Dual-Source Cooperative Optimized Energy Management Strategy for Fuel Cell Tractor Considering Drive Efficiency and Power Allocation

Abstract

To solve the problems of the low driving efficiency of a fuel cell tractor power source and the high hydrogen consumption caused by the irrational power allocation of the energy source, the power system was divided into two parts, power source and energy source, and a dual-source cooperative optimization energy management strategy was proposed. Firstly, a general energy efficiency optimization method was designed for the power source composed of a traction motor and PTO motor, and the energy source was composed of a fuel cell and power battery. Secondly, the unified objective function and constraint conditions were established, and the instantaneous optimization algorithm was used to construct the weight factor. The instantaneous optimal drive efficiency energy management strategy and the instantaneous optimal equivalent hydrogen consumption energy management strategy were designed, respectively. Finally, with the demand power as the transfer parameter, the instantaneous optimal drive efficiency energy management strategy and the instantaneous optimal equivalent hydrogen consumption energy management strategy were integrated to form a dual-source collaborative optimal energy management strategy. In order to verify the effectiveness of the proposed strategy, a rule-based energy management strategy was developed as a comparison strategy and tested in an HIL test under plowing and rotary plowing conditions. The results show that the average fuel cell efficiency of the proposed strategy increased by 7.86% and 8.17%, respectively, and the proposed strategy’s equivalent hydrogen consumption decreased by 24.21% and 9.82%, respectively, compared with the comparison strategy under the two conditions. It can significantly reduce the SOC fluctuation of the power battery and extend the service life of the power battery.

1. Introduction

As an important piece of power equipment in modern agriculture, the tractor promotes the process of agricultural modernization. With the continuous innovation of technology, tractors play an irreplaceable role in modern agriculture [1,2,3]. However, the continuous growth of human society’s demand for energy has led to an increasing scarcity of resources and environmental degradation, which have become urgent problems facing the world. Internal combustion engine tractors use fossil energy as a power source, and the exhaust and noise emissions cause serious environmental pollution, which is not in line with green requirements [4,5]. Since the fuel cell is a green machine, it is considered to be one of the ideal choices for reducing environmental pollution [6].

For fuel cell tractors, the development of efficient energy management strategies is a necessary measure to reduce the hydrogen consumption and extend the operating time [7]. Energy management techniques are currently employed extensively in a variety of fuel cell cars and can be broadly divided into the rule-based algorithms and the optimization-based algorithms [8].

The rule-based algorithms are applied to real-time state information of the hybrid power system to regulate the power allocation and operating state switching of the system by setting thresholds and logic rules. Sun Yan et al. [9] proposed an improved power-following strategy, and the simulation results showed that the proposed strategy can reduce the equivalent hydrogen consumption by 2% compared with the traditional strategy. Although the method reduces the equivalent hydrogen consumption to some extent, it ignores the weak performance of supercapacitors in storing energy, while the battery usually has a higher energy density and can store more energy. To further reduce the equivalent hydrogen consumption, Li et al. [10] proposed a fuzzy logic strategy for fuel cell hybrid vehicles (FCHVs), which was validated under typical urban driving conditions in China, and the strategy reduced the vehicle hydrogen consumption by 6.9% compared to the power-following strategy. However, the method is only optimized for state of charge (SOC) control of the battery, ignoring the low efficiency of the fuel cell when the output power is too low or too high. In order to control the switching of the fuel cell under different operating conditions, Fu-Jun Zhang et al. [11] chose a pure electric bus as the research object and proposed a switching/power-following strategy, and the simulation results showed that the range of the bus was improved by 18% compared with the energy-following control strategy. Although the rule-based algorithms are easy to implement, they rely on experimental results to build the rules, which leads to poor control results [12,13,14].

The optimization-based algorithms mainly include dynamic planning with the global optimization function and the equivalent consumption minimization strategy with the instantaneous optimization effect, etc. Du et al. [15] proposed an optimization rule for the dynamic planning strategy, and the simulation results showed that the improved control strategy led to a reduction in the equivalent hydrogen consumption of 6.46%. However, the optimization process did not consider that the improved strategy based on dynamic planning could be applied in real time. Huangfu et al. [16] introduced the rate of change of fuel cell power with weighting coefficients into the Hamiltonian function and proposed an improved real-time strategy based on Pontryagin’s minimum principle, which resulted in a reduction of 10.1% in hydrogen consumption compared to the implemented limited state machine strategy. However, the simple strategy of switching on/off the fuel cell system under the boundary condition of the battery SOC still cannot simultaneously take care of the hydrogen consumption and lifetime. Gi et al. [17] proposed an implementable control strategy for fuel cell vehicles by means of a dynamic programming approach and particle swarm optimization method. It subsequently gave the on/off moments of the fuel cell system and the relative to the battery SOC and the power demand. The appropriate modulation ratio of the fuel cell system effectively reduces the hydrogen consumption. However, the method did not accurately identify the dynamic motion conditions of the vehicle. To further increase the fuel economy, Gharibeh et al. [18] proposed an online multistage rule and optimization approach to the strategy and compared it to an optimal fuzzy logic control method, which resulted in lower fuel consumption and battery power fluctuations. Although this method reduces the fuel consumption, it does not fully consider the energy management strategy (EMS) of fuel cell electric vehicles (FCEVs) for optimizing the power distribution between multiple energy sources while taking into account aspects like the hydrogen consumption and efficiency. Rezk et al. [19] proposed an external energy maximization technique based on Harris Hawks optimization that was compared to other existing solutions. The strategy can potentially reduce the fuel consumption by 19.81% and increase the efficiency of the system by 0.09%. Although the above studies have to some extent influenced the development of strategies for fuel cell tractors, the focus of these strategies has been mainly on the passenger car segment. Given the significant differences in the energy demand characteristics and load characteristics of fuel cell tractors compared to passenger cars, further research and development of strategies for fuel cell tractors is necessary.

