**Real-time Energy Management Strategy for Oil-Electric-Liquid Hybrid System based on Lowest Instantaneous Energy Consumption Cost**

#### **Yang Yang 1,2,\*, Zhen Zhong 1,2, Fei Wang 1,2, Chunyun Fu 1,2 and Junzhang Liao 1,2**


Received: 10 January 2020; Accepted: 8 February 2020; Published: 11 February 2020

**Abstract:** For the oil–electric–hydraulic hybrid power system, a logic threshold energy management strategy based on the optimal working curve is proposed, and the optimal working curve in each mode is determined. A genetic algorithm is used to determine the optimal parameters. For driving conditions, a real-time energy management strategy based on the lowest instantaneous energy cost is proposed. For braking conditions and subject to the European Commission for Europe (ECE) regulations, a braking force distribution strategy based on hydraulic pumps/motors and supplemented by motors is proposed. A global optimization energy management strategy is used to evaluate the strategy. Simulation results show that the strategy can achieve the expected control target and save about 32.14% compared with the fuel consumption cost of the original model 100 km 8 L. Under the New European Driving Cycle (NEDC) working conditions, the energy-saving effect of this strategy is close to that of the global optimization energy management strategy and has obvious cost advantages. The system design and control strategy are validated.

**Keywords:** oil–electric–hydraulic hybrid system; lowest instantaneous energy costs; energy management; global optimization

#### **1. Introduction**

With the rise and boom of the automobile industry, the number of automobiles has been increasing, but the related problem of environmental pollution has also been growing. At present, pure electric vehicles are considered to be the cleanest automobiles, but their core technologies, such as motors and power batteries, are difficult to make great breakthrough in a short period of time, which has severely restricted their development. On the other hand, hybrid electric vehicles do not have such problems and are thus gradually being favored by more people. The main problem that needs to be solved in hybrid electric vehicles is determining how to make a reasonable allocation among the power sources under the premise that the demand torque is known. At present, the energy management strategy for hybrid electric vehicles can be roughly divided into a rule-based energy management strategy, instantaneous optimization of energy management strategies, and global optimization of energy management strategies.

Zhou et al. proposed a rule-based energy management strategy that uses dynamic programming (DP) to select control parameters. The fuel consumption per 100 km of the strategy is 12.7 L, which is very close to the global optimal value of 12.4 L [1]. Li et al. on the other hand, proposed a logic threshold strategy optimized via the pseudospectral method, which achieves the goal of reducing battery energy loss by making supercapacitors perform better with a high specific power performance [2]. Whereas

Qin et al. proposed an energy management control strategy based on working condition identification, which reduced fuel consumption by 12.77% compared with that of the strategy without working condition identification [3]. Meanwhile, Yin et al. proposed a dual-planetary hybrid electric vehicle as an object of engine torque control. This strategy can optimize the engine operating point while keeping the final battery state of charge (SOC) value within a reasonable range [4]. Although this type of energy management strategy has a simple structure and strong practicability, its advantages and disadvantages are easily affected by the experience of engineering personnel and the working conditions are poor.

For the instantaneous optimization of energy management strategy, Jiao et al. proposed an adaptive equivalent fuel consumption minimum strategy (A-ECMS), which obtains the equivalent factor under current driving conditions based on the equivalent factor map in energy distribution. The fuel consumption is minimized throughout the driving route, and the battery state of charge (SOC) is kept within a reasonable range [5]. On the other hand, Zhang et al. proposed an energy management strategy based on the minimum equivalent fuel consumption. Compared with the rule-based energy management strategy, it has a significant improvement in terms of fuel economy [6]. Meanwhile, Wang et al. proposed an energy control strategy that allows both the engine and the motor to operate in an efficient region to improve fuel economy [7]. Compared with the globally optimized energy management strategy, this strategy has a small amount of calculation and fast speed, but can only achieve instantaneous optimization.

For the global optimization energy management strategy, Xiang Zhu proposed a DP-based energy management strategy. Through online simulation, the solution of the multi-neural network model is determined to be close to the optimal solution obtained by the global optimization algorithm, and the real-time application of dynamic programming is greatly improved [8]. Meanwhile, Wang et al. considered the discrete solutions of related variables and the boundary problems of feasible domains when solving the optimal control problem of hybrid electric vehicle, and systematically studied the relationship between the optimization accuracy and the computational complexity of the dynamic programming algorithm. Compared with that of the traditional control strategy, the fuel economy based on the dynamic planning control strategy increased by about 20% [9]. Although this strategy can achieve global optimization, it needs to obtain the entire driving conditions in advance, and the amount of calculation is large, which is difficult to apply to real vehicles.

In this article, Firstly, the oil–electric–hydraulic system requires one to install a hydraulic energy storage system on the rear axle of the existing oil-electric hybrid vehicle structure, which is proposed in this article and uses a timely four-wheel-drive structure with independent driving of the front and rear axles. Secondly, based on this structure, this study focuses on a steady-state energy management strategy in the driving and braking process, proposes a logic threshold energy management strategy based on the optimal working curve, and selects the relevant threshold according to the steady-state efficiency characteristic curve of the key components. The genetic algorithm is used to jointly optimize the powertrain parameters and logic threshold energy management strategy parameters. Thirdly, for the driving mode, considering that this article mainly focuses on the fuel economy of the entire vehicle, and in the logic threshold energy management strategy, the setting of the threshold value is susceptible to expert experience, the working conditions are poor, the global optimization energy management strategy has a large amount of calculation, the driving conditions need to be known, and practical problems, a real-time energy management strategy based on the lowest energy consumption cost is proposed, whereas for the braking mode, based on the traditional four-wheel vehicle braking force distribution strategy, a braking-force allocation strategy based on the highest energy recovery is proposed. Furthermore, a global optimization energy management strategy based on dynamic programming is used as the basis for evaluating the advantages and disadvantages of other strategies. Finally, the stateflow-based control strategy model is implemented into the forward simulation model to verify the effectiveness of the strategy, and the two strategies are simulated and compared.

#### **2. Oil–Electric–Liquid Hybrid Power System Structure**

Unlike a pure electric vehicle, an oil–electric hybrid electric vehicle retains the engine and reduces the power of the battery. Although the vehicle's range is increased, the disadvantage of a reduced energy recovery rate is ignored. Under the same conditions, although the accumulator has a low energy density, it also has a high power density, which not only can quickly recover and release energy, but also has higher energy efficiency and can provide greater auxiliary power for the vehicle. If the characteristics of the high energy density of the storage battery and high power density of the accumulator are combined, not only can the vehicle's cruising range be extended, but the energy recovery rate can also be improved. Therefore, the traditional configuration is equipped with a motor and an external battery pack on the front axle, and a hydraulic energy storage system on the rear axle. In addition, continuously variable transmission (CVT) can not only adjust the operating point of the engine and motor, save fuel consumption, but also improve the ride and stability of the vehicle. Therefore, this article decided to use CVT transmission. As shown in Figure 1, the new setup is composed mainly of an integrated starter generator (ISG) motor, high-pressure accumulator, low-pressure accumulator, hydraulic pump/motor, battery, and continuously variable transmission (CVT). There are clutches at the connection between the engine and the motor, the hydraulic pump/motor, and the rear axle main reducer. The clutch status of the front and rear axles can be controlled to make the vehicle work in different modes. The vehicle working mode is outlined in Table 1.

**Figure 1.** Structure of oil–electric–hydraulic hybrid power system.

Similar to for a traditional automobile, the maximum demand power of an oil–electric hybrid electric vehicle is also determined according to the vehicle dynamics index [10]. This study uses the vehicle's basic parameters and dynamic indicators of the original model. Based on the vehicle parameters and different driving conditions, the maximum required power of the vehicle can be calculated. From these calculations, the total power of the initial power source is determined to be 120 kW.

In addition, the theoretical calculation method and the comprehensive analysis method based on the cycle condition are used to match the parameters of each key component. The matching results are listed in Table 2.


**Table 1.** Working modes of the hybrid system.

Note: <sup>ƻ</sup> means the clutch is disengaged, <sup>ƽ</sup> means the clutch is engaged.

**Table 2.** Basic parameters of each key component.


#### **3. Joint Optimization of Energy Management Strategy and Power System Component Parameters**

#### *3.1. Logic Threshold Energy Management Strategy based on Optimal Working Curve*

This study is based on the gasoline engine's universal characteristic curve, and the research object is the rechargeable oil–electric–hydraulic hybrid vehicle. *Pemin\_eco* and *Pemax\_eco* are used as the logic threshold parameters for charge-sustaining (CS) stage engine operation to optimize the working area of the engine. (*Pemin\_eco*, *Pemax\_eco*) = (9 kW, 57 kW) is initially selected, and based on the battery SOC model, the battery SOC = 0.3 is initially taken as its lower working limit.

In the parallel hybrid system, which includes a variety of working modes, to ensure that the hydraulic pump can provide sufficient regeneration capacity and improve energy recovery efficiency during braking, this study chooses the control strategy of preferential use of hydraulic energy and electric energy. The specific mode selection logic is shown in Figure 2.

**Figure 2.** Mode selection logic diagram.

Under the premise of satisfying the power requirements, obtaining the best fuel economy for the whole vehicle is one of the goals of the hybrid electric vehicle energy management strategy. Firstly, the optimal working point corresponding to different power requirements in different modes is obtained via offline optimization, and a MAP table is made. Based on the result of mode selection, the optimal working point that meets the current vehicle power demand is then determined and applied, thereby achieving the optimal power system efficiency.

When the hybrid electric vehicle is operating in the hydraulic pump/motor single drive mode, its operating point is directly determined according to the required power, because the CVT transmission efficiency model was established by interpolation, and the CVT speed ratio range was obtained, whereas when the hybrid electric vehicle is operating in the engine or motor alone drive mode, the engine or motor operating point can be adjusted via continuously variable transmission (CVT). While the demand power is satisfied, the efficiency of itself is optimized, and the working point corresponding to the optimal efficiency is the optimal working point of the engine or the motor. Under the condition that the demand power is satisfied and each key component of the power source is constrained by itself, the optimization problem, wherein the transmission system efficiency is the objective function, is solved, and the optimal working curves of the motor and the engine, when either is working alone, can be obtained. These curves are shown in Figures 3 and 4, respectively.

For hybrid systems, if the CVT efficiency loss is neglected when the engine and motor work together, Equation (1) is used.

$$\begin{aligned} P\_r &= P\_\ell + P\_{\mathfrak{m}\ell} = T\_\ell \omega \iota\_\ell + T\_{\mathfrak{m}\ell} \omega\_{\mathfrak{m}} \\ \omega\_\ell &= \omega\_{\mathfrak{m}\ell} = \omega\_r \\ \omega\_{\mathfrak{c}\\_\text{min}} &\le \omega \iota\_\ell \le \omega\_{\mathfrak{c}\\_\text{max}} \\ \omega\_{\mathfrak{m}\\_\text{min}} &\le \omega\_{\mathfrak{m}} \le \omega\_{\mathfrak{m}\\_\text{max}} \\ T\_{\mathfrak{s}\\_\text{min}} &\le T\_\ell \le T\_{\mathfrak{c}\\_\text{max}} \\ T\_{\mathfrak{m}\\_\text{min}} &\le T\_\mathfrak{m} \le T\_{\mathfrak{m}\\_\text{max}} \end{aligned} \tag{1}$$

*Pr*, *Pe*, and *Pm* represent the vehicle demand power, engine power, and motor power, respectively, ω*<sup>e</sup>* and ω*<sup>m</sup>* denote the engine and motor speeds, respectively, *icvt* indicates the transmission speed ratio, and *Te* and *Tm* refer to the engine and motor torques, respectively.

**Figure 3.** Optimal operating curve of motor.

**Figure 4.** The optimal operating curve of the engine.

When the motor is operating in the drive mode, the efficiency of the hybrid system can be expressed as

$$\eta\_1 = \frac{P\_m + P\_e}{\frac{P\_m \eta\_d}{\eta\_W} + \frac{P\_e}{\eta\_\ell}} = \frac{(T\_m + T\_s)}{\left(\frac{T\_m \eta\_d}{\eta\_W} + \frac{T\_e}{\eta\_\ell}\right)}\tag{2}$$

In the formula, η*e*, η*m*, and η*<sup>d</sup>* are engine efficiency, motor efficiency, and battery discharge efficiency, respectively.

