# Energy-Saving Control of Hybrid Tractors Based on Instantaneous Optimization

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## Abstract

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## 1. Introduction

## 2. Tractor Topology and Main Parameters

#### 2.1. Subsection Model of Hybrid Tractor Drivetraino

#### 2.2. Subsection Model of Hybrid Tractor Drivetraino

#### 2.3. Determination of Theoretical Speed and Transmission Ratio

_{0}, which is taken as 19.10. Seven forward gears are designed, including three transport gears, two working gears, and two amble gears [30,31]. The corresponding transmission ratio increases sequentially, while the theoretical speed decreases sequentially. The specific parameters used are listed in Table 2.

## 3. Hybrid Tractor Model Building

#### 3.1. Model of Hybrid Tractor Drivetraino

_{m}and T

_{e}are the motor and diesel engine torques, respectively. η

_{m}and η

_{e}represent the working efficiencies of the motor and diesel engine, respectively. T

_{req}is the torque required for the torque coupler input.

_{t}and i

_{0}are the transmission and main reducer speed ratios, respectively. n

_{tire}and n

_{e}are the drive and diesel engine speeds, respectively. v is the speed of the hybrid tractor during operation. r is the driving wheel radius of the hybrid tractor.

#### 3.2. Dyanmic Model of Rotary Tillage Unit

_{drive}and P

_{r}are the tractor travel power and rotary cultivator power consumptions, respectively. η

_{r}, η

_{zj}, η

_{b}, and η

_{o}represent the rotary tillage unit mechanical transmission efficiency, main reducer transmission efficiency, transmission efficiency, and torque-coupler efficiency, respectively. P

_{c}, P

_{th}, P

_{a}, and P

_{h}are the cutting power consumption, throwing earth power consumption, rotary cultivator forward power consumption and power required to overcome the soil horizontal reaction forces, respectively. m is the tractor mass. f is the rolling resistance coefficient. δ is the mass conversion of the factor. α is the tilt of the ground. C

_{d}and A are the tractor drag coefficient and windward area, respectively.

_{PTO}, T

_{PTO}, and n

_{PTO}are the power, torque, and speed of PTO, respectively. v

_{r}is the forward speed of the rotary cultivator.

#### 3.3. Dyanmic Model of Plowing Unit

_{TN}and various resistances when the tractor is operating is formulated as follows:

_{g}, F

_{f}, F

_{p}, F

_{Af}, and F

_{i}are the tillage, rolling, slope, air, and acceleration resistances, respectively. F

_{TN}is the driving force.

_{TN}is primarily determined by the tillage resistance F

_{g}when the supporting agricultural tools are working. The calculation formula is stated as follows:

_{l}and h

_{k}represent the individual plow width and depth, respectively. k is the soil specific resistance coefficient.

#### 3.4. Tire Model

_{q}and F

_{z}are the driving and loading forces of the drive wheel, respectively. φ and ζ represent the slip rate of the corresponding drive wheel and adhesion factor of the corresponding drive wheel, respectively. c is the horizontal distance of the hitch traction point from the center of the rear wheel.

#### 3.5. Motor Model

_{m}is the speed of the motor.

#### 3.6. Diesel Engine Model

_{e}denotes the speed of the diesel engine.

#### 3.7. Power Battery Model

_{b}and E

_{0}are the power battery output voltage and terminal voltage, respectively. I

_{b}and R

_{0}represent the output current and internal resistance of the power battery, respectively.

_{0}and setting it as a constant, the output power equation of the power battery can be stated as follows:

_{bat}(t) of the battery is positive when discharged and negative when charging. This parameter is determined as follows:

_{bat}is the battery charging and discharging efficiency.

_{b}denotes the rated power battery capacity. SOC

_{0}represents the initial the state of charge value.

#### 3.8. Power Battery Model

_{TN}and v are the resistance and travel speed of the tractor, respectively, which are determined based on the operating conditions of the tractor and are the output parameters of the dynamic model of the unit. Drivetrain model output torque and speed (T

_{req}and n

_{req}) at the input end of the torque coupler. The motor and diesel engine models receive the instructions (T

_{mreq}, n

_{mreq}, T

_{ereq}, and n

_{ereq}).

_{mreq}and T

_{ereq}are the torques required for the motor and diesel engine, respectively, at the input of the torque coupler.

## 4. Energy Saving Control Strategy Design

#### 4.1. Energy-Saving Control Strategy Based on Instantaneous Optimization

#### 4.1.1. Optimization Model of Energy-Saving Control Strategy

_{c}(t) and Q

_{f}(t) are the equivalent fuel consumption and instantaneous fuel consumption, respectively. t

_{f}represents the terminal moment. j

_{e}and j

_{m}are the prices per liter of oil and per kWh of electricity, respectively. f

_{e}is engine fuel consumption at that moment.

_{e}(t) of the diesel engine and T

_{m}(t) of the motor torque. The relationship between them and the required torque is introduced based on Equation (1).

_{m}

_{min}and T

_{m}

_{max}are the minimum and maximum torques of the motor, respectively. T

_{e}

_{min}and T

_{e}

_{max}are the minimum and maximum torque of the diesel engine, respectively. SOC

_{min}and SOC

_{max}represent the minimum and maximum values allowed by the SOC value of the power battery, respectively.

#### 4.1.2. Establish the Optimal Torque Distribution Table

_{e}and motor torque T

_{m}are taken as the control variables to address the optimal torque distribution table. The specific process is illustrated in Figure 6.