At present, there are relatively limited studies on energy management methods for fuel cell tractors. Xu Liyou et al. [20] developed a fuzzy control-based strategy for a fuel cell/battery hybrid tractor, which reduced the equivalent hydrogen consumption by 11.11% compared with the switching strategy. However, the fuzzy rules used mainly rely on the subjective experience of the designer, which has some limitations in terms of adapting to the working conditions. Valerio et al. [21] used a hybrid energy storage system combining a fuel cell and a small battery pack instead of a conventional diesel-powered tractor, which reduced the equivalent CO₂ emissions by about 50%. However, the study mentions that the control strategy used a defined way to distribute the energy demand, which makes it difficult to fully consider the dynamic changes of the system and the demand changes under real operating conditions. Xu et al. [22] used a fuel cell/battery/ultracapacitor hybrid tractor as the object and designed a multilayered decoupled control energy based on the Haar wavelet and logic rule management strategies, which reduced the whole machine hydrogen consumption by 5.4% compared with the comparison method. However, this study only considered the output efficiency of the energy system, and the studied tractor used a single motor as the power source, which makes it difficult to meet the requirement of high-efficiency operation considering the complex and variable working conditions of the tractor. Yang et al. [23] used a traction motor and a power take-off (PTO) motor as the power source but neglected the influence of the power source operation efficiency on the economy with the whole machine when formulating the energy management strategy.

In summary, there are relatively few studies on energy management strategies, and most of them only consider the power allocation methods of the fuel cell and power battery, without considering the effect of the motor drive efficiency on the economy of the whole machine. Therefore, this paper proposes a dual-source cooperative optimization energy management strategy, which achieves the cooperative optimization of the energy and power sources through the transfer of demand power variables. The main contributions are as follows. (1) Based on the instantaneous optimization algorithm, a general energy efficiency optimization method is proposed. On this basis, the instantaneous optimal drive efficiency energy management strategy and the instantaneous optimal equivalent hydrogen consumption energy management strategy are formulated for the power source and the energy source, respectively, to optimize the operation efficiency of the traction motor and PTO motor, as well as the power output modes of the fuel cell and the power battery. (2) Taking the demand power as the transfer parameter, the instantaneous optimal drive efficiency energy management strategy and the instantaneous optimal equivalent hydrogen consumption energy management strategy are integrated to form a dual-source cooperative optimization energy management strategy, which realizes the cooperative optimization of the energy source and the power source.

2. Materials and Methods

2.1. Model Building

To control the power of the fuel cell and energy storage device more accurately, and at the same time, to enhance the control of the charging condition, this paper chooses to connect a unidirectional and bidirectional DC/DC converter to the fuel cell and power battery, respectively. This configuration can bring more flexibility to energy management. The structure and parameters are shown in Figure 1 and

Table 1. Parameters of the dual-motor fuel cell tractor.

Project	Parameters/Unit	Numerical Value
Machine parameters	Effective quality/kg	2200
	Radius of the driving wheel/m	0.61
Drive system	1 gear ratio	3.42
	2 gear ratio	1.62
	PTO reducer gear ratio	5.56
	Central transmission device gear ratio	24.36

.

2.1.1. Mode Analysis

To improve the power supply stability, this paper adopts the fuel cell as the main energy source, which provides basic power to the system, and the power cell as the auxiliary energy source, which provides deficit power to the system. It has a common power supply mode, the fuel cell separates the power supply mode, and the battery separates the power supply mode and battery compensation mode, as shown in Figure 2.

In the common power supply mode, the fuel cell and the power battery supply energy together, and this mode can output a larger power, suitable for high power demand operations. The fuel cell separates the power supply mode due to the poor dynamic performance, and this mode is suitable for smoother operating conditions. The battery separates the power supply mode, also with poor power performance, and this mode is suitable for higher SOC and smoother operating conditions. The battery compensation mode will make up the excess power output from the fuel cell for the power battery to maintain the SOC, and this mode is suitable for the case when the power demand is small.

Considering the complex and variable working conditions faced by the tractor during field operation, it is hard for a single motor to satisfy the power requirements of different working conditions, so this paper adopts the dual-motor as the power source. The power source can be adjusted through the power-coupling device to realize four driving modes, which are shown in Figure 3.

In the single-motor drive mode, the traction motor provides power output independently without power coupling, and the mode output power is limited, which is applicable to the plains area of the turnaround conditions. In the dual-motor independent drive mode, the dual-motor independently provides power output without a power-coupling device. The traction motor drives the tractor, and the PTO motor is responsible for the power output, which is applicable to planting and spraying, and the power demand is not large. In the dual-motor coupled drive mode, the torque of the dual-motor is coupled by the power-coupling device to drive the tractor, and the mode is suitable for plowing and other high-load working conditions. In the dual-motor coupled PTO mode, the torque of the dual-motor is coupled by the power-coupling device to drive the tractor and carry out PTO output, and the mode of PTO can output larger power and is suitable for rotary plowing and deep loosening.