When the motor is operating in the power generation mode, the efficiency of the hybrid system can be expressed as

$$\eta\_2 = \frac{\left[P\_\varepsilon - P\_m(1 - \eta\_m \eta\_\varepsilon)\right]}{\left(P\_\varepsilon / \eta\_\varepsilon\right)} = \frac{\left[T\_\varepsilon - T\_m(1 - \eta\_m \eta\_\varepsilon)\right]}{\left(T\_\varepsilon / \eta\_\varepsilon\right)}\tag{3}$$

η*<sup>c</sup>* is the battery charging efficiency

According to Equation (1), there are multiple combinations of (ω*r*, *Tr*) on the premise that the engine and motor torques and speeds meet their constraints. The torques and speeds of the engine and motor in each combination, and the charge and discharge efficiencies of the engine, motor, and battery at this operating point can be substituted into Equation (2) or Equation (3) to calculate the total efficiency corresponding to each group of operating points. The most efficient combination (ω*e*, *Te*),(ω*m*, *Tm*) represents the best operating points of the engine and motor. In this way, the best working curves of the engine and the motor can be obtained. For the charge-depleting (CD) mode, the best working curves of the engine and motor combined drive are shown in Figures 5 and 6, respectively.

**Figure 5.** Optimal operating curve of engine.

**Figure 6.** Optimal operating curve of motor.

#### *3.2. Multi-objective optimization problems and their conversion*

Under the premise of satisfying the vehicle power performance, achieving the Pareto optimal solution of the two objective functions is equivalent to achieving the two optimal goals for hybrid electric vehicle energy consumption and vehicle manufacturing cost. This study uses a linear weighting method to convert a multi-objective function based on energy consumption and vehicle manufacturing cost into a single objective function:

$$F(\mathbf{x}) = \omega\_1 \frac{fuel(\mathbf{x})}{fuel\_{unopt}} + \omega\_2 \frac{cost(\mathbf{x})}{cost\_{unopt}} \tag{4}$$

where *f uelunopt* and *costunopt* represent the initial energy consumption and vehicle manufacturing cost, respectively, before optimization, and ω1, ω<sup>2</sup> are weighted values, wherein ω<sup>1</sup> = 0.8 and ω<sup>2</sup> = 0.2.

In terms of optimizing variable selection and constraint setting, to make the battery capacity meet the electric vehicle mileage index, the hydraulic pump/motor has to have sufficient regenerative braking force, but its corresponding cost should be reduced as much as possible. The optimization problem then becomes more convenient to solve. This study selects engine peak power *Pemax*, motor

peak power *Pmmax*, ratio *max*\_ *f actor* of maximum operating power of the engine to its peak power, ratio *min*\_ *f actor* of engine minimum operating power to peak power, and CD–CS mode switching value *Soc*\_*s*. That is, X = [*Pemax*, *Pmmax*, *max*\_ *f actor*, *min*\_ *f actor*, *Soc*\_*s*] are optimized variables for the joint optimization of energy management strategy parameters and dynamic system parameters. The vehicle's dynamic index (maximum speed is 180 km/h, 0~100 km/h acceleration time is 12.46 s, and the maximum climbable gradient is 40%) is used as an optimization constraint to ensure that the optimization results meet the vehicle power requirements.

#### *3.3. Energy Management Strategy and Optimization of Power System Components Parameters*

After the multi-objective problem is transformed into a single-objective problem, this article defines the fitness function, which simplifies the manufacturing cost of the whole vehicle power system to the cost of the engine and the motor. The following Equation (5) is obtained [11–13],

$$\cos t(X) = 849 + 12.236 P\_{\text{emax}} + 10.888 P\_{\text{mmxx}} \tag{5}$$

In the formula, *Pemax* and *Pmmax* are the peak powers of the engine and the motor, respectively. Genetic algorithms are then used to optimize energy management strategies and power system parameters:




The optimization results of the genetic algorithm are shown that the fitness value decreases with the evolution of the population, and finally converges to 0.93. The corresponding optimal individuals are *Pemax*, *Pmmax*, *max*\_ *f actor*, *min*\_ *f actor*, *Soc*\_*<sup>s</sup>* = (57.32, 32.68, 0.89, 0.16, 0.32)

According to the comparison of the simulation results of the unoptimized and GA-optimized in Table 4, the manufacturing cost of the whole vehicle power system is reduced by 1.7%, and the energy cost per 100 km is reduced by 8.3%.

Finally, to verify whether the parameter matching result of the power system is reasonable, the vehicle facing-forward simulation model is established based on the MATLAB/Simulink platform, and dynamic simulation results showed that the acceleration time to 100 km is 11.8 s, and the maximum speed is 177 km/h. The maximum grade is 40.24%, and the speed is 30km/h. At the time, the maximum gradeability can reach 39.78%; in summary, the optimized hybrid system parameters can meet the vehicle dynamic performance requirements.


**Table 4.** Comparison of simulation results.

#### **4. Energy Management Strategy based on the Lowest Instantaneous Energy Cost**

#### *4.1. Energy Management under Driving Conditions*

In this article, the minimum instantaneous energy consumption cost is the objective function; the vehicle travel demand torque *Tr*, vehicle speed v, hydraulic accumulator *Soc*1, and battery Soc are the state variables; the hydraulic pump/motor torque *Tpm*, motor torque *Tm*, engine torque *Te*, and CVT speed ratio *icvt* are the control variables. Because this study deals with not only hydraulic regenerative braking, but also motor regenerative braking [14], the hydraulic energy is equivalent to electric energy when the cost of hydraulic energy consumed is calculated, and the instantaneous cost is

$$\text{Cost} = \frac{1}{3600} \left( j\_f \frac{P\_t b\_t}{1000 \rho} + j\_c \left( \frac{P\_m}{\eta\_m \eta\_b} + \frac{P\_{pm}}{\eta\_{pm}} \right) \right) \tag{6}$$

where Cost is the sum of the costs of fuel, electricity, and hydraulic energy consumed per unit time (yuan/s), *jf* is the price of gasoline (yuan/L), and *je* is the price of electrical energy (yuan/kw·h). *Pe*, *Pm*, *Ppm* represents the output power of the engine, motor, hydraulic pump/motor (kw). *be* is the fuel consumption rate (g/(kw·h)); <sup>ρ</sup> is the density of gasoline g/cm3 ; η*<sup>m</sup>* and η*<sup>b</sup>* represent the motor, battery efficiency; η*pm* represents the mechanical efficiency of the hydraulic pump/motor in motor mode.

The objective function and constraints can be expressed as

⎧

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

$$\begin{aligned} \min \left( \text{Cost} \left( T\_{pm}, T\_m, T\_{\epsilon \epsilon} \dot{l}\_{\text{crt}} \right) \right) \\ \left( T\_{\epsilon} + T\_m \right) \cdot i\_{\text{crt}} i\_0 \eta\_{\text{crt}} + T\_{pm} \cdot i\_1 &= T\_{\eta \eta} \\ 0 \le n\_{\epsilon} &\le n\_{\text{cmax}} \\ 0 \le n\_{\text{prm}} &\le n\_{\text{prm} \text{max}} \\ T\_{\epsilon} &\le T\_{\epsilon \text{max}} (n) \\ \left| T\_m \right| &\le T\_{\eta \text{max}} (n) \\ T\_{\epsilon} + T\_m &\le T\_{\epsilon \text{cr}, \text{in}\_{\text{crt}}, \text{max}} \\ T\_{p \text{m}} &\le T\_{p \text{max}} (n) \\ \frac{P\_m}{(\eta\_{\text{m}} \eta\_{\text{p}})} &\le P\_{\text{hmax}} \\ 0.83 &\le i\_{\text{crt}} \le 2.50 \end{aligned} \tag{8}$$

To obtain the optimal values of each power source and transmission under different vehicle conditions, the grid traversal algorithm is used to solve any set of state variables, and the MAP table is made to facilitate real-time control. The algorithm flow is shown in Figure 7.

For different drive modes, the optimization results are different. In the single power source mode, because the hybrid system scheme adopted in this study does not have a transmission on the rear axle of the vehicle, the operating point cannot be optimized in the hydraulic pump/motor drive mode. Therefore, this study examines only the optimization of energy cost in the purely electric mode and engine driving mode. In the purely electric mode, the parts related to the engine and the hydraulic pump/motor in the optimization Algorithm 6 and Constraint Condition 8 are omitted, and the results shown in Figure 8a,b can be obtained via offline optimization. Similarly, for the engine mode, the optimization results are shown in Figure 9a,b.

**Figure 7.** Grid traversal algorithm flow chart.

**D** 

**Figure 8.** *Cont.*

**Figure 8.** Optimization results in the purely electric mode: (**a**) target torque of motor; (**b**) target speed ratio of continuously variable transmission (CVT).

**E** 

**Figure 9.** Optimization results in the engine mode: (**a**) target torque of engine; (**b**) target speed ratio of CVT.

The hybrid drive mode includes the electro–hydraulic hybrid drive, oil–electric hybrid drive, and oil–electro–hydraulic hybrid drive. For each mode, corresponding changes are similarly made to the optimization algorithm and constraints, and offline optimization is performed to produce the results shown in the Figures 10–12.

**F** 

**Figure 10.** Optimization results in the electro-hydraulic hybrid drive mode: (**a**) hydraulic pump/motor target torque; (**b**) motor target torque; (**c**) target speed ratio of CVT.

(**c**)

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**Figure 11.** Optimization results in oil–electro hybrid drive mode: (**a**) engine target torque; (**b**) motor target torque; (**c**) CVT of target speed ratio.

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**E** 

(**c**)

**Figure 12.** *Cont.*

**Figure 12.** Optimization results in oil-electro-hydraulic hybrid drive mode: (**a**) hydraulic pump/motor target torque; (**b**) engine target torque; (**c**) motor target torque; (**d**) CVT target speed ratio.

#### *4.2. Energy Management under Braking Conditions*

For a hybrid electric vehicle with a regenerative braking system, regarding the distribution of the braking force, it is necessary to solve the problems of not only the distribution of the braking force of the front and rear axles but also the distribution of the regenerative braking force and the frictional braking force. Thus, considering the high efficiency of the hydraulic regenerative braking system for recovering energy, this study uses the hydraulic pump/motor as the main way and the motor as the auxiliary way of providing the regenerative braking force. At the same time, the friction braking force is used to coordinate and to meet the driver's demand braking force to achieve maximum energy recovery.

Figure 13 shows the braking force distribution curve designed for the oil–electric–hydraulic hybrid electric vehicle. The OABCD curve is a braking force distribution curve for when the hydraulic accumulator is *SOC*<sup>1</sup> < 1 and the battery SOC > 0.9, the O*A BB* CD curve for when the hydraulic accumulator is *SOC*<sup>1</sup> < 1 and the battery SOC ≤ 0.9, and the O*A B* CD curve for when the hydraulic accumulator is *SOC*<sup>1</sup> = 1 and the battery SOC < 0.9. Point A indicates the maximum braking force that can be transmitted to the rear wheel when the hydraulic pump/motor is working alone; point *A* indicates the maximum braking force that can be transmitted to the front wheel when the ISG motor is working alone. Meanwhile, point B indicates the sum of the maximum braking forces that can be transmitted to the wheels when the hydraulic pump/motor and motor are simultaneously operating. *B* ,*C*, *D* are the intersections of the I curve and the braking strengths.

When the structural scheme of the hybrid system presented in this article is analyzed, the working point of the motor can be adjusted via the CVT transmission, but the working point of the hydraulic pump/motor cannot be adjusted, and thus the operating point of the motor can only be optimized. This inference considers that in the regenerative braking mode in which all motors participate, only the braking force distribution strategy is different and that there is no influence on the optimization process. Therefore, this section needs only to optimize the motor operating point in the motor regenerative braking mode. In this section, the kinetic energy recovered is used as the objective function, and the target torque of the generator and the CVT target speed ratio are optimized.

**Figure 13.** Braking force distribution curve of hybrid vehicles.

The objective function is

$$\min \left( P\_b \eta\_{\text{cv}t} \eta\_m \eta\_b \right) \tag{9}$$

In the formula, *Pb* represents the braking power required to be transmitted from the motor to the wheel.

The constraints are

$$\begin{cases} \quad T\_m = T\_{mb} / (i\_{crt} i\_1 \eta) \\ \quad 0 < n \le 6000 \\ \quad |T\_m| \le T\_{m\text{max}}(n) \\ \quad \left| P\_b \eta\_{cvt} \eta\_m \eta\_b \right| \le P\_{b\text{max}} \\ \quad 0.83 \le i\_{crt} \le 2.50 \end{cases} \tag{10}$$

The optimization results are shown in Figure 14.

**D** 

**Figure 14.** *Cont.*

**E** 

**Figure 14.** Optimization results in the regenerative braking mode: (**a**) target torque of motor; (**b**) target speed ratio of CVT.

#### *4.3. Analysis of Simulation Results*

To verify that the energy management strategy proposed in this article is effective in each mode, this study simulates under a driving cycle composed of multiple New European Driving Cycle (NEDC) working conditions. The results are shown in Figure 15.

**E Figure 15.** *Cont.*

**Figure 15.** Simulation result: (**a**) vehicle speed following curve; (**b**) hydraulic accumulator state of charge (SOC) trajectory curve; (**c**) battery SOC trajectory curve; (**d**) torque distribution curve.

