An Overview of Modelling and Energy Management Strategies for Hybrid Electric Vehicles

Abstract

With the world’s energy reserves under strain and the requirements of national carbon emission regulations, the fuel efficiency and environmental friendliness of automobiles are becoming increasingly important. Due to the combination of long cruising range and energy efficiency, hybrid electric vehicles (HEVs) have been adopted as a reliable option for improving fuel economy and reducing emissions. In order to fully exploit the advantages of hybrid electric vehicles, energy management and torque distribution have become the focus of control strategies for HEVs, while also ensuring battery life and meeting requirements for fuel consumption, emissions and driving performance. Therefore, a great deal of research has been carried out on energy management strategies and many approaches have been offered in the literature. This review provides a comprehensive assessment of the literature, highlighting its contributions and making a complete reference for scholars interested in hybrid vehicle development, control, and optimization.

1. Introduction

Because of the fast expansion of contemporary industry in recent years, ownership of gasoline-fueled automobiles has increased rapidly throughout the world, resulting in a slew of environmental pollution and energy scarcity problems [1,2,3]. Currently, nations worldwide are dedicated to advancing and manufacturing new energy vehicles, which include hybrid electric vehicles, plug-in hybrid electric vehicles (PHEV), electric vehicles, and fuel cell vehicles [4,5,6]. Hybrid technology is a novel energy technology with a low entry barrier and promising development prospects, with the benefits of low pollution emissions, low noise, and great fuel economy [7,8]. Owing to the difficulties of storing raw materials and the cost of vehicles, fuel cell vehicles cannot be mass manufactured [9,10]. Electric vehicles are limited by the power density of the battery, the consistency of cell manufacture, and the installation of infrastructure [11,12,13]. So, it will take time to completely replace the market position of fuel automobiles [14].

In this context, by incorporating extra sustainable power sources into the drive train, HEVs have been a focus of study for major vehicle manufacturers. It is seen as a practical solution to current environmental problems in the transition process [15,16]. HEVs have advantages such as improved fuel efficiency, reduced emissions, and a smoother driving experience due to the electric motor’s torque assistance. Additionally, they can operate on both gasoline and electricity, providing drivers with flexibility. On the one hand, the ability of the hybrid system to deliver output to the wheels increases freedom of control. Meanwhile, it may offer the possibility of reducing engine displacement while meeting power requirements [17]. On the other hand, the high-efficiency point of the engine is usually in the low-speed and high-load region, which might reduce the torque reserve of the engine. When the engine operates at the high-efficiency point [18,19], its low-speed constant torque characteristics can effectively compensate for the lack of acceleration performance. However, to fully realize these benefits, it is essential to establish an energy management strategy (EMS) that coordinates power sources and maximizes the use of regenerative braking energy. By doing so, fuel efficiency can be optimized, and emissions can be reduced [20,21]. Numerous studies on various elements of HEVs have been published in the literature so far [22]. Therefore, this work presents a thorough review of the literature, with an emphasis on contributions to hybrid vehicle modelling and energy management. At the same time, some outlooks on future research directions are given.

The main work of this paper is elucidated as follows: First, the emergence of HEVs is investigated, with a focus on the process and advantages of their development. Then, different hybrid vehicle configurations and their detailed modelling methods are listed, depending on different scenarios and features. Afterward, energy management strategies are broadly classified into three categories, namely rule-based energy management strategies, optimization-based energy management strategies, and deep learning-based energy management strategies. Their advantages and disadvantages are then carefully reviewed and evaluated. The purpose is to emphasize these strategies’ novelty and their contribution to satisfying several optimization objectives, including the reduction of fuel consumption and emissions, driving comfort, optimized braking energy regeneration, and improved driving performance of the vehicle. At the end, relevant research gaps within the study domain are discussed.

2. Types and Characteristics of the Powertrains for HEVs

The drive system of a hybrid vehicle usually consists of two or more sources of power energy. In general, the vast majority of hybrid vehicles have an internal combustion engine (ICE) or a fuel cell as the main source of drive energy [23]. The other source of energy, which plays a secondary role, is usually energy storage devices that recover energy, such as batteries, hydraulic pumps, super flywheels, or air compressors [24]. The most common combination of energy sources is the ICE and a battery, which is commonly known as a HEV. Based on the powertrain coupling method, there are three types of HEV powertrains: series configuration, parallel configuration, and series–parallel hybrid configuration [25,26,27,28].

2.1. Series Hybrid Electric Vehicle

The series configuration has a main motor driving the vehicle forward, while the engine is connected to a generator to generate power for the main motor or battery [2]. The ICE and the propulsion wheels cannot be connected mechanically directly in this setup [29]. During the vehicle’s movement, the engine is not directly involved in driving the whole vehicle, but in energy conversion in the form of driving the generator to generate electricity. During the vehicle braking process, the energy recovery function is carried out by the main motor and the braking energy is transferred to the power battery [30,31]. A detailed picture of this HEV is depicted in Figure 1.