2.1.2. Dynamic Modeling of Plowing Units

Plowing is a typical working condition of tractor field operations. In this working condition, the tractor needs to give full play to its power and traction capacity to cope with the resistance and load of the soil. When the tractor performs the plowing operation, the power-coupling device that needs torque and speed can be expressed as:

$$\left\{\begin{array}{l}{T}_{req}=\left(F_T+m_{s}gf\cos \theta +m_{s}g\sin \theta \right)r_w\\ N_{req}={\displaystyle \frac{i_g{i}_{0}v}{0.377r_w}}\end{array}\right.$$

(1)

where T_req denotes the torque, N·m; F_T denotes the hook traction, N; m_s denotes the service quality, kg; g denotes the gravity acceleration, m/s²; f denotes the rolling resistance coefficient; θ denotes the angle of the road, °; r_w denotes the rolling radius of the driving wheels, m; N_req denotes the required speed, r/min; i_g denotes the transmission ratio; i₀ denotes the main reduction ratio; and v denotes the speed of the tractor, km/h.

The hook pull generated by the plowing unit is related to the plowshare width and depth [24]:

$$F_T=Z{b}_l{h}_l{k}_l$$

(2)

where Z denotes the number of plowshares; b_l denotes the width of the plowshare, cm; h_l denotes the depth of the plowshare, cm; and k_l denotes the specific soil resistance, N/cm².

2.1.3. Dynamic Modeling of Rotary Plowing Units

Rotary plowing operations, in addition to overcoming rolling resistance and slope resistance, require additional power output to accomplish soil loosening, turning and mixing. Under this condition, the power-coupling device that needs torque and speed can be expressed as:

$$\left\{\begin{array}{l}{T}_{req}=\left(m_{s}gf\cos \theta +m_{s}g\sin \theta \right)r_w+T_p\\ N_{req}={\displaystyle \frac{i_g{i}_{0}v}{0.377r_w}}\end{array}\right.$$

(3)

where T_p denotes the power output shaft’s output torque, N·m.

2.1.4. Motor Model

When the power source of the parameter matches, the power source composed of the traction motor and PTO motor should firstly comply with the power requirements and then match the characteristics of the dual-motor according to the data of the operating conditions. Since plowing is the most basic and heavily loaded working condition, the rated power of the dual-motor should be designed as:

$$P_m=P_t+P_p$$

(4)

$$P_m\ge {\displaystyle \frac{F_{T}v}{3600{\eta }_T}}$$

(5)

where P_m denotes the sum of the rated power of the dual-motor, kW; P_t denotes the rated power of the traction motor, kW; P_p denotes the rated power of the PTO motor, kW; and η_T denotes the tractor traction efficiency.

In this paper, there is no need to consider the complex working mechanism inside the motor in the specific research process, only the external characteristics of the motor. The MAP diagrams of the motors are obtained by table checking and interpolation of the test data, and the efficiencies of the motors can be obtained from the table checking of the actual rotation speed and actual torque of the motors. The efficiency MAP diagrams and parameters of the dual-motor are shown in Figure 4 and

Table 2. Parameters of the dual-motor.

Project	Parameters/Unit	Numerical Value
Traction motor	Rated/Maximum power/kW	18/35
	Rated/Maximum torque/N·m	65/135
	Rated/Maximum rotation Speed/(r·min−1)	2650/6000
PTO motor	Rated/Maximum power/kW	20/40
	Rated/Maximum torque/N·m	70/140
	Rated/Maximum rotation Speed/(r·min−1)	2700/6000

.

With the motor MAP shown in the figure, the efficiency η_m can be obtained by the motor model with T the current torque and n the speed, and the relation is shown as follows:

$${\eta }_m=f_m\left(T,n\right)$$

(6)

where f_m denotes the table lookup function of the motor.

2.1.5. Fuel Cell Model

One of the most important energy sources for tractors is the fuel cell. We adopt an exchange membrane fuel cell, and according to the empirical equation, the hydrogen consumption is as follows [14]:

$${\dot{m}}_{fc}={\displaystyle \frac{1}{E_{H_2,low}}}{\displaystyle \int \frac{P_{fc}}{{\eta }_{fc}\left(P_{fc}\right)}}dt$$

(7)

where P_fc denotes the power of the fuel cell; E_H2,low denotes the low calorific value of hydrogen of 120 kJ/kg; η_fc(P_fc) denotes the efficiency of the fuel cell when its power is P_fc; and ${\dot{m}}_{fc}$ denotes the consumption of hydrogen.

Since it needs to provide energy to its air supply module, cooling module and other ancillary equipment, the overall efficiency can be expressed as:

$${\eta }_{fc}\left(P_{fc}\right)={\displaystyle \frac{P_{fc}}{P_{H_2}}}$$

(8)

where $P_{H_2}$ denotes the total power of the fuel cell.

Since the tractor is driven by the fuel cell to provide the primary driving force, it is first selected based on the steady working condition. As the plowing power demanded is large, the power design based on the plowing condition should be satisfied:

$$P_{fc}\ge {\displaystyle \frac{F_{T}v}{3600{\eta }_T}}$$

(9)

Considering the fuel cell air supply modules, cooling modules and other ancillary equipment in the whole machine using power, as well as the maximum power demand under steady state driving of the tractor, the final selected fuel cell power system has a rated power of 42 kW, and the parameters are shown in

Table 3. Parameters of the fuel cell system.

Parameters/Unit	Numerical Value
Type of fuel	Hydrogen
Cooling method	Liquid cooling
Working condition temperature/°C	40
Rated power/kW	42
Peak power/kW	45
Output voltage/V	385

.

The fuel cell model is shown in Figure 5. From the figure, we have chosen the efficient region to be in the range of about 14–38 kW. The paper’s goal is to operate in this high-efficiency region to reduce the hydrogen consumption.

