Research on Plug-in Hybrid Electric Vehicle (PHEV) Energy Management Strategy with Dynamic Planning Considering Engine Start/Stop

: The key to improving the fuel economy of plug-in hybrid electric vehicles (PHEVs) lies in the energy management strategy (EMS). Existing EMS often neglects engine operating conditions, leading to frequent start–stop events, which affect fuel economy and engine lifespan. This paper proposes an Integrated Engine Start–Stop Dynamic Programming (IESS-DP) energy management strategy, aiming to optimize energy consumption. An enhanced rule-based strategy is designed for the engine’s operating conditions, significantly reducing fuel consumption during idling through engine start–stop control. Furthermore, the IESS-DP energy management strategy is designed. This strategy comprehensively considers engine start–stop control states and introduces weighting coefficients to balance fuel consumption and engine start–stop costs. Precise control of energy flow is achieved through a global optimization framework to improve fuel economy. Simulation results show that under the World Light Vehicle Test Cycle (WLTC), the IESS-DP EMS achieves a fuel consumption of 3.36 L/100 km. This represents a reduction of 6.15% compared to the traditional DP strategy and 5.35% compared to the deep reinforcement learning-based EMS combined with engine start–stop (DDRL/SS) strategy. Additionally, the number of engine start–stop events is reduced by 43% compared to the DP strategy and 16% compared to the DDRL/SS strategy.


Introduction
Due to the global dependence on fossil fuels leading to an energy crisis, the development of new energy vehicles has become a crucial pathway.Plug-in hybrid electric vehicles (PHEVs) combine internal combustion engines and electric motors, utilizing a dual-drive system.This not only provides an environmentally friendly, efficient, and flexible energy usage method but also serves as an ideal choice for achieving energy savings, emission reductions, and enhanced driving performance [1].The design goal of hybrid electric vehicles (HEVs) is to achieve optimal energy utilization efficiency and meet power demands, which constitutes the so-called energy management (EM) control problem.
Currently, the main energy management strategies (EMSs) are divided into rule-based (RB) and optimization-based (OB) strategies [2][3][4].Rule-based strategies are widely applied in practice due to their simple and intuitive design, low computational requirements, good real-time performance, robustness, and ease of implementation and adjustment.Rule-based EMS typically relies on a set of predefined rules to execute, generating control commands based on key variable thresholds [5].Rule-based strategies can be further divided into deterministic rule-based and fuzzy rule-based strategies.The development of fuzzy logic controllers [6,7] is considered to have high application potential, but their impact is currently mainly academic.The most common deterministic rule-based control strategies, including thermostat control strategy (TCS) and power-following control strategy (PFCS) [8,9], often fail to effectively address fuel economy issues.Start-stop systems (SSSs) are now widely applied and efficient, enabling engine shutdown and startup with minimal fuel consumption.A new heuristic strategy for series HEV electromagnetic control based on an SSS, proposed by Chen, B. et al. [10], aims to bridge the gap between conventional rule-based EM strategies and SSS-optimized EM strategies.However, its improved fuel efficiency still does not reach the level of optimization-based strategies.
Optimization-based strategies not only comprehensively consider various constraints and objectives but also provide globally optimal or near-optimal solutions for the system, offering significant advantages in terms of efficiency and adaptability [11].Optimizationbased strategies can be divided into two main categories: real-time optimization strategies and global optimization strategies.Real-time optimization strategies emphasize rapid response to changes in system state or external inputs, typically updating and adjusting in real-time during system operation.Representative methods include Equivalent Consumption Minimization Strategy (ECMS) [12,13] and Model Predictive Control (MPC) [14][15][16].Li, Y. et al. [17] effectively improved fuel efficiency and energy management of commuting hybrid electric vehicles by adjusting mode switching thresholds and optimizing equivalent coefficients of ECMS.However, ECMS highly relies on precise models and parameters, is particularly sensitive to initial SOC, and lacks long-term global optimization, making its adjustment and optimization process complex.Guo, N. et al. [18] proposed using a radial basis function neural network to predict future driving speeds and generate reference values for the State of Charge (SOC) online, effectively coordinating fuel economy and battery life of PHEVs.However, MPC has high computational resource demands and relies heavily on accurate system models, making its implementation and maintenance relatively complex and costly.
The goal of global optimization strategies is to find the optimal solution for the entire system over long-term operation.Representative methods include Dynamic Programming (DP) [19][20][21], Genetic Algorithm (GA) [22], Quadratic Programming (QP) [23], and Pontryagin's Minimum Principle (PMP) [24,25].Wang, C. et al. [26] significantly improved the energy economy and system performance of electric vehicle hybrid energy storage systems by optimizing the membership functions of fuzzy control to minimize energy loss.GA is suitable for solving complex nonlinear optimization problems, with wide applicability and strong global search capability.However, its slow convergence speed, high computational cost, sensitivity to parameter adjustments, and the randomness and instability of results are major limitations.Zhang, F. et al. [27] proposed an approximate version of PMP, called A-PMP, which improves overall energy efficiency by refining shift commands and torque distribution.A-PMP particularly considers driving performance and fuel economy, optimizing engine fuel rate and State of Charge (SOC) derivatives through piecewise linear approximation, improving computational efficiency and reducing energy consumption compared to traditional PMP.PMP directly utilizes the dynamics and power system characteristics of the vehicle, providing a more accurate reflection of energy demands and distribution under actual vehicle operating conditions.However, its practical application is limited by high computational complexity, dependence on model accuracy, and constraints on real-time response capabilities.
Dynamic Programming (DP) in hybrid vehicle energy management provides globally optimal solutions and high model accuracy, making it particularly suitable for applications requiring comprehensive and detailed optimization.Patil, R.M. et al. [28] proposed a new DP method using a backward simulation model of series hybrid vehicles.This method evaluates state constraints before selecting the optimal path, focusing on transitions between finely discretized nodes in the state space rather than using penalty functions to avoid interpolation.Vinot, E. et al. [29] applied DP to optimize the system parameters of power-split hybrid electric vehicles (PS-HEVs) to precisely manage energy use, achieving an optimal balance between fuel consumption and battery size across various driving cycles.Most existing DP-related research focuses on reducing model complexity and improving computational efficiency, often neglecting the impact of the engine start-stop system on fuel consumption.
In summary, based on analyzing the impact of the engine start-stop system on PHEVs, this paper proposes establishing a PHEV model with a P2 architecture.An integrated dynamic programming method with engine start-stop control is used to optimize the fuel consumption and engine start-stop frequency of PHEVs.
The rest of this paper is structured as follows: Section 2 establishes the PHEV model with a P2 architecture.Section 3 introduces the rule-based PHEV strategy to verify the impact of the engine start-stop system on PHEV fuel consumption.Section 4 details the integration of the engine start-stop system into dynamic programming to optimize the PHEV energy management strategy.Section 5 presents a simulation study comparing the IESS-DP strategy with the RB strategy, DDRL/SS strategy, and DP strategy.Section 6 concludes the paper.