The engine shaft in this design is not directly connected to the drive shaft, resulting in a straightforward construction. This allows the engine to operate in a high-efficiency range for extended periods. However, due to the multiple conversions between fuel and motor, the energy is not utilized as effectively as possible [32]. Generally speaking, this powertrain is commonly used in large vehicles, such as miners and buses, and in a few hybrid passenger cars, such as the Toyota Corolla Twin Engine and BMW i3.

2.2. Parallel Hybrid Electric Vehicle

The engine and electric motor can both operate independently or cooperatively to provide traction in a parallel configuration. In this powertrain, the main motor is connected to the drive shaft. Meanwhile, the engine is also connected to the main motor and drive shaft via a mechanical coupling device [33]. While the vehicle is in motion, the power demand is distributed between the engine and the main motor in a particular ratio, allowing the engine to contribute directly to the overall vehicle propulsion. As the vehicle brakes, the main motor facilitates energy recovery [34]. Figure 2 shows a detailed schematic of the HEV in this setup.

Typically, a parallel HEV has the option of being powered solely by the engine, the electric motor, or a combination of both. Compared to the series configuration, the engine used in the parallel HEV system is often larger, while the electric motor is typically smaller and less potent [35]. In comparison to series HEVs, parallel ones are more efficient in terms of energy utilization, allowing for a reasonable distribution of power output between the motor and engine for different operating conditions. At the same time, their control strategy is more complex and difficult to control. Despite the parallel setup, the engine and drive wheels remain mechanically linked, resulting in the engine’s operating point being partially dependent on the power demands [36].

2.3. Series–Parallel Hybrid Electric Vehicle

The hybrid configuration uses a planetary gear mechanism or clutch to couple the engine, the main motor, and the generator. Hence, the vehicle can be driven in a variety of operating modes depending on the control strategy [4]. The advantages of series and parallel configurations are combined in a way that increases the efficiency of energy conversion. In addition, this configuration allows detachment of the engine. However, the layout is more complex and the design costs are higher, which result in higher requirements for the control strategies. It is currently the most popular configuration on the market for achieving optimum power performance and fuel economy [37,38]. The structure is displayed in Figure 3.

To provide a clearer overview,

Table 1. Comparison of the various configurations.

Configuration	References	Advantages	Disadvantages
Series hybrid electric vehicle	[29,30,31,32,39,40]	Simple structure; Optimization is relatively simple	High number of energy conversions; Not energy efficient
Parallel hybrid electric vehicle	[33,34,35,36,41]	High energy efficiency; Rational torque distribution	Complex control strategies; Large control difficulty
Series–parallel hybrid electric vehicle	[37,38,42]	Multiple working modes; High energy efficiency	Complicated arrangement structure; High computational costs

summarizes and compares all the HEV configurations mentioned above for easier visualization. The characteristics of each powertrain are presented in a concise manner, along with a list of their main advantages and disadvantages.

3. Research and Current Status of Energy Management Strategies for HEVs

Control methods can usually be divided into two types. One is the bottom-level control involving the vehicle components, which generally controls each part of the vehicle’s powertrain through the use of feedback control [43,44]. The other is the top-level control, which is responsible for planning and controlling the energy flow to ensure that physical variables such as the state of charge (SOC) are maintained within a more desirable range [45]. Specifically, energy management for HEVs requires a strategy that allows the upper-level controller to determine the amount of energy delivered at each moment, satisfying driveline, powertrain, and other constraints. Energy management strategies can calculate the required driving or braking torque at each moment based on the vehicle’s state, such as the battery SOC, vehicle speed, and the operating mode. Then, it will allocate this torque to power the components and to meet the vehicle’s moving requirements. In fact, a proper energy distribution strategy is able to improve not only the power performance but also the fuel economy of the vehicles. It is shown in Figure 4 how the energy management system acts [46,47,48].

The external control is speed control, which is the role played by the driver in a real moving vehicle and is usually replaced in a simulation model by a driver model [49]. In order to ensure that the actual vehicle speed is close to the reference working speed, the driver model controls the demanded power supplied to the vehicle by adjusting the different throttle and brake pedal openings. The internal control is the vehicle’s energy management system, which allocates the demanded power to the engine and battery via a built-in strategy [50,51].