2.1.6. Power Battery Model

In this paper, the power battery is utilized in cooperation with the fuel cell. It is usually modeled by the internal resistance model and resistive capacitance model [25,26]. The internal resistance model treats the battery pack as an ideal voltage source and a series-connected internal resistance equivalent circuit, which is a first-order model. The battery pack is treated as a circuit with two capacitors and three resistors in the resistive capacitance model, which is a second-order model. However, since the design of the state observer for the resistive capacitance model is more difficult, the internal resistance model is chosen as the modeling method for the battery in this paper [27]. The output power and output voltage can be expressed as:

$$\left\{\begin{array}{l}{P}_b=U_b{I}_b\hfill \\ U_b=E-I_b{R}_b\hfill \end{array}\right.$$

(10)

where P_b denotes the output power; U_b denotes the output voltage; I_b denotes the power battery electric current; E denotes the open circuit voltage; and R_b denotes the internal resistance.

Based on its output power, the power battery’s electric current can be expressed as:

$$I_b={\displaystyle \frac{E-\sqrt{E^2-4R_b{P}_b}}{2R_b}}$$

(11)

One of the most important settings in the battery management system is the power battery’s state of charge. The ampere–time integration approach is used in this research to compute the state of charge:

$$SOC(t)=SO{C}_0-{\displaystyle \frac{{\displaystyle {\int }_0^t{I}_b}(t)dt}{Q_b}}$$

(12)

where SOC(t) denotes the current state of charge value of the power battery; SOC₀ denotes the initial state of charge value of the power battery; and Q_b denotes the rated capacity of the power battery.

The charging and discharging efficiency during the working process can be calculated according to the following formula:

$${\eta }_{bchr}={\displaystyle \frac{2}{1+\sqrt{1-\frac{4R_{chg}{P}_{bat}}{E^2}}}}$$

(13)

$${\eta }_{bdis}={\displaystyle \frac{1+\sqrt{1-\frac{4R_{dis}{P}_{bat}}{E^2}}}{2}}$$

(14)

where η_bchr and η_bdis denote the charging and discharging efficiency; while R_chg and R_dis denote the internal resistance of the charging and discharging processes.

In summary, according to the fuel cell operating voltage range and power system configuration, a power battery system with a rated power of 18 kW is matched for the tractor, and the parameters are shown in

Table 4. Parameters of the power battery.

Parameters/Unit	Numerical Value
Rated power/kW	18
Nominal voltage/V	320
Maximum charge/Ah	17.5
Internal charge resistance/ohm	0.8
Operating temperature/°C	20

. The curves of the SOC and charging/discharging power over power battery charging/discharging efficiency are shown in Figure 6.

2.2. Dual-Source Cooperative Optimization Energy Management Strategy

To realize cooperative optimization between the energy source and the power source, this paper designs an energy efficiency optimization method with generality based on the instantaneous optimization algorithm. An instantaneous optimal drive efficiency energy management strategy and an instantaneous optimal equivalent hydrogen consumption energy management strategy are also designed. Eventually, the fusion of the two is realized by taking the demand power as the transfer parameter, forming a dual-source cooperative optimization energy management strategy.

2.2.1. General Energy Efficiency Optimization Method

At present, in the existing studies, many scholars have carried out in-depth research on the optimal distribution strategy of the energy sources; at the same time, in the field of pure electric vehicles with a dual-motor as the power source, there are also many energy management strategies to improve the efficiency. However, the existing studies have investigated energy source management and power source control independently and lack a generalized approach to both. If the existing independent research results for a single energy source or power source are directly adopted and different energy management strategies are designed separately, it will not only make the control system of the whole machine complex and redundant but also easily lead to the inefficient utilization of resources, which will affect the overall performance and stability of the system. Therefore, the objective of this paper is to explore a general method that can comprehensively consider energy source management and power source control to optimize the energy utilization efficiency and improve its overall performance.

Thus, this paper develops a general energy efficiency optimization method based on the instantaneous optimization algorithm. It can flexibly select the objective function as well as the corresponding constraints for different application objects, which greatly simplifies the design process for energy management, reducing the complexity of the control system for the whole machine.

For the method applicable to power and energy sources, a unified objective function F should first be determined:

$$F=k_{\eta }(1-{\eta }_{drive})+k_H\cdot C$$

(15)

where η_drive denotes the drive efficiency of the power source; C denotes the equivalent hydrogen consumption of the energy source; and k_η and k_H denote the weighting factors corresponding to the drive efficiency and equivalent hydrogen consumption, respectively.

Under different application objects, the optimization of the drive efficiency or equivalent hydrogen consumption can be selected by adjusting the values of k_η and k_H. During the optimization process, it is crucial to establish uniform constraints U to ensure the effectiveness and feasibility:

$$U=\{D_p,E_e\}$$

(16)

where D_p denotes a subset of power source constraints; and E_e denotes a subset of energy source constraints.

The operation process of the general energy efficiency optimization method is shown in Figure 7. The core process can be detailed as follows. First, the objective function and constraints based on the optimization object are determined. Second, the required optimization information for the optimization object are obtained. Subsequently, based on the instantaneous optimization algorithm, the operating state of the optimization object is optimized, and the objective function is calculated. Then, it is determined whether the constraints are satisfied; if no, the optimization search is continued; if yes, the minimum value of the objective function in all the operation states is calculated. Finally, the optimal operating conditions of the optimization object are output when the objective function reaches its minimal value.