- According to the typical working conditions of a tractor, a set of operating parameters (speed ratio i
_{t}, required torque T_{req}, and power source speed n_{e}) within a short period of time are used as the system input parameters; - In the value range, step sizes ΔT
_{req}and Δn_{e}are used to discretize the required torque and power source speed, respectively;$$\left\{\begin{array}{l}k=0:\Delta {T}_{req}(t):{T}_{req}(t)\\ j=0:\Delta {n}_{e}(t):{n}_{e}(t)\end{array}\right.$$ - According to the speed n
_{e}, determine the maximum torques T_{e}_{max}and T_{m}_{max}that the diesel engine and motor can achieve at this speed; - Take the SOC state value of the power battery as the state variable, the torques of motor and diesel engine as the control variable, and minimum equivalent fuel consumption as the objective function Q
_{c}, to determines the optimal instantaneous torque of the diesel engine and motor; - Record the torque of the diesel engine and motor corresponding to the required instantaneous torque and speed until the end of t
_{f}at the final moment, summarize the data at all moments, and form the optimal torque distribution table.

#### 4.1.3. Instantaneous Optimization Control

- According to the dynamic equation, calculate the required torque T
_{v}(t) and wheel speed n_{tire}(t) at the wheel of the entire machine.$${n}_{tire}(t)=\frac{v(t)}{0.377\cdot r}$$$${T}_{v}(t)=\frac{9550\cdot {P}_{v}(t)}{{n}_{tire}(t)}$$_{v}(t) is the required power at the wheels of the entire machine. - Obtain the required torque T
_{zj}(t) and speed n_{zj}(t) for the input of the main reducer.$$\left\{\begin{array}{l}{n}_{zj}(t)=\frac{{n}_{v}(t)}{{i}_{0}}\\ {T}_{zj}(t)=\frac{{T}_{v}(t)\cdot {i}_{0}}{{\eta}_{zj}}\end{array}\right.$$ - Obtain the required transmission input torque T
_{bsq}(t) and speed n_{bsq}(t).First, according to the torque required by the main reducer and the tractor speed, the transmission ratio is calculated by looking up the table. Then, the transmission efficiency is obtained by looking up the transmission ratio and torque table. Finally, the transmission input torque and speed are calculated using the transmission speed ratio and efficiency.$$\left\{\begin{array}{l}{n}_{bsq}(t)=\frac{{n}_{zj}(t)}{{i}_{t}}\\ {T}_{bsq}(t)=\frac{{T}_{zj}(t)}{{i}_{t}\cdot {\eta}_{b}}\end{array}\right.$$ - Calculate the required torque T
_{req}(t) and speed n_{req}(t) of the torque coupler input.$$\left\{\begin{array}{l}{n}_{req}(t)={n}_{bsq}(t)\\ {T}_{req}(t)=\frac{{T}_{bsq}(t)}{{\eta}_{o}}\end{array}\right.$$ - The required torque T
_{req}(t) and speed n_{req}(t) at the input end of the torque coupler obtained in the previous step are interpolated according to the optimal torque distribution table. Obtain the optimal torque distribution of the diesel engine and motor during tractor operation.

#### 4.2. Energy-Saving Control Strategy Based on Power Following

#### 4.2.1. Control Principle Based on Power Following

#### 4.2.2. Solving Process of Power Following Energy-Saving Control

_{req}and diesel engine speed n

_{e}can be obtained. Accordingly, the required torque of the entire machine T

_{req}can be obtained.

_{erated}and P

_{mrated}are the rated powers of the diesel engine and motor, respectively.

## 5. Result Analysis

#### 5.1. Analysis of Results Obtained Rotary Tillage Condition

#### 5.2. Analysis of Results Under Plow Condition

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 7.**Torque distribution under hybrid drive. (

**a**) Torque of the diesel engines. (

**b**) Torque of the motor.

Name | Parameter | Value (Unit) |
---|---|---|

Diesel engine | Rated power | 162 (kW) |

Rated speed | 2500 (rpm) | |

Maximum torque | 800 (Nm) | |

Motor | Rated power | 30 (kW) |

Rated speed | 3000 (rpm) | |

Rated torque | 96 (Nm) | |

Power battery | Energy capacity | 70 (Ah) |

Rated voltage | 360 (V) | |

SOC | 0.90–0.25 |

Forward Gear | Transport III | Transport II | Transport I | Working II | Working I | Amble II | Amble I |
---|---|---|---|---|---|---|---|

Ratio | 0.864 | 1.377 | 2.307 | 3.296 | 4.963 | 7.405 | 11.208 |

Theoretical speed (km/h) | 39.980 | 28.668 | 17.164 | 11.977 | 7.654 | 5.231 | 3.522 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, J.; Feng, G.; Xu, L.; Yan, X.; Wang, W.; Liu, M.
Energy-Saving Control of Hybrid Tractors Based on Instantaneous Optimization. *World Electr. Veh. J.* **2023**, *14*, 27.
https://doi.org/10.3390/wevj14020027

**AMA Style**

Zhang J, Feng G, Xu L, Yan X, Wang W, Liu M.
Energy-Saving Control of Hybrid Tractors Based on Instantaneous Optimization. *World Electric Vehicle Journal*. 2023; 14(2):27.
https://doi.org/10.3390/wevj14020027

**Chicago/Turabian Style**

Zhang, Junjiang, Ganghui Feng, Liyou Xu, Xianghai Yan, Wei Wang, and Mengnan Liu.
2023. "Energy-Saving Control of Hybrid Tractors Based on Instantaneous Optimization" *World Electric Vehicle Journal* 14, no. 2: 27.
https://doi.org/10.3390/wevj14020027