Machine Learning and Optimization in Energy Management Systems for Plug-In Hybrid Electric Vehicles: A Comprehensive Review

Abstract

This paper provides a comprehensive review of machine learning strategies and optimization formulations employed in energy management systems (EMS) tailored for plug-in hybrid electric vehicles (PHEVs). EMS stands as a pivotal component facilitating optimized power distribution, predictive and adaptive control strategies, component health monitoring, and energy harvesting, thereby enabling the maximal exploitation of resources through optimal operation. Recent advancements have introduced innovative solutions such as Model Predictive Control (MPC), machine learning-based techniques, real-time optimization algorithms, hybrid optimization approaches, and the integration of fuzzy logic with neural networks, significantly enhancing the efficiency and performance of EMS. Additionally, multi-objective optimization, stochastic and robust optimization methods, and emerging quantum computing approaches are pushing the boundaries of EMS capabilities. Remarkable advancements have been made in data-driven modeling, decision-making, and real-time adjustments, propelling machine learning and optimization to the forefront of enhanced control systems for vehicular applications. However, despite these strides, there remain unexplored research avenues and challenges awaiting investigation. This review synthesizes existing knowledge, identifies gaps, and underscores the importance of continued inquiry to address unanswered research questions, thereby propelling the field toward further advancements in PHEV EMS design and implementation.

1. Introduction

Investigations for more sustainable and efficient transportation solutions have stimulated the development of plug-in hybrid electric vehicles (PHEVs) as a promising alternative to traditional internal combustion engine vehicles. Typically, PHEVs integrate both electric and combustion engine powertrains, offering the flexibility to operate in electric-only mode, hybrid mode (electric plus combustion), or standalone combustion engine. This hybridization enables reduction in fuel consumption, greenhouse gas emissions, and dependency on fossil fuel while extending the driving range compared to pure electric vehicles [1].

Central to the optimal utilization of the dual power sources in PHEVs is the Energy Management System (EMS). The EMS is responsible for coordinating the power and energy distribution between the internal combustion engine and battery feeding the traction system mainly containing an electric motor driven by a converter [2]. The aim of the EMS is to achieve an optimal balance between efficiency, performance, and emissions, considering the environmental uncertainties of real driving. By optimally controlling the flow of energy based on driving conditions, user preferences, and system constraints, the EMS plays a crucial role in improving the overall efficiency and driving experience of PHEVs.

Designing an effective EMS for PHEVs presents a multifaceted optimization problem. The inherent complexity arises from the dynamic nature of driving and environmental conditions, uncertainties in traffic patterns, and the variability of energy demand [3,4,5]. Moreover, the integration of multiple component systems composed of various power sources and energy storage systems introduces additional challenges related to powertrain dynamics, component interactions, and thermal management.

Historically, early EMS designs for PHEVs primarily relied on rule-based control strategies, which prescribed fixed operating modes based on predefined rules and thresholds that depend mainly on speed, driving time, and battery’s state-of-charge (SOC) [6]. While effective to a certain extent, these strategies often lacked adaptability and struggled to fully exploit the potential benefits of hybridization.

In recent years, there has been a shift in paradigm towards data-driven and optimization-based approaches sustained by advancements in machine learning (ML) and computational optimization techniques [7,8]. These approaches leverage historical driving data, real-time sensor measurements, and predictive models to dynamically optimize energy flows, adapt to changing driving conditions, and maximize overall system efficiency [9].

By harnessing the power of machine learning algorithms and optimization frameworks, modern EMS designs for PHEVs aim to achieve higher levels of performance, responsiveness, and energy efficiency. However, realizing these objectives requires overcoming various technical and practical challenges including model complexity, computational requirements, adaptability and robustness to uncertainties, and real-system validation. These challenges have also been explored to approximate solutions to real applications [10].

In the subsequent sections of this review, we delve into the state-of-the-art machine learning and optimization techniques employed in EMS for PHEVs, examining their strengths, limitations, and potential avenues for future research and development. The paper is organized as follows: Section 2 provides an overview of PHEV configurations. Then, Section 3 expands on the concept of EMS, its importance, role, and recent advances. Section 4 details Machine Learning strategies for PHEVs EMS, while Section 5 deepens on the optimization formulations for EMS design. Section 6 describes the challenges and future directions in EMS research. Finally, Section 7 concludes the paper.

