Integrated energy, environmental, and economic optimization for energy management systems in PHEVs considering traffic conditions

Abstract

The growing dependence on fossil fuels has depleted their reserves and significantly contributed to environmental pollution. In recent years, plug-in hybrid electric vehicles (PHEVs) have garnered attention for their ability to reduce fuel consumption and emissions while offering an increased driving range, mainly due to their large battery packs. In these vehicles, critical concerns include the reduction of fuel consumption, control of pollution, and the costs associated with battery degradation. This study introduces a multi-objective optimization approach for the energy management strategy (EMS), focusing on minimizing energy consumption, environmental impact, and the economic implications of battery aging (E3). To achieve this, a plug-in hybrid electric vehicle is modeled based on the Samand vehicle using experimental data. A genetic algorithm is then employed to perform sizing optimization of the components. Additionally, a fuzzy logic controller is developed for the EMS. Ultimately, the multi-objective optimization of the energy management system is conducted across three scenarios: one objective function, two objective functions, and three objective functions evaluated over five driving cycles. The results demonstrate that the optimization approach utilizing three objective functions outperforms other scenarios. Focusing on a single objective function leads to a 13.5% reduction in average battery degradation, though fuel consumption increases by 3%. With two objective functions, battery degradation decreases by 10%, while fuel consumption and emissions rise by 1.9% and 5.7%, respectively. Considering three objective functions leads to average reductions of 3.3% in emissions and 4.4% in battery degradation, with approximately a 0.02% rise in fuel consumption.

Introduction

The increasing dependence on fossil fuels, depleting reserves, and rising environmental concerns¹ have prompted significant transformations in the automotive industry, steering a movement toward electrification². Within this evolution, PHEVs have attracted notable interest in both the industry and research due to their enhanced fuel efficiency, lower emissions, and improved travel range³ caused by high-capacity battery packs⁴. PHEVs, which utilize two power sources—an internal combustion engine (ICE) and an electric motor (EM)⁵—exhibit considerable flexibility in their power distribution⁶. This underscores the essential role of EMS in effectively allocating the required power⁷.

When developing control strategies, a range of objectives can be pursued, with the reduction of fuel consumption typically being the primary focus of most research⁸. However, with the rise of environmental regulations and the enhancement of industry standards, emissions reduction has also become an essential objective in designing control strategies for PHEVs⁹. Furthermore, given the limited lifespan of these vehicle batteries and the substantial costs associated with their replacement, significant research efforts have been directed toward mitigating battery degradation and implementing energy management strategies to extend battery life and lower replacement costs¹⁰.

In recent years, extensive research has been conducted on energy management strategies for hybrid and plug-in hybrid vehicles. Numerous studies have proposed various control strategies aimed at reducing fuel consumption. For instance, Tian et al. introduced an adaptive fuzzy control strategy to minimize fuel consumption in PHEVs. This approach employs an optimal state-of-charge (SOC) map derived from a neural network (NN), resulting in an average reduction of 9% in fuel consumption. Liu et al. proposed a novel method to improve the robustness of the PMP-based energy management system (EMS) for PHEVs through the application of fuzzy logic control. This approach resulted in a 19.94% reduction in fuel consumption compared to the charge-depleting and charge-sustaining (CD-CS) strategy and a 1.01% increase compared to dynamic programming (DP)¹¹. Lei et al. introduced a sim-to-real reinforcement learning framework that combines advanced agents with high-fidelity Simulink models¹². Their approach was validated through both simulation and real vehicle tests, resulting in hydrogen savings of 4.35–5.73% and demonstrating consistent performance in real-world conditions. Zhang et al. proposed an Integrated Thermal and Energy Management (ITEM) system that uses deep reinforcement learning (DRL) for connected PHEVs especially under varying climate and traffic conditions¹³. The designed control strategy achieved a reduction in fuel consumption of approximately 12.4%. Li et al.¹⁴ propose an online adaptive energy management strategy (EMS) for fuel cell hybrid vehicles that integrates improved driving pattern recognition with machine learning regression models trained on dynamic programming results. The proposed EMS achieved the lowest hydrogen consumption among six compared algorithms, reducing hydrogen use by up to 5.66% compared to commonly used methods. Li et al. compares four fuel cell hybrid vehicle topologies using dynamic programming-based energy management and evaluates them based on overall economic cost, including acquisition, hydrogen consumption, and component aging¹⁵. The fuel cell/battery semi-active topology is found to be the most cost-effective. Additionally, sensitivity analysis of key system parameters and the impact of driving conditions on cost are explored to guide future design improvements. Other studies have also focused on reducing fuel consumption while simultaneously extending battery life or minimizing emissions. Sarvaiya et al. conducted a comparative analysis of four distinct EMSs, focusing on optimizing battery lifespan and fuel consumption in a parallel hybrid vehicle⁶. Pourbafrani et al. proposed a traffic-based control strategy that utilizes a modified dynamic programming approach¹⁶. The main goal of the strategy was to improve fuel efficiency and reduce battery degradation. Their research findings indicate that the proposed control strategy outperforms the adaptive equivalent consumption minimization strategy (A-ECMS), achieving a 3.1% reduction in fuel consumption and a 15% decrease in battery aging. Hu et al. established a real-time optimization method employing the A-ECMS for various driving cycles, concentrating on battery degradation. The results indicated that this approach led to a 15.8% reduction in battery degradation compared to the optimized rule-based (RB) EMS optimized via a genetic algorithm¹⁷. Li et al. presents a comprehensive approach combining multi-objective optimization for HESS component sizing with an adaptive machine learning-based energy management strategy¹⁸. The proposed approach results in a reduction of total energy loss by 0.74–9.49% and a decrease in battery ampere-hour throughput by 0.5–19.83%. Jia et al.¹⁹ propose an advanced energy management strategy (EMS) for fuel cell vehicles that integrates future road and environmental information with cabin comfort control. Using a twin delayed deep deterministic policy gradient (TD3) algorithm, their EMS optimizes energy distribution among the fuel cell, battery, and air conditioning system, resulting in improved driving economy, enhanced cabin temperature regulation, extended battery lifespan, and reduced overall operating costs compared to conventional rule-based strategies. Jia et al.²⁰ propose a learning-based model predictive control (L-MPC) energy management strategy for fuel cell hybrid electric buses, combining model predictive control with machine learning to improve adaptability and efficiency. Their method incorporates a BiLSTM-based speed predictor and health-aware optimization, resulting in significant reductions in hydrogen consumption, battery and fuel cell degradation, and overall operating costs compared to conventional MPC and deep reinforcement learning approaches. In Ref²¹. Mahmoodi et al. conducted a multi-objective optimization study focused on the sizing and control strategy of a plug-in hybrid vehicle, with the goal of enhancing both fuel efficiency and emissions reduction. They utilized a fuzzy genetic algorithm, which achieved a 7% decrease in fuel consumption and a 10% reduction in emissions. Lei et al. conducted an in-depth study on carbon-free vehicle propulsion systems that leverage the synergy of ammonia and hydrogen fuels²². Their research examines a hybrid powertrain that integrates fuel cells and internal combustion engines, aiming to optimize energy utilization and manufacturing costs through multi-objective algorithms. The study highlights the potential of ammonia-hydrogen blends to realize carbon-neutral heavy-duty transportation, offering enhanced efficiency and reduced emissions. Mr. Kim et al. proposed an optimal model-based control strategy for parallel hybrid electric vehicles (HEVs)²³. In comparison to the dynamic programming strategy, their method achieved a 9.09% reduction in NOx emissions, though it resulted in a 4.52% increase in hydrocarbon (HC) emissions. Moreover, when assessed against real-world driving data, the strategy demonstrated a remarkable 29.73% reduction in NOx emissions, alongside a 1.10% increase in hydrocarbon emissions. Lei et al. proposed a modular theory-constrained neural network for fuel cell vehicle modeling, highlighting the potential of hybrid frameworks in vehicle energy analysis²⁴. Their model improved voltage prediction accuracy by 33.7% compared to theoretical models and enhanced hydrogen consumption estimation accuracy by up to 63.7% over traditional methods.

