Dual-Layer Energy Management Strategy for a Hybrid Energy Storage System to Enhance PHEV Performance

Abstract

Plug-in hybrid electric vehicles (PHEVs) typically employ batteries with relatively small capacities due to constraints on chassis space and vehicle cost. Consequently, under conditions such as acceleration and hill climbing, these vehicles often experience high-current battery discharges, which can significantly compromise the battery’s lifespan. To address this issue, this paper focuses on a plug-in hybrid passenger vehicle, introducing supercapacitors to form a hybrid energy storage system (HESS) in conjunction with the PHEV battery, and it proposes a dual-layer energy management strategy for PHEVs. First, a PHEV model is developed, and a rule-based energy management strategy is designed. By conducting simulation comparisons of the CLTC under three control rules with different thresholds, the strategy yielding the lowest fuel consumption is selected, and its battery discharge characteristics are analyzed. Subsequently, the required power parameters of the supercapacitor are calculated, and, taking chassis space constraints into account, the number and specifications of the supercapacitors are determined. Subsequently, a dual-layer energy distribution strategy for PHEVs equipped with supercapacitors is proposed. In the upper layer, an equivalent fuel consumption minimization method is applied to optimize the torque distribution between the engine and the motor, while the lower layer employs a rule-based strategy for power allocation between the battery and the supercapacitor. A proportional feedback factor is introduced for the real-time adjustment of the engine and motor torque distribution, and simulations under the CLTC are conducted to evaluate the PHEV’s torque distribution and fuel consumption. The results indicate that the dual-layer energy management strategy reduces the duration of high-current battery discharge in the supercapacitor-equipped PHEV by 73.61%, decreases the peak current by 30.76%, and lowers the overall vehicle fuel consumption by 5%. Unlike other studies, this paper analyzes and calculates the specifications, dimensions, and quantity of supercapacitors based on the available chassis space of the PHEV passenger car. The results demonstrate that the designed supercapacitor array effectively mitigates the high-current discharge of the PHEV battery, and the proposed dual-layer energy management strategy is capable of reducing the overall fuel consumption of the vehicle.

1. Introduction

With the intensification of global environmental pollution and the gradual depletion of non-renewable resources, effectively utilizing clean energy and improving the efficiency of non-renewable energy consumption have become urgent issues that need to be addressed. In the automotive industry, achieving energy conservation and emission reduction and developing innovative energy solutions are at the core of current research. Currently, with the continuous advancement of new energy vehicle technologies, hybrid electric vehicles are receiving increasing attention due to their significant advantages in energy conservation and emission reduction.

The energy management strategy is one of the key technologies for hybrid vehicles, with its core goal being the rational allocation of power between the motor and the engine to ensure that the engine operates in its high-efficiency range while using the pure electric mode in low-torque output conditions [1]. To achieve these goals, researchers have proposed various control strategies. Jia H et al. [2] proposed a cascade fuzzy control strategy. This strategy aims to slow down the load change rate of the fuel cell system and increase the driving range through particle swarm optimization. Lü X et al. [3] conducted research on the application of model predictive control in the energy management system of hybrid electric vehicles. They analyzed the advantages and limitations of various prediction techniques and solutions, and they verified their practical performance under different system optimization objectives through case studies. Qi C et al. [4] developed an energy management strategy based on reinforcement learning. They introduced an auxiliary agent to meet the energy requirements of hybrid electric vehicles, which significantly improved the applicability of the model. Hou S et al. [5] utilized the data support of the intelligent transportation system to optimize the fuel economy of plug-in hybrid electric vehicles and adopted the equivalent consumption minimization strategy for energy management. Zhu Z et al. [6] proposed a fuzzy adaptive equivalent fuel consumption minimization strategy to optimize energy distribution. By employing a fuzzy PI controller to adjust the equivalent factor in real time, the simulation results indicated that the strategy could reduce fuel consumption by 6.71% (for farming operations) and 5.04% (for transportation) while improving the battery SOC balance and enhancing fuel economy. Zhou J et al. [7] designed an energy management scheme for hybrid electric vehicles based on reinforcement learning. They established the power system model and the Markov probability transition model, effectively improving the fuel efficiency. Zhu Z et al. [8] designed a mechanical–electronic–hydraulic power transmission system that integrates hydro-mechanical composite transmission with a hybrid electric motor system. By analyzing three typical operations—cultivation, harvesting, and transportation—the results indicated that the system operated in a high-load region with fuel consumption lower than that of conventional PowerShift and CVT tractors. However, such optimization may lead to an excessively high power being allocated to the motor at certain moments, which, in turn, causes a high-current discharge of the battery and thus affects the battery’s service life.

