# Determination of the Performance Characteristics of a Traction Battery in an Electric Vehicle

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## Abstract

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## 1. Introduction

_{2}emissions [1,3], and the mathematical modelling of the state of the batteries in cargo electric vehicles [10], are devoted to determining performance characteristics of the traction battery in an electric truck.

## 2. Materials and Methods

- The degree of charge of the battery;
- Torques of asynchronous electric motors;
- Temperature of electric motors and inverters;
- The battery voltage;
- The rotation frequency of the electric motor.

- Determining the depth of discharge of batteries during vehicle operation;
- Modelling the traction electrical system of an electric truck;
- Traction battery modelling;
- Modelling a system for the calculation of traction forces on a shaft in the electric motors.

## 3. Determining the Depth of Discharge of Batteries during Vehicle Operation

_{bat}is the battery current;

_{bat}is the supplied battery power;

_{bat}is the battery voltage.

_{bat}is the energy given by the battery;

## 4. Mathematical Modelling of the Traction Electrical System in an Electric Truck

- The development of a mathematical model that takes into account the mechanical characteristics of the vehicle;
- Verification of the obtained data with the results of vehicle test runs by comparing the acceleration characteristics in the simulation with real characteristics when driving according to an acceleration cycle along a straight road;
- The integration of a mechanical model into the electrical model in order to calculate the energy performance, reliable traction electrical system (TES) parameters and vehicle dynamics (VD).

- -
- Required traction force ${F}_{k}$ on the drive wheels

_{f}is the rolling resistance force of the vehicle;

_{α}is the force of resistance to uphill movement:

- -
- the required torque on drive wheels is:$${M}_{k}={F}_{k}\cdot {r}_{k};$$
- -
- the speed of the TM shaft rotation is:$${n}_{k}=\frac{30\cdot {i}_{gb1}{i}_{gb2}{V}_{a}}{\pi \cdot {r}_{k}};$$
- -
- the required torque on the TM shaft is:$${M}_{e}=\frac{{M}_{k}}{i\cdot {\eta}_{gb}};$$
- -
- the drag torque on the electric vehicle (EV) shaft is:$${M}_{C}=\frac{{F}_{f}+{F}_{v}+{F}_{a}}{{i}_{gb1}\cdot {i}_{gb2}\cdot {\eta}_{gb}}{r}_{k};$$
- -
- the required power on the shaft of the TM is calculated by the following formula, kW:$${P}_{e}=\frac{{M}_{e}\cdot {n}_{e}}{9550}.$$
- -
- The actual speed of the vehicle is calculated according to the speed of the TM shaft using the following expression:$${V}_{a}=\frac{\pi \cdot {r}_{k}\cdot {n}_{k}}{30\cdot {i}_{gb1}\cdot {i}_{gb2}}.$$
- -
- EV acceleration is as follows:$$a=\frac{d{V}_{a}}{dt}.$$

_{c,}serves as an input parameter for the mathematical model of EV. Data on the required values of torque, speed and power on the EV shaft are used in the calculation of load moments in the TM [41,42,43].

- Model of a traction electric machine;
- Model of an electric energy conversion and a control system for the traction electrical equipment (two inverters for each electric motor);
- Traction battery model;
- Model of a system for calculating traction forces on the shaft of electric motors.

#### 4.1. Mathematical Model Considering the Mechanical Characteristics of the Vehicle, and Subsequent Verification of Traction Characteristics

- A vehicle characterisation unit;
- A block for calculating the torque in a cycle;
- A vehicle dynamics calculation unit;
- A braking system unit;
- A dynamic characteristics calculation block;
- A block for calculating energy characteristics;
- An oscilloscope unit.

- A motion cycle setting unit;
- A unit for calculating the moment of resistance to vehicle movement;
- A vehicle inertia calculation unit.

_{t}is the coefficient of viscous friction for the motor shafts (F

_{t}is 0.03 Nms).

#### 4.2. Verification of the Mechanical Model with Real Test Results

- Torques of electric motors;
- Motor shaft speed;
- Actual speed of the electric vehicle.

#### 4.3. Verification of the Energy Performance of an Electric Bus

#### 4.4. Verification of Speed Characteristics with a Test Report

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Energy characteristics of an electric vehicle propulsion system (route #1): W

_{recup}is the regeneration energy stored while an electric vehicle is in motion, W

_{bat}is the battery energy used to move an electric vehicle, W

_{con}is the consolidated battery and regenerative energy used for driving.

