# Simulation Tool for Assessing Driving Strategies for Electric Racing Vehicles

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Dynamic Modelling of the Electric Vehicle

_{a}), the force due to an inclined surface (F

_{hc}), the rolling force (F

_{rr}) and the aerodynamic force. (F

_{ad}).

- Overcoming rolling resistance.
- Overcoming aerodynamic resistance.
- Overcoming the component of the weight of the vehicle that acts on the slope.
- Accelerating the vehicle if the speed is not constant.

- Rolling resistance force

_{RR}is the coefficient of rolling resistance.

_{RR}value taken for light vehicles over asphalt road is 0.0055. Other typical values used according to the surface conditions encountered can be found in [31].

- Force due to aerodynamic drag

_{d}is a constant called the drag coefficient.

_{d}is a dimensionless factor that quantifies the resistance that a solid presents to penetrate and move through a fluid, usually air. This coefficient is independent of the size of the body and the velocity of the fluid up to a certain point. After this point, noticeable variations in C

_{d}are experienced.

^{−3}is usually used in most cases.

- Force on an inclined surface

_{ωa}) can be obtained by combining this equation with Equation (5). In addition, if the system consists of a gear one, the efficiency will never be 100%, so it is necessary to integrate the efficiency η

_{g}of the gear system. The required force can be written as:

- Tractive force

#### 2.2. Modelling of Vehicular Dynamics

#### 2.3. Electric Vehicles Performance Modelling

_{te}) to move the vehicle for one second is equal to the power; therefore, the energy required each second is:

_{m}), the necessary electrical power (P

_{electric}) is:

_{mot}is the mechanical power of the engine.

_{mot}

_{in}) is greater than the mechanical output power (P

_{motout}), according to the equations:

#### 2.4. Engine Modelling

^{-6}to obtain good results. This fact means that the complete execution of the vehicle simulation model will take a long time, this being of little use for the purpose of this project. For this reason, a simplified engine model was chosen that would allow for obtaining results in a more reasonable time frame.

_{a}) is proportional to the motor speed in rad/s:

_{s}) is equal to the voltage generated by the motor plus the voltages that are conducted through the resistance (R) and inductance (L):

_{0}is the vacuum intensity and V

_{nom}is the motor nominal voltage.

_{v}) and the number of pole pairs of the motor.

#### 2.4.1. Stator Resistance (R_{s})

^{−1}) is needed to find the value at another specific temperature.

#### 2.4.2. Inductance (L)

_{d}< L

_{q}). This is due to the low reluctance on the q axis. However, the inductances at the surface are usually the same because the magnets are mounted on the surface and the reluctance is the same for any position.

_{a}, R

_{a}and I

_{a}are the armature voltage, armature resistance and armature intensity of the motor, respectively.

#### 2.4.3. Electrical Constant of the Engine

_{v}(V/krpm), is as follows. Firstly, two phases of the motor are connected through the probe to the oscilloscope and, secondly, the hub motor is rotated in such a way that a sinusoidal type of signal is generated.

_{v}is obtained from the amplitude and angular velocity:

#### 2.4.4. Pole Pairs

#### 2.5. Battery Modelling

- Nominal voltage;
- Nominal capacity;
- Initial state of charge.

#### 2.6. Aerodynamics Modelling

_{d}to be calculated by applying Equation (2). In this equation, the value of 1.225 Kg/m

^{3}was taken for the air density and 0.02 m

^{2}for the front area of the model. The results are shown in Figure 8 and, from them, it can be concluded that the value of the coefficient C

_{d}is quite stable regarding speed. We took the average value of these results as the definitive C

_{d}, obtaining a value of C

_{d}= 0.49.

#### 2.7. Circuit Modelling

#### 2.8. Simplifications to the Model

## 3. Simulink Model Development

- Total length: 230 cm.
- Maximum width: 85 cm.
- Maximum height: 98 cm.
- Number and configuration of wheels: 3 wheels (2 steering front, 1 driving rear).
- Front axle width: 80 cm.
- Wheelbase: 110 cm.

- Manufacturer/model: EcityPower/S12S.
- Rated voltage: 48 V.
- Maximum power: 500 W.

- Manufacturer/model: Crystalyte/406.
- Rated voltage: 48 V.
- Rated power: 500 W.

- Manufacturer/model: Custom/Samsung.
- Nominal voltage: 48 V.
- Maximum voltage: 54.6 V.
- Capacity: 12 Ah.
- Weight: 4.8 Kg.

#### 3.1. Vehicle Model

#### 3.2. Battery Block Model

#### 3.3. Engine Block Model

_{s}, which provides the voltage from the battery. In addition, the engine has an input speed ‘n’ in r.p.m that is fed back from vehicle dynamics. As outputs, the motor block presents the current, the electromotive force, the torque and the power of the motor.

#### 3.4. Control Modes

#### 3.4.1. Duty Cycle Control

#### 3.4.2. Torque Control

#### 3.4.3. Battery Power Control

#### 3.4.4. Vehicle Speed Control

#### 3.4.5. Controller

_{ss}) for the electric motor supply and the discharge current (beta) of the battery.

_{ss}) is the product of the battery voltage (V

_{s}) times the duty cycle (Duty):

_{m}) times the duty cycle and divided by the controller efficiency (Rend):

#### 3.5. Block Model of the Road

## 4. Description of the Graphical Interface

## 5. Results and Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 8.**(

**a**) Longitudinal force as a function of speed. (

**b**) Drag coefficient as a function of speed.

k_{v} | Pole Pairs | L | R |
---|---|---|---|

147.96 (V/krpm) | 22 (Pole pairs) | 62 (µH) | 0.42 (Ω) |

Real Strategy Simulation | Constant Power | Constant Speed | Constant Torque | |
---|---|---|---|---|

Total Consumption (Wh) | 9.93 | 9.67 | 8.02 | 10.91 |

Consumption per km (Wh/km) | 4.72 | 4.60 | 3.81 | 5.19 |

Range (km/kWh) | 211.86 | 217.39 | 262.47 | 192.68 |

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## Share and Cite

**MDPI and ACS Style**

Rosas-Cervantes, D.; Fernández-Ramos, J.
Simulation Tool for Assessing Driving Strategies for Electric Racing Vehicles. *World Electr. Veh. J.* **2023**, *14*, 198.
https://doi.org/10.3390/wevj14080198

**AMA Style**

Rosas-Cervantes D, Fernández-Ramos J.
Simulation Tool for Assessing Driving Strategies for Electric Racing Vehicles. *World Electric Vehicle Journal*. 2023; 14(8):198.
https://doi.org/10.3390/wevj14080198

**Chicago/Turabian Style**

Rosas-Cervantes, Daniel, and José Fernández-Ramos.
2023. "Simulation Tool for Assessing Driving Strategies for Electric Racing Vehicles" *World Electric Vehicle Journal* 14, no. 8: 198.
https://doi.org/10.3390/wevj14080198