Considering the issue of battery service life, some scholars have developed battery capacity degradation models based on the battery’s capacity degradation characteristics and the actual charging and discharging characteristics of vehicles. This makes the energy management strategy more comprehensive and the power distribution between the motor and the engine more reasonable. Shi D et al. [9] developed a fuzzy adaptive strategy based on Pontryagin’s minimum principle, using real-time traffic data (such as the average road speed and speed fluctuation) for dynamic optimization. Compared with the traditional state of charge (SOC) feedback correction strategy, it showed better fuel economy. Nguyễn BH et al. [10] proposed a torque distribution strategy for parallel hybrid trucks based on real-time optimization, using a linear quadratic regulator in closed-loop control to minimize the engine’s fuel consumption while ensuring the stability of the battery’s SOC. Xie S et al. [11] developed a model predictive control method for an energy management system to optimize the battery discharge depth in order to enhance the battery’s lifecycle value, effectively balancing the relationship between the energy consumption cost and the equivalent battery life loss cost. Sarvaiya S et al. [12] conducted a comparative study on the battery life optimization of parallel hybrid electric vehicles under different control strategies. They also considered the influence of various factors such as temperature and current on battery aging, providing a more scientific basis for an accurate prediction of battery life. However, in some cases, due to the consideration of the impact of battery life attenuation, the efficiency of the engine is sacrificed, which results in the energy management strategy failing to achieve the expected improvement in fuel economy as designed. Regarding the power distribution between the engine and the motor, although the energy balance between the two is achieved, the efficiency of the engine may be affected to some extent.

Therefore, researchers have drawn on the application experience of supercapacitors in pure electric vehicles and proposed to introduce supercapacitors into hybrid electric vehicles to reduce the high-current discharge of the battery. This strategy helps to extend the battery’s service life without affecting the engine’s efficiency. Yu YB et al. [13] and Tavakol-Sisakht et al. [14] used fuzzy control as the main control strategy for energy distribution. However, the former divided the engine’s operating range in a rule-based manner, focusing on the battery charging situation. They derived an equivalent fuel consumption model during charging and established a fuzzy logic-based control strategy, proposing an adjustable energy management system. The latter conducted experiments on different topological structures and made comparisons, aiming to improve the battery’s service life and the overall performance of the system. Fuzzy controllers rely on rule-setting specific to the application, which makes it difficult for them to adapt to new situations or those not previously learned. Different driving conditions and environments may require different fuzzy control strategies. Therefore, in the integrated control strategy, Zhang S et al. [15] adjusted the output power between the battery pack and the supercapacitor pack through the model predictive control strategy and optimized it using the dynamic programming algorithm. Meanwhile, they adopted a rule-based strategy to distribute the output power between the auxiliary power unit and the composite energy storage system. However, when the capacity of the supercapacitor is low, the optimization effect of dynamic programming will be limited. Azeem MK et al. [16] designed a complete mathematical model of a composite energy storage system including a charging unit for plug-in hybrid electric vehicles. They also proposed an adaptive terminal sliding mode control strategy based on an adaptive law. By using a genetic algorithm to adjust the controller parameters, the adaptability and accuracy of the control strategy were enhanced. However, this strategy is only applicable to the charging state. Truong HVA et al. [17] proposed an enhanced extremum-seeking algorithm that effectively optimizes the reference power allocation for each power source. The results showed that, with this approach, the power of the proton exchange membrane fuel cell could be optimally regulated, with efficiency improving by approximately 46.7% and hydrogen consumption reducing by about 31.2%. Moreover, the SOC of the energy storage device was effectively balanced at the end of the driving cycle.

Most of the above studies have focused on buses, which generally have ample chassis space and do not face issues with the installation of supercapacitors. This study focuses on a mass-produced hybrid passenger vehicle, which has limited chassis space, allowing for only a small number of compact supercapacitors. As a result, the total capacity of the supercapacitors is relatively low, making the aforementioned control strategies less adaptable to low-capacity supercapacitors. This limitation may lead to situations where the supercapacitors fail to effectively mitigate high-current battery discharges. Therefore, this paper proposes a hierarchical control-based dual-layer energy management strategy for PHEVs. In the upper layer, the equivalent fuel consumption minimization (ECMS) method is employed to optimize the torque distribution between the engine and the motor, aiming to minimize the overall fuel consumption of the PHEV. In the lower layer, a rule-based strategy is used to allocate power between the battery and the supercapacitor, effectively preventing high-current battery discharges and frequent charging events.