2. Plug-In Hybrid Electric Vehicles (PHEVs) Overview

Plug-In Hybrid Electric Vehicles (PHEVs) are a type of hybrid vehicle that combines an internal combustion engine (ICE) with an electric motor (EM) and a battery. The PHEV configuration allows for various modes of operation, enabling the vehicle to run on electricity alone, the internal combustion engine alone, or a combination of both [11].

On the other hand, the PHEVs have the capability to recharge their batteries directly from the utility grid and are equipped with larger battery capacities. Furthermore, they can utilize charge depletion (CD) mode, allowing them to run either purely on electric power or in a blended mode where the electric motor is prioritized over the internal combustion engine (ICE) [12]. Figure 1 depicts the main architectures for a series PHEV and a parallel PHEV. The terms “series” and “parallel” indicate whether the ICE is used solely to charge the battery or to provide traction directly to the vehicle, respectively. Each component of the PHEVs is described below according to the architectures presented for PHEVs:

• Internal Combustion Engine (ICE): The vehicle is equipped with a traditional internal combustion engine, which runs on gasoline or another fuel. The engine is responsible for providing power to the vehicle and, in some cases, recharging the battery [13].
• Electric Motor/Generator: PHEVs have an electric motor that can propel the vehicle using electricity stored in the battery. Additionally, the motor can act as a generator during regenerative braking or when the internal combustion engine is running to generate electricity and recharge the battery [14].
• Transmission System: A PHEV features a unique transmission system that allows power to be split and distributed between the internal combustion engine, electric motor, and wheels. This system enables different operating modes, such as series and parallel hybrid modes [15].
• Battery Pack: PHEVs have a high-voltage battery pack that stores electrical energy. This battery is rechargeable, typically through an external power source such as a wall outlet or charging station [16].
• Power Split Device (PSD): The power split device is a key component that allows the distribution of power between the internal combustion engine and the electric motor. It consists of a planetary gear set that can adjust the power split ratio, enabling efficient power delivery to the wheels [17].
• Power Electronics: Power electronics components, including an inverter, are essential for converting the direct current (DC) stored in the high-voltage battery to alternating current (AC). This provides three-phase power to the electric motor [18].
• Onboard Charger: PHEVs are equipped with a charging system that allows the high-voltage battery to be charged from an external power source. Charging can occur through a standard electrical outlet (Level 1 charging), a dedicated charging station (Level 2 charging), or, in some cases, through fast charging stations (Level 3 charging) [19].
• Energy Management System (EMS): The EMS plays a crucial role in controlling and optimizing the power flow between the internal combustion engine and the electric motor. It determines when to use electric power, when to rely on the internal combustion engine, and when to switch between different modes to maximize efficiency and performance [20].

2.1. Series PHEV Configuration

The transmission of the PHEV series consists of the ICE, Energy Storage System (ESS), and two electric machines, where one is the motor and the other is the generator. The electric motor is directly connected to the transmission system as shown in Figure 1a. The engine is coupled to the generator to produce electrical energy, which can be stored in the ESS or directed to the electric motor to propel the vehicle. The electric motor receives energy from both the battery and the generator. Thanks to the decoupling between the engine and the wheels in this architecture, the engine can operate in its optimal efficiency range [21]. In the series configuration of a PHEV, an additional generator and a more powerful battery pack are required compared to the parallel configuration. This increases both the weight and the cost of the vehicle. Additionally, greater energy losses occur due to the multiple conversion processes involved in the transmission. On the other hand, the engine can be smaller due to its decoupling from the transmission system. Therefore, series PHEVs are suitable for driving conditions with frequent stops and starts, such as delivery vehicles and public transportation [22].