Vehicle Model
This study selects a Plug-in Hybrid Electric Vehicle (PHEV) with a P2 configuration for research.As shown in Figure 1, the powertrain includes critical components such as the engine, P2 drive motor, and power battery pack.The configuration employs two clutches, and an automated manual transmission (AMT) to efficiently manage power transmission.The vehicle parameters are listed in Table 1.
World Electr.Veh.J. 2024, 15, x FOR PEER REVIEW 3 of 18 use, achieving an optimal balance between fuel consumption and battery size across various driving cycles.Most existing DP-related research focuses on reducing model complexity and improving computational efficiency, often neglecting the impact of the engine start-stop system on fuel consumption.In summary, based on analyzing the impact of the engine start-stop system on PHEVs, this paper proposes establishing a PHEV model with a P2 architecture.An integrated dynamic programming method with engine start-stop control is used to optimize the fuel consumption and engine start-stop frequency of PHEVs.
The rest of this paper is structured as follows: Section 2 establishes the PHEV model with a P2 architecture.Section 3 introduces the rule-based PHEV strategy to verify the impact of the engine start-stop system on PHEV fuel consumption.Section 4 details the integration of the engine start-stop system into dynamic programming to optimize the PHEV energy management strategy.Section 5 presents a simulation study comparing the IESS-DP strategy with the RB strategy, DDRL/SS strategy, and DP strategy.Section 6 concludes the paper.

Vehicle Model
This study selects a Plug-in Hybrid Electric Vehicle (PHEV) with a P2 configuration for research.As shown in Figure 1, the powertrain includes critical components such as the engine, P2 drive motor, and power battery pack.The configuration employs two clutches, and an automated manual transmission (AMT) to efficiently manage power transmission.The vehicle parameters are listed in Table 1.In the P2 configuration, the engine and the electric motor are connected in series with the transmission.They can be decoupled using clutches, with the engine connected to clutch 1, and the electric motor positioned between clutch 1 and clutch 2. This arrangement allows the engine and the electric motor to engage or disengage from the transmission independently.In the P2 configuration, the engine and the electric motor are connected in series with the transmission.They can be decoupled using clutches, with the engine connected to clutch 1, and the electric motor positioned between clutch 1 and clutch 2. This arrangement allows the engine and the electric motor to engage or disengage from the transmission independently.