Contrary to pure electric and fuel vehicles, HEVs have various power sources and driving modes, which complicates their structural layout and increases the complexity of their control variables [52]. HEVs have demonstrated a significant improvement in vehicle fuel economy and emission reduction while still meeting power requirements and maintaining satisfactory vehicle performance and driving comfort. As the technology has advanced, existing energy management strategies are broadly categorized into three groups: rule-based energy management strategies, optimization-based energy management strategies, and learning-based energy management strategies [34,53,54,55]. The main classifications and theoretical distributions are shown in Figure 5.

3.1. Rule-Based Energy Management Strategies

The rule-based energy management control strategy is also known as a logic threshold control strategy. The main idea is to determine the operating state of the powertrain by defining a set of rules for the operation of the vehicle’s powertrain, usually in the form of a flowchart with a table of control parameters [56,57,58]. The two main types of control are deterministic rules and fuzzy rules. Neither method involves direct optimizing or minimizing control [59,60]. The design of rules is often based on heuristic algorithms or engineering experience, and the effectiveness of control is dependent on the strength of the rule design [61].

3.1.1. Deterministic Rule-Based Energy Management Strategies

Deterministic rule-based control determines the operating mode and energy distribution of the vehicle by setting a series of logical judgment rules [62]. In this kind of strategy, rules are determined on the basis of the engine’s fuel economy or emission map. Rule-based energy management strategies are generally executed using a pre-calculated look-up table. Such strategies are currently used in thermostat control methods, power-following control methods, and state machine control methods [63].

The state machine model developed and built by Banvait implemented power distribution by executing predefined control rules or logical thresholds [64]. In this strategy, the maximum power was extracted through the electric motor to drive the vehicle with the rest of the power being provided by the engine. Wang et al. demonstrated a cyber-physical energy optimization management system [65]. Deterministic rule-based energy management strategies allocate power tasks for the engine and electric motor based on the battery’s state of charge (SOC) and the power demanded by the vehicle. To enhance the performance of energy management systems (EMS), an enhanced firework algorithm (EFWA) has been proposed to optimize controller parameters and obtain better parameters more quickly, making it better suited for the complex optimization of EMS. In [66], the rules were extracted from recognized algorithms and their control parameters were optimized offline and corrected online for series–parallel hybrid systems with automatic mechanical transmissions (AMT) to maintain fuel economy and the SOC balance of the battery.

3.1.2. Fuzzy Rule-Based Energy Management Strategies

Fuzzy rule-based control establishes the choice of variables for domain partitioning in advance and builds a library of fuzzy rules [67]. The inputs to the controller are transformed into control outputs for each part of the vehicle’s energy source through two processes of fuzzy inference and defuzzification [68]. The relative simplicity of fuzzy rule controllers enables tweaking and adaptation when required, increasing the degree of control. Because of its non-linear structure, it is even more beneficial in complicated systems including modern powertrains. Fuzzy rule-based control currently comes in a variety of forms, including conventional fuzzy control strategies, adaptive fuzzy control strategies, and predictive fuzzy control strategies [69,70].

Conventional fuzzy control is frequently employed to enhance fuzzy efficiency and, as a result, make the engine operate efficiently. This method is assisted by an electric motor, which forces the ICE to work in a high-efficiency area at all times while remaining within the battery SOC. In [71], a fuzzy controller was created for a HEV with a parallel structure. A set of principles were created in a fuzzy controller to efficiently determine the divide between the two powerplants, i.e., the electric motor and ICE, which referred to the driving instruction, the SOC of the energy store, and the motor speed.

Today, the use of adaptive fuzzy control strategies is increasingly widespread as they have the potential to enhance both fuel economy and emissions. Individual targets can be controlled by adaptive fuzzy controllers by altering the value of the weights given to them. Reference [72] presented an adaptive fuzzy logic-based energy management strategy (AFEMS) to estimate the power delivery between the ultracapacitor charge and the battery pack. Due to the intricate real-time control problem, a fuzzy logic system was used, which is shown in Figure 6. The fundamental goals of this adaptive fuzzy logic controller were to increase system effectiveness, reduce battery current variance, and maintain SOC. In [73], Lin et al. proposed a new adaptive control strategy for driving styles by using particle swarm optimization (PSO) combined with fuzzy expert algorithms. The aim of this strategy was to explore the influence of driving style on the fuel economy of a PHEV.

For energy management, predictive fuzzy controllers utilize information provided by a global positioning system from scheduled transportation trips. Frequently, vehicle speed, vehicle condition, and route location are used as inputs to the predictive controller. The predictive fuzzy controller calculates the optimal torque distribution on the basis of the existing vehicle movement history, as well as speculation on the possible future movements of the vehicle. In [74], a series HEV (SHEV) with batteries capable of supporting the maximum traction power needs was taken into consideration. Fuzzy logic was used to predictably lower the amount of SHEV initiates, strengthening the system performance and component lifespan. An online predictive control strategy named dual-loop online intelligent programming (DOIP) has been proposed for velocity prediction and energy-flow control [75]. In this approach, a deep fuzzy predictor was developed to predict driver-oriented velocity using fuzzy granulation technology. The vehicle performances with different control strategies are summarized in

Table 2. Vehicle performance with different control strategies over WLTP (Data from the source [75]).