2.2.2. Instantaneous Optimal Drive Efficiency Energy Management Strategy

Different torque allocations result in different operating efficiencies. To improve the efficiency of the power source, this section develops an instantaneous optimal drive efficiency control strategy based on the general energy efficiency optimization method.

When the fuel cell tractor is operating, different power source operation modes require different management strategies. In the single-motor drive mode or the dual-motor independent drive mode, the motors are independently responsible for providing power output without power coupling. At this time, the operating state and performance parameters (such as the speed and torque) of each motor directly depend on the demand index of the current specific operation task. In this case, since there is no dynamic coupling and mutual coordination between the motors, there is no need to adjust the motors, and it is only necessary to ensure that they can actually operate. However, when it comes to the dual-motor coupled drive mode and the dual-motor coupled PTO mode, there is a power-coupling effect, and varying torque methods of distribution will result in different driving efficiencies of the power sources. To improve the driving efficiency of the power source, an instantaneous optimal drive efficiency energy management strategy is proposed.

Under the condition of satisfying the constraints, there are a variety of different torque combinations to choose from, and these different torque combinations will affect the driving efficiency of the power source. Therefore, in the optimization process, the maximum utilization efficiency of the dual-motor is used as the optimization goal, and the operating efficiency of the power source can be effectively improved by optimizing the torque distribution of the dual-motor. At this time, the objective function F is determined by adjusting the weighting factor based on the optimization object:

$$F=1-{\eta }_{drive}$$

(17)

For the drive efficiency of the power source η_drive, first define the power-coupling device’s output power P_w as:

$$P_w={\displaystyle \frac{T_t{N}_t}{9550}}+{\displaystyle \frac{T_p{N}_p}{9550}}$$

(18)

where T_t and T_p denote the torque of the traction motor and PTO motor, N·m; and N_t and N_p denote the speed of the traction motor and PTO motor, r/min.

Therefore, the power source’s drive efficiency, η_drive, can be expressed as follow:

$${\eta }_{drive}={\displaystyle \frac{P_w}{\frac{T_t{N}_t}{9550{\eta }_t}+\frac{T_p{N}_p}{9550{\eta }_p}}}$$

(19)

where η_t denotes the traction motor efficiency; and η_p denotes the PTO motor efficiency.

Therefore, the objective function F is:

$$F({\eta }_{drive})=1-{\displaystyle \frac{P_w}{\frac{T_t{N}_t}{9550{\eta }_t}+\frac{T_p{N}_p}{9550{\eta }_p}}}$$

(20)

The optimization objects in this section are the traction motor and PTO motor, so the constraints select the subset of power source constraints in the unified constraints with the following expressions:

$$\left\{\begin{array}{l}{T}_{tmin}\le T_t\le T_{tmax}\\ N_{tmin}\le N_t\le N_{tmax}\\ T_{pmin}\le T_p\le T_{pmax}\\ N_{pmin}\le N_p\le N_{pmax}\end{array}\right.$$

(21)

where T_tmin denotes the minimum torque of the traction motor, N·m; T_tmax denotes the maximum torque of the traction motor, N·m; N_tmin denotes the minimum speed of the traction motor, r/min; N_tmax denotes the maximum speed of the traction motor, r/min; T_pmin denotes the minimum rotational torque of the PTO motor, N·m; T_pmax denotes the maximum rotational torque of the PTO motor, N·m; N_pmin denotes the minimum speed of the PTO motor, r/min; and N_pmax denotes the maximum speed of the PTO motor, r/min.

A flowchart of the instantaneous optimal drive efficiency energy management strategy is shown in Figure 8. Firstly, calculate the power-coupling device’s output required torque T_req and speed N_req. Second, obtain the maximum of the traction motor output torque T_tmax and the PTO motor output torque T_pmax at this speed N_req by checking the table. Subsequently, traverse the combination of the output torque of the dual-motor and calculate the efficiency of the power source for each combination of the torque. Then, determine whether the constraints are satisfied; if no, continue traversing the combination of the output torque of the dual-motor; if yes, calculate the maximum value of the objective function in all the operation states. Finally, output the optimal point of the torque distribution at the time with maximum efficiency from the power source.

2.2.3. Instantaneous Optimal Equivalent Hydrogen Consumption Energy Management Strategy

To achieve an efficient output, an instantaneous optimal equivalent hydrogen consumption energy management strategy is proposed based on the general energy efficiency optimization method. Based on the theory of equivalent hydrogen consumption, the strategy optimizes the output power in real time within the unit control cycle, so that the energy source has the minimum equivalent hydrogen consumption [28,29,30].

At this time, the optimization object is the energy source, and the objective function F is determined by adjusting the weighting factor based on the drive efficiency and equivalent hydrogen consumption:

$$F=C$$

(22)

The power required at the input of the power source should be calculated as:

$$P_{req}={\displaystyle \frac{P_t}{{\eta }_t}}+{\displaystyle \frac{P_p}{{\eta }_p}}$$

(23)

where P_req denotes the power demanded of the power source, kW; P_t denotes the output power of the traction motor, kW; P_p denotes the output power of the PTO motor, kW; η_t denotes the efficiency of the traction motor; and η_p denotes the efficiency of the PTO motor.

The fuel cell is mainly used to provide stable energy output, while the power battery is used to provide transient energy output, and the combination of the two can satisfy the energy demand. Therefore, the total instantaneous hydrogen consumption of the system is composed of two components, where the relationship can be expressed as follows:

$$C=C_{fc}+C_{bat}$$

(24)

where C_fc denotes the instantaneous hydrogen consumption of the fuel cell, kg; and C_bat denotes the instantaneous equivalent hydrogen consumption of the power battery, kg.