Engine Model
This paper focuses on calculating gasoline engine fuel consumption while neglecting the complex internal engine dynamics.Using experimental data from the hybrid power system's engine, this study employs an experimental modeling approach.Figure 2

Engine Model
This paper focuses on calculating gasoline engine fuel consumption while neglecting the complex internal engine dynamics.Using experimental data from the hybrid power system's engine, this study employs an experimental modeling approach.Figure 2 illustrates the engine's fuel consumption characteristics.The technical characteristics of the engine are listed in Table 2.As shown in Figure 2, the red line indicates the maximum engine torque ( ), while the colored contour lines represent various levels of Brake Specific Fuel Consumption (BSFC) from low to high.This figure effectively demonstrates the engine's fuel efficiency under various operating conditions, which is critical for optimizing the energy management strategy of hybrid vehicles.As shown in Figure 2, the red line indicates the maximum engine torque (T e−max ), while the colored contour lines represent various levels of Brake Specific Fuel Consumption (BSFC) from low to high.This figure effectively demonstrates the engine's fuel efficiency under various operating conditions, which is critical for optimizing the energy management strategy of hybrid vehicles.
The engine's output power, fuel consumption rate, and fuel consumption per unit time are defined in Equations ( 1)- (3).
•n e 9550 ( 1) where P e denotes the engine output power (kW), T e represents the engine torque (N•m), n e indicates the engine speed (r/min), b e signifies the engine fuel consumption rate (g/kW•h), ρ refers to the fuel density (kg/L), and g corresponds to the acceleration due to gravity (m/s²).The product of ρ and g, denoted as ρg, is assumed to range from 6.96 to 7.15 (N/L).

Motor Model
This paper develops a motor model based on data from a permanent magnet synchronous motor (PMSM) test bench.A three-dimensional lookup table model was developed based on motor characteristics data collected in the laboratory.The inputs to the model include the PMSM's speed and torque, while the output is the motor's efficiency.The efficiency characteristics of the PMSM are depicted in Figure 3.The engine's output power, fuel consumption rate, and fuel consumption per unit time are defined in Equations ( 1)- (3).

Cylinder
where  denotes the engine output power (kW),  represents the engine torque (N•m),  indicates the engine speed (r/min),  signifies the engine fuel consumption rate (g/kW•h),  refers to the fuel density (kg/L), and  corresponds to the acceleration due to gravity (m/s²).The product of  and , denoted as , is assumed to range from 6.96 to 7.15 (N/L).

Motor Model
This paper develops a motor model based on data from a permanent magnet synchronous motor (PMSM) test bench.A three-dimensional lookup table model was developed based on motor characteristics data collected in the laboratory.The inputs to the model include the PMSM's speed and torque, while the output is the motor's efficiency.The efficiency characteristics of the PMSM are depicted in Figure 3.Following control system commands, the motor control system drives the motor to generate the required torque.The motor's operating characteristics define the maximum torque supply as follows: Following control system commands, the motor control system drives the motor to generate the required torque.The motor's operating characteristics define the maximum torque supply as follows: , n e < n ≤ n max (4) where n is the instantaneous speed, T peak is the maximum torque of the motor, P peak is the maximum power of the motor, n e is the rated speed, and n max is the maximum speed.
Furthermore, T m (motor torque) is defined as: where T order is the requested torque.

Battery Model
The PHEV under study uses lithium iron phosphate batteries, known for their high safety, long lifespan, and excellent high-temperature performance.Neglecting temperature fluctuations and battery aging effects, a simple yet effective internal resistance model of the battery is proposed [30] and used to construct the fundamental dynamic model, as follows: where V OC is the open circuit voltage of the battery, R int is the internal resistance of the battery, P batt is the load power of the battery, and Q ESS is the nominal capacity of the battery.
Based on the symbol definitions above, the State of Charge (SOC) update formula under discrete time conditions is as follows:

The Rule-based Strategy
The plug-in hybrid vehicle examined in this study is capable of operating in five distinct modes: pure electric drive, engine direct-drive, hybrid drive, charge sustaining, and regenerative braking.This paper categorizes the operating modes into two primary categories: EV mode and engine start-stop strategy modes, based on whether the engine participates.

EV Mode
The PHEV operates in EV mode when the SOC is greater than 30% and the torque provided by the traction motor is sufficient to meet the vehicle's demand.As illustrated in Figure 4, the energy is solely supplied by the power battery, and the traction motor fulfills the driving demand.where  represents the overall vehicle demand torque,  is the engine output torque,  indicates the engine operating status, and  is the motor output torque.where T req represents the overall vehicle demand torque, T Eng is the engine output torque, S Eng indicates the engine operating status, and T EV is the motor output torque.

Engine Start/Stop Strategy
In the event that the SOC is below 30% or T req is greater than T EV , the PHEV will operate in this mode if the motor output torque does not meet the overall vehicle demand torque.The engine start-stop mode integrates the remaining four operating modes and facilitates the transition between pure electric drive, pure engine drive, hybrid drive, charge sustaining, and regenerative braking through the engine start-stop module.The corresponding control strategy is illustrated in Figure 5. where  represents the overall vehicle demand torque,  is the engine output torque,  indicates the engine operating status, and  is the motor output torque.

