# Research on Global Optimal Energy Management Strategy of Agricultural Hybrid Tractor Equipped with CVT

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## Abstract

**:**

## 1. Introduction

## 2. Topology and Principal Parameters of Hybrid Tractors

#### 2.1. Hybrid Tractor Topology

#### 2.2. Main Performance Parameters of Hybrid Tractor

## 3. Model Construction of Hybrid Tractor

#### 3.1. Hybrid Tractor Transmission System Model

_{ereq}and P

_{mreq}are the diesel engine and motor required power, respectively. n

_{req}and T

_{req}denote the required speed and torque at the input end of the torque coupler, respectively. η

_{e}and η

_{m}are the working efficiencies of the diesel engine and motor, respectively. P

_{e}and P

_{m}denote the power required for the diesel engine and motor, respectively. T

_{e}, T

_{m}, n

_{e}and n

_{m}denote the torques and speeds of the diesel engine and motor, respectively.

_{0}and i

_{cvt}denote the main reducer and CVT speed ratios, respectively. n

_{e}and n

_{tire}represent the diesel engine and driving wheel speeds, respectively. r denotes the driving wheel radius of the hybrid tractor. v represents the speed of the hybrid tractor during working.

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

_{zy}, η

_{cvt}, and η

_{o}represent the central drive efficiency, CVT efficiency, and torque-coupler efficiency, respectively. P

_{r}and P

_{drive}denote the rotary cultivator power and tractor travel power consumptions, respectively.

#### 3.3. Motor Model

#### 3.4. Diesel Engine Model

#### 3.5. CVT Model

_{cvt_in}is the input torque of the CVT.

_{cvt_in}and n

_{cvt_out}are the CVT driving pulley and driven pulley speeds, respectively. T

_{cvt_out}is the CVT output torque.

#### 3.6. Power Battery Model

_{bat}denotes the battery charging or discharging efficiency. P

_{m}greater than 0 is discharging, and P

_{m}less than 0 is charging. P

_{bat}represents the required power of the power battery.

_{b}denotes the rated power battery capacity. SOC(t) and SOC(t + 1) are the SOC at the current and next moment, respectively. ∆t is the time step.

#### 3.7. Machine Simulation Model

_{req}and n

_{req}) of the whole machine are obtained through calculation and processing according to Equations (1), (4) and (6). Inside the controller, the required power of the whole machine is allocated according to the established control strategy (including the proposed and compared strategies). Then output the corresponding motor required power (P

_{mreq}) and diesel engine required power (P

_{ereq}) as the input of the motor model and diesel engine model.

_{mreq}, n

_{mreq}, T

_{ereq}, and n

_{ereq}) and transmit the power to the rotary tiller dynamic model (P

_{drive}and P

_{r}) through the transmission system model. At the same time, the power battery model performs energy transfer according to the required power of the motor model (P

_{bat}).

## 4. Energy Management Strategy Design

#### 4.1. Global Optimal Energy Management Strategy Based on Dynamic Programming

#### 4.1.1. Energy Management Optimization Model

_{c}(t) is the total cost of energy consumption. Q

_{f}(t) denotes the instantaneous fuel consumption. t

_{f}denotes the end moment. j

_{m}and j

_{e}represent the prices per kWh of electricity and liter of oil, respectively.

#### 4.1.2. Dynamic Programming Algorithm

_{m}

_{min}, T

_{m}

_{max}, T

_{e}

_{min}, and T

_{e}

_{max}represent the minimum and maximum torques of the electric motor and diesel engine at the current moment, respectively. n

_{m}

_{min}, n

_{m}

_{max}, n

_{e}

_{min}, and n

_{e}

_{max}represent the minimum and maximum speeds of the electric motor and diesel engine at the current moment, respectively. i

_{cvt}

_{min}and i

_{cvt}

_{max}denote the minimum and maximum speed ratios of the CVT, respectively. SOC

_{min}and SOC

_{max}are the least and greatest values permitted by the SOC, respectively.