**Figure 14.**Block for calculating the required torque in a motion cycle taking into account the motor-operating mode.

**Figure 18.**Motor torque graph obtained from the experimental study: black line—engine torque; blue line—resistance torque.

**Figure 19.**Comparison of electric vehicle speeds in simulation and real tests: black line—simulation movement; blue line—real car movement.

**Figure 20.**Comparison of electric vehicle speeds in simulation and real tests after correcting a moment of inertia: black line—simulation movement; blue line—real car movement.

**Figure 22.**Matching battery energy without considering regeneration in real tests and in driving cycle: black line—simulation movement; blue line—real car movement.

**Figure 23.**External characteristic obtained from testing an electric vehicle: black line—engine torque; blue line—resistance torque.

**Figure 24.**Experimental estimation of velocities in a motion cycle: black line—simulation movement; blue line—real car movement.

Route Number | Distance, km | Average Speed, km/h | Energy in Cycle, kW | Recovery Energy, kW∙h | Energy Consumption, kWh/km |
---|---|---|---|---|---|

1 | 15.01 | 31.22 | 12.75 | 2.65 | 0.85 |

2 | 16.34 | 28.81 | 17.55 | 3.68 | 1.08 |

Parameter | Designation | Significance | Unit |
---|---|---|---|

Wheel arrangement | 4 × 2 | ||

Gross weight | m_{a} | 16,000 | kg |

Curb weight | m_{c} | 10,000 | kg |

Frontal projection area of the EV | S_{a} | 7.53 | m^{2} |

Aerodynamic drag coefficient | c_{x} | 0.86 | |

Dynamic radius of the EV wheel | r_{k} | 0.451 | m |

Gearbox efficiency | ${\eta}_{gb}$ | 0.958 | |

Gear ratio of the first gearbox | i_{gb1} | 5.82 | |

Gear ratio of the second gearbox | i_{gb2} | 3.92 | |

Rolling resistance coefficient | f | 0.013 | |

Speed of EV movement | V_{a} | defined by a cycle | m/s |

Maximum speed | V_{max} | 80 | m/s |

Traction motor (TM) torque, nom/peak | M_{e} | 260/450 | N m |

Maximum speed of the TM | n_{max} | 11,500 | min^{−1} |

Nominal/maximum battery voltage | U_{BAT} | 460 | V |

Battery capacity | C | 140 | A·h |

Tyres | 245/70R 19.5 | ||

Acceleration (deceleration) of the EV when driving | a | defined by a loop | m/s^{2} |

Air density | r | 1.31 | kg/m^{3} |

Free-fall acceleration | g | 9.81 | m/s^{2} |

Angle of a track profile inclination | $\alpha $ | defined by a track profile | radians |

Parameter | Unit | Significance |
---|---|---|

Maximum motor shaft torque including intermediate gearboxes | Nm | 485 |

Maximum speed at a maximum torque | 1/min | 11,000 |

Maximum power per shaft | kW | 120 |

Maximum short-term effective current based on the maximum power rating | A | 350 A |

Minimum DC voltage value | V | 580 |

Maximum DC voltage value | V | 800 |

Permissible ambient operating temperatures from −40 to 85 °C | °C | −40.85 |

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**MDPI and ACS Style**

Malozyomov, B.V.; Martyushev, N.V.; Kukartsev, V.V.; Konyukhov, V.Y.; Oparina, T.A.; Sevryugina, N.S.; Gozbenko, V.E.; Kondratiev, V.V.
Determination of the Performance Characteristics of a Traction Battery in an Electric Vehicle. *World Electr. Veh. J.* **2024**, *15*, 64.
https://doi.org/10.3390/wevj15020064

**AMA Style**

Malozyomov BV, Martyushev NV, Kukartsev VV, Konyukhov VY, Oparina TA, Sevryugina NS, Gozbenko VE, Kondratiev VV.
Determination of the Performance Characteristics of a Traction Battery in an Electric Vehicle. *World Electric Vehicle Journal*. 2024; 15(2):64.
https://doi.org/10.3390/wevj15020064

**Chicago/Turabian Style**

Malozyomov, Boris V., Nikita V. Martyushev, Vladislav V. Kukartsev, Vladimir Yu. Konyukhov, Tatiana A. Oparina, Nadezhda S. Sevryugina, Valeriy E. Gozbenko, and Viktor V. Kondratiev.
2024. "Determination of the Performance Characteristics of a Traction Battery in an Electric Vehicle" *World Electric Vehicle Journal* 15, no. 2: 64.
https://doi.org/10.3390/wevj15020064