# An Energy Management Strategy and Parameter Optimization of Fuel Cell Electric Vehicles

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## Abstract

**:**

## 1. Introduction

- (1)
- The optimization of an energy management strategy is always combined with the size matching of key vehicle components. A rule-based strategy or optimal control strategy can be used for optimization, or it can be regarded as a low-level optimization problem in the cycle of vehicle parameter matching.
- (2)
- A variety of algorithms can be used, such as convex optimization and PSO, which can solve the combinatorial optimization problems of parameter matching and energy management at the same time.

## 2. System Description and Methodology

#### 2.1. Powertrain Structure

#### 2.2. Matching of Composite Power Supplies

- ${P}_{cap1}$: Required power of composite power supply;
- ${\eta}_{1}$: Efficiency of the motor control system;
- ${P}_{\mathrm{max}}$: Maximum power required by the vehicle;
- ${P}_{at}$: Other power requirements;
- ${P}_{f}$: Fuel cell system power;
- ${\eta}_{D}$: DC converter efficiency.

- P
_{cap2}: Required power from the composite power supply; - P
_{rat}: Rated power of the power source (motor).

_{cap}= max (P

_{cap1}, P

_{cap2}) = P

_{cap1}

#### 2.3. PEMFC Model

- $-\Delta {\overline{\mathrm{g}}}_{f}^{0}$: Change in molar concentration of the hydrogen;
- $T$: Cell temperature (K);
- $R$: Gas constant = $8.134{\mathrm{Jmol}}^{-1}{K}^{-1}$;
- ${P}_{{H}_{2}}$: Partial pressure of hydrogen;
- ${P}_{{O}_{2}}$: Partial pressure of oxygen;
- ${a}_{{H}_{2}O}=1$: Ratio of gas to liquid water;
- ${P}_{{O}_{2}}=0.21$.

- ${E}_{0}$: Open-circuit voltage;
- ${V}_{act}$: Activation loss;
- ${V}_{ohmic}$: Ohmic loss;
- ${V}_{con}$: Concentration loss.

#### 2.4. Lithium Battery Model

- ${V}_{\mathrm{oc}}$: Open circuit voltage;
- ${I}_{bat}$: Internal current;
- ${R}_{\mathrm{bat}}$: Equivalent internal resistance;
- ${P}_{bat}$: External output power.

_{bat}and V

_{bat}can be calculated as follows [24]:

- $SO{C}_{0}$: Initial SOC;
- ${Q}_{\mathrm{t}}$: Battery capacity (Ah);

- ${n}_{b}$: Number of battery cells in series.

#### 2.5. Ultra-Capacitors Model

- ${E}_{sc}$: Stored energy;
- ${U}_{sc}$: Terminal voltage;
- ${I}_{sc}$: Internal current;
- ${R}_{sc}$: Internal resistance;

#### 2.6. Characteristic Analysis and Experiment of Air Compressor

- ${G}_{c}$: Mass flow;
- ${\rho}_{in}$: Air density;
- ${d}_{c}$: Diameter of the impeller;
- ${U}_{c}$: Blade tip speed;
- ${\omega}_{c}$: Rotating speed;

#### 2.7. Drive Cycle

#### 2.8. Vehicle Performance

#### 2.8.1. Maximum Speed

- m: Weight (including energy management system components);
- f: Rolling resistance coefficient;
- u: Speed;
- $\alpha $: Climbing angle;
- C
_{D}: Drag coefficient; - A: Frontal area;
- $\rho $: Air density;
- ${P}_{m}$: Motor inverter input power;
- ${\eta}_{T}$: Transmission system efficiency;
- ${\eta}_{md}$: Battery drive efficiency;

- ${P}_{aux}$: Accessory power;
- ${P}_{fce}$: FCS output power;
- ${\eta}_{dc}$: Converter efficiency;
- ${P}_{bat}$: Battery output power;
- ${P}_{uc}$: Ultra-capacitors output power;

#### 2.8.2. Acceleration Time

- ${F}_{a}$: Traction;
- ${T}_{m\_\mathrm{max}}$: Maximum torque output by the energy management system;
- ${R}_{tire}$: Tire rolling radius;
- ${T}_{m\_allowed}$: Maximum torque of motor external characteristic curve;
- $\Delta t$: Sampling interval;
- $\omega $: Rotating speed;
- ${t}_{acc}$: Acceleration time;
- $N$: Discrete time matrix;
- ${P}_{m\_\mathrm{max}}$: Maximum input power of the motor inverter.

#### 2.8.3. Mileage

- ${E}_{\mathrm{fce}}$: Output energy of the fuel cell system;
- ${\eta}_{dc}$: Efficiency of the DC converter;
- ${E}_{aux}$: Energy consumed by the accessorial components of the vehicle;
- ${m}_{hydro}$: Hydrogen mass;
- LHV: Low heat value of hydrogen;
- ${\eta}_{fce}$: Net efficiency of the fuel cell system.
- $Driving\_m$: Driving distance.