In the literature, various aspects of energy management strategies have been examined. Some studies, such as²⁵propose EMS designed primarily to reduce fuel consumption. Others, like²⁶develop EMS with dual objectives: minimizing energy consumption and addressing environmental issues, particularly in terms of emissions reduction. Additionally, certain studies, such as²⁷focus on the dual aims of reducing energy consumption while also minimizing economic costs, particularly prolonging battery life and decreasing replacement expenses.

As mentioned before, most research has concentrated on reducing energy consumption, minimizing emissions, or lowering the economic costs associated with battery degradation, either as standalone objectives or in pairs. However, a significant gap persists in the development of EMS that simultaneously tackles all three of these objectives: managing energy consumption, addressing environmental challenges, and controlling economic costs. Therefore, the main idea of this paper is to optimize the control strategy for PHEVs from three perspectives: energy, environment, and economy (E3), while taking driving conditions into account. Energy considerations include the fuel consumption of the ICE as well as the equivalent fuel consumption of the battery. From an economic perspective, battery degradation, which can impose significant costs on consumers, is also considered. Furthermore, the paper aims to optimize pollutant emissions to address environmental concerns comprehensively. The remainder of this study is structured as follows. Section two covers vehicle configuration, the equivalent circuit model (ECM) of the battery, the battery life model, and the development of the driving cycle. Section three focuses on the optimization of vehicle component sizing. In section four, the discussion turns to the design of the EMS. Section five shifts the emphasis to the optimization of the control strategy. Section six presents and analyzes the results, while section seven offers a summary and conclusions.

PHEV configuration

In this research, a parallel PHEV configuration is developed based on the national Samand platform. As illustrated in ‎Fig. 1, the ICE map for the vehicle is generated using data from the IKCO engine test²⁸. The default specification of the main components and the vehicle parameters are provided in ‎Table 1. To effectively model the vehicle, a parallel PHEV approach is employed, and the simulation is carried out using Simulink/Advisor.

[See PDF for image]

Fig. 1

Experimental set-up for engine dynamometer test²⁸.

Table 1. PHEV parameters and default component specifications.

Parameter	Value
ICE power	82	W
Motor power	75	W
Battery capacity	40	Ah
Cell voltage	3.7	V
Glider mass	905
	0.318	–
	1.2
Front area	2.1
Wheelbase	2.6

Energy storage model

In the design of PHEVs, the energy storage system is a critical component, representing a substantial investment in vehicle technology. Lithium-ion batteries have emerged as the preferred choice for energy storage due to their impressive specific energy, high power output, and extended cycle life, contributing to their reliability and efficiency²⁹.

Equivalent circuit model (ECM)

A mathematical model is necessary to accurately describe the behavior of a battery³⁰. In this paper, an ECM is utilized for this purpose. A series resistance (Rint) ECM is employed to model the battery, with the corresponding equation outlined below. As mentioned in ‎Table 1. a 40 Ah lithium-ion battery cell, Kokam SLPB100216216H, is used as the battery cell of the vehicle.