As can be seen from Figure 15a, the driver model based on the PI controller has higher control accuracy. From a comparison of (a) and (b), it can be found that during the driving process, when the hydraulic accumulator SOC1 > 0, the hydraulic accumulator releases energy. Therefore, the hydraulic mode-based drive mode selection strategy proposed in this article achieves the expected control effect. From a comparison of (a), (b), and (c), it can be seen that during the braking process, the hydraulic accumulator SOC1 or the battery SOC has a significant rise, which indicates that the braking force distribution strategy not only can meet the braking demand but also can fully recover energy. It can also be seen from (c) that the battery SOC can still be maintained within a reasonable range after falling to a certain value. It can also be seen from (a), (d) that the torque distribution of the engine, the motor, and the hydraulic pump/motor can satisfy the torque demand of the entire vehicle. In the whole simulation process over the driving distance, because the hydraulic accumulator SOC1 returns to the initial state, the energy consumption includes only electric energy and fuel, wherein the electric energy is 5.88 degrees, the fuel is 4.99 L, and the total energy consumption cost is 38 yuan. Compared with the fuel consumption cost of the original model 100 km 8 L, the strategy proposed in this article saves costs by about 32.14%.

#### *4.4. Simulation Comparison under Two Di*ff*erent Strategies*

To better compare the proposed strategy with the minimum energy consumption cost strategy, the initial Soc of the battery is selected to be 0.8, and the initial value of the hydraulic accumulator Soc1 is set to 1. Furthermore, the DP-based global optimized energy management strategy is simulated under the NEDC working conditions. The results are shown in Figure 16.

**Figure 16.** *Cont.*

**Figure 16.** *Cont.*

**Figure 16.** Simulation results of the energy management strategy based on dynamic programming (DP): (**a**) battery Soc; (**b**) accumulator Soc; (**c**) motor torque; (**d**) engine torque; (**e**) hydraulic pump/motor torque; (**f**) CVT speed ratio.

The simulation result Figure 16 shows that the DP-based energy management strategy can extend the cruising range by rationally utilizing the electric energy and can also maintain the balance when the battery Soc is low. The control effect of the strategy is also good, which can provide a certain evaluation point for the advantages and disadvantages of other strategies. Therefore, this strategy is compared with the instantaneous energy consumption cost minimum energy management strategy. The simulation results are shown in Figure 17.

**Figure 17.** Comparison of simulation results under two strategies: (**a**) battery SOC versus time curve; (**b**) energy consumption cost versus time curve.

It can be seen from Figure 17 that the instantaneous optimized energy management strategy has a faster rate of lowering the Soc in the pre-simulation battery, uses more power, and lowers the energy consumption cost, which has obvious cost advantages compared with the global optimized energy management strategy. When the battery Soc drops to around 0.3, its value is balanced, and the energy consumption cost increases significantly and gradually exceeds the energy consumption cost under the global optimized energy management strategy.

#### **5. Conclusions**

In this study, a new type of oil–electric–hydraulic hybrid power system is examined as the research object, and a driving mode based on hydraulic energy and electric energy is selected. A logic threshold energy management strategy based on the optimal working curve is proposed, and then the linear weight method is adopted. The multi-objective function, which aims at the energy consumption cost and the manufacturing cost of the whole vehicle power system, is converted into a single objective function, the optimization variables are selected, and the constraints are set. The genetic algorithm is used to optimize the energy management strategy parameters and power system components. The optimized power system parameters can meet the power performance requirements of the vehicle.

Aiming at managing energy when the vehicle is under driving condition, a real-time energy management strategy based on the lowest instantaneous energy consumption cost is proposed. The strategy uses the instantaneous energy consumption cost in the single power source driving mode or the hybrid driving mode as the objective function and utilizes the grid. The ergodic method solves the target values of different vehicle demand torques and vehicle speeds to form a MAP table for real-time control. For braking conditions, based on the braking force distribution strategy and ECE regulations for traditional four-wheel-drive vehicles, a braking force distribution strategy based on the highest energy recovery is proposed. The simulation results show that the energy management strategy proposed in this article can achieve reasonable distribution of torque and achieve the expected control effect, and saves about 32.14% compared with the fuel consumption cost of the original model 100 km 8 L.

Simulation analysis of global optimization energy management strategy based on dynamic programming is performed, and the results prove that this strategy can be used as the basis for evaluating other strategies. The simulation comparisons under the NEDC working conditions show that the energy-saving effect of the real-time energy management strategy based on the minimum instantaneous energy consumption cost is similar to that of the global optimized energy management strategy.

**Author Contributions:** Y.Y. designed the oil–electric–hydraulic system and proposed the energy management control strategies; Z.Z. conducted model building, calculation, and analysis based on proposed control strategies; F.W. and C.F. matched the parameters of the oil–electric–hydraulic system and analyzed system performance. J.L. helped Z.Z. verify the energy management control strategies, and organized the manuscript format. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Key R&D Program of China (Grant No. 2018YFB0106100) and the National Natural Science Foundation of China (Grant No. 51575063).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **E**ffi**ciency Optimization and Control Strategy of Regenerative Braking System with Dual Motor**

#### **Yang Yang 1,2,\*, Qiang He 2, Yongzheng Chen <sup>2</sup> and Chunyun Fu 1,2**


Received: 10 January 2020; Accepted: 5 February 2020; Published: 6 February 2020

**Abstract:** The regenerative braking system of electric vehicles can not only achieve the task of braking but also recover the braking energy. However, due to the lack of in-depth analysis of the energy loss mechanism in electric braking, the energy cannot be fully recovered. In this study, the energy recovery problem of regenerative braking using the independent front axle and rear axle motor drive system is investigated. The accurate motor model is established, and various losses are analyzed. Based on the principle of minimum losses, the motor control strategy is designed. Furthermore, the power flow characteristics in electric braking are analyzed, and the optimal continuously variable transmission (CVT) speed ratio under different working conditions is obtained through optimization. To understand the potential of dual-motor energy recovery, a regenerative braking control strategy is proposed by optimizing the dynamic distribution coefficient of the dual-electric mechanism and considering the restrictions of regulations and the I curve. The simulation results under typical operating conditions and the New York City Cycle (NYCC) proposed conditions indicate that the improved strategy has higher joint efficiency. The energy recovery rate of the proposed strategy is increased by 1.18% in comparison with the typical braking strategy.

**Keywords:** electric vehicle; dual-motor energy recovery; regenerative braking system; CVT speed ratio control; motor minimum loss; energy consumption and efficiency characteristics; braking force distribution

#### **1. Introduction**

Given the limitations of oil resources and the importance of environmental protection, governments around the world have enacted stringent regulations on fuel consumption and emissions. Electric vehicles, as environmentally friendly vehicles, have attracted a considerable amount of attention from researchers and corporations, and regenerative braking technology as one of the key technologies of energy conservation and emission reduction has been widely studied and applied [1–3]. The regenerative braking system can use the motor to convert the braking kinetic energy into electric energy and store it in the battery. This electric energy can be released during the driving process, which can not only improve the energy utilization rate and extend the driving range but also reduce the driver's range anxiety. Therefore, maximization of the braking energy recovery under safe braking conditions has been the focus and challenge of energy management of electric vehicles.

Zhang et al. proposed an improved regenerative braking control strategy for rear-drive electric vehicles. In the deceleration braking test, the improved regenerative braking efficiency could reach 47% [4]. Cheng et al. verified a new series control strategy, and the experimental results confirmed that the steady and dynamic contribution of the strategy to the improvement of energy efficiency reached 58.56% and 69.74%, respectively [5]. Itani et al. compared flywheels with supercapacitors as the second energy source of front axle driven electric vehicles, and the results demonstrated that ultra-capacitors performed better in weight, specific energy and specific power. It was more convenient to reuse the braking energy and provided a solution to reduce the damage of the large current to batteries during regenerative braking [6]. For the control of specific components, Yuan et al. proposed a new scheme of the line control dynamic system considering the functional requirements of regenerative braking in the structural development stage and adopted the current amplitude modulation control to improve the accuracy of hydraulic regulation and eliminate vibration noise. The maximum regeneration efficiency of the bench test was 46.32% of the total recoverable energy [7]. Chen proposed a feedback hierarchical controller that tracked the desired speed and distributed the braking torque to four wheels to improve the energy recovery [8]. In terms of overall optimization, Deng et al. analyzed the relationship between the battery, motor, CVT and comprehensive efficiency, and proposed a regenerative braking control strategy for the CVT hybrid electric vehicle. In comparison with the typical strategy, the average power generation efficiency of the motor increased by 2.91% [9]. Shu et al. developed a maximum energy recovery energy management strategy and used the sequential quadratic programming (SQP) algorithm to optimize the CVT ratio control strategy, which achieved a good control effect [10]. To expand the scope of braking energy recovery, Bera et al. used the motor and hydraulic system to jointly adjust the braking process of an anti-lock braking system (ABS) and obtained a good effect [11]. The above literatures have all conducted relevant studies on the improvement of energy recovery in the regenerative braking process, which has improved the regenerative braking performance of vehicles. However, there are a greater number of studies on a single model than on a joint model and more studies on regenerative braking of a single motor than on regenerative braking of vehicles with a dual-motor drive system.

As a key device of the regenerative braking system, the efficiency of the motor directly affects energy recovery. Hence, improving the efficiency of the motor is conducive to the increase of energy recovery. Many scholars have conducted relevant studies on improving motor efficiency. Tripathi et al. conducted a detailed study on the model-based loss minimization algorithm (MLMA), and the results confirmed that this method could not only effectively improve motor efficiency but also exhibit good dynamic performance [12]. Uddin et al. used a model-based loss minimization algorithm (LMA) to compare the efficiency of permanent magnet synchronous motors based on direct torque flux linkage control (DTFC) and vector control (VC). The simulation results showed that the former had higher efficiency [13]. Inoue et al. studied the control performance of the permanent magnet synchronous motor (PMSM) drive system based on current control and direct torque control. Their results showed that the latter, combined with the control law of the M-T framework, had the advantages of control stability [14]. Wang et al. introduced the integral balance of the sine value of the torque angle such that the speed and the electromagnetic torque could be controlled to converge at the same time by adjusting the speed only once and to obtain the optimal dynamic response of the speed [15]. Vido and Le Ballois [16] and Lee et al. [17] also conducted relevant studies and improved the efficiency of the motor to a certain extent. The above literatures have conducted research on the efficiency of the motor and obtained various results. However, in the process of regenerative braking, it is necessary to analyze the influencing factors of motor loss to maximize system efficiency.

To minimize the power loss in the process of electric braking, this study analyses the automobile with an independent motor drive system of the front and rear axles. First, the accurate motor model is established, and various losses are analyzed. Based on the principle of minimum loss, the motor control strategy is designed. The characteristics of power flow in the electric braking process are analyzed, and the combined efficiency model of the front and rear axles is established. The optimal transmission ratio of CVT under different working conditions is obtained through optimization, and the input and output characteristics of the front and rear axles are analyzed. Finally, by optimizing the brake force distribution coefficient of the front and rear motors and considering the ECE regulations and I curve as the limit, a new control strategy of dual motor regenerative braking is proposed to maximize the energy recovery.

#### **2. Hybrid Electric Vehicle System Structure and Parameters**

In comparison with pure electric vehicles and fuel cell vehicles, hybrid electric vehicles are widely used in production and by consumers without the disadvantages of short driving range, long charging time, high fuel cell price and difficult hydrogen re-filling [18]. The structural schematic diagram of the hybrid vehicle system studied here is shown in Figure 1, and it should be noted that the schematic diagram is not the layout of the real vehicle.

**Figure 1.** Schematic diagram of dual motor hybrid electric vehicle. ISG—Integrated Starter Generator.

This configuration can be driven by the engine alone or by the motor. During high power demand, the motor and the engine can work simultaneously to meet the needs of the vehicle. The front axle and rear axle of this configuration have motors, which can make the vehicle exhibit better dynamic performance in pure electric mode and can recover more energy when braking. The vehicle controller is responsible for collecting the speed, brake pedal, brake master cylinder pressure and other signals and corresponding responses. When the brake pedal signal is detected, the driving state of the car is quickly determined, and the control signal is sent to the lower controller through the controller area network (CAN) bus. The lower controller makes correlation identification according to the control signal and sends signals to the hydraulic control unit and motor control unit according to the established algorithm to complete the driver's instructions. The vehicle parameters and component parameters are shown in Table 1.



**Table 1.** *Cont.*

#### **3. Motor Loss Model and Control Strategy**

#### *3.1. Motor Loss Model*

Permanent magnet synchronous motors with the high-power density and high-efficiency advantages of small volume and light quality have been widely used in new energy vehicles [19]. To obtain a more accurate model, it must be considered that the iron loss in the model is important. Hence, the equivalent iron loss resistance is introduced parallel to the magnetizing branch in the circuit [20], as depicted in Figure 2. Certain idealized conditions are assumed; for example, saturation is ignored, and the electromotive force is sinusoidal [18]. Motor losses mainly include mechanical losses, copper losses, iron losses and stray losses. Since stray losses are difficult to measure and control and account for a small percentage of the total loss [21], they are not considered in this study.