Engine Start/Stop Strategy
In the event that the SOC is below 30% or  is greater than  , the PHEV will operate in this mode if the motor output torque does not meet the overall vehicle demand torque.The engine start-stop mode integrates the remaining four operating modes and facilitates the transition between pure electric drive, pure engine drive, hybrid drive, charge sustaining, and regenerative braking through the engine start-stop module.The corresponding control strategy is illustrated in Figure 5.When the SOC is greater than the minimum threshold, if the vehicle's demand torque is greater than the motor torque threshold and the vehicle demand torque T req is greater than the optimal engine output torque T opt , it is also necessary to ensure that the vehicle demand torque T req is less than the optimal engine output torque T opt and the sum of the peak positive torque of the electric motor T EvMax .The diagram of T opt is shown in Figure 6.
As shown in Figure 6, the optimal torque diagram is derived from a series of engine performance tests under various load conditions.These tests measure the Brake Specific Fuel Consumption (BSFC) across a range of engine speeds and torques.The optimal torque curve T opt is then plotted to identify the torque values at which the engine operates most efficiently (i.e., lowest BSFC).This curve represents the engine operating points that maximize fuel efficiency while meeting the vehicle's torque demands.
Once the aforementioned operational conditions are satisfied, the vehicle operates in hybrid drive, with both the engine and the electric motor functioning at optimal torque output.
When the SOC is below the minimum threshold and the vehicle demand torque T req is equal to or less than the optimal engine output torque T opt , the vehicle will operate in engine direct-drive mode, provided that the aforementioned operational conditions are met.In this mode, the engine will continue to run along the optimal curve. is greater than the motor torque threshold and the vehicle demand torque  is greater than the optimal engine output torque  , it is also necessary to ensure that the vehicle demand torque  is less than the optimal engine output torque  and the sum of the peak positive torque of the electric motor  .The diagram of  is shown in Figure 6.As shown in Figure 6, the optimal torque diagram is derived from a series of engine performance tests under various load conditions.These tests measure the Brake Specific Fuel Consumption (BSFC) across a range of engine speeds and torques.The optimal torque curve  is then plotted to identify the torque values at which the engine operates most efficiently (i.e., lowest BSFC).This curve represents the engine operating points that maximize fuel efficiency while meeting the vehicle's torque demands.
Once the aforementioned operational conditions are satisfied, the vehicle operates in hybrid drive, with both the engine and the electric motor functioning at optimal torque output.
When the SOC is below the minimum threshold and the vehicle demand torque  is equal to or less than the optimal engine output torque  , the vehicle will operate in engine direct-drive mode, provided that the aforementioned operational conditions are met.In this mode, the engine will continue to run along the optimal curve.
When the SOC is between the minimum and maximum thresholds, if the vehicle demand torque  is greater than the motor torque threshold and  is less than or equal to the optimal output torque of the engine  , the vehicle will operate in charge sustaining mode once the above operating conditions are met.At this time, the engine continues to run along the optimal curve to ensure that the battery is not overcharged.Concurrently, the motor generates negative torque to facilitate battery charging.
When the BSP exceeds 0, the operating mode switches to regenerative braking mode, which recovers the kinetic energy generated during braking or deceleration, with the aim of increasing energy utilization efficiency, reducing energy waste, and improving fuel efficiency.
In this instance, the upper limit of the threshold for pure electric drive mode is determined by the sum of the pure electric drive mode torque switching threshold and the EV mode compensation threshold.This is carried out to prevent the operating mode from switching frequently between pure electric drive mode and engine start-stop mode, thereby avoiding transmission losses.When the SOC is between the minimum and maximum thresholds, if the vehicle demand torque T req is greater than the motor torque threshold and T req is less than or equal to the optimal output torque of the engine T opt , the vehicle will operate in charge sustaining mode once the above operating conditions are met.At this time, the engine continues to run along the optimal curve to ensure that the battery is not overcharged.Concurrently, the motor generates negative torque to facilitate battery charging.
When the BSP exceeds 0, the operating mode switches to regenerative braking mode, which recovers the kinetic energy generated during braking or deceleration, with the aim of increasing energy utilization efficiency, reducing energy waste, and improving fuel efficiency.
In this instance, the upper limit of the threshold for pure electric drive mode is determined by the sum of the pure electric drive mode torque switching threshold and the EV mode compensation threshold.This is carried out to prevent the operating mode from switching frequently between pure electric drive mode and engine start-stop mode, thereby avoiding transmission losses.This finding led us to conclude that an optimization method capable of comprehensively capturing complex driving conditions and vehicle state changes is necessary to achieve higher levels of energy utilization and further reduce fuel consumption.Consequently, this study employs a dynamic programming (DP) algorithm as a global optimi- This finding led us to conclude that an optimization method capable of comprehensively capturing complex driving conditions and vehicle state changes is necessary to achieve higher levels of energy utilization and further reduce fuel consumption.Consequently, this study employs a dynamic programming (DP) algorithm as a global optimization framework to ensure optimal energy allocation throughout the driving cycle.The core strength of the DP algorithm lies in its ability to comprehensively evaluate future states in a multi-step decision-making process.This provides a powerful tool for plug-in hybrid vehicles to precisely adjust energy flow.