1

where is the battery voltage, is the battery current, is the inner resistance, and is the battery open circuit voltage. The ECM model is shown in ‎Fig. 2.

[See PDF for image]

Fig. 2

Schematic representation of a Rint equivalent circuit model.

Cycle life model

Battery aging is a critical phenomenon that leads to the gradual degradation of battery performance, primarily reflected in capacity loss and increased internal resistance. This degradation occurs due to two main factors: calendar aging, which happens during storage or idle periods, and cycle aging, which is a result of repeated charge and discharge cycles³¹. Accurately predicting capacity loss and resistance growth caused by calendar and cycle aging is crucial for improving battery performance and lifespan. Modeling these degradation processes allows for better optimization of battery design and management strategies by simulating behavior under various conditions. Integrated aging models that capture multiple degradation mechanisms have proven effective for precise lifecycle assessment and extending battery durability³². Battery degradation models can be categorized into two primary types: electrochemical and semi-empirical. Electrochemical models provide a more precise representation of battery behavior but come with greater computational complexity. In contrast, semi-empirical models, which also rely on experimental data, are less computationally intensive and offer an acceptable level of accuracy. As a result, they have been widely employed in numerous studies, such as³³.In this study, a semi-empirical model is used to model battery aging that incorporates variables such as temperature, SOC, and C-rate³⁴.

2

where represent the battery aging, and are constant terms, is the activation energy (), is the dependence, determines the current rate, is the molar gas constant (), is the battery temperature (°C), is the ampere-hour throughput, represent the dependence, refers to the battery current, and denotes the battery capacity ()³⁵.

Driving cycle development

A driving cycle is a speed-time profile representing a particular region’s driving behavior characteristic. It comprises a series of vehicle operating conditions, including acceleration, cruising, deceleration, and idling phases³⁶. The primary goal in developing a driving cycle is to accurately estimate fuel consumption, emissions, and other pollutants a vehicle produces under driving conditions³⁷.

One approach to developing a driving cycle is through the use of a “micro-trip” definition. Each micro-trip is comprised of two segments: a moving segment and a stationary segment. The stationary segment includes the starting and ending points where the vehicle remains idle, while the moving segment encompasses acceleration, constant speed, and deceleration. Notably, the endpoint of each micro-trip serves as the starting point for the subsequent micro-trip³⁸. The Tehran driving cycle is developed according to the concept of micro-trip using real-world traffic data gathered from various locations within the city of Tehran, as illustrated in ‎Fig. 3. Also, ‎Fig. 4 shows the Idle Time/Total Time vs. Average Speed.

In real-world driving scenarios, traffic conditions vary significantly and can be broadly classified into three main categories: congested conditions, moderate-speed scenarios typically found in suburban areas, and high-speed situations commonly experienced on highways. Each of these conditions presents distinct dynamic and operational challenges for vehicle EMS. By integrating these traffic scenarios into the development and optimization of the control strategies, we can ensure that the EMS is both practical and applicable in real-world driving, thereby enhancing the overall performance of the vehicle. The present study aims to examine the effect of traffic varying conditions on optimization problems using five distinct driving cycles, including FTP-75, NEDC, Tehran-Long, Tehran-Short, and WLTP-Class3. These driving cycles are depicted in ‎Fig. 5, and their characteristics are detailed in ‎Table 2.

[See PDF for image]

Fig. 3

The routes selected for data collection within Tehran city³⁹. Map data: Google Maps © 2017 Google.

[See PDF for image]

Fig. 4

Idle time/total time vs. average speed for real-world traffic data gathered within the city of Tehran.

Table 2. Characteristics of the driving cycles.

Driving cycle	Time ()	Distance ()	Maximum speed ()	Average speed ()
Tehran short	1797	13.42	83.93	26.87
Tehran long	4146	31.03	113.66	26.95
FTP-75	2477	17.17	91.25	25.82
NEDC	1184	10.93	120	33.21
WLTP-Class3	1800	23.26	131.3	46.5

[See PDF for image]

Fig. 5

Representation of driving cycles: (a) FTP-75, (b) NEDC, (c) Tehran-Long, (d) Tehran-Short, (e) WLTP-Class3.

PHEV component sizing

The initial step in designing a PHEV is to identify the appropriate sizes for the main mechanical and electrical components used for power generation. These essential components include the ICE, the electric motor, and the energy storage system. Choosing the correct size for these components is critical, as it greatly influences the overall performance and characteristics of the vehicle.

Various objectives may be pursued in sizing optimization, including reducing fuel consumption, minimizing emissions, and enhancing overall cost efficiency. This study aims to optimize these parameters, specifically decreasing fuel consumption and lowering emissions. Accordingly, the objective function is developed with these aims in mind.

3

where , , and are the weighting coefficients, indicates the length of the driving cycle, while is the equivalent fuel consumption. CO, HC, and refer to carbon monoxide, hydrocarbon, and nitrogen oxide emissions, respectively. The symbols , , and represent the reference values for fuel consumption, carbon monoxide emissions, and the sum of hydrocarbon and nitrogen oxide emissions.

PNGV constraints

Vehicle performance should also be considered during the optimization process. Thus, in this study, the PNGV constraints, according to ‎Table 3., are used to examine vehicle performance.

Table 3. Optimization constraints according to PNGV⁹.