**Figure 2.** d-q axes equivalent circuits for the PMSM model with iron losses.

In steady-state, the voltage balance equation of the d-q axis is as follows:

$$
\mu\_d = \mathcal{R}\_c \dot{t}\_d - a\psi\_q \tag{1}
$$

$$
\mu\_q = \mathcal{R}\_\mathcal{C} i\_q + a\nu \psi\_d \tag{2}
$$

Here, *Rc* is the stator winding resistance, *uq* and *ud* are the d-q axis components of the stator voltage, *id* and *iq* are the d-axis and q-axis current components, respectively, ω is the angular velocity of the stator, and ψ*<sup>d</sup>* and ψ*<sup>q</sup>* are the d-q axis components of the stator flux, respectively. The permanent magnet flux ψ*<sup>a</sup>* has the following relationship:

$$
\psi\_d = L\_d i\_{od} + \psi\_d \tag{3}
$$

$$
\psi\_q = L\_q i\_{\alpha q} \tag{4}
$$

The electromagnetic torque can be calculated using Equation (5).

$$T\_{\varepsilon} = \frac{3}{2} p \{ \psi\_d i\_{\alpha \eta} - \psi\_q i\_{\alpha d} \} = \frac{3}{2} p \left[ \psi\_a i\_{\alpha \eta} + \left( L\_d - L\_q \right) i\_{\alpha \eta} i\_{\alpha d} \right] \tag{5}$$

where *p* is the number of pole pairs, *iod* and *ioq* are the d-q axis magnetization current components, respectively, and *Ld* and *Lq* are the d-q axis inductance components, respectively. For surface-mounted permanent magnet synchronous motors, *Ld* = *Lq*.

Then, copper loss and iron loss can be calculated by the Equations (6) and (7), respectively.

$$P\_{cu} = \frac{3}{2} R\_c \left[ \left( \dot{\iota}\_{od} - \frac{\alpha L\_d \dot{\iota}\_{\alpha \eta}}{R\_f} \right)^2 + \left[ \dot{\iota}\_{\alpha \eta} + \frac{\alpha \left( \psi\_a + L\_d \dot{\iota}\_{\alpha l} \right)}{R\_f} \right]^2 \right] \tag{6}$$

$$P\_{Fe} = \frac{3}{2} R\_f \left( l\_{cd}^2 + l\_{cq}^2 \right) = \frac{3}{2} R\_f \left[ \left( -\frac{wL\_q i\_{aq}}{R\_f} \right)^2 + \left( \frac{\omega \left( \psi\_a + i\_{od} L\_d \right)}{R\_f} \right)^2 \right] \tag{7}$$

When the motor is working, the load and power factor are the key factors influencing the size of the copper loss. Therefore, when the current speed and torque are given, the current optimal *iod* (minimum loss) can be obtained:

$$i\_{od} = -\frac{\psi\_d L\_{il} \alpha^2 \left(\mathcal{R}\_c + \mathcal{R}\_f\right)}{\mathcal{R}\_c \mathcal{R}\_f^2 + \alpha^2 L\_d^2 \left(\mathcal{R}\_c + \mathcal{R}\_f\right)}\tag{8}$$

Mechanical loss has an approximately linear relationship with motor speed [22]. By setting the value of *K* as constant, the mechanical loss model of permanent magnet synchronous motor can be obtained:

$$P\_M = \mathbb{K}n\tag{9}$$

#### *3.2. Motor Control Strategy*

The motor control method has an important influence on motor performance. Hence, it is necessary to improve it to get higher motor efficiency. In comparison with most conventional proportional-integral-derivative (PID) control method, to obtain better performance and reduce energy losses here, the motor speed loop adopts the sliding mode control and the current loop uses the minimum loss control method (LMA). The total efficiency of the former motor for η*isg* is set as

$$\eta\_{\rm ieg}(i\_{\rm qq}) = \frac{\mathcal{T}\_{\rm td}\omega}{\mathcal{T}\_{\rm td}\omega + P\_{\rm cu} + P\_{\rm Fc} + P\_{\rm M}} = \frac{\frac{3}{2}p\psi\_{\rm a}i\_{\rm qq}\omega}{\frac{3}{2}p\psi\_{\rm a}i\_{\rm qq}\omega + P\_{\rm cu}(i\_{\rm qq}) + P\_{\rm Fc}(i\_{\rm qq}) + P\_{\rm M}}\tag{10}$$

It can be observed that the total efficiency is a quadratic function of the stator q-axis excitation current. By using the mathematical method, it is observed that there is always a value of *ioq*, which can minimize the total loss under different torque and electric angular speed. When the motor loss is set to be the lowest, it is as follows:

$$\gamma = \frac{\partial P\_{\rm is\%\\_loss}}{\partial i\_{\rm oq}} \frac{\partial T}{\partial i\_{\rm od}} - \frac{\partial P\_{\rm is\%\\_loss}}{\partial i\_{\rm od}} \frac{\partial T}{\partial i\_{\rm oq}} = 0 \tag{11}$$

The constraints are

$$\begin{cases} \begin{array}{c} w\_1 = T = \frac{\eta}{2} p \Big[ \psi\_{al} i\_{aq} + \left( L\_d - L\_q \right) i\_{aq} i\_{od} \Big] \\\ w\_2 = \gamma = \frac{\partial P\_{i q \text{-} lasa}}{\partial i\_{aq}} \frac{\partial T}{\partial i\_{al}} - \frac{\partial P\_{i s \text{-} lasa}}{\partial i\_{al}} \frac{\partial T}{\partial i\_{aq}} \end{array} \tag{12}$$

The voltage state equation of the d-q axis can be obtained by calculating the time derivative of each side of the loss constraint as follows:

$$
\begin{pmatrix}
\dot{w}\_1\\\dot{w}\_2
\end{pmatrix} = \begin{pmatrix}
X\_{11} & X\_{12} \\
X\_{21} & X\_{22}
\end{pmatrix} \begin{pmatrix}
\underline{U}\_d \\
\overline{U}\_q
\end{pmatrix} + \begin{pmatrix}
Y\_1 \\
Y\_2
\end{pmatrix} \tag{13}
$$

The elements *X*11, *X*12, *X*21, *X*22, *Y*<sup>1</sup> and *Y*<sup>2</sup> are, respectively:

$$X\_{11} = \frac{3PR\_c(L\_d - L\_q)i\_{oq}}{2L\_d(R\_s - R\_c)}\tag{14}$$

$$X\_{12} = \frac{3pR\_c \left[\psi\_a i\_{\alpha\eta} + \left(L\_d - L\_q\right)i\_{\alpha\eta}i\_{\alpha d}\right]}{2L\_d(R\_s + R\_c)}\tag{15}$$

$$X\_{21} = \frac{9P}{2L\_d R\_c} \left[ 2 \left( \frac{R\_f R\_c^2}{R\_f + R\_c} + L\_q^2 \alpha^2 \right) \left( L\_d - L\_q \right) i\_{ad} + \frac{R\_f R\_c^2}{R\_f + R\_c} \psi\_d + L\_d \left( 2L\_d - L\_q \right) \psi\_d \alpha^2 \right] \tag{16}$$

$$X\_{22} = \frac{9P\left(L\_d - L\_q\right)}{2L\_d R\_c} \left(\frac{R\_f R\_c^2}{R\_f + R\_c} + L\_q^2 \omega^2\right) i\_{aq} \tag{17}$$

$$Y\_{1} = \frac{3P}{2L\_{d}R\_{\mathbf{c}}} \begin{bmatrix} -\frac{R\_{f}R\_{\mathbf{c}}\left(L\_{d}^{2} - L\_{q}^{2}\right)}{L\_{d}l\_{\mathbf{c}q}\left(R\_{f}R\_{\mathbf{c}}\right)}i\_{0q}i\_{ad} - \frac{R\_{f}R\_{\mathbf{c}}}{R\_{f} + R\_{\mathbf{c}}}\psi\_{d}i\_{aq} \\ + \frac{\left(L\_{d}l\_{q}\right)\left(L\_{q}^{2}L\_{dq}^{2} - L\_{q}^{2}\right)\omega}{L\_{d}l\_{\mathbf{q}}} - \frac{\psi\_{d}\omega\left(\psi\_{q} + 2L\_{d}i\_{dq} - L\_{d}i\_{ad}\right)}{L\_{q}} \end{bmatrix} \tag{18}$$

$$\begin{split} Y\_{2} &= X\_{21} \Biggl[ -R\_{f} i\_{\alpha d} + \frac{I\_{q} \omega i\_{\alpha q} \left( R\_{f} + R\_{c} \right)}{R\_{c}} \Biggr] \\ &+ X\_{11} \Bigl[ -R\_{f} i\_{\alpha d} - \frac{I\_{d} \omega i\_{\alpha q} \left( R\_{f} + R\_{c} \right)}{R\_{c}} - \frac{\omega \psi\_{a} \left( R\_{f} + R\_{c} \right)}{R\_{c}} \Biggr] \end{split} \tag{19}$$

If all the above influential elements depend on the motor parameters and state, assuming that the X and Y elements meet the braking requirements, the output equation of the controller can be expressed as follows:

$$
\chi\left(\frac{lI\_d}{lI\_q}\right) = \frac{\begin{pmatrix} X\_{22} & -X\_{12} \\ -X\_{21} & X\_{11} \end{pmatrix} \begin{pmatrix} \bar{w}\_1 - Y\_1 \\ \bar{w}\_2 - Y\_2 \end{pmatrix}}{\begin{vmatrix} X\_{11} & X\_{12} \\ X\_{21} & X\_{22} \end{vmatrix}} \tag{20}
$$

To obtain the stable torque closed-loop output, the PI (Proportional-Integral) algorithm is used as follows:

$$
\begin{pmatrix}
\dot{w}\_1 \\
\dot{w}\_2
\end{pmatrix} = \begin{pmatrix}
K\_{Pl}\Delta T + K\_{It} \int \Delta T \mathrm{d}t \\
\end{pmatrix} \tag{21}
$$

where Δ*T* = *T*<sup>∗</sup> − *T* and Δγ = γ<sup>∗</sup> − γ can be brought into the above equation to get

$$\Delta I\_d = \frac{\left(K\_{Pl}\Delta T + K\_{Il}\int \Delta T \, \mathrm{d}t - Y\_1\right)X\_{22} + \left(K\_{Pl}\Delta \gamma + K\_{l\gamma}\int \Delta \gamma \, \mathrm{d}t - Y\_2\right)X\_{12}}{X\_{11}X\_{22} - X\_{12}X\_{21}}\tag{22}$$

$$\mathrm{dI}\_{q} = \frac{-\left(-\mathrm{K}\_{\mathrm{P}\gamma}\Delta\gamma + \mathrm{K}\_{\mathrm{I}\gamma}\int \Delta\gamma \mathrm{d}t - \mathrm{Y}\_{1}\right)\mathrm{X}\_{21} + \left(-\mathrm{K}\_{\mathrm{P}\mathrm{I}}\Delta T - \mathrm{K}\_{\mathrm{I}\mathrm{I}}\int \Delta T \mathrm{d}t - \mathrm{Y}\_{2}\right)\mathrm{X}\_{11}}{\mathrm{X}\_{11}\mathrm{X}\_{22} - \mathrm{X}\_{12}\mathrm{X}\_{21}}\tag{23}$$

The optimal PI parameters can be obtained after multiple debugging. The overall control model of the motor is shown in Figure 3.

**Figure 3.** Minimum loss control model of motor.

The analysis shows that when the motor runs without load, the copper loss accounts for a small proportion, and the iron loss increases linearly with the increase of the speed. When the motor is loaded, the copper loss of the motor increases in square shape relative to the load torque, while the iron loss increases slowly. The efficiency of the former PMSM can be simulated in Simulink, as depicted in Figure 4.

**Figure 4.** Efficiency map of the ISG.

#### **4. Optimization of the Electric Braking Power Flow E**ffi**ciency and the Braking Force Distribution**

#### *4.1. Optimization of the Electric Braking Power Flow E*ffi*ciency*

#### 4.1.1. Power Flow Analysis of Electric Braking

To improve the recovery of braking energy, it is necessary to analyze the loss of power flow in the process of electric braking. Here, the electric braking system is mainly composed of a front and rear motor, battery pack, CVT transmission, clutch and other vehicle parameters. The parameters of each component are shown in Table 1. Furthermore, as both front and rear motors can participate in the process, it means that more energy can be recovered, and the driving range can be effectively increased. The power flow of the vehicle's electric braking loss is shown in Figure 5.