Strategy	Initial SOC	Final SOC	Used Fuel Energy (108 J)	Savings (%)
Rule-based	0.8	0.2893	2.2730	-
DP	0.8	0.3339	2.0146	11.37%
DOIP	0.8	0.3093	2.0644	9.18%
Rule-based	0.2	0.2893	3.0951	-
DP	0.2	0.3891	2.6383	14.76%
DOIP	0.2	0.3348	2.7300	11.80%

.

The main benefits of rule-based control methods for energy management include their simplicity and usability, which make it simple to comprehend and accomplish the primary control goals in actual automobiles [76]. Rule-based control strategies are now commonly used in the production vehicle market because of their low computational effort, adaptability, and good reliability [77]. Despite its widespread use, there are still several major issues that need to be addressed in the rules-based approach to HEV control. Typically, the development of such strategies requires a great deal of time and qualified engineers due to the long process of defining and calibrating the rules. However, the driving conditions of vehicles are often highly variable, which also leads to a necessity to redefine the rules for each driving condition and powertrain, so placing high demands on the robustness of the strategies [78,79,80]. At the same time, rule-based strategies always suffer from poor fuel economy compared to the following strategies based on optimization. This is most probably owing to their inability to adjust their control strategy in real-time [81].

3.2. Optimization-Based Energy Management Strategies

An optimization-based EMS is one that uses optimization algorithms to search for and apply optimal or sub-optimal control sequences after establishing the system control objective function and constraints. This type of strategy usually employs known or predicted driving condition information to calculate the actuator settings that minimize the set cost function as the global or local optimum solution [82,83,84,85,86,87]. The core problem is generally expressed as finding the objective function’s minimal value in the feasible domain. Presently, optimization-based energy management strategies consist mainly of global optimization and instantaneous optimization [88,89].

Control strategies based on global optimization generally require an optimized action search under conditions where the global disturbances are known, such as in dynamic programming (DP), genetic algorithms, and game theory methods [90,91,92]. However, due to its computationally intensive and complex preview, this class of algorithms is not usually supported for real-time applications. As such, the results of global optimization strategies might be used as benchmarks for evaluating the merits of other energy management algorithms [93,94,95]. Meanwhile, the strategy based on instantaneous optimization defines a transient cost function at each moment and solves for the optimal amount of control for the vehicle, which is able to achieve the target of a global cost function approximation through iterative and roll optimization [96]. The main methods based on real-time optimization include equivalent consumption minimization strategies (ECMS), robust control, model predictive control (MPC), and Pontryagin’s minimum principle (PMP). The expansion of these techniques is already a hot topic of current research in the field [97,98,99,100].

3.2.1. Equivalent Consumption Minimization Strategies

ECMS is a strategy for optimizing the powertrain control method to minimize the equivalent fuel consumed by the vehicle’s powertrain while achieving a specific driving objective [101,102,103]. For the vehicle system, the internal energy flow can be divided into the following two states: When the battery output power is positive, the motor is in the traction motor state and the motor outputs positive torque outwards. At this point, the mechanical energy provided by the electrical energy consumed by the motor will equivalently replace some of that provided by the engine [104,105,106,107]. When the battery output is negative, the motor is in generator mode and the motor outputs negative torque outwards. The electrical energy obtained from this regenerative energy recovery can replace part of the fuel energy in the future, and this replacement power is also determined by the operating state of the engine at this time [108,109].

Based on this, the basic principle of the ECMS is to allocate part of the consumed energy to the battery so that the consumption or storage of this electrical energy is equivalent to the use or saving of a certain amount of fuel [110,111]. To obtain the control strategy that minimizes the instantaneous equivalent fuel consumption, a cost function for equivalent fuel consumption is defined, and the traversal of each instantaneous state quantity is solved [112]. For HEVs, the energy path of the ECMS is shown in Figure 7.