Dynamic Programming Energy Management Strategy
Dynamic programming (DP) can find globally optimal solutions and effectively handle constraints and nonlinearities.Therefore, compared to rule-based strategies, DP can better exploit the advantages of PHEVs [31].
This study employs the DP method to achieve precise control and optimization, reducing fuel consumption and enhancing overall operational efficiency and performance.

Formulating Dynamic Programming
In discrete time, the state equation of the PHEV model is expressed as follows: where x represents the state variables, k represents the discrete time steps, u represents the control variables, and n Eng represents the engine speed.
The design of PHEVs typically features a larger capacity battery pack, allowing more electrical energy to be drawn from the grid, thus reducing dependence on fossil fuels and lowering overall fuel consumption.During urban driving, PHEVs can operate purely on battery power, reducing the frequency of engine startups, thereby decreasing fuel consumption and emissions.To minimize fuel consumption, the goal of the optimal control problem is to identify the control sequence that minimizes the following cost function: where N denotes the stage number of the driving cycle, L denotes the instantaneous cost, and Fuel k denotes the instantaneous fuel consumption of each stage.
To ensure the smooth operation of the engine, motor, and battery, constraint condition (10) must be applied during the optimization process.
where η EV represents motor efficiency, n EV represents motor speed, T b represents braking torque, and the subscripts min and max denote the minimum and maximum values of the respective variables.

Implementing Dynamic Programming
When solving backward to obtain the minimum cost function, the DP problem can be described by recursive Equations ( 11) and (12).The sub-problem at the (N − 1)-th step is: For the k-th step (0 ≤ k < N − 1), the sub-problem can be described as: where J * k (x k ) is the optimal cost function at state x k at the k-th step, leading to the end of the driving cycle.x k+1 is the state at the (k + 1)-th step after applying the control variable u k to state x k at the k-step, as in Equation ( 12).

Integrated Engine Start-Stop Dynamic Programming
To further optimize the PHEV's energy management strategy, this study introduces engine start-stop control within the framework of dynamic programming (DP).The engine start-stop strategy aims to minimize the engine's operating time under low-efficiency conditions, thus lowering fuel consumption and emissions.In the DP algorithm, the engine's state is considered an additional control variable denoted as u eng , where u eng = 1 indicates the engine is running and u eng = 0 indicates the engine is stopped.
Therefore, the control variable vector is updated to u = T Eng T EV n Eng u eng ; the state equation and cost function are correspondingly adjusted.Specifically, an additional item representing the engine start-stop cost is added to the cost function to account for the energy consumption and wear associated with engine starts and stops.The updated cost function is expressed as follows: where λ is a weighting coefficient used to balance fuel consumption and the engine startstop cost, and ∆u eng,k represents the change in engine state at step k, engine start or stop.
In the optimization process, in addition to existing state and control variable constraints, engine start-stop logic constraints must also be considered.For example, the engine must run for a minimum duration after starting to avoid frequent start-stops, which can affect engine lifespan.
In this manner, the DP algorithm can provide a globally optimal solution for the energy management of PHEVs while considering the engine start-stop strategy.

Methodology for Determining Weighting Factors
Following the integration of engine start-stop control into the DP framework, an important issue we face is how to balance fuel consumption and engine start-stop costs.To address this issue, we introduce a weighting coefficient λ, which influences the trade-off between the number of engine start-stop events and fuel consumption in the cost function.
The Entropy Weight Method (EWM) is an important information weight model that avoids human interference in weighting indicators, enhancing the objectivity of evaluation results.Additionally, the EWM requires only one calculation to address the weighting problem of multiple indicators and obtain applicable weights for each [32].Therefore, this study adopts EWM to determine the weighting coefficients for each term in the cost function (Equation ( 14)).
where λ start−stop is the weighting coefficient of the number of engine starts and stops, λ f uel is the weighting coefficient of the fuel consumption, C start−stop,k is the cost of the engine starts and stops at the kth step, and C f uel,k is the corresponding fuel consumption cost.
To optimize the energy distribution strategy, this study simulates different driving cycles to fine-tune the weighting coefficients.The goal is to identify coefficients that minimize energy consumption across various driving scenarios while reducing engine start-stop events.This enhances energy efficiency and extends engine lifespan.The optimal weighting coefficients are presented in Table 3.   MIL testing integrates the control algorithm into a simulation model to verify the algorithm's performance in a virtual environment before implementation in real hardware.This approach allows for the identification and correction of potential issues early in the development process.
Similarly, the primary goal of SIL testing is to ensure behavioral consistency between the auto-generated code and the models used for code generation.This method enables verification that the code and model perform identically under the same test data inputs, which is essential for confirming the reliability of the generated code.During SIL testing, we ensured comprehensive coverage of various paths and signal ranges with the input test data.This extensive data coverage is crucial for validating the behavioral equivalence MIL testing integrates the control algorithm into a simulation model to verify the algorithm's performance in a virtual environment before implementation in real hardware.This approach allows for the identification and correction of potential issues early in the development process.
Similarly, the primary goal of SIL testing is to ensure behavioral consistency between the auto-generated code and the models used for code generation.This method enables verification that the code and model perform identically under the same test data inputs, which is essential for confirming the reliability of the generated code.During SIL testing, we ensured comprehensive coverage of various paths and signal ranges with the input test data.This extensive data coverage is crucial for validating the behavioral equivalence between the model and the generated code.
Figures 9 and 10 show the validation results of the control strategies for the engine and motor under the IESS-DP strategy using both Model-in-the-Loop (MIL) and Softwarein-the-Loop (SIL) testing approaches.The high degree of consistency between the MIL and SIL results confirms that the power, torque, and speed of the engine and motor match the expected performance under the proposed IESS-DP strategy, validating the accuracy and reliability of our control method.MIL testing integrates the control algorithm into a simulation model to verify the algorithm's performance in a virtual environment before implementation in real hardware.This approach allows for the identification and correction of potential issues early in the development process.
Similarly, the primary goal of SIL testing is to ensure behavioral consistency between the auto-generated code and the models used for code generation.This method enables verification that the code and model perform identically under the same test data inputs, which is essential for confirming the reliability of the generated code.During SIL testing, we ensured comprehensive coverage of various paths and signal ranges with the input test data.This extensive data coverage is crucial for validating the behavioral equivalence between the model and the generated code.
Figures 9 and 10 show the validation results of the control strategies for the engine and motor under the IESS-DP strategy using both Model-in-the-Loop (MIL) and Softwarein-the-Loop (SIL) testing approaches.The high degree of consistency between the MIL and SIL results confirms that the power, torque, and speed of the engine and motor match the expected performance under the proposed IESS-DP strategy, validating the accuracy and reliability of our control method.