Description	Value
Acceleration time for 0–97 kph (0–60 mph)	≤ 12 s
Acceleration time for 64–97 kph (40–60 mph)	≤ 5.3 s
Acceleration time for 0-137 kph (0–85 mph)	≤ 23.4 s
Maximum speed at 0% grade	≥ 137 kph
Gradeability at 88.5 kph for 1200 s	≥ 6.5%

Genetic algorithm (GA)

This study employs a genetic algorithm for sizing. To effectively apply a GA to an optimization problem, it is essential to establish the objective function and a chromosomal representation of the variables involved. Here, the chromosome contains , , and as the decision variables:

4

where is the torque scaling factor applied to adjust the size of the ICE, is the torque scaling factor utilized to modify the size of the electric motor. denotes the total number of modules that constitute the battery package. The genetic algorithm begins with a population of 20 individuals and proceeds through 40 generations of optimization. In each generation, the decision variables , , and are modified for each individual to assess their corresponding objective function values with specified lower and upper bounds as shown in ‎Table 4. Based on their fitness levels, individuals are selected to form the next generation. For each new set of decision variables, acceleration and slope performance tests are conducted. If these performance criteria are not met, a penalty is applied to the corresponding objective function values to discourage infeasible solutions during the optimization process. The penalty values are illustrated in ‎Table 5.

Table 4. Optimization variables for sizing optimization.

Variable	Lower bound	Upper bound
	0.1	1
	0.1	1
	30	100

Table 5. Penalty values for unsatisfied constraints.

Description	Value
For acceleration 0–97 kph
For acceleration 64–97 kph
For acceleration 0-137 kph
For maximum speed
For gradeability

Energy management strategy

Fuzzy logic is a powerful tool based on expert knowledge used to control complex and nonlinear systems⁴⁰. This approach has already demonstrated its effectiveness in the control of EVs, HEVs, and PHEVs. In a PHEV application, a fuzzy logic controller manages power distribution between the ICE and electric motor using two inputs: the required power and the battery SOC. The structure of the fuzzy logic controller is depicted in ‎Fig. 6.

[See PDF for image]

Fig. 6

Schematic of fuzzy control system.

In this study, three membership functions are defined for both the inputs and the output, leading to nine fuzzy rules. Since the output of the fuzzy strategy is the ICE’s torque, its membership functions are designed to be similar to those of the requested torque. The initial membership functions are illustrated in ‎Fig. 7, and the corresponding rules are presented in ‎Table 6.

[See PDF for image]

Fig. 7

Initial membership functions: (a) Required torque, (b) SOC.

Table 6. Rules of the fuzzy control strategy.

	Req. torque
SOC		Low	Opt.	High
	Low	Opt.	High	High
	Opt.	Low	Opt.	High
	High	Low	Opt.	Opt.

Among the two power sources in a PHEV, the ICE functions as the main power source, while the electric motor serves as an assistant. To enhance overall efficiency, the ICE must operate within its optimal range. Thus, the requested torque is compared to the optimal torque of the ICE. The requested torque is defined on a scale from zero to one, with a value of 0.5 indicating the optimal torque. Furthermore, the state of charge (SOC) is assessed on a scale from zero to one, with zero indicating the minimum value and one denoting the maximum. ‎Fig. 8 illustrates the optimal torque of the ICE.

[See PDF for image]

Fig. 8

The ICE’s area of operation.

Optimization procedure

Developing a fuzzy control strategy primarily relies on the designer’s knowledge, which may not guarantee optimal performance. Therefore, it is essential to integrate this knowledge with optimization methods, mainly when designing control strategies for complex systems like PHEVs. This research aims to utilize genetic algorithms to optimize the fuzzy control strategy. The objective of optimizing the control strategy is to minimize fuel consumption, emissions, and battery degradation by formulating and evaluating different objective functions. The outcomes of the optimization are subsequently compared.

In the preceding section, it was noted that the control strategy involves the SOC and the requested torque as inputs, with the output representing the torque delivered by the ICE. Three membership functions have been assigned to both the inputs and output, utilizing a total of five variables to define these membership functions, as illustrated in ‎Fig. 9. Specifically, one variable is utilized for the triangular membership function, while two variables are allocated for each of the trapezoidal membership functions. Assuming that the membership functions for both the requested torque and the ICE torque are identical, a total of ten optimization variables are required.

[See PDF for image]

Fig. 9

Variables used to define the membership functions.

Each of the ten decision variables is restricted by defined lower and upper bounds, as detailed in ‎Table 7.

Table 7. Optimization variables for EMS optimization.

Variable	Lower bound	Upper bound
,	− 0.2	0
,	0	0.5
,	0	0.45
,	0.5	1
,	1	1.2

Single objective function

The initial objectives include minimizing equivalent fuel consumption and extending battery life. To achieve these objectives, the corresponding equation can be formulated as follows:

5

where and are the weighting coefficients, denotes the battery aging, and indicates the equivalent fuel consumption, defined as the total of the ICE’s fuel consumption and the equivalent fuel consumption of the battery. The symbols and correspond to the reference values for equivalent fuel consumption and battery aging, respectively.

Multi-objective functions

Two objective functions

To assess the impact of emissions in conjunction with fuel consumption and battery degradation, two distinct objective functions are considered. The first objective function encompasses the normalized sum of equivalent fuel consumption and emissions, while the second focuses on battery degradation. The objective functions are given as:

6

7

Three objective functions

To evaluate the impact of each optimization objective independently, each can be formulated as a separate objective function. As a result, the objective functions can be defined as follows:

8

9

10

Given the specified objective functions, it is not necessary to normalize fuel consumption and battery degradation. Consequently, the results will be derived independently of any reference values. In each objective function, the weights assigned will be considered equal.