For the ECMS, the key is to associate electrical energy with the equivalent fuel consumption during the charging and discharging of the battery [113]. The instantaneous fuel consumption can be divided by the source into actual and virtual fuel consumption, the expression of which can be described as:

$${\dot{m}}_{f,eqv}(t)={\dot{m}}_f(t)+{\dot{m}}_{ress}(t)$$

(1)

where ${\dot{m}}_{f,eqv}(t)$ is the instantaneous equivalent fuel consumption, ${\dot{m}}_f(t)$ and ${\dot{m}}_{ress}(t)$ are the instantaneous actual fuel consumption and the instantaneous equivalent fuel consumption, respectively [114]. Meanwhile, ${\dot{m}}_f(t)$ can be formulated as:

$${\dot{m}}_f(t)=\frac{P_{eng}(t)}{{\eta }_{eng}(t)Q_{lhv}}$$

(2)

where Q_lhv is the low calorific value of the fuel, which is the available energy per unit mass of fuel. P_eng represents the power generated when the engine is in operation. Also, ${\dot{m}}_{ress}(t)$ should be calculated as:

$${\dot{m}}_{ress}(t)=\frac{EF}{Q_{lhv}}{P}_{batt}(t)$$

(3)

where EF is the equivalence factor for the oil-to-electric conversion and P_batt(t) is the power generated by the battery. A number of studies have reported changes in ECMS optimization strategies. These include adaptive ECMS and telemetric ECMS, which adjust EF based on past driving data and future predictions [115,116,117].

In [118], an adaptive EMS based on ECMS was proposed, incorporating real-time traffic information such as average speed, average acceleration, and the standard deviations of speed for different road sections. Markov speed prediction models were then established to predict velocity and applied to the energy management of a PHEB. The adoption of adaptive ECMS (AECMS) overcame the limitations of fixed ECMS, which cannot change in real time. Finally, the method was evaluated using three real road sections, and the fuel consumption rates were notably reduced when compared to traditional ECMS, as shown in

Table 3. Comparison of the fuel economy for three road segments (Data from the source [118]).

	ECMS			Adaptive ECMS
Type	1	2	3	1	2	3
Fuel (L/100 km)	10.56	9.39	8.95	9.42	8.66	8.52
∆Fuel (%)				−10.76	−7.79	−4.78

.

Tian et al. improved the fuel economy of HEVs through driving style recognition in synergy with ECMS [119]. To accurately identify the driving style of the driver in real-time, a hybrid recognition algorithm based on feature samples was presented. After the successful identification of the driving style level, the obtained driving style level and the correction function associated with SOC are exploited to adjust the EF and establish an adaptive ECMS strategy. The framework was divided into two parts, which is shown in Figure 8.

Reference [120] developed an adaptive EMS for PHEB by using a clustering algorithm. Road types were classified and the corresponding categories were assigned to actual roads. Using a trained neural network model, the different road categories were combined to optimize the equivalent fuel consumption coefficient in the ECMS. This was achieved by calculating and planning the SOC reference trajectory. The torque distribution of the strategy under WLTC and UDDS conditions can be seen in Figure 9. The simulation results showed that the fuel economy was improved while guaranteeing a reduction in computational effort. The approach can be practically applied in specific urban conditions provided that sufficient road information is collected.

For HEVs with dual-motor powertrains, wang et al. propose an EMS that takes into account the mode transition constraints [121]. This EMS could balance the fuel economy of a hybrid vehicle with the mode-switching frequency of a dual motor. A multi-criterion cost function J_EMS-MTC was established as:

$$\begin{array}{cc}\hfill J_{over}& =J_{eco}+J_{com}+J_t\hfill \\ & ={\displaystyle {\int }_{t_0}^{t_f}\left[{\dot{m}}_f\left(x\left(t\right),u\left(t\right),t\right)+{\dot{m}}_{ress}\left(x\left(t\right),u\left(t\right),t\right)\right]} dt+\alpha \left(\delta v+\overline{\Delta v^2}\right)+\beta e^{-\frac{1}{1-\left|\frac{t-t_l}{t_e}\right|}}\hfill \end{array}$$

(4)

where t₀ and t_f are the initial time and the final time. J_eco, J_com, and J_t represent the cost of fuel economy, driving comfort, and mode transitions, respectively. t_e and β represent the effect time and amplitude of the penalty function. Usually, the extra penalty function can be restricted by adjusting these two parameters. t_l is the moment when the latest change happened.

Experiments and tests have shown that this adaptive ECMS could reduce mode switching by more than 60% and achieve a trade-off between mode switching frequency and fuel economy. At the cost of a slight increase in fuel consumption, its practical application potential was demonstrated. Similar observations were studied by Liu et al. [122] and Tang et al. [123].

ECMS is a mathematical model and optimization algorithm that transforms the control strategy of a vehicle powertrain into a mathematical optimization problem in order to minimize the objective cost function and obtain the optimal control sequence [124]. With the development of hybrid technology in recent years, ECMS is gradually being used increasingly in HEVs. In global terms, the algorithm’s fuel economy optimization results are closer to those of the global optimum, but compared to the global optimum control, the algorithm does not require prior knowledge of the full operating conditions, greatly reducing the amount of computation required to calculate the optimum power distribution and making the application of ECMS to real vehicles more possible [125,126,127].