Analysis of Simulation Results
To evaluate the superiority of the IESS-DP strategy, a comparative analysis was conducted against the RB strategy, DP strategy, and DDRL/SS strategy [33].The simulation results are illustrated in Figure 11, where the trend of SOC changes over time clearly reflects the energy consumption of each strategy.
As shown in Figure 11, the DP strategy exhibits a more gradual decline in the SOC of the battery compared to the RB strategy and DDRL/SS strategy.The robustness of the DP strategy is reflected in its conservative SOC consumption, indicating a significant improvement in efficiency for avoiding over-discharge and optimizing regenerative energy utilization.The IESS-DP strategy shows a similar amplitude of SOC fluctuations compared to the DP strategy, indicating that both have comparable energy management effectiveness in dynamically responding to various driving conditions.

Analysis of Simulation Results
To evaluate the superiority of the IESS-DP strategy, a comparative analysis was conducted against the RB strategy, DP strategy, and DDRL/SS strategy [33].The simulation results are illustrated in Figure 11, where the trend of SOC changes over time clearly reflects the energy consumption of each strategy.
As shown in Figure 11, the DP strategy exhibits a more gradual decline in the SOC of the battery compared to the RB strategy and DDRL/SS strategy.The robustness of the DP strategy is reflected in its conservative SOC consumption, indicating a significant improvement in efficiency for avoiding over-discharge and optimizing regenerative energy utilization.The IESS-DP strategy shows a similar amplitude of SOC fluctuations compared to the DP strategy, indicating that both have comparable energy management effectiveness in dynamically responding to various driving conditions.
the battery compared to the RB strategy and DDRL/SS strategy.The robustness of the DP strategy is reflected in its conservative SOC consumption, indicating a significant improvement in efficiency for avoiding over-discharge and optimizing regenerative energy utilization.The IESS-DP strategy shows a similar amplitude of SOC fluctuations compared to the DP strategy, indicating that both have comparable energy management effectiveness in dynamically responding to various driving conditions.It is noteworthy that the SOC curves for each strategy in the simulation graph change after  = 1550 seconds.The rate of SOC decline for the RB, DP, and DDRL/SS strategies becomes consistent after  = 1550 seconds, indicating that these strategies exhibit similar energy consumption patterns when the battery level approaches depletion.This may be due to all strategies entering a common energy-saving mode when the battery charge falls below a certain threshold, in order to extend battery life.
Despite the convergence in trends among the other strategies, the IESS-DP strategy consistently maintained a relatively high SOC level, demonstrating its superior performance throughout the simulation.This trend indicates that as battery power decreases, It is noteworthy that the SOC curves for each strategy in the simulation graph change after t = 1550 s.The rate of SOC decline for the RB, DP, and DDRL/SS strategies becomes consistent after t = 1550 s, indicating that these strategies exhibit similar energy consumption patterns when the battery level approaches depletion.This may be due to all strategies entering a common energy-saving mode when the battery charge falls below a certain threshold, in order to extend battery life.
Despite the convergence in trends among the other strategies, the IESS-DP strategy consistently maintained a relatively high SOC level, demonstrating its superior performance throughout the simulation.This trend indicates that as battery power decreases, the performance differences between the RB, DP, and DDRL/SS strategies gradually diminish, whereas the IESS-DP strategy continues to exhibit effective energy management capabilities.
As shown in Figure 12, the motor operating points under the IESS-DP strategy are concentrated in the high-efficiency region.This minimizes deviation and effectively improves motor efficiency.This phenomenon indicates that, under most conditions, the motor operates close to its theoretical efficiency peak.
World Electr.Veh.J. 2024, 15, x FOR PEER REVIEW 14 of 18 the performance differences between the RB, DP, and DDRL/SS strategies gradually diminish, whereas the IESS-DP strategy continues to exhibit effective energy management capabilities.