**Figure 5.** Schematic diagram of power loss during regenerative braking.

The overall efficiency of the vehicle's electric brake energy recovery can be calculated using Equation (24):

$$\eta = \frac{\left(P\_f + P\_r\right) - P\_{ft} - P\_{rt} - P\_{\text{isg\\_loss}} - P\_{\text{pmsum\\_loss}} - P\_{\text{crt\\_loss}} - P\_{\text{buttery\\_loss}}}{P\_f + P\_r} \tag{24}$$

Among them, η is the total efficiency of the electric brake of the whole vehicle, *Pf* and *Pr* are the front and rear axle braking input powers, respectively; *Pf t* and *Prt* are the front and rear axle transmission power losses, respectively; *Pisq*\_*loss* and *Ppmsm*\_*loss* are the power loss of the front and rear motors, respectively; *Pcvt*\_*loss* is the CVT transmission loss; *Pbattery*\_*loss* is the battery charging power loss.

As the power loss of the driving system is primarily related to the speed, whereas the loss of the motor and the inverter is a function of the electric angular speed and torque and the CVT loss is related to the input torque and the speed ratio, the equation can be rewritten as Equation (25).

$$\eta = \frac{\left[\beta T \omega\_f + (1 - \beta) T \omega\_r\right] - Q\_{f\\_\text{loss}}\left(\beta\_r \omega\_{f\text{r}}, i\right) - Q\_{r\\_\text{loss}}\left(\beta\_r \omega\_{r\text{}}\right) - Q\_{t\\_\text{loss}}\left(\upsilon\right) - Q\_{b\\_\text{loss}}\left(\text{SOC}\right)}{\beta T \omega\_f + (1 - \beta) T \omega\_r} \tag{25}$$

where *T* is the braking torque of the vehicle; β is the distribution coefficient of forward and backward torque; ω*<sup>f</sup>* and ω*<sup>r</sup>* are the front and rear motor angular velocity, respectively; *i* is the CVT transmission speed ratio; *<sup>v</sup>* is the speed; *Qf* \_*loss* β, ω*<sup>f</sup>* , *i* is the CVT-ISG combined loss; *Qr*\_*loss*(β, ω*r*) is the loss of the rear motor; *Qt*(*v*) is the loss of the transmission system; and *Qb*(*SOC*) is the loss of the battery.

4.1.2. Establishment of the Joint Efficiency Model and Optimization of the CVT Speed Ratio

The combined front axle model is mainly composed of CVT and front motor and hence, its loss is calculated as Equation (26):

$$P\_{f\_{\text{\\_loss}}} = P\_{\text{crit\\_loss}}(T\_{\text{crit\\_in\\_in\\_out\\_in}}) + P\_{\text{isg\\_loss}}(\omega\_{\text{crit\\_out}}, T\_{\text{crit\\_out}}) \tag{26}$$

*Pf* \_*loss* is the total power loss of the front axle. *Tcvt*\_*out* is the input torque of the front motor. ω*cvt*\_*in* and ω*cvt*\_*out* are CVT input and output speed, respectively. The torque loss of the CVT mainly includes the slip loss of the steel belt, the loss caused by the deformation of the belt wheel and the slip loss of the metal sheet [23]. When the speed is fixed at 2000 rpm, its efficiency changes, as shown in Figure 6. It can be observed that the efficiency of CVT is mainly related to the speed ratio. When the speed ratio is approximately 1, the efficiency reaches a maximum, but when it is less than 1, there is a significant decline in the efficiency.

**Figure 6.** Transmission efficiency of the CVT.

Through the established CVT-ISG joint efficiency model, the CVT speed ratio with the highest joint efficiency can be determined. When the number ratio is 1.5, the joint efficiency changes are shown in Figure 7.

**Figure 7.** CVT–ISG motor combined efficiency at a speed ratio of 1.5.

It can be found that the efficiency of the combined model in the region with high speed and low torque is lower than that of the single motor model. Since the CVT has lower efficiency in the region with low torque, it results in lower overall efficiency. Further, under different torques and rotating speeds, the combined efficiency changes with the CVT speed ratio. By seeking the CVT speed ratio

that makes the combined efficiency reach maximum, the system efficiency can be maximized. The results are shown in Figure 8.

**Figure 8.** Optimal CVT ratio under different working conditions.

Therefore, by calculating the braking power of the motor through the pedal's opening degree, the optimal CVT speed ratio under this braking torque can be obtained under the combined efficiency model. However, it should be noted that when the vehicle starts, the motor speed should be set greater than 500 rpm, and the speed ratio should be adjusted to the maximum to protect the motor from irreversible damage. When the vehicle is in an emergency braking state (*z* > 0.7), the CVT speed ratio should be adjusted to the minimum to ensure the safety and stability of the vehicle.

The rear axle joint model is mainly composed of a motor, which is relatively simple and similar to the front axle motor model. Therefore, it is not to be introduced separately.

4.1.3. Input and Output Characteristics of the Front and Rear Axis Joint Models

According to the joint model established above, the input and output characteristics of the front and rear axles are analyzed to provide a basis for formulating the braking force distribution strategy.

The braking strength allocated by the front axle during simulation is set to 0.3, and the energy recovery and energy consumption rate of the front axle braking system at different initial velocities are depicted in Figure 9.

**Figure 9.** (**a**) Energy recovery rate and (**b**) energy loss rate of front axle braking system at different vehicle speeds.

It can be found that the higher the initial braking speed, the higher the energy recovery rate. This is because when the vehicle is at a higher speed, the motor is in an efficient working area, and the energy recovered is more than when it is at a lower speed. With the increase of the initial braking speed, the energy loss rate of the motor, CVT and battery decreases slowly, and the biggest loss is the motor loss. This indicates that the loss of the front axle is relatively small at higher speeds.

Under the same conditions, the characteristics of the rear axle joint model are depicted in Figure 10.

**Figure 10.** (**a**) Energy recovery rate and (**b**) energy loss rate of rear axle braking system at different vehicle speeds.

In comparison with the combined loss model of the front shaft, the recovery rate of the rear shaft is relatively higher, because there is no CVT to affect the efficiency of the motor, so the recovery rate is higher. Further, the loss rate of the rear shaft is lower than that of the front shaft, but the larger torque will cause the larger charging current of the battery, larger battery loss and lower charging efficiency.

#### *4.2. The Braking Force Distribution Strategy with the Maximum Joint E*ffi*ciency*

#### 4.2.1. Front and Rear Motors Braking Force Distribution

Since the front and rear motors are different, it implies that the optimal operating range of the motor is different during the braking process. It is necessary to adjust the braking force of the front and rear motors to achieve a higher recovery rate. The utilization efficiency of regenerative braking of front and rear shafts is defined as follows:

$$\eta\_{\text{sys}} = \frac{P\_{\text{inf}}\eta\_{\text{inf}} + P\_{\text{inv}}\eta\_{\text{inv}}}{P\_{\text{inf}} + P\_{\text{inv}}} \tag{27}$$

where *Pin f* and *Pinr* are the braking power of the front and rear shafts, respectively. η*in f* and η*inr* are the combined braking efficiency of front and rear axles, respectively. A biaxial regenerative braking model was established.

$$\text{Max } \eta\_{\text{sys}} = \frac{P\_{\text{inf}} \eta\_{\text{inf}} + P\_{\text{inv}} \eta\_{\text{inv}}}{P\_{\text{inf}} + P\_{\text{inv}}} = \frac{T\_{\text{inf}} \eta\_{\text{inf}} + T\_{\text{inv}} \eta\_{\text{inv}}}{T\_{\text{inf}} + T\_{\text{inv}}} \tag{28}$$

$$\begin{cases} \quad 0 \le P\_{\text{inf}} \le P\_{\text{inf}} \\_{\text{max}} \\\quad 0 \le P\_{\text{inv}} \le P\_{\text{inv}} \\_{\text{max}} \\\quad 0 \le T\_{\text{inf}} \le T\_{\text{inf}} \\_{\text{max}} \\\quad 0 \le T\_{\text{inv}} \le T\_{\text{inv}} \\_{\text{max}} \\\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \end{cases} \tag{29}$$

$$\text{s.t.} \begin{cases} 0 \le T\_{\text{inv}} \le T\_{\text{inv\\_max}} \\ \quad q = \frac{T\_{\text{inv}}}{T\_{\text{reg}}} \\ P\_{\text{inv}} = (1 - q) \times P\_{\text{reg}} \\ \quad n\_{\text{inf}} = f(T\_{\text{inf}}, n\_f) \\ \quad n\_{\text{inv}} = f(T\_{\text{inv}}, n\_r) \end{cases} \tag{29}$$

where *q* is the braking force distribution coefficient of the rear axle; *Pin f* \_*max* and *Pinr*\_*max* are, respectively, the maximum braking power that the front and rear axles can provide. *Preg* is the total regenerative braking power. The distribution coefficient of the optimal posterior axis is calculated as shown in Figure 11.

**Figure 11.** Optimal rear axle distribution coefficient.

It can be observed that the surrounding dark blue part is the separate working area of the front motor during regenerative braking, the middle bright yellow part is the separate working area of the rear motor during regenerative braking and the remaining part is the joint working area of the front and rear axle joint model.

#### 4.2.2. Vehicle Braking Force Distribution Strategy

Based on the above analysis, the mode switching point of regenerative braking of the front and rear axles can be obtained by fitting the boundary of the separate working area of the rear axles. Thus, the relationship between braking torque and speed is

$$T\_{\theta}(\upsilon) = 19.06 \cdot \cos\left(\upsilon \times 1.052 \times 10^{-3}\right) - 13.15 \sin\left(\upsilon \times 1.052 \times 10^{-3}\right) - 41.29 \tag{30}$$

As illustrated in Figure 12, when the regenerative braking torque of the vehicle is located in the envelope region of the curve and the coordinate axis, i.e., when *Tq*(*v*) <sup>&</sup>gt; <sup>|</sup>*Tb*|, the rear axis is used for braking alone. When the braking torque is outside the curve, that is, *Tq*(*v*) <sup>&</sup>lt; <sup>|</sup>*Tb*|, the braking force is allocated according to the *p*-value, and the peak power peak torque of the front and rear motors should be limited by the threshold value to prevent overload of the front and rear motors. Considering the braking stability and regulatory restrictions, the braking force distribution strategy is as follows:

**Figure 12.** Front and rear axle braking force distribution coefficient boundary curve.

(1) When *z* < 0.2, the braking force is distributed by the distribution coefficient of the rear shaft.


$$\begin{cases} F\_r = \frac{T\_k}{r} \\ F\_f = 0 \\ F\_{\mu f} = 0 \\ F\_{\mu r} = 0 \end{cases} \tag{31}$$

*Fr* is the rear axle braking force; *Ff* is the braking force of the front axle; *F*μ*<sup>f</sup>* is the hydraulic braking force of the rear shaft; *F*μ*<sup>r</sup>* is the hydraulic braking force of the front shaft; *r* is the vehicle radius; *v* is the speed of the vehicle. At this point, the braking force will be provided by the rear motor alone. The front motor and the hydraulic braking system of the front and rear shafts do not participate in the braking.


$$\begin{cases} \begin{array}{c} F\_{re\xi r} = q \times \frac{T\_k}{r} \\ F\_{re\xi f} = (1 - q) \times \frac{T\_k}{r} \\ F\_{\mu f} = 0 \\ F\_{\mu r} = 0 \end{array} \end{cases} \tag{32}$$

The braking force is distributed through the distribution coefficient q of the rear shaft. At this point, the front motor starts to participate in the regenerative braking, while the hydraulic braking system still does not participate in the braking.

When the braking strength is between 0.15 and 0.8, the Economic Commission of Europe (ECE) regulations stipulate that the curve of the rear axle using the adhesion coefficient should not be above the front axle. Hence, if the set distribution is reasonable, it should be considered here. According to the braking force distribution strategy in this study,

$$
\beta = 1 - q \tag{33}
$$

The relationship between the braking value and ECE braking regulations can be obtained [22], and the relation curve between the braking force distribution coefficient and the braking intensity z can be illustrated as shown in Figure 13. When the speed is 30 km/h and 100 km/h, it can be seen that the curve changes within the range permitted by regulations.

**Figure 13.** The relationship of the β and *z* when no-load.

The upper limit curve A is to ensure that the adhesion coefficient of the front axis meets the requirements. Curve B is to limit the locking order of the front and rear wheels of the car. When the β value appears above curve B, the front wheels can always be locked to the rear wheels in braking. However, when the β value is lower than the curve C, the adhesion coefficient of the rear axis will be insufficient and hence, the contact value should be kept above the curve C at all times.