3.2.2. Pontryagin’s Minimum Principle

The PMP specifies that the optimal solution to a global optimization problem has to fulfill optimality conditions, which are related to the transient minimal value of the Hamiltonian function [128,129,130,131]. Assuming that the trajectory calculated through PMP is deterministic and satisfies the corresponding constraints and boundary conditions, the optimal trajectory is usually considered to be the global optimal one [132,133]. Thus, the Hamiltonian function can be described:

$$H\left(x\left(t\right),u\left(t\right),t\right)={\dot{m}}_f\left(x\left(t\right),u\left(t\right),t\right)+\lambda \left(t\right)f\left(x\left(t\right),u\left(t\right),t\right)$$

(5)

where λ(t) denotes the co-state. The state and co-state of the system must satisfy the following conditions:

$$\{\begin{array}{l}\dot{x}\left(t\right)=\frac{\partial H}{\partial \lambda }=f\left(x\left(t\right),u\left(t\right),t\right)\\ \dot{\lambda }\left(t\right)=-\frac{\partial H}{\partial x}=-\lambda \left(t\right)\frac{\partial f}{\partial x}\end{array}$$

(6)

On the basis of PMP, Onori adopted an adaptive supervision controller to optimize the online energy management of a PHEV [134]. The suggested algorithm depended on the adaptation of the control parameter from the SOC input and incorporates minimum driving information. This new method operated in a distance-based domain and was equipped with rules. The purpose is to prevent the actual SOC from deviating from the reference linear SOC profile, by appropriately resetting the common state.

In [135], an optimal EMS built on the approximate PMP algorithm was developed for parallel plug-in hybrid electric vehicles (HEVs). The authors were inspired to use a novel piecewise linear approximation strategy, which specified the turning point of the engine fuel rate for Hamiltonian optimization. The optimization process using the A-PMP strategy is presented in the flow diagram shown in Figure 10, and the results are summarized in

Table 4. Optimization results comparison (Data from the source [135]).

Configuration	AE-CS	A-PMP	PMP
Fuel consumption (L/100 km)	1.1333	1.0577	1.0618
Final SOC	0.3038	0.3043	0.3050
Corrected fuel consumption (L/100 km)	1.1333	1.0544	1.0538
Corrected final SOC	0.3038	0.3038	0.3038
Fuel saving rate (%)	0	6.96	7.01
Time step (s)	0.1	0.1	0.1
Process time for the whole simulation	2 min	4 min	6 h
Real time capability	Yes	Yes	Hardly

.

Chen et al. presented an energy management approach for power-split PHEVs. A series of quadratic equations were formulated to approximately calculate the fuel rate of the vehicle by analyzing the PHEV powertrain, with the battery current as an input. PMP was introduced to find the battery current command from the solution of the Hamiltonian function [43].

Strategies based on PMP optimize the vehicle state and simplify the whole vehicle control strategy under vehicle braking and stopping conditions. By defining the instantaneous cost function at each moment, the instantaneous optimal control volume for the vehicle is solved and the objective of approximate optimality of the global cost function is achieved.

3.2.3. Model Predictive Control Strategy

Model predictive control (MPC), used to be known as rolling time domain control, is a powerful theoretical tool for solving non-linear strongly constrained control problems [136,137,138,139,140,141]. This method keeps the computational effort within a feasible range within a predefined finite moving sight distance. It also improves control accuracy and performance through reasonable prediction of future work disturbances. MPC has now been widely studied and applied in the field of control, especially in the control of motors [142,143]. The method works by rapidly calculating the optimal control of the forecast level and applying only the first element. The forecast horizon is then shifted to the future in the subsequent time step [144].

Machacek proposed a model predictive controller for a PHEB with two electric motors that were online-capable. The goal was to reduce the fuel consumption while performing an anticipated driving objective [145]. The proposed multi-level controller structure is indicated in Figure 11. This method integrated a static Hamiltonian function solution with a convex optimization problem while accounting for dynamic states. For a typical driving cycle of 30 min, it took around 3 s to solve the MPC optimization. Meanwhile, the driver-behavior-aware modified stochastic MPC was proposed for EMS in PHEBs [146]. The modified stochastic MPC defeats the limitations of the traditional rolling optimization approach used in MPC.

In [147], Zhang suggested an approach based on MPC that possessed high computational efficiency to obtain the optimal torque distribution and gear shift timing. Figure 12 illustrates the overall schematic of the EMS. As a result of this, it is possible to find the roughly global optimal solution with a seemingly reduced processing overhead, indicating a tremendous potential for real-time applications.

