# An Optimal Approach to Energy Management Control of a Fuel-Cell Vehicle

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## Abstract

**:**

## 1. Introduction

_{2}politO. Further details regarding the vehicle characteristics are presented in Table A1.

## 2. Problem Formulation

## 3. Tank-to-Wheel Model

#### 3.1. Equation Model

#### 3.2. Model Validation

## 4. Reference Speed Profile Optimization

## 5. MPC Design for Energy Management

Algorithm 1 Armature state prediction algorithm. |

Algorithm 2 EMS algorithm. |

## 6. Testing and Simulations

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

CAD | Computer-Aided Design |

CFD | Computational Fluid Dynamics |

EM | Electric Motor |

EMS | Energy Management System |

FC | Fuel Cell |

LUT | Look-Up Table |

MPC | Model Predictive Control |

PS | Power Source |

SC | Super Capacitor |

SEM | Shell Eco-Marathon |

## Appendix A

Quantity | Value |
---|---|

Maximum speed | 35 km/h |

Maximum range | 60 km |

Drag coefficient | 0.088 |

Empty mass | 39 kg |

FC nominal power | 500 W |

DC motor nominal power | 200 W |

Variable | Symbol | Unit |
---|---|---|

FC voltage | ${V}^{fc}$ | V |

FC current | ${I}^{fc}$ | A |

SC voltage | ${V}^{sc}$ | V |

SC current | ${I}^{sc}$ | A |

Armature voltage | ${V}^{a}$ | V |

Armature current | ${I}^{a}$ | A |

Rotor torque | ${T}^{m}$ | Nm |

Rotor speed | ${\omega}^{m}$ | rad/s |

Driving torque | ${T}^{d}$ | Nm |

Slip speed | $\Delta \omega $ | rad/s |

Pinion torque | ${T}^{p}$ | Nm |

Pinion speed | ${\omega}^{p}$ | rad/s |

Annular gear torque | ${T}^{ag}$ | Nm |

Annular gear speed | ${\omega}^{ag}$ | rad/s |

Driving force | ${F}^{d}$ | N |

Vehicle speed | v | rad/s |

Vehicle traveled distance | s | m |

DC-DC duty cycle | ${d}^{a}$ | - |

Switching variable | $\Omega $ | - |

PS voltage | ${V}^{ps}$ | V |

PS current | ${I}^{ps}$ | A |

Parameter | Symbol | Unit |
---|---|---|

Open circuit voltage | ${E}_{oc}$ | V |

Number of cells | ${N}_{c}$ | - |

Tafel slope | A | V |

Exchange current | ${I}_{0}$ | A |

Internal resistance | ${R}_{ohm}$ | $\Omega $ |

SC capacitance | ${C}_{sc}$ | F |

Armature inductance | ${L}_{a}$ | H |

Armature resistance | ${R}_{a}$ | $\Omega $ |

Speed constant | ${k}_{e}$ | rad/sV |

Torque constant | ${k}_{t}$ | Nm/A |

Rotor inertia | ${J}_{m}$ | kgm^{2} |

DC motor driver efficiency | ${\eta}_{a}$ | - |

Freewheel coefficients | $a,b,c$ | - |

Transmission ratio | ${i}_{t}$ | - |

Annular gear teeth | ${n}_{ag}$ | - |

Pinion teeth | ${n}_{p}$ | - |

Transmission efficiency | ${\eta}_{t}$ | - |

Vehicle equivalent mass | ${m}_{eq}$ | kg |

Air density | ${\rho}_{air}$ | kg/m^{3} |

Frontal area | S | m^{2} |

Drag coefficient | ${c}_{x}$ | - |

Vehicle mass | m | kg |

Gravitational acceleration | g | m/s^{2} |

Road inclination | $\alpha $ | rad |

Asymptotic rolling resistance coefficient | ${\mu}_{0}$ | - |

Rolling radius | ${r}_{r}$ | m |

Threshold speed | ${v}_{th}$ | m/s |

Maximum speed | ${v}_{max}$ | m/s |

Number of phases | ${N}_{phase}$ | - |

Maximum armature current | ${I}_{max}^{a}$ | A |

Track length | ${l}_{track}$ | m |

Sample time | ${T}_{s}$ | s |

Prediction horizon | ${H}_{p}$ | - |

Scailing factor | $\gamma $ | A/V |

Recharge current | ${I}_{rch}$ | A |

Average vehicle speed | ${v}_{avg}$ | m/s |

Minimum allowed SC voltage | ${\overline{V}}_{sc}^{min}$ | V |

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**Figure 2.**Schematic diagram illustrating the main components of the IDRAkronos powertrain, with arrows indicating the energy flow direction.

**Figure 5.**(

**A**) Discretization of the track into sectors. (

**B**) Elevation and discretization of the road profile. (

**C**) Road gradient of each sector.

**Figure 6.**(

**A**,

**C**) Optimal armature current as a function of track position and time. (

**B**,

**D**) Optimal speed profile as a function of track position and time.

**Figure 9.**Full run attempt results. (

**A**) Comparison between the reference speed profile and the simulated vehicle speed. (

**B**) Simulated SC voltage and constraint. (

**C**) Computed control action at each sample time. (

**D**) Comparison of hydrogen consumption with and without the designed EMS.

**Figure 10.**(

**A**) Variation in road inclination angle compared to the reference angle during the simulation. (

**B**) Random resistive force exerted on the vehicle during the simulation. (

**C**) Fuel consumption results obtained from simulations under specified conditions.

Set-Up | Consumption | ||||
---|---|---|---|---|---|

Scenario | Test | $\gamma $ | Only FC (NL) | MPC (NL) | Saving (%) |

simplified | ${H}_{p}=2$ | 0.44 | 6.9 | 6.2 | 10.1 |

simplified | ${H}_{p}=3$ | 0.39 | 6.9 | 6.2 | 10.1 |

simplified | FC delayed | 0.24 | 6.7 | 6.1 | 8.9 |

full | run attempt | 0.12 | 19.4 | 18.4 | 5.1 |

full | disturbances | 0.12 | 20.8 | 20.2 | 2.9 |

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**MDPI and ACS Style**

Cerrito, F.; Canale, M.; Carello, M.
An Optimal Approach to Energy Management Control of a Fuel-Cell Vehicle. *World Electr. Veh. J.* **2024**, *15*, 55.
https://doi.org/10.3390/wevj15020055

**AMA Style**

Cerrito F, Canale M, Carello M.
An Optimal Approach to Energy Management Control of a Fuel-Cell Vehicle. *World Electric Vehicle Journal*. 2024; 15(2):55.
https://doi.org/10.3390/wevj15020055

**Chicago/Turabian Style**

Cerrito, Francesco, Massimo Canale, and Massimiliana Carello.
2024. "An Optimal Approach to Energy Management Control of a Fuel-Cell Vehicle" *World Electric Vehicle Journal* 15, no. 2: 55.
https://doi.org/10.3390/wevj15020055