(2) 0.2 < *z* ≤ 0.5

At this point, the braking force will be distributed according to the I curve. If the braking torque provided by the front and rear motors is insufficient to meet the braking task, the remaining braking power required will be supplemented by the hydraulic braking system.

$$\begin{cases} \begin{aligned} F\_{\varGamma} &= \frac{T\_b \cdot i}{r} \\ F\_f &= m \text{g} \text{z} - F\_r \\ F\_{\varPi} &= F\_r - F\_{\text{regr}} \\ F\_{\mu f} &= F\_f - F\_{\text{regr}f} \end{aligned} \tag{34}$$

where *i* represents the braking force distribution coefficient under the I curve.

(3) *z* > 0.5

When the braking strength is greater than 0.5, the braking stability is most important. Therefore, reducing the braking force of the motor at a constant speed gradually withdraws the motor from the braking work. Simultaneously, the missing braking force is supplemented by the hydraulic pressing force to ensure that when *z* = 0.7, the motor completely exits the braking, without affecting the hydraulic pressure to provide the full braking force in case of emergency braking. The specific allocation strategy is shown in Figure 14.

**Figure 14.** Braking force distribution diagram.

#### **5. Vehicle Performance Simulation and Analysis**

Based on the joint loss model, the simulation model of the whole system was established in Simulink/MATLAB, as shown in Figure 15. The simulation analysis was conducted under typical working conditions and cyclic working conditions, respectively, to verify the effectiveness of the strategy.

**Figure 15.** Vehicle simulation model.

#### *5.1. Simulation of Typical Braking Conditions*

The initial condition of the vehicle speed is 100 km/h and the SOC (State of charge) value of the power battery is 0.7. In addition, the influence of other resistances other than braking force, such as wind resistance, is not considered temporarily in the braking process. According to the analysis of power flow on the above analysis, the loss of each component in the braking process is made into an energy consumption diagram as shown in Figure 16.

**Figure 16.** Brake energy flow diagram.

#### 5.1.1. Braking Strength *z* = 0.2

When the braking strength is 0.2, the change in SOC and the overall efficiency during the entire process from the beginning of braking to the end are depicted in Figure 17a and the loss of key components is depicted in Figure 17b.

**Figure 17.** Simulation results when the *z* = 0.2. (**a**) Change in the SOC and joint efficiency; (**b**) Energy loss of the key components.

It can be found that at the initial time, the joint efficiency decreases slowly, the efficiency is higher, and the energy can be fully recovered. According to the data in the figure, at this time, the loss of braking energy mainly comes from the motor. Since the front motor has a short working time, the focus is on the rear motor, which is the same as the CVT loss. It can be seen that 298.745 kJ energy has been recovered from the driver stepping on the brake pedal to the vehicle parking, 395.71 kJ energy has been lost and the recovery rate has reached 43.02%.

#### 5.1.2. Braking Strength *z* = 0.4

When the braking strength is 0.4, the change in SOC and the overall efficiency during the entire process from the beginning of braking to the end are depicted in Figure 18a and the loss of key components is depicted in Figure 18b.

**Figure 18.** Simulation results when the *z* = 0.4 (**a**) Change in the SOC and joint efficiency (**b**) Energy loss of the key components.

When the braking starts, the regenerative braking efficiency of the dual motors has a short period of platform area, and the efficiency is relatively high. As the speed decreases, the electric braking efficiency decreases, while the mechanical braking proportion increases. According to the data in the figure, due to the addition of hydraulic braking, the energy loss of most regenerative braking is hydraulic braking loss accounting for 69.06%. Both the front and rear motors are in the peak operating state. The loss of the front motor is higher than that of the rear motor due to the CVT, and the loss of the front and rear motors is smaller than that of the rear motor when the braking strength is 0.2 because the motor has a shorter working state.

#### 5.1.3. Braking Strength *z* = 0.6

When the braking strength is 0.6, the change in SOC and the overall efficiency during the entire process from the beginning of braking to the end are depicted in Figure 19a and the loss of key components is depicted in Figure 19b.

**Figure 19.** Simulation results when the *z* = 0.6. (**a**) Change in the SOC and joint efficiency; (**b**) energy loss of the key components.

It can be observed that at this point, due to the gradual withdrawal of the motor braking, the increase in SOC is not large. According to the data in the figure, the hydraulic braking loss accounts for a larger proportion, accounting for 85.64%. Furthermore, due to the short braking time, the overall loss of the front and rear motors decreases in comparison with the braking strength, and the CVT loss also decreases.

From the simulation of typical working conditions, it can be observed that despite the braking strength of 0.2, 0.4 or 0.6, the SOC increases to different degrees during the braking process, and the lower the braking strength and the longer the braking time under the same speed, the more energy will be recovered.

#### *5.2. Cycle Simulation*

To verify the distribution strategy in this study, NYCC was selected for cycle simulation, and the ideal braking force distribution method of motor first braking was compared. The braking torque, power, total system efficiency and SOC of the front and rear motors are analyzed. NYCC has the characteristics of low speed, high acceleration and frequent braking, and its braking environment and braking strength can be obtained as shown in Figure 20 [24].

**Figure 20.** NYCC (**a**) operating speed and (**b**) braking strength.

The braking torque changes of the front and rear motors are depicted in Figure 21. To recover energy more efficiently, the rear motors often work in the state of peak torque, whereas the front motors often work in the state below the rated torque, so as to not be involved in braking as frequently as the rear motor.

**Figure 21.** The torque of (**a**) the front and (**b**) rear motors.

The braking power changes of the front and rear motors are shown in Figure 22. It can be seen that the maximum power of the front motor is approximately 6.7 kW and that of the rear motor is approximately 14.8 kW. The braking frequency of the rear motor is relatively large. In comparison with the ideal braking strategy, the front motor did not participate in the braking in the early stage and the rear motor braking power increased.

**Figure 22.** The power of (**a**) the front and (**b**) rear motors.

The efficiency and SOC changes are depicted in Figure 23. The overall efficiency of the rear motor can reach approximately 0.8 when it works alone. As the selection of the CVT speed ratio can adjust the efficiency of the front motor, the overall efficiency of the front and rear motors is higher when they work together to effectively recover energy. After the complete working condition, the SOC rises by approximately 0.003.

**Figure 23.** The changes in (**a**) joint efficiency and (**b**) SOC.

From the changes in efficiency and SOC, it can be observed that under the condition of low braking strength, the braking force distribution method discussed here has a high recovery efficiency and can recover maximum energy. Additionally, the motor loss minimization algorithm was adopted to maximize the use of the front and rear motors, system efficiency and SOC were improved, and the energy recovery of NYCC increased by 1.18% in comparison with the typical braking strategy.

#### **6. Conclusions**

(1) In this study, the front axle and rear axle independent motor drive system vehicle was considered as the research objective, the accurate motor model was established, various losses were analyzed and a new motor control method was proposed based on the principle of minimum loss.

(2) The characteristics of power flow in the process of electric braking were analyzed in detail, the combined efficiency model of the front axle (CVT–ISG) and rear axle (PMSM) was established, the braking force distribution of the front and rear motors was optimized based on the input and output characteristics of the front and rear axles. It was found that the optimal braking force distribution coefficient of the front and rear axles will change with the change of the working conditions. According to this change rule, a dual-motor regenerative braking force distribution strategy based on the optimal braking energy recovery was designed.

(3) In the MATLAB/Simulink simulation platform, the double motor regenerative braking system model was developed, and the simulation analyze was carried out under three typical braking conditions and NYCC conditions, respectively. It was observed that when the braking strength was 0.2, the braking energy recovery rate could reach 43.02%, and the energy recovery rate of the improved strategy was 1.18% higher than that of the typical braking strategy under NYCC conditions, which verify the effectiveness of the strategy proposed in this study.

**Author Contributions:** Conceived the research ideas and put forward the research methods, Y.Y.; Build the model and simulated it, Q.H. and Y.C.; Analyzed the simulation data, C.F. All authors have read and agreed to the published version of the manuscript.

**Funding:** The research was supported by (1) the National Key R&D Program of China (grant No. 2018YFB0106100) (2) the National Natural Science Foundation of China (grant No. 51575063). The authors would also like to acknowledge the support from the State Key Laboratory of Mechanical Transmission of Chongqing University, China.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

*Article*

### **Energy Control Strategy of Fuel Cell Hybrid Electric Vehicle Based on Working Conditions Identification by Least Square Support Vector Machine**

#### **Yongliang Zheng 1, Feng He 1,\*, Xinze Shen <sup>1</sup> and Xuesheng Jiang <sup>2</sup>**


Received: 23 November 2019; Accepted: 12 January 2020; Published: 15 January 2020

**Abstract:** Aimed at the limitation of traditional fuzzy control strategy in distributing power and improving the economy of a fuel cell hybrid electric vehicle (FCHEV), an energy management strategy combined with working conditions identification is proposed. Feature parameters extraction and sample divisions were carried out for typical working conditions, and working conditions were identified by the least square support vector machine (LSSVM) optimized by grid search and cross validation (CV). The corresponding fuzzy control strategies were formulated under different typical working conditions, in addition, the fuzzy control strategy was optimized with total equivalent energy consumption as the goal by particle swarm optimization (PSO). The adaptive switching of fuzzy control strategies under different working conditions were realized through the identification of driving conditions. Results showed that the fuzzy control strategy with the function of driving conditions identification had a more efficient power distribution and better economy.

**Keywords:** fuel cell hybrid electric vehicle; least squares support vector machines (LSSVM); driving conditions identification; power distribution

#### **1. Introduction**

The introduction of a power battery can make up for the shortcomings of fuel cell hybrid electric vehicles (FCHEV), such as the inability to recover braking energy, slow start speed and soft output characteristics. The dual power source (fuel cell and battery pack) can make the fuel cell hybrid electric vehicles (FCHEVs) produce a better power performance, but how to make the power source power distribution more reasonable and better improve the economy is a research difficulty. Based on previous experience, researchers developed rule-based energy management algorithms, such as thermostatic control strategy (TCS) [1] and a power following control strategy (PFCS) [2,3]. Fuzzy control strategy (FCS) [4–6] and fuzzy control strategy optimized by other algorithms [7] can adapt to the requirements of vehicle nonlinear control and effectively distribute the power between the power sources of fuel cell hybrid vehicles. However, due to the lack of road condition information, they are difficult to further improve the working efficiency and the economy of power sources in complex working conditions. Another control strategy based on optimization, such as dynamic programming (DP) [8–10], are widely used in hybrid electric vehicle energy management strategy because they can achieve global optimization. However, those methods will increase the computational burden and make it difficult to realize the online application. In order to simplify the calculation, some strategies, such as equivalent consumption minimization strategy (ECMS) [11–13], Pontryagin minimum principle strategy (PMPS) [14,15] and stochastic dynamic programming (SDP) [16], further improve the energy management performance on the basis of effectively reducing the calculation amount. For some

intelligent algorithms, such as particle swarm optimization (PSO) [17] and genetic algorithm (GA) [18], the fuel economy can also be improved by optimizing some relevant parameters based on the rule-based control strategy.

Working conditions have a profound impact on the economy and power source performance of FCHEVs. Ahmadi et al. [19] investigated the influence of driving patterns, and they found that various driving patterns under different conditions could affect the degradation of a fuel cell, and then affect the economy of the fuel cell vehicles. Raykin et al. [20] investigated the influence of driving patterns under different working conditions and an electric power supply on the well-to-wheel energy use and greenhouse gases of a plug-in hybrid electric vehicle (PHEV). When formulating the FCHEVs' energy control strategy, some references mentioned that they took single working condition into account, and there were certain limitations in improving the economy under different working conditions. Moreover, they did not consider the efficient working area of a fuel cell (FC) and battery pack to give full play to their respective advantages. Under the condition that working conditions can be identified, the energy management strategy of FCHEV should be adjusted according to the actual situation to achieve efficient and reliable power distribution among power sources, improve economy and extend the service life of power sources.

A lot of scholars have studied working condition identification. References [21–24] based on a fuzzy control recognizer, realized the identification of driving conditions. However, membership functions and rules of the fuzzy controller were selected and formulated based on personal experience, and the ideal effect could be achieved after multiple debugging. Clustering methods also play a role in the field of driving conditions recognition [25,26]. In [25], working conditions were divided into five typical working conditions by way of a clustering analysis method, then working conditions were identified by a Euclid approach degree. Yu et al. [26] identified high impact factors affecting pattern characteristics from static and quasi-static environment and traffic information, then proposed a trip/route division algorithm based on data clustering method. However, the selection of initial clustering center affected the clustering analysis results. Recently, machine learning has been further applied. Neural networks, such as back-propagation (BP) neural network [27] and learning vector quantization (LVQ) neural network [28,29], involve first, characteristic parameters that have an important influence on driving conditions being selected as the input, then, the identification period of the working condition samples are classified. After training the samples, the prediction of future working conditions can be realized. However, the accuracy of neural network depends on its structure. Chen [30] et al. proposed an improved hierarchical clustering algorithm to divide the driving cycle data into four groups, and then applied a support vector machine (SVM) to predict driving conditions based on the clustering results.