The instantaneous hydrogen consumption of the fuel cell system is an important indicator in the hybrid system, and the equation for it can be expressed as follows:

$$C_{fc}={\displaystyle \frac{1}{E_{H_2,low}}}{\displaystyle \frac{P_{fc}}{{\eta }_{fc}}}$$

(25)

where η_fc denotes the fuel cell efficiency.

The equivalent hydrogen consumption equates the consumption of the power battery to the hydrogen consumption. The equation can be expressed as follows [31]:

$$C_{bat}=\left\{\begin{array}{cc}{\displaystyle \frac{1}{E_{H_2,low}}}{\displaystyle \frac{P_{bat}}{{\eta }_{dis}\cdot \overline{{\eta }_{fc}}}},& P_{bat}\ge 0\\ {\displaystyle \frac{1}{E_{H_2,low}}}{\displaystyle \frac{P_{bat}{\eta }_{chg}}{\overline{{\eta }_{fc}}}},& P_{bat}<0\end{array}\right.$$

(26)

where P_bat denotes the power battery power, kW; η_dis denotes the fuel cell discharge efficiency; $\overline{{\eta }_{fc}}$ denotes the average fuel cell discharge efficiency; and η_chg denotes the fuel cell charge efficiency.

To avoid excessive charging and discharging of the power battery, it is necessary to ensure that the power battery stays within a certain SOC range during actual operation. Therefore, Equation (20) can be corrected by adding a compensation factor:

$$C(t)=C_{fc}+\alpha C_{bat}$$

(27)

where α denotes an SOC compensation factor.

$$\alpha =1-\beta {\displaystyle \frac{2SOC-\left(SO{C}_H+SO{C}_L\right)}{SO{C}_H-SO{C}_L}}$$

(28)

where β denotes the SOC adjustment factor with a value range from 0 to 1; SOC denotes the current instantaneous SOC value; SOC_H denotes the maximum limit value of the SOC; and SOC_L denotes the minimum limit value of the SOC.

Therefore, the objective function F of the instantaneous optimal equivalent hydrogen consumption energy management strategy is:

$$F=C_{fc}+\alpha C_{bat}$$

(29)

The constraints should be selected as a subset of the energy source constraints in the unified constraints with the expression:

$$\left\{\begin{array}{l}{P}_{f{c}_{\_}\min }\le P_{fc}(t)\le P_{f{c}_{\_}\max }\\ P_{ba{t}_{\_}\min }\le P_{bat}(t)\le P_{bat\_\max }\\ SO{C}_L\le SOC(t)\le SO{C}_H\end{array}\right.$$

(30)

A flowchart of the instantaneous optimal equivalent hydrogen consumption energy management strategy is shown in Figure 9. First, calculate the required power P_req at the input of the power source. Second, traverse each possible fuel cell and power battery power allocation scheme and calculate the hydrogen consumption of the fuel cell C_fc(t) and power battery C_bat(t). Then, determine whether the constraints are satisfied; if no, continue traversing each possible fuel cell and power battery power allocation scheme; if yes, calculate the minimum value of the objective function in all the operation states. Finally, select the scheme with the lowest hydrogen consumption from all the power allocation schemes that satisfy the constraints and output the optimal power of the fuel cell and power battery.

2.2.4. Dual-Source Cooperative Optimization Energy Management Strategy

Based on the general energy efficiency optimization method, the instantaneous optimal drive efficiency energy management strategy and the instantaneous optimal equivalent hydrogen consumption energy management strategy are designed. Since the energy source output allocation scheme and the energy source drive efficiency have an important effect on the economy of a fuel cell tractor, these two factors must be comprehensively considered when formulating the strategy. This paper proposes a dual-source cooperative optimization energy management strategy that takes the required power as the transfer parameter and realizes cooperative optimization between the energy source and the power source. A flowchart of this is shown in Figure 10.

The specific process of the dual-source cooperative optimization energy management strategy is as follows. First, according to the plowing and rotary plowing working condition information, the output side of the power-coupling device’s required torque and speed information is obtained and transmitted to the instantaneous optimal drive efficiency energy management strategy. The strategy traverses the torque combination of the dual-motor and outputs the torque combination with the highest efficiency. Then, based on the torque and speed information of the dual-motor in this combination, the power required of the power source is calculated. The instantaneous optimal equivalent hydrogen consumption energy management strategy traverses the power allocation methods of the energy source according to the demanded power by the power source and calculates the equivalent hydrogen consumption of each allocation scheme. Finally, the power source and energy source allocation scheme with the minimum equivalent hydrogen consumption is selected as the optimal scheme among multiple power allocation schemes.

2.3. Comparative Method Design

To verify the effectiveness, a rule-based energy management strategy is formulated in this paper and simulation experiments are conducted under plowing and rotary plowing conditions.

In this section, firstly, the torque equal distribution strategy is developed; secondly, the power-following strategy is designed. Finally, the comparative strategy is formed using the demand power as the transfer parameter.

For the power source, the dual-motor coupled drive mode and the dual-motor coupled PTO mode, the torque of the dual-motor is coupled by the power-coupling device and then output. For this reason, the torque equal distribution strategy is developed in this paper. The ratio of the rated power of the dual-motor is used to distribute the torque of the dual-motor.

The output torques T_t and T_p are, respectively:

$$\left\{\begin{array}{l}{T}_t=k{T}_v\\ T_p=(1-k)T_v\end{array}\right.$$

(31)

where k denotes the torque distribution coefficient, which can be expressed as:

$$k={\displaystyle \frac{P_{et}}{P_{ep}+P_{et}}}$$

(32)

where P_et and P_ep denote the rated power of the traction motor and PTO motor, kW.