Results and analysis

Sizing optimization

As previously mentioned, a genetic algorithm has been employed to optimize the size of each vehicle component. The initial population size is set to 20, and the number of iterations is 40. At each step, the new size of each component is determined using scaling factors, and after simulation, the objective function value is calculated. The PNGV constraints are then evaluated through slope and acceleration tests. As shown in ‎Fig. 10, the objective value during the optimization process is presented for five driving cycles, including FTP, NEDC, Tehran-Long, Tehran-Short, and WLTP-Class3. The optimized values of the variables for the driving cycles are shown in ‎Table 8. ‎Table 9. presents the results obtained from the evaluation of the performance constraints.

[See PDF for image]

Fig. 10

The objective function values against generations for driving cycles: (a) FTP-75, (b) NEDC, (c) Tehran-Long, (d) Tehran-Short, and (e) WLTP-Class3.

Table 8. Concluding values of optimization variables for the driving cycles.

Design variable	FTP-75	NEDC	Tehran long	Tehran short	WLTP-Class3
	0.64	0.86	0.63	0.63	0.63
	0.57	0.67	0.57	0.58	0.83
	92	97	99	99	100

Table 9. The evaluation of vehicle performance within the optimal solution scenario.

Constraints	WLTP-Class3	NEDC	FTP	Tehran long	Tehran short
Acceleration time (0–60 mph)	9.73	10.06	10.27	10.26	10.23
Acceleration time (40–60 mph)	4.95	5.17	5.3	5.28	5.27
Acceleration time (0–85 mph)	20.4	21.32	21.83	21.61	21.54
Maximum speed (0% grade)	181.29	181.42	181.55	181.52	181.52
Gradeability	6.5	8.81	6.52	6.5	6.5

Control strategy optimization

The results of the control strategy optimization with the genetic algorithm are presented in this section. The optimizations are performed to examine the effect of traffic conditions over five different driving cycles. In this study, for single-objective optimization, the Genetic Algorithm (GA) is used due to its effectiveness in exploring large and complex search spaces. For multi-objective optimization, the Non-dominated Sorting Genetic Algorithm II (NSGA-II) is employed, as it efficiently generates a diverse set of trade-off solutions representing the Pareto front.

Single objective function

As in the previous section, optimization is carried out through the Genetic Algorithm with a population of 20 individuals and 40 generations. The values of ICE fuel consumption, battery equivalent fuel consumption, total equivalent fuel consumption, and battery degradation for the initial and optimized states across five driving cycles are provided in ‎Table 10. ‎Figure 11 offers a comparison of these values in their normalized form.

Table 10. Analysis of fuel consumption and battery degradation: initial state vs. optimized state.

Parameter	State	FTP-75	NEDC	Tehran-short	Tehran-long	WLTP-Class3
Fuel	Initial	3/28	2/91	3/43	2/81	2/95
	Optimized	4/16	3/17	4/57	3/66	3/88
Fuel_ESS	Initial	1/9	1/97	3/52	2/38	2/61
	Optimized	1/23	1/75	2/62	1/69	1/88
Fuel_eqv	Initial	5/18	4/88	6/95	5/19	5/56
	Optimized	5/39	4/92	7/19	5/35	5/76
ESS_aging	Initial	0/016	0/012	0/017	0/024	0/021
	Optimized	0/014	0/011	0/015	0/020	0/017

[See PDF for image]

Fig. 11

Analysis of fuel consumption and battery degradation in normalized form: initial vs. optimized.

As shown in ‎Fig. 11, optimizing the control strategy results in an increase in fuel consumption for the ICE as well as total equivalent fuel consumption across all driving cycles. However, it simultaneously reduces the battery’s equivalent fuel consumption and degradation. Furthermore, after optimization, there is a slight increase in equivalent fuel consumption compared to the initial state. At the same time, battery degradation demonstrates a more significant decrease, highlighting the effectiveness of the optimization algorithm. Specifically, the optimization leads to an average reduction of 13.5% in battery degradation while resulting in an average increase in fuel consumption of approximately 3%.

Following the optimization, as shown in Fig. 12, the ICE has successfully operated within its optimal range, thereby achieving enhanced efficiency.

[See PDF for image]

Fig. 12

Operating points of the combustion engine before and after optimization: (a) FTP-75, (b) NEDC, (c) Tehran-long, (d) Tehran-short, and (e) WLTP-Class3.

Two objective functions

This section presents the optimization results based on two objective functions. As mentioned earlier, the first objective function captures the normalized sum of fuel consumption and emissions, while the second focuses on the normalized degradation of the battery.

‎Figure 13 illustrates the optimal solutions along with their corresponding Pareto front for the five distinct driving cycles. The trade-offs reveal that a reduction in fuel consumption and emissions is linked to an increase in battery degradation. Conversely, efforts to minimize battery degradation result in higher fuel consumption and emissions.

[See PDF for image]

Fig. 13

Optimal solutions and fitted Pareto curve for the driving cycles using two objective functions: (a) FTP-75, (b) NEDC, (c) Tehran-long, (d) Tehran-short, and (e) WLTP-Class3.