#### 4.1.3. Dynamic Programming Control Strategy Solution Process

- 1.
- Based on the operative circumstances, the dynamic programming algorithm is set to 1800 stages (m = 1800). According to the known vehicle speed and vehicle parameters in each stage, the required torque T
_{v}(k) of the tractor at the wheels of each stage is obtained through the dynamic equation.

_{v}(k) denotes the required power at the wheel of the tractor.

- 2.
- Obtain the required torque T
_{zy}(k) at the input end of the central drive.

_{zy}(k) represent the required torque at the input end of the central drive.

- 3.
- Obtain the required torque T
_{cvt_in}at the input end of the CVT. Firstly, the CVT speed ratio is obtained according to the central transmission demand torque and the tractor speed look-up table, and the output torque of the CVT is calculated on the basis of the known speed ratio. Then the CVT efficiency is obtained through the CVT speed ratio and torque look-up table. Accordingly, the CVT input torque is calculated from the CVT speed ratio and efficiency. - 4.
- Obtain the required torque T
_{req}(k) at the input end of the torque coupler.

_{PTO}(k) denotes the PTO gear ratio inside the torque coupling.

- 5.
- According to the required torque T
_{req}(k) and speed n_{req}(k), based on the set SOC upper and lower limits, CVT speed ratio, maximum and minimum torque values of diesel engine and electric motor, diesel engine fuel consumption rate, and electric motor efficiency, interpolation calculation each stage may control variables. - 6.
- From all the possible control variables calculated, select the speed and torque of the diesel engine and motor that satisfy the constraints of the Equation (22). Calculate the control variables and state parameter values of each component when the objective Equation (21) is the minimum value. The state change and interpolation calculation of the control variables are shown in Figure 8.

_{k}. In the k + 1 stage, the optimal control variable u

_{k}

_{+1}is obtained by interpolating u

_{k}

_{+1}(j) and u

_{k}

_{+1}(j + 1). The red line in Figure 8 shows that in the k + 1 stage, the state variable x(i + 1) exceeds the set upper and lower limits of the SOC.

- 7.
- Let m = m − 1, carry out the operation of the next stage until k = 0, get the optimal control parameter and SOC value, and the operation ends.

#### 4.2. Power following Energy Management Strategy

## 5. Simulation Results and Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 5.**(

**a**) The relationship curve between electromotive force and SOC; (

**b**) The relationship curve between charge or discharge internal resistance and SOC.

**Figure 13.**CVT speed ratio change diagram. (

**a**) Based on dynamic programming strategy; (

**b**) Based on power-following strategy.

Component | Parameter | Value (Unit) |
---|---|---|

Diesel engine | Rated power | 60 (kW) |

Rated speed | 2200 (rpm) | |

Maximum torque | 280 (Nm) (1700 rpm) | |

Motor | Maximum power | 40 (kW) |

Rated speed | 2800 (rpm) | |

Maximum torque | 140 (Nm) | |

Power battery | Rated capacity | 70 (Ah) |

Rated voltage | 320 (V) | |

SOC | 0.25–0.90 | |

Central drive | Speed ratio | 19.27 |

CVT | Speed ratio | 0.864–9.728 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, J.; Feng, G.; Liu, M.; Yan, X.; Xu, L.; Shang, C.
Research on Global Optimal Energy Management Strategy of Agricultural Hybrid Tractor Equipped with CVT. *World Electr. Veh. J.* **2023**, *14*, 127.
https://doi.org/10.3390/wevj14050127

**AMA Style**

Zhang J, Feng G, Liu M, Yan X, Xu L, Shang C.
Research on Global Optimal Energy Management Strategy of Agricultural Hybrid Tractor Equipped with CVT. *World Electric Vehicle Journal*. 2023; 14(5):127.
https://doi.org/10.3390/wevj14050127

**Chicago/Turabian Style**

Zhang, Junjiang, Ganghui Feng, Mengnan Liu, Xianghai Yan, Liyou Xu, and Chengyan Shang.
2023. "Research on Global Optimal Energy Management Strategy of Agricultural Hybrid Tractor Equipped with CVT" *World Electric Vehicle Journal* 14, no. 5: 127.
https://doi.org/10.3390/wevj14050127