For the energy source, this paper designs a power-following strategy. It is a key technology applied to hybrid energy systems that satisfies the dynamic power demand of the system by utilizing the power of different energy units. Based on the SOC and the power demand of the power source, the fuel cell’s operating state is adjusted to realize the control. The switching control is shown in Figure 11.

The details of the power-following strategy are as follows:

I Working range: SOC > SOC_H and P_req < P_min (the lower limit threshold of power). To ensure that the power battery does not remain in a high SOC state for a long time, the fuel cell is turned off and the power battery provides energy.

II Operating range: SOC > SOC_H and P_min < P_req < P_max (the upper limit threshold of power). The fuel cell maintains the operating state of the previous moment.

III Working range: SOC > SOC_H and P_req > P_max. A single energy source cannot be fully satisfied. The fuel cell is started to meet the high power demand. The fuel cell system and the power battery both work together to meet the energy supply needs of the machine.

IV Working range and V Working range: SOC_L < SOC < SOC_H and P_req < P_min. The fuel cell maintains the operating state of the previous moment.

VI Operating range: SOC_L < SOC < SOC_H and P_req > P_max. Then, the power required by the power source cannot be supplied by a single power source, so the fuel cell is in the open state and shares the task of power supply with the power battery.

VII Working range, VIII Working range and IX Working range: SOC < SOC_L. The power battery stops working and the fuel cell is switched on to charge it in order to ensure that the power battery can continue to provide energy in the case of subsequent high energy demand.

A flowchart of this is shown in Figure 12. First, according to the plowing and rotary plowing working condition information, the output side of the power-coupling device’s required torque and speed information is obtained, and this information is fed into the torque equal distribution strategy. In this strategy, the output torque of the dual-motor is allocated according to the ratio of the rated power. Then, the actual power required at the input of the power source is calculated based on the allocated torque and speed. Meanwhile, the thermostat energy management strategy is regulated based on the SOC state to determine the operating state, and it outputs energy according to the required power from the power source.

3. Results and Discussion

To verify the effectiveness of the dual-source cooperative optimization energy management strategy, this paper uses the MATLAB simulation platform and the hardware in the loop (HIL) test platform to test and verify the dual-source cooperative optimization energy management strategy and the rule-based energy management strategy. The HIL test platform is mainly composed of the control model and the controlled object, and it can simulate the actual operation process of the fuel cell tractor to realize real-time experimental validation of the performance of the power source and energy source.

The HIL test platform is mainly composed of an HIL test cabinet and a PC and controller. The HIL test cabinet is mainly composed of power management units, a signal conditioning module, a real-time processor, etc. The real-time processor adopts the NI PXIe-8880 controller. The PC adopts the Windows 10 operating system, connects to the HIL test cabinet based on Ethernet, and controls the HIL test cabinet to carry out test experiments through the VeriStand software control.

According to the test needs, the HIL test environment is first configured through the PC, the strategies are written into the controller, and then the tractor controlled object and the controller are loaded into the real-time processor, and the data of the HIL test are observed and exported through the VeriStand software of the PC. A flowchart of the specific HIL test validation is shown in Figure 13.

3.1. Plowing Condition

In this paper, the measured data of a 38 kW tractor under the plowing condition are selected as the load of a dual-motor fuel cell tractor for a simulation test. The cooperating velocity and traction resistance curve under the plowing condition are shown in Figure 14. The simulation length of this condition is 600 s, the average resistance generated by the ploughshare is 12.23 kN, and the average operating velocity is 6.6 km/h. The sampling step is set to 1 s in the plowing condition, and the dual-source cooperative optimization energy management strategy and the rule-based energy management strategy are verified by MATLAB simulation experiments and HIL tests, respectively.

The dual-motor operating points under the plowing condition are shown in Figure 15. From the figure, compared with the comparative strategy, the dual-source cooperative optimization energy management strategy makes the motors work more in the high-efficiency area, which is because the dual-source cooperative optimization can traverse the optimal dual-motor torque combination scheme, which improves the operating efficiency. Through optimization, the dual-source cooperative optimization energy management strategy provides an improvement in the driving efficiency of the power source. As verified by the HIL test, the obtained efficiency scatter distributions are similar to the simulation results.

The output power of the fuel cell and power battery under the plowing condition is shown in Figure 16. From the figure, the output power of the fuel cell under the dual-source cooperative optimization energy management strategy is smoother and more stable than the comparative strategy, which can provide more stable power for the fuel cell tractor while reducing the damage to the fuel cell. In contrast, the power cell provides rapidly varying power to satisfy temporarily high power demands. By rationally allocating the power outputs, the dual-source cooperative optimization energy management strategy achieves the optimal utilization of both. The results obtained by the HIL test verification are the same as the simulation results.

The fuel cell efficiency curves under the plowing condition are shown in Figure 17. The average efficiency of the fuel cell with dual-source cooperative optimized energy management is 0.5736, which is 7.86% higher than the average efficiency of 0.5318 of the comparative strategy. The HIL verification is the same as the simulation results. The results show that the dual-source cooperative optimized energy management can significantly improve the efficiency of fuel cell operation.

The SOC variation curve of the power battery under the plowing condition is shown in Figure 18. Compared with the comparative strategy, the SOC fluctuation under the proposed strategy is smoother. The comparative strategy reaches the SOC min at 454 s and enters the charging state. The end-state values of the power battery are 44.04% and 37.24% under the proposed and compared strategies, respectively. This is consistent with the results obtained by the HIL test validation. The above results show that the damage to the power battery due to the SOC fluctuation is less under the proposed strategy.