The least square support vector machines (LSSVM) based on support vector machines (SVM), compared with SVM, can complete a prediction in a shorter time and has a great generalization ability. Moreover, LSSVM is not subject to the set of algorithm structures and has good robustness in handling regression and classification problems.

In order to improve the performance of FCHEV, this paper proposes a driving condition recognizer. By extracting feature parameters and segmenting recognition segments from driving conditions information, LSSVM optimized by CV is used to realize working condition recognition. Energy management controllers based on a fuzzy control under different working conditions are established and optimized. Combined with the driving conditions identification, the energy management controller adopts corresponding fuzzy control strategy according to driving conditions to improve the performance of FCHEV.

#### **2. Vehicle Structure and Parameters**

The FCHEV was a front-drive vehicle with the structure shown in Figure 1. The fuel cell system was connected to the Controller Area Network (CAN) bus through a one-way DC/DC converter, while the battery pack was directly connected to the CAN bus. The motor drives the vehicle through

the final drive and differential. The complete vehicle parameters of a fuel cell hybrid electric vehicle are shown in Table 1.

**Figure 1.** Fuel cell hybrid electric vehicle transmission structure diagram.


**Table 1.** Vehicle parameters.

In this paper, the vehicle model of FCHEV was established in AVL Cruise, as shown in Figure 2, and the control strategy model was established in Matlab/Simulink, shown in Figure 3. In Figure 2, the overall simulation model includes driver module, fuel cell system, power battery pack, motor and controller, one-way DC/DC converter, final drive, and energy management module. The blue line and red line represent mechanical connection electrical connection, respectively.

**Figure 2.** Vehicle structure diagram in AVL Cruise.

**Figure 3.** Control module in Simulink.

#### *2.1. Fuel Cell Module*

The fuel cells in this paper were proton exchange membrane fuel cells (PEMFC), and they were built out of membrane electrode assemblies (MEA), which included the electrodes, electrolyte, anode catalyst layer, cathode catalyst layer (CCL), and gas diffusion layer (GDL). The detailed modeling process is found in references [31,32]. In the fuel cell component, in addition to the fuel cell, there was a simple compressor model, and its properties are shown in Table 2. The compressor delivered hydrogen continuously to the fuel cell stack, which generated electricity to drive the motor.

**Table 2.** Compressor properties.


The voltage of the fuel cell electrochemical model is calculated as follows:

$$
\mathcal{U}\_{\rm fc} = \mathcal{U}\_{\rm oc} - \eta\_0 - j\_0 \mathcal{R} \tag{1}
$$

$$
\eta\_0 = V\_{\text{act}} + V\_{\text{CCL}} + V\_{\text{GDL}} \tag{2}
$$

$$j\_0 R = \frac{I\_{\rm st}}{A\_{\rm area}} R \tag{3}$$

where *U*fc is the output voltage, *U*oc is the ideal open circuit voltage, η<sup>0</sup> is the cathode voltage loss, *V*act is the activation over potential, *V*CCL is the voltage loss caused by the oxygen transmission loss in the cathode catalyst layer (CCL), *V*GDL is the voltage loss caused by the oxygen transmission loss in the anode catalyst layer, *j*<sup>0</sup> and *I*st are the electric flow density and current of the stack, while *A*area is the effective area of the fuel cell, *R* is the ohmic internal resistance of the fuel cell. The activation loss can be defined as follows.

$$V\_{\text{act}} = \left| b\_{\text{Tf}} \cdot \text{arcsinh}(\frac{\left(\frac{j\_0}{j\_a}\right)^2}{2\frac{c\_{\text{cr}}}{c\_{\text{ci}}}(1 - \exp(\frac{-j\_0}{2j\_b}))}) \right| \tag{4}$$

where *b*Tf is the Tafel slope which describes the speed of the chemical reaction, and *c*cc is the oxygen concentration in the cathode channel, while *c*ci is the oxygen concentration at the channel inlet. Moreover, *j*<sup>a</sup> and *j*\* can be defined as

$$j\_a = \sqrt{2i\_\* S\_{\text{pc}} b\_{\text{Tf}}} \tag{5}$$

$$j\_\* = \ S\_{\rm pc} b\_{\rm Tf} / l\_{\rm CCL} \tag{6}$$

where *i*\* is the volumetric exchange current density, and *S*pc is the CCL proton conductivity, in addition, *l*CCL is the thickness of the CCL.

The voltage loss *V*CCL can be defined as

$$V\_{\rm CCL} = \frac{\frac{S\_{\rm Fe} h\_{\rm f\_f}^2}{4FD\_{\rm CCL}c\_{\rm cr}} \left(\frac{\dot{j}\_0}{\lambda} - \ln(1 + \frac{\dot{j}\_0^2}{\dot{j}\_\*^2 B^2})\right)}{1 - \frac{\dot{j}\_0}{\dot{j}\_l^\* \dot{s} c\_{\rm ci}}} \tag{7}$$

where *F* is the Faraday constant, *D*CCL is the oxygen diffusion coefficient in the CCL. *j*\* *l* and *B* can be defined as

$$j\_l^\* = \frac{4FD\_{\rm GDL}c\_{ci}}{l\_{\rm GDL}} \tag{8}$$

$$B = 2 \arctan(\frac{\hat{j}\_0}{2 \arctan(\frac{\hat{j}\_0}{2 \arctan(\frac{\hat{j}\_0}{2 \arctan(\frac{\hat{j}\_0}{2 \arctan(\frac{\hat{j}\_0}{2})})})})}) \tag{9}$$

where *D*GDL is the oxygen diffusion coefficient in the GDL, while *l*GDL is the thickness of GDL.

The voltage loss *V*GDL can be defined as

$$V\_{\rm GDL} = -b\_{\rm Tf} \ln(1 - \frac{j\_0}{j\_l^\* \frac{\mathcal{C}\_{\rm cr}}{\mathcal{C}\_{\rm ci}}}) \tag{10}$$

Assuming that the fuel cell stack consists of *n* fuel cell cells, the output power of the fuel cell stack is

$$P\_{\rm fc} = n \times (\mathcal{U}\_{\rm fc} \times I\_{\rm st}) \tag{11}$$

The efficiency of fuel cell stack can be expressed as follows:

$$
\eta\_{\text{fc}} = (\mathcal{U}\_{\text{oc}} - \mathcal{U}\_{\text{fc}}) / \mathcal{U}\_{\text{oc}} \tag{12}
$$

The single fuel cell properties are shown in Table 3.


**Table 3.** The properties of a single fuel cell.

#### *2.2. Power Battery Pack*

The lithium battery selected in this paper had a capacity of 24 Ah and a rated voltage of 3.3 V, and its specific parameters are shown in Table 4. Its equivalent circuit model adopted the Rint model, as shown in Figure 4a. The voltage of the battery output to the CAN bus is:

$$
\mathcal{U}\_{\rm out} = \mathcal{U}\_{\rm ocV} - I\_{\rm b} \mathcal{R}\_0 \tag{13}
$$

where *U*OCV is the open circuit voltage of lithium battery, *U*Out is the output voltage, *I*<sup>b</sup> and *R*<sup>0</sup> are the current and ohmic internal resistance of lithium battery respectively.


Upper/lower cut-off voltage 3.65 V/2 V Operating temperature −5–50 ◦C

#### **Table 4.** Battery parameters.

**Figure 4.** Battery model and parameters relationship: (**a**) Rint equivalent circuit model; (**b**) relationship of the relevant parameters of the lithium battery.

SOC, an important parameter of a lithium battery, is expressed by the following equation:

$$\text{SOC}(t) = \text{SOC}\_0 - \frac{\eta I \Delta t}{\mathcal{C}\_{\text{P}}} \tag{14}$$

where η is the coulomb efficiency, in this paper, η = 1, SOC0 was the initial value, sampling time Δ*t* = 1 s, and *C*<sup>P</sup> was the actual capacity of the battery. Through experiments, the parameters relationships of the battery are shown in Figure 4b.

#### **3. Typical Driving Conditions**

Working conditions of a vehicle have an important impact on economy and power distribution. Therefore, a more efficient energy management strategy can be developed by predicting the future working conditions.

In this paper, three typical driving conditions were selected, namely UDDS (Urban Dynamometer Driving Schedule), EUDC (Extra Urban Driving Cycle) and US06 (Highway Driving Schedule), as shown in Figure 5, which corresponded to an urban condition, suburban condition and highway condition, respectively. In an urban working condition, the vehicle speed is low and frequent parking occurs. The average vehicle speed is less than 35 km·h−1, moreover, the vehicle is in a state of low power output. The speed is fast in highway conditions, and the average speed is about 70 km·h−1, in addition, the output power of the car is relatively large. The suburban working condition is in the middle of the two, with an average speed of about 60 km·h<sup>−</sup>1.

**Figure 5.** Typical driving cycles: (**a**) city driving cycle—UDDS; (**b**) rural driving cycle—EUDC; (**c**) highway driving cycle—US06.

#### *3.1. Selection of Working Condition Characteristic Parameters*

The selection of characteristic parameters of working conditions is the key to accurately identifying future working conditions. In principle, more characteristic parameters is more helpful for prediction, but that requires high computational power. In contrast, too few characteristic parameters cannot cover the information of working conditions, which may lead to a large prediction deviation. Many scholars have studied the selection of characteristic parameters of driving conditions [25,30,33–35]. Based on some research and the importance of each parameter in driving conditions identification, six common characteristic parameters were selected, i.e., acceleration time/total time (*r*c), deceleration time/total time (*r*dc), time of uniform speed/total time (*r*u), average speed (*v*a), average acceleration (*a*c) and average deceleration (*a*dc). Six characteristic parameters of three working conditions are shown in Table 5.


**Table 5.** Characteristic parameters of typical working conditions.

#### *3.2. Dividing of Working Condition Samples*

The time length of the working conditions samples, namely, the identification cycle and update of identification cycle, will also have an impact on the working condition recognition. The specific segmentation of the working condition recognition samples is shown in Figure 6. *T* is the identification period, therefore, six characteristic parameters in this period of time can be calculated to identify the working conditions of this sample. While *s* is the update of the period, that is, the time difference between the beginning of the previous cycle segmentation and the beginning of the current cycle segmentation. If *T* is too long, although it contains more information, it will increase useless information and calculation burden, which will reduce the effect of recognition. If *T* is too short, it will not accurately reflect the real situation of working conditions. Similarly, a too small *s* leads to frequent cycle switching, which will cause a burden on the processor, while a too large *s* is not conducive to the timely switching of working conditions. References [35,36] studied in detail the effect of *T* and *s* on the accuracy of working conditions identification. Based on considering the accuracy and calculation cost, *T* = 100 s, *s* = 3 s.

**Figure 6.** Selection of working condition samples.

#### **4. Working Condition Identification Model Based on LSSVM**

#### *4.1. Least Squares Support Vector Machine*

LSSVM is able to classify samples by mapping them into high-latitude feature Spaces. LSSVM replaces the inequality constraints of problems in SVM with a set of linear equality constraints, thus simplifying the solution of Lagrange multipliers. A training set is considered with *n* data samples to be (*X*i, *y*i), where input data *X*<sup>i</sup> ∈ R*n*, output data *y*<sup>i</sup> ∈ R. A linear function in the high-level feature space will be used to fit the samples.

$$g(X\_{\mathbf{i}}) = \omega^{\mathrm{T}} \varphi(X\_{\mathbf{i}}) + b \tag{15}$$

where ϕ(*X*) is a nonlinear mapping function, ω is the weight vector in the feature space, and *b* is the bias term.

According to the principle of structural risk minimization and taking into account the complexity of function and fitting error, the optimization problem of LSSVM can be expressed as:

$$\begin{array}{rcl}\min\_{\boldsymbol{\omega}, \boldsymbol{b}, \boldsymbol{\xi}} J(\boldsymbol{\omega}, \boldsymbol{\xi}) &=& \frac{1}{2} \boldsymbol{\omega}^{\mathrm{T}} \boldsymbol{\omega} + \frac{1}{2} \mathrm{C} \sum\_{i=1}^{n} \boldsymbol{\xi}\_{i}^{2} \\ \text{s.t.} \quad y(\boldsymbol{X}) &=& \boldsymbol{\omega}^{\mathrm{T}} \boldsymbol{\varphi}(\boldsymbol{X}) + \boldsymbol{b} + \boldsymbol{\xi}\_{i} \ \boldsymbol{i} = \boldsymbol{1}, 2, \dots, n \end{array} \tag{16}$$

where ξ<sup>i</sup> is the error variable and *C* is the penalty factor.