The overall structure of this paper is arranged as follows: Section 2 focuses on the PHEV modeling, Section 3 discusses the supercapacitor parameter calculation and the rule-based PHEV energy management strategy simulation, Section 4 covers the design and simulation of the PHEV dual-layer energy management strategy, and Section 5 presents the discussion and conclusion.

2. Modeling of Plug-in Hybrid Electric Vehicle

PHEV models are classified into various types based on the location of the clutch. The subject of this study is a parallel-type P2 hybrid passenger vehicle, as shown in Figure 1. In this type of PHEV, the clutch can disconnect at low speeds, allowing the motor to independently provide power. When high-power output is required, the clutch closes, and the engine and motor work together to provide the necessary power. Additionally, under certain conditions, the engine can also charge the battery. This model ensures that the engine and motor can operate either independently or together, offering the advantage of high energy utilization efficiency.

2.1. Electric Motor and Engine

Some of the technical data of the engine and electric motor of the PHEV studied in this paper are presented in

Table 1. Some parameters of the engine and electric motor.

Maximum engine speed	6000 rpm	Maximum motor speed	10,000 rpm
Maximum engine torque	250 N·m	Maximum motor torque	230 N·m
Maximum engine power	125 kW	Maximum motor power	80 kW

. The performance curves of the engine and electric motor are shown in Figure 2.

In the engine’s external characteristic curve, it can be observed that the engine reaches its peak torque within the speed range of 2300–4700 rpm, defining the constant torque region. Beyond this range, the torque gradually decreases as the speed increases; however, the engine’s power continues to rise. The engine reaches its maximum power at approximately 5000 rpm, after which the power gradually declines. According to the fuel consumption map, the engine exhibits better fuel economy within the speed range of 2000–4000 rpm. Although fuel consumption is lower at engine speeds below 2000 rpm, the torque output is also reduced, resulting in suboptimal power performance. Conversely, at speeds above 5000 rpm, power decreases while fuel consumption increases, making prolonged operation at high speeds undesirable. Therefore, PHEVs should avoid sustained high-speed engine operation to minimize energy consumption.

In the motor’s external characteristic and efficiency maps, it can be observed that the motor can deliver near-maximum torque in the low-speed range, which explains its ability to provide significant power during vehicle startup. However, as the speed increases beyond 4000 rpm, the maximum torque gradually decreases. Considering the three-dimensional efficiency map, the motor should operate within high-efficiency regions (such as the yellow-highlighted areas in the figure) to balance power demand and energy utilization efficiency.

2.2. A Hybrid Energy Storage System Consisting of Supercapacitors and Batteries

The structure of an HESS composed of supercapacitors and batteries has a significant impact on the internal power distribution during its operation. Reference [18] introduces several different topologies, among which the passive topology allows for simple power output but cannot control the energy of the two components. Conversely, the active topology enables power distribution between the supercapacitors and the battery. The active topology is further divided into supercapacitor semi-active and battery semi-active configurations. In the supercapacitor semi-active configuration, the supercapacitor and the DC/DC converter are connected in series and then parallel to the lithium battery. Due to the advantage of the lithium battery in maintaining a stable terminal voltage, which shows little variation in a single cycle, it can serve as the source of the DC bus voltage. Meanwhile, the terminal voltage of the supercapacitor can be regulated by the DC/DC converter and then integrated into the DC bus, enabling its flexible application. This paper adopts the supercapacitor semi-active topological structure, and the specific connection method is shown in Figure 3.

In this semi-active supercapacitor topology, the battery is directly connected to the motor, while the supercapacitor is linked to the motor side through a bidirectional DC/DC converter. When the motor requires high power, the supercapacitor is activated, discharging and boosting its voltage via the DC/DC converter to meet the motor’s operating voltage requirements. During charging or regenerative braking, the DC/DC converter steps down the voltage to store excess energy in the supercapacitor. This approach enables the system to flexibly utilize the supercapacitor during transient high-power demands or energy recovery, thereby reducing the instantaneous load on the battery and improving overall energy utilization efficiency.

The battery model selected in this study consists of an equivalent internal resistance in series with the battery cell. The relationship between the charging/discharging voltage of a single battery cell and its SOC during the charging and discharging process is shown in Figure 4, while the overall battery pack parameters are listed in

Table 2. Battery model parameters and connection configuration.

Battery pack capacity	35 Ah
Nominal voltage	3.2 V
Maximum voltage	3.7 V
Number of series-connected cells	110
Number of parallel-connected cells	1

.