3.2.4. Dynamic Programming

DP is a class of algorithms for solving optimization problems. The main step is to break the original problem down into several smaller problems, solve each one recursively, and then combine the answers to all of the smaller questions to arrive at the original problem’s solution. The algorithm is mainly applied to problems with overlapping sub-problems and optimal substructures [91,148,149,150,151]. DP has the advantage of being effective in avoiding double counting and solving large-scale problems. However, it requires a large amount of time and space to compute state variables and state transfer equations. Overall, the results of DP are often used as an optimal benchmark for other controllers, or as a basis for developing and improving other sub-optimal controllers [152,153].

In [154], an effort was made to develop an energy-efficient supervisory control method for the HEV to improve fuel economy and decrease emissions of exhaust gases. In order to achieve efficient power distribution, a global solution was obtained by means of deterministic DP. Similarly, Li et al. applied a controller based on action-dependent heuristic dynamic planning (ADHDP) to acquire ecological speed profiles and implement active distance control under normal driving conditions [155]. The ADHDP was able to adjust internal parameters online, thereby enabling the handling of systems with perturbations. Power distribution is achieved through ADHDP by enumerating the design shift commands. In [156], Zhu et al. provided benchmark results on how to balance conflicting objectives corresponding to identification and system efficiency through the DP strategy. This method monitored battery parameters and identified vehicle status to ensure battery safety and efficient operation of the HEV.

For a given driving condition, DP can find the globally optimal EMS for a hybrid powertrain and calculate the optimal control variable results. Therefore, DP is often used in hybrid powertrain energy management analysis to obtain optimal fuel economy results and thus to analyze more rational power allocation strategies and power component behavior. At the same time, the hybrid powertrain energy management problem is typically a non-linear multi-disturbance control problem and is usually expressed as a multi-constraint non-linear optimization problem, which is then solved by DP to obtain the optimum fuel economy performance.

3.3. Learning Based Energy Management Strategies

With the development of artificial intelligence, energy management problems are becoming increasingly integrated with computer technology [157,158,159]. Among them, a learning-based EMS is a kind of energy management strategy with highly adaptive learning capability [160,161]. It is well suited to the control of highly non-linear systems due to its good adaptability, robustness, and other characteristics, and has also gained the attention of many industries in recent years [162,163,164,165]. As for HEVs, learning-based EMS is mostly used for optimizing rule-based control, predicting vehicle states, and learning optimal control behavior [166,167,168].

In [169], Wu et al. introduced an EMS for a series–parallel PHEV that utilizes deep deterministic policy gradients. This algorithm is an actor-critic, model-free reinforcement learning approach that can determine the optimal energy distribution for a vehicle over continuous spaces. The authors used traffic-simulation-generated travel cycles to train and evaluate the intelligence and performed flexible power allocation to the PHEV. Wang et al. integrated computer vision and deep reinforcement learning to enhance the financial efficiency of HEVs [170]. The approach was able to learn the optimal control strategy autonomously from the visual input. State-of-the-art convolutional neural-network-based target inspection methods are used to extract available visual information from the camera. The detected visual information was taken as state input to output an EMS. In [171], a study was presented by Xu et al. for pattern recognition. The 2-D visualization of training data was achieved by the t-distributed stochastic neighbor embedding algorithm.

Table 5. Vehicle performance with different control strategies over WLTP.

Strategy	References	Advantages	Disadvantages
Rule-based	[56,61,64,172,173]	Low technical difficulty of the method; low online calculation volume; wide industrial application.	Difficult to ensure charge maintenance; requires extensive tuning; poor robustness.
ECMS, PMP	[105,116,132,174,175,176,177,178,179]	Little calculation; no need for full working conditions information; good fuel economy.	No guarantee of global optimality; high impact of equivalence factors
MPC	[137,144,180,181]	Combining real-time and optimality; a wide range of applications.	Computationally intensive; over-simplified model
DP	[149,155,182,183,184]	Obtains the global optimal solution; performs directly multi-objective optimization.	Requires a high amount of computational power; no real-time optimization possible
Learning-based	[163,185,186,187,188]	Excellent adaptability and robustness; suitable for high non-linearity.	Complex calculations and low maturity.

provides a comprehensive overview and comparison of various EMS used in HEVs. The table summarizes the features of each EMS topology in a clear and concise manner. The EMS topologies covered in the table include rule-based, optimization-based, and learning-based strategies. The advantages and disadvantages of each strategy are also listed to help readers make informed decisions based on their needs and preferences. The table provides valuable information for researchers and engineers working in the field of HEVs, as it offers a quick reference guide to help them choose the most appropriate EMS for their specific application.

4. Future Challenges

The application of EMS for hybrid vehicles in real vehicles is characterized by a strong systemic nature, wide synergy, and high complexity. At present, most EMS remain at the level of theoretical research and have not been applied in real vehicles. This is due to the fact that energy management requires not only innovation in algorithm principles but also multi-dimensional engineering issues such as access to multi-source information, prediction of future driving conditions, constraints on control objectives, functions supported by the control platform and software architecture, chip computing power, and communication mechanisms.