## 3. Wavelet-Fuzzy Logic Energy Management System

#### 3.1. Energy Split Based on a Wavelet Transform

_{1}(Z) is a high-pass filter and H

_{2}(Z) is a low-pass filter. In the decomposed signal, x

_{0}(t) is a low-frequency signal; x

_{1}(t), x

_{2}(t) and x

_{3}(t) are high-frequency signals, where the sum of the three high-frequency signals is output as the required power of the ultra-capacitors; and x

_{0}(t) is the sum of the required power of the FCS and the battery, where the two are distributed in a certain proportion. The FCS cannot recover energy, and the negative part of x

_{0}(t) is allocated to the battery for energy recovery. After the decomposition is completed, the inverse process signal reconstruction is completed through a reconstruction filter.

#### 3.2. Fuzzy Logic Energy Management System

_{ref}) and ultra-capacitors SOCs. Under specific fuzzy rules, through fuzzification and defuzzification, accurate battery output power and FCS output were obtained. The control rules under the driving conditions were as follows: (1) When the P

_{ref}is small, most of the P

_{ref}is provided by the FCS, or provided by the FCS alone. The output power of the battery and the ultra-capacitors should be adjusted in conjunction with their own SOC. The power supply with the higher SOC value is the first to supply energy. (2) When the P

_{ref}is medium, the fuzzy rule should first keep the FCS in the optimal efficiency range, and at the same time, batteries and ultra-capacitors are used as auxiliary energy sources to provide part of the energy. (3) When the P

_{ref}is high, the fuzzy rule should first ensure that the vehicle energy demand is met, and the FCS, battery and ultra-capacitors work at the same time. In the braking mode, the battery and the ultra-capacitors recover the braking energy. The fuzzy rules are shown in Table 4. The larger instantaneous power is mainly recovered by the ultra-capacitors to prevent the battery from being impacted by a larger current; when the braking energy is medium or small, the energy is first recovered by the power source with a smaller SOC. The distribution of MFs is consistent over the entire discourse in the primary FLC. Thus, it is not expected to perform optimally over different parameters. In this study, the MFs of the FLC were optimized with the help of the PSO algorithm, and the construction parameters of the input MFs were regarded as design variables, as shown in Figure 13. The input MFs of SOC

_{uc}and SOC

_{bat}could be represented by four parameters (x1, x2, x3, x4), and the input MFs of PREF-bat could be represented by eight parameters (y1, y2, y3, y4, y5, y6, y7, y8).

## 4. Parameter Optimization Based on the Particle Swarm Algorithm (PSO)

#### 4.1. PSO

- t: Number of iterations;
- ${v}_{i}(t)$: The velocity of the ith particle in t iterations;
- $\omega $: Inertia weight;
- ${c}_{1}$,${c}_{2}$: Cognitive coefficients;
- ${R}_{1}$,${R}_{2}$: Uniformly distributed random numbers;
- ${R}_{i}^{b}(t)$: The historical optimal position of the individual particle i;
- ${R}_{g}^{b}$: The best position in the history of the group;
- $\varphi $: Shrinkage factor.

#### 4.2. Definition of Multi-Objective Parameter Optimization Problem

#### 4.2.1. Objective Function

- ${E}_{md}$: Motor drive energy;
- ${\eta}_{md}$: Motor efficiency;
- ${E}_{\mathrm{aux}}$: Ancillary energy consumption;
- ${E}_{batloss}$: Battery charge and discharge energy consumption;
- ${E}_{mb}$: Regenerative braking to recover energy;
- ${\eta}_{mb}$: Regenerative braking efficiency;
- ${\eta}_{fce}$: FCS efficiency;
- n
_{dc}: Converter efficiency.

- LHV: Low calorific value of hydrogen.

#### 4.2.2. Restrictions

- $SO{C}_{L}$: Lower limits of battery SoC;
- $SO{C}_{H}$: Upper limits of battery SoC;
- $SO{C}_{0}$: Initial SoC value;
- $SO{C}_{end}$: End SoC value;
- ${U}_{bus\_\mathrm{min}},{U}_{bus\_\mathrm{max}}$: Minimal and maximal voltages of the bus;
- ${P}_{dc\mathrm{max}}$: Maximal power of the DC converter;
- $Speed\_Max$: Maximal speed.

#### 4.2.3. Optimization Variables

- ${P}_{\mathrm{fc}\_net}$: The maximum power of the FCS should not be higher than the required power when the vehicle is running at the highest speed so as to avoid capacity waste when the FCS is driven alone;
- ${x}_{cp}$: Compressor diameter scale;
- ${n}_{bp}$: Number of parallel-connected battery cell stings;
- ${n}_{b\mathrm{s}}$: Number of series-connected battery cells;
- ${n}_{up}$: Number of parallel-connected UC cell stings;
- ${n}_{us}$: Number of series-connected UC cells.