2.2. Parallel PHEV Configuration

In this configuration, both the internal combustion engine (ICE) and the electric motor are directly connected to the transmission system with a fixed speed ratio, providing the necessary torque to the wheels. According to the energy management strategy, the ICE and the electric motor can propel the vehicle either individually or together. This makes the parallel architecture more suitable for highway driving than for urban driving. This architecture has several advantages compared to the series one. A parallel PHEV experiences fewer losses in transmission. Additionally, the electric motor can be smaller since it is not designed to propel the vehicle throughout the entire trip [21]. A parallel PHEV is also more cost-effective because it requires only one electric machine to function as both a motor and a generator. However, the direct mechanical connection between the motor and the transmission system means that the motor cannot always operate in its optimal region [23]. Furthermore, the design of the EMS control strategy in a parallel PHEV is more complex.

3. Energy Management Systems (EMS) in PHEVs

The Energy Management System (EMS) of PHEVs encompasses a multi-system assembly of hardware and software components vital for managing optimal energy utilization. Central to this system are sensors and data acquisition modules responsible for monitoring vehicle parameters such as vehicle speed, battery State-of-Charge (SoC), engine load, and environmental conditions. There sensors provide real-time data inputs that are essential for EMS decision making. Coupled with complex control algorithms, EMS processes the sensor data to make informed decisions regarding power distribution and system operation. Their control algorithms, ranging from model-based to machine learning-based approaches, serve as the brain of the EMS, facilitating dynamic adjustments to powertrain operation based on driving conditions and user preferences. Actuators and powertrain components constitute another integral aspect of EMS, acting upon the control commands generated by the algorithm to regulate the operation of the ICE, electric motor, transmission, and Energía storage system (ESS). Furthermore, EMS relies on communication interfaces to seamlessly interact with other vehicle subsystems, enabling data exchange and coordination for optimized performance. These components collectively form the foundation of EMS, enabling efficient energy management and improving the overall performance of PHEVs. The EMS for PHEVs is practically a cyber-physical system given the integration of cyber- and specialized hardware and software.

3.1. Importance of Energy Management Systems

The EMS plays a pivotal role in PHEVs in optimizing energy utilization and enhancing vehicle performance. Through dynamic adjustments to power distribution, EMS can optimize efficiency considering current operating conditions based on real-time data and driving conditions. This optimization leads to a reduction in fuel consumption and emissions, contributing to environmental sustainability and economic savings. EMS enhances vehicle performance by fine-tuning power delivery, torque distribution, and acceleration characteristics to meet driver demands and ensure a smooth driving experience. Nevertheless, EMS is instrumental in protecting powertrain components from excessive stress and wear, thereby extending their operational lifespan, and reducing maintenance costs. Its adaptability and flexibility enable optimal performance across diverse driving scenarios, ranging from city commuting to highway cruising, while also accommodating variations in driver behavior and preferences.

The EMS should prioritize efficiency optimization, leveraging predictive algorithms and real-time sensor data to minimize fuel consumption, reduce emissions, and maximize system efficiency. The optimization extends to power and energy distribution within the hybrid powertrain, ensuring seamless transitions between power sources and modes of operation to minimize energy losses. EMS should also exhibit robustness and reliability. Robustness extends to fault detection and diagnosis capabilities, enabling the system to detect and mitigate anomalies in real-time to prevent system failures and ensure vehicle safety. EMS also supports interoperability and scalability, allowing for seamless integration with other vehicle subsystems and facilitating upgrades and expansions.

Integrating fault detection and diagnosis in EMS for PHEVs involves several steps and methodologies to ensure seamless operation. Integrations require data collection and preprocessing, feature selection and extraction of parameters, ML model training, real-time fault detection, diagnosis and prognostics, integration with EMS and continuous improvement. Real-time fault detection includes online monitoring, anomaly detection, and decision-making to trigger alerts and initiate predefined responses to mitigate the issues. By developing adaptive algorithms that can learn from new patterns, fault detection capabilities are improved, thus, improving the system’s reliability and enhancing safety for the user. An early alert base could potentially improve predictive maintenance to calculate the remaining useful life of components, allowing for timely maintenance before a fault occurs.