As shown in Figure 12, the motor operating points under the IESS-DP strategy are concentrated in the high-efficiency region.This minimizes deviation and effectively improves motor efficiency.This phenomenon indicates that, under most conditions, the motor operates close to its theoretical efficiency peak.Figures 13 and 14 illustrate the engine's operating conditions.Figure 13 shows the distribution of engine operating points, while Figure 14 compares the number of engine start-stop events under the DP, DDRL/SS, and IESS-DP strategies.Figure 13a,b indicate that the DP strategy concentrates the engine operating points more in the optimal performance region.Concentration indicates that the DP strategy effectively guides the engine to operate closer to its optimal performance zone, thereby improving overall fuel efficiency.
As shown in Figure 13b,d, the IESS-DP strategy further optimizes engine operation by adding additional constraints and enhanced functionalities, reducing deviations from the optimal efficiency zone.Figure 13c shows that although the DDRL/SS strategy enables Figures 13 and 14 illustrate the engine's operating conditions.Figure 13 shows the distribution of engine operating points, while Figure 14 compares the number of engine start-stop events under the DP, DDRL/SS, and IESS-DP strategies.Figure 13a,b indicate that the DP strategy concentrates the engine operating points more in the optimal performance region.Concentration indicates that the DP strategy effectively guides the engine to operate closer to its optimal performance zone, thereby improving overall fuel efficiency.Additionally, the IESS-DP strategy reduces the number of engine start-stop by approximately 43% compared to the DP strategy, and by about 16% compared DDRL/SS strategy.This not only enhances the engine system's lifespan and reliabil also improves fuel efficiency by keeping the engine within its optimal operating ran longer periods.
Table 4 shows that the fuel consumption per 100 kilometers under the RB stra 3.97L.Fuel consumption decreases to 3.49L under the DP strategy and further to under the IESS-DP strategy, representing a reduction of approximately 6.15%.Add ally, the IESS-DP strategy reduces fuel consumption by 5.35% compared to the DD strategy.Additionally, the IESS-DP strategy reduces the number of engine start-stop events by approximately 43% compared to the DP strategy, and by about 16% compared to the DDRL/SS strategy.This not only enhances the engine system's lifespan and reliability but also improves fuel efficiency by keeping the engine within its optimal operating range for longer periods.
Table 4 shows that the fuel consumption per 100 kilometers under the RB strategy is 3.97L.Fuel consumption decreases to 3.49L under the DP strategy and further to 3.36L under the IESS-DP strategy, representing a reduction of approximately 6.15%.Additionally, the IESS-DP strategy reduces fuel consumption by 5.35% compared to the DDRL/SS strategy.As shown in Figure 13b,d, the IESS-DP strategy further optimizes engine operation by adding additional constraints and enhanced functionalities, reducing deviations from the optimal efficiency zone.Figure 13c shows that although the DDRL/SS strategy enables some operating points to fall in higher efficiency areas, their distribution is not as extensively concentrated on the engine's optimal working curve as with the IESS-DP strategy.
Additionally, the IESS-DP strategy reduces the number of engine start-stop events by approximately 43% compared to the DP strategy, and by about 16% compared to the DDRL/SS strategy.This not only enhances the engine system's lifespan and reliability but also improves fuel efficiency by keeping the engine within its optimal operating range for longer periods.
Table 4 shows that the fuel consumption per 100 km under the RB strategy is 3.97 L. Fuel consumption decreases to 3.49 L under the DP strategy and further to 3.36 L under the IESS-DP strategy, representing a reduction of approximately 6.15%.Additionally, the IESS-DP strategy reduces fuel consumption by 5.35% compared to the DDRL/SS strategy.Simulation results show that the IESS-DP strategy maintains significantly lower cumulative fuel consumption over time.This indicates that the IESS-DP optimization effectively reduces fuel consumption, enhances vehicle energy efficiency, and alleviates the cost and efficiency issues associated with frequent engine start-stop events.

