a 50% drop.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**(

**a**) Fitness value searching for balanced optimization. (

**b**) Fitness value searching for battery performance degradation preferred optimization. (

**c**) Fitness value searching for system cost preferred optimization. (

**d**) Fitness value searching for hydrogen consumption preferred optimization.

**Figure 6.**(

**a**) Fitness value searching for balanced optimization. (

**b**) Fitness value searching for battery performance degradation preferred optimization. (

**c**) Fitness value searching for system cost preferred optimization (

**d**) Fitness value searching for hydrogen consumption preferred optimization.

**Figure 8.**Training process of EMS agent with weighting factors a

_{1}= 0.34, a

_{2}= 0.33, a

_{3}= 0.33.

**Figure 9.**Power distribution between FC and battery in WLTC in selected training episode with weighting factors a

_{1}= 0.34, a

_{2}= 0.33, a

_{3}= 0.33 (

**a**) Complete cycle; (

**b**) Part of the cycle.

**Figure 10.**Training process of EMS agent with weighting factors a

_{1}= 0.2, a

_{2}= 0.2, a

_{3}= 0.6.

**Figure 11.**Power distribution between FC and battery in WLTC in selected training episode with weighting factors a

_{1}= 0.2, a

_{2}= 0.2, a

_{3}= 0.6, (

**a**) Complete cycle; (

**b**) Part of the cycle.

**Figure 12.**Power distribution between FC and battery in UDDS in selected training episode with weighting factors a

_{1}= 0.34, a

_{2}= 0.33, a

_{3}= 0.33.

**Figure 13.**Power distribution between FC and battery in UDDS in selected training episode with weighting factors a

_{1}= 0.2, a

_{2}= 0.2, a

_{3}= 0.6.

Parameter | Value | Unit |
---|---|---|

Front area | 2.18 | m^{2} |

Aerodynamic drag coefficient | 0.32 | N/A |

Coefficient of rolling resistance | 0.0105 | N/A |

Equipped mass | 1750 | kg |

Correction coefficient of rotating mass | 1.05 | N/A |

Acc performance (0–100 km/h) | 10 | s |

Hill-climbing capability | 30@30 km/h | ° (degree) |

Top speed | 120 | km/h |

Parameter | Value | Unit |
---|---|---|

Rated power | 50 | kW |

Peak power | 120 | kW |

Rated speed | 5500 | rpm |

Max speed | 14,000 | rpm |

Rated torque | 90 | Nm |

Max torque | 215 | Nm |

Parameter | Variable | Value | Unit |
---|---|---|---|

Cell numbers | N | 80 | |

Peak power | P_{fc,Max} | 45 | kW |

Peak current | I_{st,Max} | 300 | A |

Stack mass | FC_{Mass} | 13.1 | kg |

Battery Parameters | DoH < Threshold | DoH > Threshold |
---|---|---|

Energy density | 0.156 kWh/kg | 0.156 kWh/kg |

Power density | 2.4 kW/kg | 0.96 kW/kg |

Weight | 31.25 kg | 125 kg |

Voltage | 375 V | 375 V |

DoH Range | Weight Coefficients | Optimal DoH | Fitness Value |
---|---|---|---|

[0, 0.375] | a_{1} = 0.34_{,} a_{2} = 0.33, a_{3} = 0.33 | 0.2016 | 1.1088 |

a_{1} = 0.2_{,} a_{2} = 0.2, a_{3} = 0.6 | 0.2323 | 0.6703 | |

a_{1} = 0.2_{,} a_{2} = 0.6, a_{3} = 0.2 | 0.0347 | 0.7399 | |

a_{1} = 0.6_{,} a_{2} = 0.2, a_{3} = 0.2 | 0.3493 | 1.711 | |

[0.375, 1] | a_{1} = 0.34_{,} a_{2} = 0.33, a_{3} = 0.33 | 0.3755 | 1.1337 |

a_{1} = 0.2_{,} a_{2} = 0.2, a_{3} = 0.6 | 0.3821 | 0.6794 | |

a_{1} = 0.2_{,} a_{2} = 0.6, a_{3} = 0.2 | 0.3750 | 0.8507 | |

a_{1} = 0.6_{,} a_{2} = 0.2, a_{3} = 0.2 | 0.3750 | 1.7060 |

Weighting Factors (a_{1},a_{2},a_{3}) | Equivalent Hydrogen Consumption | Battery Capacity Degradation | FC Performance Degradation |
---|---|---|---|

0.34–0.3–0.33 | 0.558 kg | 0.0126 | 0.0073 |

0.2–0.2–0.6 | 0.629 kg | 0.0142 | 0.0068 |

Weighting Factors (a_{1},a_{2},a_{3}) | Equivalent Hydrogen Consumption | Battery Capacity Degradation | FC Performance Degradation |
---|---|---|---|

0.34–0.3–0.33 | 0.4284 kg | 0.0036 | 0.0618 |

0.2–0.2–0.6 | 0.6447 kg | 0.0061 | 0.0535 |

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## Share and Cite

**MDPI and ACS Style**

Zhou, J.; Feng, C.; Su, Q.; Jiang, S.; Fan, Z.; Ruan, J.; Sun, S.; Hu, L.
The Multi-Objective Optimization of Powertrain Design and Energy Management Strategy for Fuel Cell–Battery Electric Vehicle. *Sustainability* **2022**, *14*, 6320.
https://doi.org/10.3390/su14106320

**AMA Style**

Zhou J, Feng C, Su Q, Jiang S, Fan Z, Ruan J, Sun S, Hu L.
The Multi-Objective Optimization of Powertrain Design and Energy Management Strategy for Fuel Cell–Battery Electric Vehicle. *Sustainability*. 2022; 14(10):6320.
https://doi.org/10.3390/su14106320

**Chicago/Turabian Style**

Zhou, Jiaming, Chunxiao Feng, Qingqing Su, Shangfeng Jiang, Zhixian Fan, Jiageng Ruan, Shikai Sun, and Leli Hu.
2022. "The Multi-Objective Optimization of Powertrain Design and Energy Management Strategy for Fuel Cell–Battery Electric Vehicle" *Sustainability* 14, no. 10: 6320.
https://doi.org/10.3390/su14106320