# Fuzzy-Energy-Management-Based Intelligent Direct Torque Control for a Battery—Supercapacitor Electric Vehicle

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## Abstract

**:**

## 1. Introduction

## 2. Hybrid Electric Vehicle Dynamics

_{ext}is the sum of all of the external forces acting on the EV, m represents vehicle mass, and “a” is the EV acceleration.

_{traction}and the net resistive force Fr, as it is shown in the equation below:

_{aero}is the aerodynamic force, F

_{g}is the road slope force, F

_{tire}is the friction force between the vehicle tires and ground surface, and F

_{acc}represents the acceleration force required to achieve maximum vehicle speed from rest.

_{d}represents the aerodynamic coefficient, V

_{wheel}is the EV longitudinal speed, and V

_{wind}is the wind speed.

## 3. DTC Algorithm

_{sα}and V

_{sβ}are calculated using Equation (14), as shown below:

_{a}and i

_{b}current sensors and V

_{DC}voltage sensor). In addition, the position sensor is needed to sense and control the EV speed. So, the total number of required sensors is equal to four. In this work, an estimator that requires less sensors and that does not involve any integral terms was used, and it is shown in the figure below (Figure 1).

_{a}, i

_{b}, and θ (IC is deduced from i

_{a}, i

_{b}), whereas the classical estimator needs another extra sensor for the DC bus voltage measurement, as already stated in Equation (14).

## 4. Cost Function and GA Adaptation

_{i}and T

_{i}represent the HEV reference speed and torque, respectively. $\widehat{{T}_{i}}$ and $\widehat{{\Omega}_{i}}$ represent the measured HEV speed and torque, respectively. φ

_{ref}is the reference flux and it is equal to the permanent magnet flux, and φ

_{i}is the measured PMSM flux at a given instant, n represents the length of speed, and torque absolute error vectors. Figure 5 depicts the genetic algorithm pseudo code used in this paper.

## 5. Power Management

## 6. Simulation and Results

^{5}, 15.77), respectively. The speed of the HEV is presented in Figure 14. One can notice that HEV speed precisely follows its reference, which contains slow, medium, and aggressive acceleration and decelerations.

## 7. Real Time Simulation

_{dc}in green color along with FC power control signal ${k}_{fuzzy}^{FC}$ in fuchsia color. It can be seen that each time FC toggles from one operating point to another, significant and acceptable DC bus ripples occur.

## 8. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

HEV | Hybrid electric vehicle |

EV | Electric vehicle |

FC | Fuel cell |

DC | Direct current |

RT | Real time |

PMSM | Permanent magnet synchronous machine |

DTC | Direct torque control |

SVM | Space vector modulation |

GA | Genetic algorithm |

SOC | State of charge |

FLC | Fuzzy logic control |

Symbols | |

F_{ext} | External force [N] |

F_{r} | Resistive force [N] |

F_{t} | Tractive force [N] |

F_{aero} | Aerodynamic force [N] |

F_{g} | Gravitational force [N] |

F_{tire} | Tire force [N] |

F_{acc} | Acceleration force [N] |

m | Vehicle mass [kg] |

a | Vehicle acceleration [m/s^{2}] |

A | Vehicle front area [m^{2}] |

C_{d} | Aerodynamic coefficient [s^{2}/m^{2}] |

V_{wheel} | Wheel speed [m/s] |

V_{wind} | Wind speed [m/s] |

ρ | Air density [kg/m^{3}] |

t_{a} | Vehicle time constant [s] |

α | Road slope angle |

Φ_{d} | Direct axis flux [Wb] |

Φ_{q} | Quadratic axis flux [Wb] |

Φ_{PM} | Permanent magnet flux [Wb] |

L_{d} | Direct axis inductance [H] |

L_{q} | Quadratic axis inductance [H] |

i_{d} | Direct axis current [A] |

i_{q} | Quadratic axis current [A] |

T_{e} | Electromagnetic torque [N·m] |

ϴ_{s} | Stator flux angle [°] |

V_{DC} | DC bus voltage [V] |

[S_{a} S_{b} S_{c}]^{T} | Inverter switching state vector |

α, β, γ | Weighting factors |

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**Figure 13.**Candidate solutions in the search space (

**a**) PI1 at first iteration (

**b**) PI1 at last iteration (

**c**) PI2 at first iteration (

**d**) PI2 at last iteration (

**e**) PI3 at first iteration (

**f**) PI3 at last iteration.

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

Weight | 1200 kg |

Wheel radius | 0.32 m |

Gravity | 9.81 m/s^{2} |

Maximum torque | 110 N·m |

Maximum speed | 200 km/h |

Frontal area | 2.6 m^{2} |

Air density | 1.2 kg/m^{3} |

Aerodynamic coefficient | 0.3 |

Parameter | Population | Iterations | Selection | Selection Rate | Mutation Rate |
---|---|---|---|---|---|

Value | 100 | 50 | Roulette wheel | 0.5 | 0.5 |

Supercapacitor | Battery (Li-Ion) | ||
---|---|---|---|

Nominal voltage | 24 V | Nominal voltage | 24 V |

Capacitance | 9 F | Capacitance | 9 Ah |

ESR | 0.139 Ohm | ESR | 1.5 Ohm |

N_{serie} | 15 | N_{serie} | 15 |

N_{parallel} | 1 | N_{parallel} | 2 |

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**MDPI and ACS Style**

Oubelaid, A.; Alharbi, H.; Humayd, A.S.B.; Taib, N.; Rekioua, T.; Ghoneim, S.S.M.
Fuzzy-Energy-Management-Based Intelligent Direct Torque Control for a Battery—Supercapacitor Electric Vehicle. *Sustainability* **2022**, *14*, 8407.
https://doi.org/10.3390/su14148407

**AMA Style**

Oubelaid A, Alharbi H, Humayd ASB, Taib N, Rekioua T, Ghoneim SSM.
Fuzzy-Energy-Management-Based Intelligent Direct Torque Control for a Battery—Supercapacitor Electric Vehicle. *Sustainability*. 2022; 14(14):8407.
https://doi.org/10.3390/su14148407

**Chicago/Turabian Style**

Oubelaid, Adel, Hisham Alharbi, Abdullah S. Bin Humayd, Nabil Taib, Toufik Rekioua, and Sherif S. M. Ghoneim.
2022. "Fuzzy-Energy-Management-Based Intelligent Direct Torque Control for a Battery—Supercapacitor Electric Vehicle" *Sustainability* 14, no. 14: 8407.
https://doi.org/10.3390/su14148407