The calculation formula for the battery output current is

$$P_{require}=U_{SOC}·I-I^2·R_{battery}$$

(1)

In the above equation, $P_{require}$ is the required power, with the unit of W; $U_{SOC}$ is the battery voltage, with the unit of V; I is the current, with the unit of A; and $R_{battery}$ is the internal resistance of the battery, with the unit of $\Omega$.

This paper adopts the model proposed in Reference [19] to determine the DC/DC efficiency based on the current and power. The efficiency data obtained under different operating conditions are shown in

Table 3. DC/DC efficiency.

	10 kW	20 kW	30 kW	40 kW	50 kW
10 A	92%	95%	97%	95%	94%
50 A	91%	93%	96%	93%	92%
100 A	88%	91%	95%	92%	91%
>=150 A	82%	89%	92%	91%	90%

.

3. Supercapacitor Parameter Calculation and Rule-Based PHEV Energy Management Strategy Simulation

3.1. Calculation of Supercapacitor Parameters

In this study, the PHEV passenger car uses a rule-based method to control the torque and power of both the engine and motor. To select an appropriate supercapacitor for the PHEV, the first step is to perform a CLTC (China Light-Duty Vehicle Test Cycle) simulation on the PHEV model without a supercapacitor. This simulation helps analyze the impact of different control rules on the fuel consumption of the PHEV. Based on the control rule that results in the lowest fuel consumption, the maximum power of the supercapacitor is calculated according to the battery’s high-current discharge periods. This value serves as the basis for determining the number and specifications of the supercapacitor cells. When determining the physical dimensions of the supercapacitor cells, it is also important to consider the available space on the vehicle’s chassis for supercapacitor installation.

The PHEV passenger car without a supercapacitor adopts a rule-based control method for energy management. The energy management strategy for its engine and electric motor is shown in Figure 5.

The rule-based energy management strategy first selects the primary power source based on the current SOC value. If the SOC is greater than a predefined threshold, the motor is chosen as the primary power source. Then, based on the relationship between the required torque and the motor’s maximum torque, the strategy determines whether the engine needs to intervene. If the required torque exceeds the motor’s torque limit, the engine assists by providing the remaining torque. If the motor can provide the entire required torque, the vehicle operates in the pure electric mode. If the required torque is less than 0, the vehicle enters the regenerative braking mode to recover energy. The braking energy recovery mode adopts a fixed-proportion recovery rule, as shown in Figure 6.

All subsequent experiments in this paper are based on the CLTC conditions, and the condition curve is shown in Figure 7. The specific characteristics are described in

Table 4. Overview of CLTC.

Characteristics	Values	Characteristics	Values
Runtime (s)	1800	Distance (km)	14.8
Maximum Speed (km/h)	114	Maximum Acceleration (m/s2)	1.47
Maximum Deceleration (m/s2)	−1.47	Average Speed (km/h)	28.96
Operating Average Speed (km/h)	37.18	Acceleration Segment Average Acceleration (m/s2)	0.45
Deceleration Segment Average Deceleration (m/s2)	−0.49	Relative Positive Acceleration (m/s2)	0.17
Acceleration Ratio (%)	28.61	Deceleration Ratio (%)	26.44
Constant Speed Ratio (%)	22.83	Idle Ratio (%)	22.11

below.

Based on the PHEV model without a supercapacitor, three rule-based control strategies are designed in Simulink, and fuel consumption simulations under the CLTC are carried out. The SOC thresholds of the three control rules are shown in

Table 5. SOC thresholds of the three control rules.

Rule	${\mathit{SOC}}_{\mathit{high}}$	${\mathit{SOC}}_{\mathit{low}}$
rule1	0.5	0.3
rule2	0.6	0.3
rule3	0.7	0.3

.

After setting the corresponding control rules in Simulink, simulations are conducted under the CLTC conditions, and the fuel consumption results per 100 km are shown in Figure 8. As shown in Figure 8, Rule 1 results in the lowest fuel consumption. Therefore, Rule 1 is chosen as the basis for the subsequent study. The battery operating current under Rule 1 is shown in Figure 8. By analyzing Figure 8, the specifications of the supercapacitor can be determined.

The battery capacity of the PHEV studied in this paper is 35 Ah. Based on the experimental results of Reference [20], which examined the effects of different discharge rates on capacity reduction and temperature rise, the discharge rate is controlled within the range of 1.5 C to 2 C, with a maximum discharge current of 56 A. At this point, the voltage is approximately 350 V, and the total power of the supercapacitor is calculated to be at least 7.5 kW.