The average values of fuel consumption, emissions, and battery degradation at the optimal points for the various driving cycles are illustrated in normalized form in ‎Fig. 14. As shown in the figure, following optimization, fuel consumption saw an average increase for the Tehran-Short and WLTP-Class3 driving cycles, while it remained relatively stable for the other driving cycles. Emissions also experienced an average increase for the NEDC, Tehran-Short, and WLTP-Class3 driving cycles, but decreased for the remaining driving cycles. Furthermore, all driving cycles, after optimization, showed an average reduction in battery degradation. Consequently, the optimization resulted in an approximate average increase of 1.9% in fuel consumption, a roughly 5.7% rise in emissions, and about 10% reduction in battery degradation.

[See PDF for image]

Fig. 14

Analysis of fuel consumption, emissions, and battery degradation in normalized form considering two objective functions: initial vs. optimized.

Three objective functions

The optimization results are presented in this section, with a focus on three objective functions: equivalent fuel consumption, emissions, and battery degradation. Throughout the optimization process, vehicle performance is systematically evaluated through an evaluation of relevant performance constraints. The optimal solutions corresponding to five driving cycles are illustrated in ‎Fig. 15.

[See PDF for image]

Fig. 15

3D representation of Optimal points for the driving cycles using three objective functions: (a) FTP-75, (b) NEDC, (c) Tehran-Long, (d) Tehran-Short, and (e) WLTP-Class3.

As illustrated in ‎Fig. 15, there is no single point where all three objectives achieve their most optimal values simultaneously. For instance, during the NEDC driving cycle, the point that minimizes emissions and fuel consumption corresponds to the maximum capacity fade. Therefore, it is essential to establish a priority among these objectives when designing an optimal control strategy.The average values of fuel consumption, emissions, and battery degradation at the optimal points for the driving cycles are depicted in normalized form in ‎Fig. 16.

[See PDF for image]

Fig. 16

Analysis of fuel consumption, emissions, and battery degradation in normalized form considering three objective functions: initial vs. optimized.

As depicted in ‎Fig. 16, the optimization process that incorporates three objective functions has resulted in an increase in average fuel consumption for the Tehran-Long, Tehran-Short, and WLTP-Class3 driving cycles. Conversely, a decrease in fuel consumption is noted for the other driving cycles. Emissions have also increased on average for the WLTP-Class3 cycle, while no changes are observed for the Tehran-Short, with reductions seen in the remaining driving cycles. In terms of average battery degradation, no alterations are noted for the FTP-75 driving cycle, whereas reductions are recorded for the other cycles. Therefore, the results indicate that the optimization of the control strategy, focusing on the three objective functions, has led to an average increase in fuel consumption of 0.02%. However, emissions and battery degradation have been reduced by 3.3% and 4.4%, respectively, highlighting a superior performance compared to other optimization scenarios.

Given that vehicles encounter a variety of traffic and environmental conditions throughout their journey, an optimal approach involves switching between multiple controllers. In heavily congested areas, the controller can operate in a fuel optimization mode, effectively reducing fuel consumption. In polluted urban environments, the controller can focus on emissions optimization, contributing to decreased air pollution. Furthermore, on routes where the vehicle can maintain a steady speed, the controller can operate in a battery life optimization mode, extending the lifespan of the battery and delaying its degradation, which ultimately reduces replacement costs.

Conclusion

This paper presents a multi-objective optimization approach for the EMS in PHEVs, focusing on minimizing energy consumption, mitigating environmental impacts, and reducing battery economy (extending battery life). To achieve this, a parallel model of the PHEV version of the Samand vehicle is developed using empirical data, and optimal component sizing is determined through a genetic algorithm. Subsequently, a fuzzy control strategy is introduced as the control strategy, which is optimized through a genetic algorithm across three scenarios: single objective function, two objective functions, and three objective functions. The optimization aims to reduce energy consumption, emissions, and battery degradation across five different driving cycles (FTP-75, NEDC, Tehran-Long, Tehran-Short, and WLTP-Class3) while accounting for traffic conditions.

The findings indicate that focusing on a single objective function results in an average reduction of 13.5% in battery degradation, although this is accompanied by a 3% increase in fuel consumption. When two objective functions are incorporated, there is an average reduction of 10% in battery degradation, along with increases of 1.9% in fuel consumption and 5.7% in emissions. Lastly, optimizing with three objective functions achieves average reductions of 3.3% in emissions and 4.4% in battery degradation, with only a negligible increase of approximately 0.02% in fuel consumption. This clearly illustrates the superior performance of the optimization strategy when utilizing three objective functions compared to the other scenarios.

For future works, it is recommended to conduct comparative evaluations with other advanced optimization methods to further validate and benchmark the proposed approach. In addition, incorporating detailed cost modeling—including initial component costs, energy consumption, battery replacement, and residual vehicle value—will enhance the comprehensiveness of the analysis. The evaluation of the fuzzy logic controller’s computing performance and real-time execution on embedded vehicle platforms is feasible and can be addressed in future work. Finally, future studies could explore the simultaneous optimization of both system sizing and control strategy, allowing for a more integrated approach and enabling comparisons with the results of the sequential optimization adopted in this research.

Acknowledgements

All figures were created by the authors, except Figs. 1 and 3, as cited in the figure captions.

Author contributions

M.M.: Conceptualization, data curation, formal analysis, investigation, methodology, project administration, resources, software, supervision, validation, visualization, writing-review and editing. E.A.: Conceptualization, data curation, formal analysis, investigation methodology, resources, software, validation, visualization, writing-original draft, writing-review and editing.

Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.