Converting Equation (16) to unconstrained functions by building Lagrange functions and solving this Lagrange function, the classification prediction model of LSSVM can be obtained, as shown in Equation (8), and its structure is shown in Figure 7. Combined with Section 3, six characteristic parameters are taken as the input of the LSSVM, and the output is the working condition categories:

$$y = \text{sign}(\sum\_{i=1}^{n} \alpha\_i y\_i K(X, \text{Xi}) + b) \tag{17}$$

where the radial basis function (RBF) is selected as the kernel function, namely *K*(*X*, *Xi*) = *exe*(− *X* − *Xi* 2/(2σ2)), α is the Lagrange multiplier.

**Figure 7.** The LSSVM structure diagram.

#### *4.2. The Influence of Key Parameters on the Accuracy of LSSVM*

If σ→0, then *K*(*X*, *X*i)→0, which means that all the mapped points have the same distance from each other, that is, there is no clustering phenomenon. However, If σ→∞, then *K*(*X*, *X*i)→1, which means that all sample points will be divided into the same class and cannot be distinguished. As for the penalty factor *C*, if *C* is too large, ξi→0, the tolerance of samples between boundaries is very low, and there are less misclassifications, which means the fitting of samples is good, however, the prediction effect is not always good; on the other hand, if the value of C is too small, there are more samples between two boundaries, resulting in a greater possibility of misclassification, and the fitting of samples decreases.

The accuracy of LSSVM's model depends on the kernel parameter σ and the penalty factor *C*. A too large σ will reduce the model's accuracy, but a too small σ will lead to overfitting. The penalty factor *C* will affect the error and complexity of the model. Therefore, in this study, the cross-validation method was used to obtain the optimal parameters.

#### *4.3. The K-Fold Cross-Validation for Optimizing LSSVM*

Cross-validation has been widely used to estimate prediction errors. In this work, *K*-fold cross-validation combined with grid search was applied to optimize LSSVM, which could overcome the limitations of the holdout validation [37]. The steps to optimize LSSVM were as follows:


In order to present equidistant grid search results more clearly, grid coordinates (σ, *C*) are converted to logarithmic coordinates (log2σ, log2*C*).

#### **5. Fuzzy Energy Management Strategy Based on Working Condition Identification**

Fuzzy control based on the theory of fuzzy mathematics, fuzzes the actual input and output, and formulates rules through experience. These kinds of simulation of a human's approximate reasoning and comprehensive decision-making process has good robustness and adaptability. Fuzzy energy management strategies [4–6] developed by some researchers were aimed at a single working condition. In addition, fuzzy control rules based on personal experience are difficult to deal with complex multi-working conditions. Therefore, on the basis of condition identification, three fuzzy energy management strategies were formulated to deal with urban, suburban and expressway conditions, respectively. Besides, PSO is used to optimize the fuzzy control under various working conditions with total equivalent energy consumption as the objective function, and the adaptive switching effect is achieved through the identification of working conditions. It should be noted that the following fuzzy controller and optimization take the urban working condition as an example.

#### *5.1. Fuzzy Controller Design*

(1) Selection of input and output variables of fuzzy controller.

The SOC of the battery pack and the total power demand *P*r of FCHEV were selected as the input of the fuzzy controller, while the output is the output power *P*fc of the fuel cell. The power demand relationship is as follows:

$$P\_{\rm b} = P\_{\rm r} - P\_{\rm fc} \tag{18}$$

where *P*<sup>b</sup> is the output power of the battery, and *P*<sup>r</sup> includes the power of the drive motor and the power consumed by accessories.

(2) Fuzzy distribution of input and output variables.

The range of FCHEV's total power demand *P*r is [0, 60] (kw), and its fuzzy subsets are very small, small, medium, large and very large, i.e., {VS, S, M, L, VL}; the SOC range of power battery is [0, 1], and the fuzzy subsets are {VL, L, M, H, VH}, representing very low, low, medium, high and very high; the range of fuel cell's output power *P*fc is [0, 50] (kw), hence its fuzzy subsets {VL, L, M, H, VH} represent very low, low, medium, high and very high.

(3) Fuzzy control rules.

The fuzzy control rules of FCHEV are formulated according to the following principles:


#### *5.2. Fuzzy Controller Optimization Based on PSO*

As an optimization algorithm, PSO is a solution to reducing the influence of making fuzzy control strategy based on personal experience. In this paper, the membership functions of the input and output of the fuzzy controller were selected as the parameters to be optimized, and the objective function was total equivalent energy consumption (TEEC) of the power sources, i.e.,

$$\begin{cases} \min E(\mathbf{x}) = E\_{\text{fc}}(\mathbf{x}) + E\_{\text{b}}(\mathbf{x})\\ \text{s.t.} \ G\_{\text{i}}(\mathbf{x}) \ge 0, \mathbf{i} = 1, \dots, \mathbf{m} \end{cases} \tag{19}$$

where *E*fc(*x*) and *E*b(*x*) are the equivalent electric energy consumption of the fuel cell and electric energy consumption of battery, respectively, while *G*i(*x*) is the constraint condition of the vehicle, such as the time of acceleration and SOC fluctuation range of the battery pack.

The distributions of control rules under urban working condition before and after optimization are shown in Figure 8.

**Figure 8.** Control rules under a city driving condition. (**a**) before optimization; (**b**) after optimization.

#### *5.3. Fuzzy Energy Management Based on Condition Identification*

After identifying working conditions by LSSVM, the corresponding fuzzy control rules are selected by the fuzzy controller according to the working conditions. The flow chart of the energy management strategy based on working conditions identification is shown in Figure 9. Firstly, the characteristic parameters were extracted from the working condition information and sample segmentations were determined, and then working condition identifications were carried out by LSSVM. Fuzzy control strategies were optimized under three working conditions, and corresponding fuzzy control rule was selected under a specific working condition to realize the adaptive switching of the control strategy under complex working conditions.

**Figure 9.** Flow chart of energy management strategy.

#### **6. Results and Discussion**

#### *6.1. Results of Working Conditions Identification*

The samples of three typical working conditions were divided into 730 samples, of which 547 were training samples and the other 183 were validation samples.

Figure 10a describes the iterative optimization process of LSSVM's parameters under grid search and cross-validation. Among the 183 validation samples shown in Figure 10b, the recognition accuracy reached 98.36%. The key parameters of LSSVM optimized by CV were σ = 2.64, *C* = 25.61. Figure 10c shows the randomly generated driving conditions, where the LSSVM could identify the random driving conditions with an accuracy of 100%.

**Figure 10.** Results of working conditions recognition by LSSVM: (**a**) iterative process of training samples; (**b**) validation samples identification result; (**c**) identification result of mixed working conditions.

#### *6.2. Fuzzy Control Energy Management Strategy Based on Driving Conditions Identification*

In order to verify the effectiveness of the proposed energy management strategy, it was compared with the power follow control strategy in the efficiency of fuel cell stack, the SOC fluctuation of battery pack and the economy, at medium SOC level (SOC = 60%) and high SOC level (SOC = 85%).

#### 6.2.1. The Initial SOC of Battery Pack Was 60%

As shown in Figure 11a, the vehicle speed of the proposed fuzzy control strategy (FC1) can well follow the real vehicle speed. In Figure 11b, for total equivalent energy consumption, the power following control strategy (PFCS) was 3.99 (kW·h), which was 5.26% higher than that of the traditional fuzzy control strategy (FC2) (3.78/kW·h). In Figure 11c,d and Table 6, the average efficiency of the fuel cell stack of the FC2 was 67.62%, which was 2.05% higher than that of PFCS. The fluctuation range of SOC of FC2 was 58.56–61.55%, which was gentler than that of PFCS, for the ΔSOC of FC2 improved by 6.67% compared with PFCS.

In Figure 11b, for total equivalent energy consumption, FC1 was 3.65 (kW·h), which was 3.44% lower than that of FC2. In Figure 11c,d and Table 6, the average efficiency of the fuel cell stack for FC1 was 68.71%, which was 1.09% higher than of FC2. The fluctuation range of SOC of the FC1 was 58.15–61.00%. Compared with FC2, the ΔSOC of FC1 improved by 0.47%, which was conducive to the durability of the battery pack. Therefore, when the SOC initial value was 60%, the FC1 was better

than the FC2 and PFCS in improving the efficiency and durability of power sources and the economy of FCHEV.

**Figure 11.** Comparison of results when SOC = 60%: (**a**) comparison of vehicle velocity; (**b**) comparison of overall equivalent energy consumption; (**c**) comparison of fuel cell stack efficiency; (**d**) comparison of SOC.

**Table 6.** Comparison of results of mixed random driving conditions when SOC = 60%.


Note: Total equivalent energy consumption (TEEC); average efficiency of fuel cell stack (AEFCS); ΔSOC = SOCmax − SOCmin; power following control strategy (PFCS); proposed fuzzy control (FC1); traditional fuzzy control (FC2).

#### 6.2.2. The Initial SOC of the Battery Pack Is 85%

As shown in Figure 12a, the speed of FC1 can also follow the actual speed well, which is similar to the case of SOC = 60%. In Figure 12b, for total equivalent energy consumption, the PFCS was 4.45 (kW·h), but the figure for FC2 was 3.95 (kW·h), which was 11.24% lower than that of PFCS. In Figure 12c,d and Table 7, the average efficiency of the fuel cell stack of the FC2 was 68.22%, which was 2.66% higher than that of PFCS (65.56%). The fluctuation range of SOC of PFCS was 80.55–86.12%, while the range of SOC for FC2 was 74.80–85.00%, so the ΔSOC of PFCS improved by 4.63% compared with FC2.

**Figure 12.** Comparison of results when SOC = 85%: (**a**) comparison of vehicle velocity; (**b**) comparison of overall equivalent energy consumption; (**c**) comparison of fuel cell stack efficiency; (**d**) comparison of SOC.


**Table 7.** Comparison of results of mixed random driving conditions when SOC = 85%.

In Figure 12b, for total equivalent energy consumption, FC1 was 3.85 (kW·h), which was 2.53% lower than that of FC2. In Figure 12c,d and Table 7, the average efficiency of the fuel cell stack for FC1 was 68.62%, which was 0.40% higher than of FC2. The fluctuation range of SOC of the FC1 was 75.64–85.00%, which meant the ΔSOC of FC1 improved by 0.84% compared with FC2, so FC1 was more conducive to the durability of the battery pack. Therefore, when SOC = 85%, PFCS was better than FC1 and FC2 in controlling the fluctuation of SOC, on the other hand, FC1 showed that it had better performances on the average efficiency of the fuel cell stack and the economy than the other two control strategies.

To summarise, in order to verify the effectiveness of the proposed fuzzy control strategy, it was compared with the traditional fuzzy control and power following control strategy in the case of SOC = 60% and SOC = 85%. It can be seen form Tables 6 and 7, when SOC = 85%, the total equivalent energy consumption of PFCS, FC1 and FC2 were much more than these of SOC = 60%, particularly for PFCS, where the largest difference of the equivalent energy consumption occurred between SOC = 60% and SOC = 85%. At a high SOC level (SOC is above 80%), the battery pack has sufficient power, and the braking energy recovery rate of the FCHEV is low, so as to avoid overcharging of the battery pack. In terms of the operating efficiency of the fuel cell stack, when SOC = 85%, though the average

efficiency of the fuel cell stack of FC1 is slightly lower than that of SOC = 60%, the figure for FC1 is still the highest, which indicates the stability of the proposed fuzzy control to maintain the high efficiency of the fuel cell stack. As for the fluctuation of SOC, the expected SOC range of the battery pack of FCHEV was 40–80%, which can prevent the overcharging and over-discharging of the battery pack, thus extending the life of the power battery. It can be seen from Figure 12d that more hydrogen was consumed to reduce the fluctuation of SOC, so the SOC of PFCS was kept above 80%. Although the fluctuation of SOC became smaller, it did not fall rapidly to the expected range, which showed that the power distribution of PFCS was insufficient at a high SOC level. On the contrary, the SOC of FC1 and FC2 decreased from 85% to 75.64% and 74.80% respectively, moreover the fluctuation of SOC for FC1 was smaller, which was more conducive to extending the life of the power battery. It was noted that at a high SOC level, the performance gap between FC1 and FC2 had narrowed. However, at a high SOC level or medium SOC level, the proposed fuzzy control strategy showed the better performances on the working efficiency of fuel cell stack, controlling SOC fluctuation and the economy of FCHEV.

#### **7. Conclusions**

In order to deal with the influence of complex working conditions on economy and power distribution between power sources on FCHEV, an energy management strategy based on driving condition identification was developed.


**Author Contributions:** Conceptualization, F.H. and Y.Z.; Methodology, Y.Z.; Software, Y.Z.; Validation, X.S., Y.Z.; Formal Analysis, Y.Z.; Resources, X.S.; Data Curation, X.S. and X.J.; Writing—Original Draft Preparation, Y.Z.; Writing—Review & Editing, F.H.; Supervision, F.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was funded by the Guizhou Province Science and Technology Support Program, grant number (2018)2177.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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