3.2. Supercapacitor Selection and Installation

According to the total power requirement of the supercapacitor obtained from the above calculation, the supercapacitor cell parameters are calculated. The formula for calculating its discharge current is as follows:

$$\mathrm{E}={\displaystyle \frac{1}{2}}C{U}_{SC}^2$$

(2)

$$P_{SC}=U_{SC}·I_{SC}$$

(3)

In the above equation, C is the capacitance, with the unit of F; $\mathrm{E}$ is the stored energy, with the unit of J; $P_{SC}$ is the power of the capacitor, with the unit of W; $I_{SC}$ is the current of the capacitor; and $U_{SC}$ is the voltage across the capacitor.

Considering the chassis space constraints of the PHEV, the selected supercapacitor cell parameters are shown in

Table 6. Main parameters of the supercapacitor cell.

Stored energy	3.04 Wh
Cell voltage	2.7 V
Typical heat capacity	643 J/°C
Single-cell mass	545 g
Single-cell capacity	3000 F

. When using 2.7 V, 3000 F supercapacitor cells, 18 cells are typically connected in series to meet high-voltage requirements, forming a supercapacitor module with a voltage of approximately 48 V and a total capacitance of about 150 F. This series connection method utilizes the additive effect of individual cell voltages, with each cell bearing approximately 2.7 V. The total capacitance is calculated by dividing the capacitance of a single cell by the number of series-connected cells, resulting in approximately 166.67 F, which is practically around 150 F. The final selected supercapacitor module, which ensures sufficient power while meeting system constraints, is detailed in

Table 7. Main parameters of the supercapacitor bank.

Total length	416 mm
Total width	132 mm
Total height	187 mm
Voltage	48 V
Current	100 A
Capacitor bank capacity	150 F

.

In this study, there is a space on the chassis of the PHEV passenger car with length, width, and height dimensions of 60 cm, 50 cm, and 30 cm, respectively, which can be used to install the required supercapacitor bank.

3.3. Simulation of Rule-Based Energy Management Strategy for PHEV with Supercapacitor

Based on the previously selected supercapacitor, a simulation of the energy management strategy for the PHEV equipped with the HESS is conducted using the rule-based energy management strategy. In this simulation, the energy management strategy for the PHEV’s engine and motor is as shown in Figure 5, while the power distribution strategy between the supercapacitor and the battery is as illustrated in Figure 9.

To prevent the battery from undergoing high-current discharge under high-power demand, the supercapacitor is activated when the motor power exceeds the predefined rated threshold. Specifically, when the system’s required power is greater than zero, it first determines whether the power demand exceeds the predefined limit. If it does, the decision to activate the supercapacitor is made based on its SOC level (the supercapacitor can output power if its SOC exceeds a certain threshold), thereby reducing the load on the battery. Additionally, when the required power is less than zero, regenerative braking is activated. If the supercapacitor’s SOC is below 1, it can store the recovered energy, further improving energy recovery efficiency. This approach helps extend the battery lifespan and increases the driving range of the PHEV [21]. This control strategy dynamically adjusts the charging and discharging states of the battery and supercapacitor based on real-time power demand and the SOC levels of both components. This approach effectively prevents high-current battery discharge while optimizing energy recovery and utilization, thereby enhancing overall system performance and economic efficiency.

Based on the PHEV model shown in Figure 1, the supercapacitor bank (parameters are shown in Table 7) is connected in parallel with the battery (as shown in Figure 3) to establish a PHEV model equipped with a supercapacitor. Using the CLTC, a simulation of the rule-based energy management for the PHEV with the HESS is carried out. The following is the presentation and analysis of the simulation results.

As shown in Figure 10, the supercapacitor operates between 750 s and 1500 s, preventing the battery from experiencing significant high-current discharge. Statistics indicate that the high-current discharge time of the battery is reduced by 58.85%, and the peak current decreases from 107.01 A to 87.57 A. Due to the supercapacitor’s advantage in regenerative braking, the braking energy during the first 500 s is stored in the supercapacitor. After the supercapacitor is fully charged between 600 s and 1000 s, the battery begins to charge, reducing the number of charge cycles and avoiding the negative impact of frequent charging on the battery.

Clearly, equipping the selected supercapacitor on the PHEV passenger car studied in this paper alongside the original battery to form the HESS neither affects the torque distribution between the PHEV motor and the engine nor increases the number of battery charge cycles. It also prevents high-current battery discharges, which is beneficial for extending the battery’s lifespan.