Conclusions
This paper focuses on a PHEV with a P2 architecture and proposes the IESS-DP energy management strategy.By precisely controlling the energy flow of the plug-in hybrid electric vehicle (PHEV), this strategy significantly improves fuel economy and system performance.Comprehensive simulations and experimental validations demonstrate that this strategy shows superior performance metrics compared to traditional rule-based (RB) and dynamic programming (DP) strategies.The specific details are as follows: Firstly, this paper addresses various engine operating states by designing an enhanced rule-based strategy.By precisely controlling engine start-stop cycles, it significantly reduces fuel consumption during idle periods.
We propose the IESS-DP strategy, an integrated DP energy management approach that incorporates engine start-stop functionality.It comprehensively considers different operational states of engine start-stop control and introduces weighting coefficients to balance fuel consumption and engine start-stop costs.This strategy achieves precise energy flow control through a global optimization framework, significantly improving fuel economy.
The simulation validation under WLTC conditions demonstrates that the proposed IESS-DP energy management strategy achieves a fuel consumption rate of 3.36 L/100 km, which is a reduction of 18.15%, 6.15%, and 5.35% compared to the RB, DP, and DDRL/SS strategies, respectively.Additionally, the corresponding number of engine start-stop events is reduced by 43% and 16% compared to the DP and DDRL/SS strategies, respectively.Therefore, the IESS-DP strategy not only optimizes PHEV fuel efficiency but also effectively mitigates the costs and efficiency issues associated with frequent engine start-stop events.
However, this study has several limitations.Model simplifications, such as neglecting internal engine dynamics and battery temperature effects, may affect accuracy.The significant computational complexity of the dynamic programming algorithm restricts its real-time application.Additionally, the long-term effects of battery aging have not been considered.Future research will explore applying this strategy to a broader range of vehicle models and more complex driving scenarios to achieve comprehensive energy management and higher fuel efficiency.Additionally, considerations for battery health management and the effects of battery aging will be crucial in subsequent studies, enhancing the long-term operational performance and reliability of plug-in hybrid electric vehicles.

Figure 4 .
Figure 4. Energy management control strategy in EV mode.

Figure 4 .
Figure 4. Energy management control strategy in EV mode.

Figure 4 .
Figure 4. Energy management control strategy in EV mode.

Figure 5 .
Figure 5. Energy management control strategy under engine start-stop strategy.Figure 5. Energy management control strategy under engine start-stop strategy.

Figure 5 .
Figure 5. Energy management control strategy under engine start-stop strategy.Figure 5. Energy management control strategy under engine start-stop strategy.

Figure 7 18 Figure 7
Figure 7 illustrates that the Engine Start-Stop (ESS) Control Strategy significantly optimizes fuel economy.In various driving cycles, it exhibits lower fuel consumption compared to traditional strategies without ESS.Simulation results indicate that with the ESS control strategy, the fuel consumption of the PHEV under the WLTC cycle condition decreased from 3.97 L/100 km to 3.76 L/100 km, representing a reduction of 5.29%.However, the RB strategy is limited in its ability to adequately respond to changes in driving modes, potentially causing fluctuations in optimization effectiveness under various real-world conditions.

Figure 7 .
Figure 7.Comparison of fuel economy between RB strategy and ESS strategy.

Figure 7 .
Figure 7.Comparison of fuel economy between RB strategy and ESS strategy.

3 . 5 .
Values of weighting factors.Simulation Test and Results Analysis 5.1.Verification of Simulation Results This study uses the Worldwide Harmonized Light Vehicle Test Cycle (WLTC) to validate the IESS-DP algorithm.The WLTC simulates modern driving conditions, including frequent acceleration and braking, to more accurately reflect daily vehicle use.It is divided into four parts based on vehicle speed: low, medium, high, and extra-high.The total duration of the WLTC test is approximately 1800 s, covering about 23.25 km.Vehicle speed varies frequently during the test, reaching up to 131 km per hour, ensuring coverage of various driving conditions from low to high speeds.

Figure 8 18 Figure 8
Figure 8 shows the driving cycle, featuring results from the reference, Model-in-the-Loop (MIL), and Software-in-the-Loop (SIL) tests.The alignment of both MIL and SIL results with the reference data substantiates the accuracy and reliability of the IESS-DP strategy in managing vehicle speed across varying driving conditions.

Figure 9 .
Figure 9.Comparison of Engine MIL and SIL Results under IESS-DP Strategy: (a) Engine power; (b) Engine torque; (c) Engine speed.Figure 9. Comparison of Engine MIL and SIL Results under IESS-DP Strategy: (a) Engine power; (b) Engine torque; (c) Engine speed.

Figure 10 .
Figure 10.Comparison of MIL and SIL Results under IESS-DP Strategy: (a) Electric motor power; (b) Electric motor torque; (c) Electric motor speed.

Figure 14 .
Figure 14.Comparison of engine start-stop events.

Figure 14 .
Figure 14.Comparison of engine start-stop events.

Figure 14 .
Figure 14.Comparison of engine start-stop events.
illustrates the engine's fuel consumption characteristics.The technical characteristics of the engine are listed in Table2.

Table 2 .
Technical characteristics of the engine.

Table 2 .
Technical characteristics of the engine.

Table 4 .
Energy consumption under different control strategies.