4.1. Multi-Source Information Acquisition and Processing

Traffic information is highly time-variant, random, and uncertain. Moreover, the information gathered from various sensing devices in HEVs is often unstructured, irregular, and unstandardized. Hence, it is a significant challenge to integrate information from multiple sources, filter it, and fuse it to meet the computing platform’s information format requirements. Additionally, the energy management of HEVs requires different decision and control platforms, such as human–vehicle–road–cloud, to operate together seamlessly, which requires effective communication and coordination among them. Therefore, the development of an efficient and robust system that can handle such complex tasks is crucial for the successful implementation of energy management in HEVs. To address these challenges, researchers have proposed various approaches, such as data fusion, machine learning, and cloud computing, which can help integrate and analyze the data from different sources to make effective energy management decisions. Ensuring real-time interactions between platforms with low latency and high reliability is crucial. Additionally, it is essential to establish effective communication mechanisms among various heterogeneous platforms. Therefore, the accurate acquisition and efficient processing of information is a prominent prerequisite for the efficient use of energy.

4.2. Power Demand Forecasting for Different Airspace

The accuracy of the predicted working conditions is critical for determining the performance of HEVs. However, predicting such conditions is challenging due to their dynamic and uncertain nature, which includes factors such as the state of traffic signals, traffic flow, and road surface conditions, all of which are subject to change. Therefore, forecasting must consider the impact of complex traffic scenarios in future spatial and temporal domains on energy management, as well as the marginal benefits of such forecasts. Achieving accurate prediction information is a demanding task that requires careful consideration of multiple factors, including the cost of collecting data from various sources and the computational resources required to process this data, all while ensuring the accuracy and real-time performance of the forecast results.

4.3. Vehicle Control Capability and Constraints

Energy management control objectives include the engine, motor, battery, clutch, and other physical objects. It is an important prerequisite for the energy management of hybrid vehicles to ensure that the vehicle is safe to drive. A stalled or deadlocked solution process can directly affect the instability of the driving process. Consequently, functional safety, expected functional safety, and information security are of great importance. The design of the electrical and electronic control architecture plays a crucial role in determining the computational real-time and reliability of the energy management system. Similarly, the software architecture is equally important as it determines whether the energy management strategy can be continuously upgraded online. A well-designed architecture is essential for achieving high efficiency and robustness of the energy management system.

5. Conclusions

Due to the good fuel economy of hybrid vehicles and the versatility of control strategies, hybrid technology is one of the powerful measures needed to achieve peak carbon and carbon neutrality from now to the long term. Hence, extensive attention has been paid to HEVs from both academic and industrial researchers. This paper provides a comprehensive review of various aspects related to HEVs, with a specific focus on their modelling, power structure, and EMS. The aim is to analyze and present the advantages and disadvantages of different EMS categories in HEVs.

In this paper, we investigate three different categories of EMS in-depth and summarize the findings. We discuss and compare the control structure, innovation, and application environment of each strategy in detail. To illustrate the effectiveness of these strategies, we select the results of several papers that have optimized different objectives such as fuel economy, driving comfort, and battery power maintenance. The modelling of HEVs includes the development of mathematical models that simulate the behavior of different components, such as the engine, electric motor, and battery, under various operating conditions. The power structure of HEVs includes the design and integration of these components, taking into account their individual characteristics and constraints. The EMS of HEVs involves the control and coordination of the power sources, energy storage, and power distribution systems to achieve optimal performance and efficiency. The three categories of EMS we investigate in this paper are rule-based EMS, optimization-based EMS, and artificial intelligence-based EMS. Rule-based EMS utilizes predefined rules to control the operation of the power sources and energy storage system. Optimization-based EMS employs mathematical optimization techniques to determine the optimal power distribution strategy based on predefined objectives and constraints. Artificial intelligence-based EMS uses machine learning algorithms to learn and adapt to the driving conditions and optimize the power distribution strategy in real time. By analyzing and comparing the different EMS categories, we aim to provide a comprehensive understanding of their advantages and disadvantages. Furthermore, by presenting the results achieved in previous studies, we demonstrate the effectiveness of different EMS categories in achieving different objectives. Overall, this paper provides valuable insights for researchers, engineers, and policymakers involved in the development and implementation of HEVs.

Although many strategies, including ECMS, MPC, and rule-based strategies, have been extensively researched and applied, there are still a number of gaps in the current research on control strategies of HEVs. Future research directions will also be more and more closely integrated with computer technology, which will break through previous limitations and further realize the optimization effect and real-time of EMS.