4. PHEV Dual-Layer Energy Management Strategy Design and Simulation

To further reduce the fuel consumption of the PHEV, this paper proposes a dual-layer energy management strategy based on hierarchical control. The upper layer uses the ECMS to optimize the torque distribution between the engine and the motor, while the lower layer employs a rule-based approach to manage the power distribution between the battery and the supercapacitor. The rule-based power distribution strategy for the HESS and its effects were previously introduced. This section mainly focuses on the principle of the ECMS and its application in optimizing the torque distribution between the engine and the motor. Based on this, a hierarchical control-based energy management strategy for the PHEV is designed and simulated under CLTC conditions.

4.1. Principle of the Equivalent Fuel Consumption Minimization Method

The ECMS is a control strategy suitable for energy management in PHEVs. Its primary objective is to minimize the total energy consumption over the entire driving cycle by optimizing the power distribution between the motor and the engine. The ECMS achieves this by continuously adjusting the power split to ensure that the engine operates in its most efficient range while balancing the contribution of the motor and engine in a way that minimizes fuel consumption [22]. In the implementation of the ECMS, the first step is to define a factor called the “equivalent fuel consumption value”, which is used to convert electrical energy consumption into equivalent fuel consumption. Then, the power corresponding to the minimum equivalent fuel consumption is used to determine the power output of the engine and motor. The ECMS is an effective energy management approach that optimizes the energy use of the PHEV by dynamically distributing power between the engine and motor. This strategy achieves both economic and environmental benefits by minimizing fuel consumption while maximizing energy efficiency [23].

The objective function of the equivalent fuel consumption minimization method is

$$\mathrm{m}\left(t\right)=m_{\mathrm{fuel}}+m_{\mathrm{elc}}=m_{\mathrm{fuel}}+{\displaystyle \frac{P_{\mathrm{motor}}·\alpha }{3600}}$$

(4)

In the formula, $m\left(t\right)$ is the theoretical fuel consumption of the whole vehicle, with the unit of g/s; $m_{fuel}$ is the fuel consumption of the engine, with the unit of g/s; $P_{motor}$ is the current power of the electric motor, with the unit of kW; and $\alpha$ is the equivalent fuel consumption value for converting the motor power into fuel mass, which is specified as 82 g/kWh. Additionally, 3600 is used to convert the resulting unit from g/h to g/s.

The calculation formula for the motor power is

$$P_{\mathrm{motor}}=T_m·{\omega }_m$$

(5)

In the above equation, $P_{motor}$ is the motor power, with the unit of W; $T_m$ is the motor torque, with the unit of N·m; and ${\omega }_m$ is the angular velocity of the motor, with the unit of rad/s. The relationship between the angular velocity and rotational speed is given by

$${\omega }_m={\displaystyle \frac{2\pi N_m}{60}}$$

(6)

In the above equation, $N_m$ is the motor speed, with the unit of RPM.

Combining the above two equations, we obtain the relationship between the motor power, torque, and speed as follows:

$$P_{\mathrm{motor}}={\displaystyle \frac{2\pi T_m{N}_m}{60}}$$

(7)

At this point, the unit of $P_{motor}$ is W, and converting the unit to kW gives

$$P_{\mathrm{motor}}={\displaystyle \frac{2\pi T_m{N}_m}{60\times 1000}}$$

(8)

After performing the corresponding calculations, we finally obtain the relationship between the required motor power, speed, and torque as follows:

$$P_{\mathrm{motor}}={\displaystyle \frac{T_m{N}_m}{9549}}$$

(9)

Depending on rounding conventions, some sources round this to 9549, while others may round it to 9550 for simplicity. This small difference has a negligible impact on practical calculations. Based on the motor’s charge and discharge states and the corresponding efficiency, the final motor power calculation formula is

$$P_{\mathrm{motor}}\left(t\right)=(1-\beta )·{\displaystyle \frac{T_m\left(t\right)·N_m\left(t\right)}{9550}}·\eta +\beta ·{\displaystyle \frac{T_m\left(t\right)·N_m\left(t\right)}{9550·\eta }}$$

(10)

In the above equation, $\eta$ represents the charge and discharge efficiency, and $\beta$ represents the charge or discharge state: 0 represents the charging state, and 1 represents the discharging state.

The constraints of Equation (10) are as follows:

$$\left\{\begin{array}{c}\mathrm{SOC}min\le SO{C}_t\le SO{C}_{max}\hfill \\ SO{C}_{min}\le SO{C}_t\le SO{C}_{max}\hfill \\ P_{min}\le P_{bat}\left(t\right)\le P_{max}\hfill \\ T_{m,min}\le T_m\left(t\right)\le T_{m,max}\hfill \\ T_{e,min}\le T_e\left(t\right)\le T_{e,max}\hfill \\ T_{req}\left(t\right)=T_e\left(t\right)+T_m\left(t\right)\hfill \end{array}\right.$$

(11)

In the above equation, $T_{req}$ is the required torque; $T_e$ is the engine torque; the value of $SO{C}_{min}$ is 0.3; the value of $SO{C}_{max}$ is 1; the value of $T_{(m,min)}$ is −230 N·m; the value of $T_{(m,max)}$ is 230 N·m; the value of $T_{(e,min)}$ is 0; and the value of $T_{(e,max)}$ is 250 N·m.