List of symbols

Acronyms

PHEV

Plug-in hybrid electric vehicle

E3

Energy, environment, economy

ICE

Internal combustion engine

IKCO

Iran khodro company

OCV

Open circuit voltage

SOC

State-of-charge

FC

Fuel consumption

CO

Carbon monoxide

HC

Hydrocarbon

NOx

Nitrogen oxide

GA

Genetic algorithm

Eqv

Equivalent

HEV

Hybrid electric vehicle

DP

Dynamic programming

AECMS

Adaptive equivalent consumption minimization strategy

ECMS

Equivalent consumption minimization strategy

WLTP

Worldwide harmonized light vehicles test procedure

FTP

Federal test procedure

NEDC

New European driving cycle

ECM

Equivalent circuit model

NN

Neural network

EMS

Energy management strategy

PNGV

Partnership for a new generation of vehicles

CD-CS

Charge-depleting and charge-sustaining

EM

Electric motor

ESS

Energy storage system

RB

Rule-based

Symbols

Battery aging

Open circuit voltage

Current passing through the circuit

Weighting factor

Ampere-hour throughput

Air density

Internal resistance

ICE scale

Electric motor scale

Module number of battery

grd

Grade

acc. 1

First acceleration time

acc. 2

Second acceleration time

acc. 3

Third acceleration time

,

Constant term

Activation energy

Current rate

Battery temperature

Molar gas constant

dependence parameter

Battery current

Battery capacity

Drag coefficient

Duration of the driving cycle

ICE scale

Electric motor scale

Module number of battery

grd

Grade

acc. 1

First acceleration time

acc. 2

Second acceleration time

acc. 3

Third acceleration time

Weighting factor

SOC

State of charge

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

References

1. Xiao, G; Liu, H; Nabatalizadeh, J. Optimal scheduling and energy management of a multi-energy microgrid with electric vehicles incorporating decision making approach and demand response. Sci. Rep.; 2025; 15, 5075.1:CAS:528:DC%2BB2MXjvVGls7Y%3D [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/39934186][PubMedCentral: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11814307]

2. Tawfik, MI; Ali, A; Asfoor, M. A combined trade-off strategy of battery degradation, charge retention, and driveability for electric vehicles. Sci. Rep.; 2024; 14, 21995.1:CAS:528:DC%2BB2cXitVertLbE [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/39313498][PubMedCentral: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11420351]

3. Aggarwal, S. & Singh, A. K. Electric vehicles the future of transportation sector: a review. Energy Sources Part. Recover. Util. Environ. Eff. 1–21. https://doi.org/10.1080/15567036.2021.1976322 (2021).

4. Chen, Z; Li, SJ; Cai, X; Zhou, N; Cui, J. Online state of health monitoring of lithium-ion battery based on model error spectrum for electric vehicle applications. J. Energy Storage; 2022; 45, 103507.

5. Plötz, P; Funke, SA; Jochem, P; Wietschel, M. CO2 mitigation potential of Plug-in hybrid electric vehicles larger than expected. Sci. Rep.; 2017; 7, 16493.2017NatSR..716493P [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/29184118][PubMedCentral: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5705705]

6. Sarvaiya, S; Ganesh, S; Xu, B. Comparative analysis of hybrid vehicle energy management strategies with optimization of fuel economy and battery life. Energy; 2021; 228, 120604.

7. Recalde, A; Cajo, R; Velasquez, W; Alvarez-Alvarado, MS. Machine learning and optimization in energy management systems for Plug-In hybrid electric vehicles: A comprehensive review. Energies; 2024; 17, 3059.

8. Lü, X et al. Hybrid electric vehicles: A review of energy management strategies based on model predictive control. J. Energy Storage; 2022; 56, 106112.

9. Du, A; Han, Y; Zhu, Z. Review on multi-objective optimization of energy management strategy for hybrid electric vehicle integrated with traffic information. Energy Sources Part. Recover. Util. Environ. Eff.; 2022; 44, pp. 7914-7933.

10. Zhou, L; Yang, D; Zeng, X; Zhang, X; Song, D. Multi-objective real-time energy management for series–parallel hybrid electric vehicles considering battery life. Energy Convers. Manag.; 2023; 290, 117234.

11. Liu, X; Du, J; Ma, J; Liu, G; Xiong, Y. An adaptive co-state design method for PMP-based energy management of plug-in hybrid electric vehicles based on fuzzy logical control. J. Energy Storage; 2024; 102, 114118.

12. Lei, N., Zhang, H. & Wang, Z. Sim-to-real design and development of reinforcement learning-based energy management strategies for fuel cell electric vehicles. (2025). https://doi.org/10.1016/j.apenergy.2025.126030.

13. Zhang, H et al. Integrated thermal and energy management of connected hybrid electric vehicles using deep reinforcement learning. IEEE Trans. Transp. Electrif; 2024; 10, pp. 4594-4603.

14. Li, M; Wang, Y; Yu, P; Sun, Z; Chen, Z. Online adaptive energy management strategy for fuel cell hybrid vehicles based on improved cluster and regression learner. Energy Convers. Manag.; 2023; 292, 117388.

15. Li, M; Yu, P; Wang, Y; Sun, Z; Chen, Z. Topology comparison and sensitivity analysis of fuel cell hybrid systems for electric vehicles. IEEE Trans. Transp. Electrif.; 2023; 9, pp. 5111-5121.

16. Pourbafarani, Z., Montazeri-Gh, M. & Khasheinejad, M. Improvement of PHEV equivalent fuel economy and battery life by applying traffic-based SOC management. IEEE Trans. Transp. Electrif. https://doi.org/10.1109/TTE.2021.3109083 (2021).