## 5. Simulation and Test Result

- (1)
- Construction of the energy management strategy

- (2)
- Calculation of the parameters related to the lithium battery and supercapacitor

- (3)
- Compilation and download of the energy management strategy

- (4)
- ControlDesk design

- (5)
- Working condition simulation

- (6)
- Data acquisition

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

BRM | Braking energy recovery mode |

CDM | Composite power supply separate driving mode |

DP | Dynamic programming |

FC | Fuel cell |

FCEVs | Fuel cell electric vehicles |

FCS | Fuel cell system |

FCDM | Fuel cell combined driving mode |

FDM | Fuel cell separate driving mode |

PEMFC | Proton exchange membrane fuel cell |

PSO | Particle swarm optimization |

SOC | State of charge |

UDDS | Urban Dynameter Driving Schedule |

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**Figure 1.**Structure of power system of FCEVs and an FCS: (

**a**) Power system structure (

**b**) FCS structure.

**Figure 4.**Characteristic curves of ultra-capacitors (

**a**) Charging characteristic curves (

**b**) Discharging characteristic curves.

**Figure 10.**Energy split of a three-level wavelet transform: (

**a**) demand power decomposition (

**b**) Haar wavelet decomposition (

**c**) Haar wavelet reconstruction.

**Figure 15.**Optimization results of the membership function: (

**a**) adjusted MFs of SOCuc and SOCbat and (

**b**) adjusted MFs of PREF-bat.

Parameter | Units | Value |
---|---|---|

Nominal cell voltage V_{B} | V | 3.5 |

Cell capacity Q_{B} | As | 8500 |

Cell resistance R_{B} | Ω | 0.02 |

Cell unit cost c_{b} | USD | 7.0 |

Cell mass m_{b} | kg | 0.08 |

Parameter | Units | Value |
---|---|---|

Nominal voltage | V | 18.2 |

Electrical capacitance | F | 600 |

Electrical series resistance | mΩ | 2.5 |

Max power | kW | 40 |

Mass | kg | 6 |

Parameter | Units | Value |
---|---|---|

Time | s | 1369 |

Mileage | km | 11.99 |

Maximum speed | km/h | 91.25 |

Average speed | km/h | 31.51 |

Maximum acceleration | m/s^{2} | 1.48 |

Average acceleration | m/s^{2} | 0.5 |

Maximum deceleration | m/s^{2} | −1.48 |

Average deceleration | m/s^{2} | −0.58 |

Idling time | s | 259 |

Stop times | - | 17 |

P_{bat} | SOC_{uc} | |||
---|---|---|---|---|

LOW | M | HIGH | ||

SOC_{bat} | LOW | P_{bat} < P_{REF-bat} | P_{bat} < P_{REF-bat} | P_{bat} < P_{REF-bat} |

M | P_{bat} > P_{REF-bat} | P_{bat} > P_{REF-bat} | P_{bat} > P_{REF-bat} | |

HIGH | P_{bat} > P_{REF-bat} | P_{bat} > P_{REF-bat} | P_{bat} > P_{REF-bat} |

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

Population size | 30 | Lower bound [Nbatt Nfcp] | [1 2] |

Max iteration | 100 | Upper bound [Nbatt Nfcp] | [10 60] |

Max weight | 1.5 | Lower bound [Kfc] | 0 |

Min weight | 0.1 | Upper bound [Kfc] | 1 |

Lower bound (Ksoc) | 0 | Upper bound [Ksoc] | 15 |

Parameter | Units | Value |
---|---|---|

m, weight of the vehicle | kg | 1700 |

l, wheelbase | mm | 2550 |

A, front area | m^{2} | 2.2 |

C_{D}, air drag coefficient | - | 0.29 |

R, wheel rolling radius | m | 0.32 |

f, rolling resistance coefficient | - | 0.02 |

η_{T}, transmission system efficiency | - | 0.96 |

i, gear ratio | - | 4.41 |

Parameter | Units | Value |
---|---|---|

${P}_{\mathrm{fc}\_net}$ | kW | 83 |

${x}_{cp}$ | - | 0.8 |

${n}_{bp}$ | - | 40 |

${n}_{b\mathrm{s}}$ | - | 35 |

${n}_{up}$ | - | 1 |

${n}_{us}$ | - | 60 |

Parameter | Not Optimized | Optimized |
---|---|---|

System cost (US$) | 150,000 | 146,000 |

System quality (kg) | 1700 | 1625 |

Hydrogen consumption (g) | 380 | 368 |

Average battery current (A) | 35 | 32 |

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**MDPI and ACS Style**

Li, W.; Feng, G.; Jia, S.
An Energy Management Strategy and Parameter Optimization of Fuel Cell Electric Vehicles. *World Electr. Veh. J.* **2022**, *13*, 21.
https://doi.org/10.3390/wevj13010021

**AMA Style**

Li W, Feng G, Jia S.
An Energy Management Strategy and Parameter Optimization of Fuel Cell Electric Vehicles. *World Electric Vehicle Journal*. 2022; 13(1):21.
https://doi.org/10.3390/wevj13010021

**Chicago/Turabian Style**

Li, Wenguang, Guosheng Feng, and Sumei Jia.
2022. "An Energy Management Strategy and Parameter Optimization of Fuel Cell Electric Vehicles" *World Electric Vehicle Journal* 13, no. 1: 21.
https://doi.org/10.3390/wevj13010021