4.2. Design of the Dual-Layer Energy Management Strategy for PHEV

A flowchart of the dual-layer energy management strategy for the PHEV based on hierarchical control designed in this paper is shown in Figure 11. The required torque for the vehicle is calculated based on the difference between the current speed and the target speed. The upper layer uses the ECMS to determine the individual torques for the engine and motor, thus controlling them to provide power to the vehicle. The lower layer employs a rule-based approach to allocate the output power between the battery and the supercapacitor.

The solution process for the ECMS is shown in Figure 12. First, the required torque during normal driving is input. Then, the strategy iterates through each torque value in the engine model’s torque range, calculating the corresponding fuel consumption at each moment based on the current engine speed. The required motor torque is then determined, and the motor power is determined using the current speed. Depending on the charging and discharging state, the real motor power is adjusted. The corresponding equivalent fuel consumption is calculated, allowing the total fuel consumption for each engine torque to be determined. After iterating through all engine torque values, the minimum total fuel consumption is selected as the fuel consumption output for that moment. The corresponding motor torque and engine torque are then used as the output for that time. This process is repeated to complete the optimal torque distribution for the entire test cycle.

4.3. Setting of the Feedback Factor in the Torque Distribution Between the Engine and the Motor

During the simulation of the CLTC, the SOC of the battery changes continuously. Therefore, referring to the adaptive equivalent consumption minimization strategy proposed in similar research [24,25,26], this paper sets a proportional feedback factor for the real-time adjustment of the torque distribution between the engine and the motor:

$$\mathrm{S}(\mathrm{t}+1)=1-{\left({\displaystyle \frac{SOC\left(t\right)-SO{C}_h}{SO{C}_h-SO{C}_l}}\right)}^3$$

(12)

In the above equation, S represents the value of the feedback factor at the current moment, which is only related to the battery SOC value in the previous moment; $SO{C}_h$ and $SO{C}_l$ are the set high and low SOC values, with values of 0.8 and 0.2, respectively.

Therefore, the calculation formula for the equivalent fuel consumption is obtained as follows:

$$\mathrm{m}\left(\mathrm{t}\right)=m_{fuel}+m_{elc}+=m_{fuel}+{\displaystyle \frac{P_{motor}·\alpha ·S\left(t\right)}{3600}}$$

(13)

When the SOC is greater than 0.5, the feedback factor decreases as the SOC increases. At this point, the motor’s energy share in the equivalent fuel consumption increases, and the motor becomes the primary power output unit. As the SOC continues to decrease, the feedback factor gradually increases. When the SOC reaches 0.5, the power contribution from the engine and the motor is equal. When the SOC is less than 0.5, the feedback factor exceeds 1, and the engine becomes the primary power output unit. At this stage, excess power can also be used to charge the battery. The actual fuel consumption is still calculated using Equation (4), while Equation (13) is only used for optimization during the solution process.

4.4. Simulation of the CLTC

Based on the previously established PHEV model equipped with a supercapacitor, a simulation calculation of the PHEV torque distribution and equivalent fuel consumption using the equivalent fuel consumption minimization method is carried out under the CLTC. An analysis of the simulation results is presented below.

An analysis of Figure 13 reveals that, under the same required torque, the fuel consumption of the dual-layer management strategy based on hierarchical control is 5% lower than that of the rule-based strategy. This indicates that the PHEV dual-layer management strategy not only ensures a reasonable distribution of torque between the engine and the motor but also helps reduce fuel consumption.

As shown in Figure 14, both the rule-based and hierarchical control-based torque outputs are primarily driven by the motor, but the engine’s operating time differs. In the rule-based control method, the engine only provides power when the required torque is large, which can result in some motor output points operating at lower efficiency, thereby increasing the equivalent fuel consumption. In contrast, the hierarchical control method ensures that the motor operates in a higher efficiency range, with the engine acting as auxiliary power. This not only ensures that the total fuel consumption is minimized but also optimizes the efficiency of both the engine and the motor.