17. Hu, J., Zhu, P., Wu, Z. & Tian, J. A real-time multi-objective optimization method in energy efficiency for plug-in hybrid electric vehicles considering dynamic electrochemical characteristics of battery and driving conditions. J. Energy Storage. 84, (2024).

18. Li, M; Wang, L; Wang, Y; Chen, Z. Sizing optimization and energy management strategy for hybrid energy storage system using multiobjective optimization and random forests. IEEE Trans. Power Electron.; 2021; 36, pp. 11421-11430.2021ITPE..3611421L

19. Jia, C; Liu, W; He, H; Chau, KT. Deep reinforcement learning-based energy management strategy for fuel cell buses integrating future road information and cabin comfort control. Energy Convers. Manag.; 2024; 321, 119032.

20. Jia, C et al. Learning-based model predictive energy management for fuel cell hybrid electric bus with health-aware control. Appl. Energy; 2024; 355, 122228.

21. Mahmoodi-k, M; Montazeri, M; Madanipour, V. Simultaneous multi-objective optimization of a PHEV power management system and component sizing in real world traffic condition. Energy; 2021; 233, 121111.

22. Lei, N; Zhang, H; Chen, H; Wang, Z. A comprehensive study of various carbon-free vehicle propulsion systems utilizing ammonia-hydrogen synergy fuel. eTransportation; 2024; 20, 100332.

23. Kim, J et al. Economic nonlinear predictive control for Real-Time optimal energy management of parallel hybrid electric vehicles. IEEE Access.; 2020; 8, pp. 177896-177920.

24. Lei, N et al. Theory-Constrained neural network with modular interpretability for fuel cell vehicle modelling. IEEE Trans. Veh. Technol.; 2025; PP, pp. 1-13.

25. Lei, Z et al. An adaptive equivalent consumption minimization strategy for plug-in hybrid electric vehicles based on traffic information. Energy; 2020; 190, 116409.

26. Hu, X; Zhang, X; Tang, X; Lin, X. Model predictive control of hybrid electric vehicles for fuel economy, emission reductions, and inter-vehicle safety in car-following scenarios. Energy; 2020; 196, 117101.1:CAS:528:DC%2BB3cXjtF2gu74%3D

27. Valenti, G; Pagot, E; De Pascali, L; Biral, F. Battery aging-aware online optimal control: an energy management system for hybrid electric vehicles supported by a bio-inspired velocity prediction. IEEE Access.; 2021; 9, pp. 164394-164416.

28. Montazeri-Gh, M., Fotouhi, A. & Naderpour, A. Driving patterns clustering based on driving feature analysis. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 225, 1301–1317 (2011).

29. Çorapsiz, MR. PV-fed multi-output Buck converter-based renewable energy storage system with extended current control for lifetime extension of Li-ion batteries. Comput. Electr. Eng.; 2024; 120, 109757.

30. Sultan, YA; Eladl, AA; Hassan, MA; Gamel, SA. Enhancing electric vehicle battery lifespan: integrating active balancing and machine learning for precise RUL estimation. Sci. Rep.; 2025; 15, 777. [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/39755722][PubMedCentral: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11700096]

31. Li, Y et al. Evolution of aging mechanisms and performance degradation of lithium-ion battery from moderate to severe capacity loss scenarios. Chem. Eng. J.; 2024; 498, 155588.1:CAS:528:DC%2BB2cXhvFKjtbnE

32. Patrizi, G et al. A review of degradation models and remaining useful life prediction for testing design and predictive maintenance of Lithium-Ion batteries. Sensors; 2024; 24, 3382.1:CAS:528:DC%2BB2cXhtlOmsr3M [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/38894170][PubMedCentral: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11174798]

33. Lei, N; Zhang, H; Wang, H; Wang, Z. An improved co-optimization of component sizing and energy management for hybrid powertrains interacting with high-fidelity model. IEEE Trans. Veh. Technol.; 2023; 72, pp. 15585-15596.

34. Tian, X., Cai, Y., Sun, X. & Zhu, Z. Collaborative optimization of fuel economy and battery life for plug-in hybrid electric buses considering traffic condition. J Energy Storage90, (2024).

35. Montazeri-Gh, M; Alimohammadi, E. Online battery aging calculation in plug-in hybrid electric vehicle considering driving condition. Energy Sources Part. Recover. Util. Environ. Eff.; 2024; 46, pp. 5324-5343.

36. Ibrahim, N. A. et al. Data collection and data management approach for developing a driving cycle: a review. J. Adv. Res. Appl. Sci. Eng. Technol.46, 39–49 (2024).

37. Bishop, JDK; Axon, CJ. Using natural driving experiments and Markov chains to develop realistic driving cycles. Transp. Res. Part. D Transp. Environ.; 2024; 137, 104507.

38. Yang, D; Liu, H; Li, M; Xu, H. Data-driven analysis of battery electric vehicle energy consumption under real-world temperature conditions. J. Energy Storage; 2023; 72, 108590.

39. Montazeri-Gh, M; Pourbafarani, Z; Near-Optimal, SOC. Trajectory for traffic-based adaptive PHEV control strategy. IEEE Trans. Veh. Technol.; 2017; 66, pp. 9753-9760.

40. Dawei, M; Yu, Z; Meilan, Z; Risha, N. Intelligent fuzzy energy management research for a uniaxial parallel hybrid electric vehicle. Comput. Electr. Eng.; 2017; 58, pp. 447-464.