The comparison results of the equivalent hydrogen consumption under the plowing condition are shown in Figure 19. The consumption of the proposed strategy is 196.21 g, which is 24.21% lower compared to the 258.89 g consumed by the comparative strategy. The equivalent hydrogen consumption of the dual-source cooperative optimization energy management strategy and the comparative strategy is verified by the HIL test to be 196.22 g and 258.89 g, respectively, which is a little different from the simulation results. This result shows that the proposed strategy has a significant advantage in terms of the energy savings.

3.2. Rotary Plowing Condition

In addition to the plowing condition, rotary plowing is another important condition of the tractor in field operations. The power-coupling device’s torque and operation velocity under the rotary plowing condition are shown in Figure 20. The simulation length of this working condition is 600 s, the average output torque of the power-coupling device is 110.76 Nm, and the average operation velocity is 5.59 km/h. In the same way, the sampling step is set to 1 s in the rotary plowing condition, and the dual-source cooperative optimization energy management strategy and the rule-based energy management strategy are verified by MATLAB simulation experiments and HIL tests, respectively.

The dual-motor operating points under the rotary plowing condition are shown in Figure 21. The proposed strategy makes the operating points of the dual-motor more densely distributed in the high-efficiency region, and this centralized distribution indicates that the fuel cell tractor utilizes the energy more efficiently in actual operation, which improves the energy utilization efficiency of the whole machine and further verifies that the proposed energy management strategy can improve the operating efficiency. As verified by the HIL test, the obtained efficiency scatter distributions are similar to the simulation results.

The output power of the fuel cell and power battery under the rotary plowing condition is shown in Figure 22. As shown in the figure, compared with the comparative strategy, the dual-source cooperative optimization energy management strategy makes the output power of the fuel cell show smoother characteristics, thus ensuring a stable power supply for the fuel cell tractor and reducing the possible losses of the fuel cell. The results obtained by the HIL test verification are the same as the simulation results.

The fuel cell efficiency curves under the rotary plowing condition are shown in Figure 23. The figure shows that after implementing the dual-source cooperative optimization energy management strategy, the fuel cell system achieves an average efficiency value of 0.5867, which is a significant improvement of 8.17% compared to the average efficiency of 0.5424 obtained by the comparative strategy. The HIL verification is the same as the simulation results. It is shown that the dual-source cooperative optimization strategy proposed in this paper can significantly improve the efficiency of fuel cell operation.

The SOC variation curve under the rotary plowing condition is shown in Figure 24. The initial SOC is 55%, and the comparative strategy reaches the SOC in 447 s and enters the charging state. The end-state values of the power battery are 41.04% and 37.04% under the proposed and compared strategies, respectively. This is consistent with the results obtained by the HIL test validation. The SOC fluctuation under the proposed strategy in this paper is smoother and can significantly reduce the SOC fluctuation of the power battery, which is conducive to prolonging the service life of the power battery and improving its efficiency, which reflects a more effective protection measure for the power battery.

The comparison results of the equivalent hydrogen consumption under the rotary plowing condition are shown in Figure 25. The equivalent hydrogen consumption of the dual-source cooperative optimization energy management strategy is 233.93 g, which is 9.82% lower than that of the comparative strategy (259.39 g). The equivalent hydrogen consumptions of the dual-source cooperative optimization energy management strategy and comparative strategy are verified by the HIL test to be 233.93 g and 259.39 g, respectively, which are the same as the simulation results. This result further verifies the superiority of the energy management strategy proposed in this paper in reducing the equivalent hydrogen consumption and improving the energy utilization efficiency.

4. Conclusions

To realize the cooperative optimization of the power source and energy source to reduce the equivalent hydrogen consumption, this paper designs a dual-source cooperative optimization energy management strategy for the power source composed of a traction motor and PTO motor, as well as the energy source composed of a fuel cell and power battery. To verify the effectiveness of the proposed strategy, a rule-based energy management strategy is formulated as a comparison strategy and MATLAB simulation and HIL simulation tests are performed to validate the results. The following conclusions are drawn from this study:

(1)

The plowing and rotary plowing conditions, compared with the comparative strategy, improve the average fuel cell efficiency of the proposed strategy by 7.86% and 8.17%, and the equivalent hydrogen consumption is reduced by 24.21% and 9.82%, respectively. The dual-source cooperative optimization energy management strategy can improve efficiency and reduce hydrogen consumption.

(2)

Under the plowing condition, the end-state values of the power battery are 44.04% and 37.24% for the proposed and comparison strategies, respectively. Under the rotary plowing condition, the end-state values of the power battery are 41.04% and 37.04% for the proposed and comparison strategies, respectively. The proposed strategy can significantly reduce the SOC fluctuation of the power battery, which is conducive to prolonging the service life of the power battery and improving its utilization efficiency.

(3)

The equivalent hydrogen consumption of the two strategies was verified by HIL tests to be 196.22 g and 258.89 g for plowing as well as 233.93 g and 259.39 g for rotary plowing. This result is similar to that obtained by the simulation, which is 196.21 g and 258.89 g for plowing as well as 233.93 g and 259.39 g for rotary plowing. The simulation results are basically consistent with the HIL test results, which verifies the effectiveness of the strategies.

In addition, in the future, the energy output of a fuel cell tractor can be investigated under many different operating conditions, taking into account the driver’s state and the dynamic degradation characteristics of the fuel cell.