By analyzing Figure 15, which reflects the battery current, it can be seen that, although the engine output torque is reduced, causing the motor power to be higher at certain points, the supercapacitor still plays a role in suppressing large-current discharge from the battery. The period of large-current discharge from the battery is shortened by 73.61%, and the peak current decreases from 107.01 A to 74.09 A. This indicates that the dual-layer energy management strategy for the PHEV, based on hierarchical control, is effective.

As shown in Figure 16, the hierarchical control-based strategy optimizes the torque distribution between the engine and the motor, resulting in reduced energy consumption by the battery. Figure 16 shows that, for the first 600 s, the supercapacitor is responsible for recovering the braking energy, while the battery does not engage in energy recovery. Only after the supercapacitor is fully charged does the battery begin to recover the braking energy. This reduces the number of times that the battery needs to be charged, which helps extend its lifespan.

As shown in Figure 17, the feedback factor continuously increases, indicating that, when the battery charge is sufficient, the motor torque is prioritized. As the battery charge decreases, the feedback factor increases, meaning that the motor’s weight becomes more significant. When the battery SOC reaches 0.5, the motor and engine have equal weight. If the SOC continues to decrease, the engine becomes the primary torque output unit. Clearly, the feedback factor change curve shown in Figure 17 corresponds to the SOC change curve of the battery shown in Figure 16, suggesting that the real-time adjustment of the torque distribution between the engine and motor, as controlled by the feedback factor, works effectively.

4.5. Comparison Experiment

To further validate the applicability of the proposed strategy for small-capacity capacitors, this study references the battery–supercapacitor control strategy in [15], which employs the Dynamic Programming (DP) algorithm to optimize power allocation between the battery and supercapacitor. Owing to the power losses caused by the internal resistances of the battery and supercapacitor, the strategy determines their instantaneous power outputs based on the principle of minimizing the total power loss. Identical driving cycle simulations are conducted, and comparative results between the proposed control strategy and the referenced method are illustrated in the figure below.

An analysis of Figure 18 reveals that the smaller capacity of the supercapacitor leads to rapid depletion during prolonged operation, thereby causing ineffective power output during discharge. This phenomenon forces the battery to sustain high-current discharge, which significantly degrades its service life. In contrast, the proposed control strategy ensures that the supercapacitor discharges promptly when required to shoulder the power demand, effectively mitigating high-current battery discharge and extending the battery’s lifespan.

5. Conclusions and Discussion

Through modeling, simulation, and analyses of hybrid electric vehicles under different configurations and control strategies, the main conclusion drawn is that equipping such vehicles with a supercapacitor and adopting an appropriate control strategy has a positive impact on their performance. This is particularly evident in aspects such as mitigating large-current discharge from the battery, enhancing battery lifespan, and reducing fuel consumption.

In terms of alleviating the large-current discharge of the battery: In hybrid vehicles equipped with an HESS, when the motor demands excessive power, the supercapacitor can assume part of the power load, effectively mitigating high-current discharges from the battery. Simulation results indicate that, under identical CLTC conditions, the proportion of the high-current discharge time reduces to approximately 73.61%, and the peak current decreases by 30.76%, significantly alleviating the stress on the battery, thereby contributing to its protection and extended lifespan.

In terms of extending the battery’s service life:By leveraging the advantages of the supercapacitor in braking energy recovery, an effective braking energy recovery control strategy can prevent the battery from frequent charging. This, in turn, provides further evidence of the positive impact of the supercapacitor on enhancing the battery’s lifespan.

In terms of reducing fuel consumption:By comparing the fuel consumption under different control strategies, it is found that the ECMS shows excellent results. Under the CLTC conditions, fuel consumption is reduced by approximately 5%. This strategy not only ensures a reasonable distribution of torque between the motor and the engine but also mitigates large-current discharge from the battery while simultaneously reducing fuel consumption.

Future research plans:Conducting real vehicle bench tests to evaluate and refine the proposed hierarchical control-based dual-layer energy management strategy for PHEVs is essential. This will further validate the feasibility and practicality of integrating supercapacitors into PHEVs. In addition, considering that current rule-based battery–supercapacitor power distribution strategies suffer from a lack of flexibility—which hinders the full exploitation of the supercapacitor’s high-power output capabilities—this study plans to further optimize the energy distribution between the battery and supercapacitor by employing an intelligent control strategy based on predicted speeds. In Reference [27], research on the application of an MPC strategy for battery–supercapacitor power distribution was conducted; the proposed method introduced a Koopman Linear Predictor to optimize the vehicle’s speed profile and trajectory, thereby achieving more refined energy management. This approach offers a promising new perspective for the rational allocation of power between the battery and supercapacitor.