3.2. Key Challenges in EMS for PHEVs

The EMS for PHEVs dynamically allocates power between the ICE and energy storage systems based on factors such as vehicle speed, load, battery SoC, and driver input. EMS also implements predictive and adaptive control strategies, leveraging predictive models and real-time data to anticipate driving conditions and adjust powertrain operation in an anticipatory manner. Key indicators and parameters used to quantify performance include fuel economy (expressed in miles per gallon equivalent, MPG-e), electric range (measured in miles or kilometers), emissions (in grams per kilometer), and overall system efficiency (in percentage). Additionally, EMS monitors and manages component health, detecting anomalies and implementing preventive measures to ensure system reliability and extended lifespan. Furthermore, EMS facilitates energy harvesting through regenerative braking, capturing, and storing kinetic energy during deceleration for later use, which enhances efficiency and performance.

The design and implementation of EMS for PHEVs presents several complex challenges. One significant challenge lies in the complexity and integration of components that encompass intricate interactions and dependencies between diverse hardware and software elements. Besides, EMS faces challenges in modeling and prediction because accurate predictive models and algorithms are essential for forecasting future driving conditions and optimizing powertrain operation. Furthermore, ensuring real-time performance and computational efficiency is critical, as EMS must execute complex control algorithms and optimization strategies within stringent time constraints while meeting efficiency requirements.

The integration of real-time sensor data into machine learning models for EMS in PHEVs faces several primary challenges. First, the complexity of the hybrid powertrain system, as highlighted in [24], presents a significant obstacle due to its highly non-linear nature. Second, the need to output both continuous and discrete variables simultaneously adds another layer of complexity to the integration process. In addition, uncertainties encountered in model uncertainty, environmental uncertainty, and adversarial attacks [25] can impact the performance of machine learning models utilizing real-time sensor data. Lastly, the degradation of energy storage systems over time [26] poses a challenge in ensuring the accuracy and reliability of the data used in these models. Addressing these challenges is crucial for enhancing the efficiency and effectiveness of EMS in PHEVs. Several proposals have been put forward in the latest research to address challenges like latency, accuracy, and computational burden in machine learning techniques for EMS in PHEVs. One approach involves utilizing reinforcement learning (RL) algorithms to generate policies offline from historical datasets, reducing sample inefficiency, unsafe exploration, and simulation-to-real gap [27]. Another proposal suggests utilization of the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm for integrating co-recognition for driving style and traffic conditions, thus, enhancing the generalization ability and self-learning efficiency in EMS [28]. It has been shown that TD3-based EMS outperforms DDQN and DDPG in terms of convergence speed and energy-saving performance. Additionally, hybrid algorithms combining data-driven and simulation-based RL methods have been recommended to learn from both real logging data and simulated models, achieving near-optimal policies with reduced fuel consumption in PHEVs [29].

3.3. Recent Advances and Formulations of EMS for PHEVs

Energy and power are carefully determined in an EMS formulation for PHEVs. The problem can be addressed as an energy management or power management control problem [30,31]. There are plenty of algorithms and heuristics to solve this problem. These algorithms have included deterministic rule-based or methods based on fuzzy logic [6,32], equivalent consumption minimization strategy (ECMS) [33], Pontryagin’s maximum (or minimum) principle (PMP) [34], and dynamic programming [35]. A Rule-Based control strategy uses heuristic “if-then” procedures, relying on human intuition or models without drive cycle pre-information. They require low computation, common in vehicles like the Honda Insight and Toyota Prius [36]. The use of convex optimization has gained attention due to its relatively faster and more reliable way of solving optimization problems. However, there are some drawbacks, i.e., it is challenging to reach an accurate convex model due to the uncertainties of approximations. Also, there are discrete parameters (e.g., clutch or gear state) so that, even if a model has been obtained, the optimization problem is expressed as a mixed-integer set, which is known to be an NP-hard problem. The approach to these issues has been to develop complex methods composed of two or more algorithms, e.g., dividing the problem into two or more stages whose complexity can be tackled by the solving strength of two or more heuristics. Recently, in addition to the methods mentioned above, machine learning (ML) and artificial intelligence (AI) have gained relevance due to the vertiginous development of neural networks experienced lately. AI techniques show high potential for designing Energy Management Systems (EMS) for Hybrid Electric Vehicles (HEVs). In [37], an EMS using deep learning with Recurrent Neural Networks (RNNs) is presented to minimize CO2 emissions. This methodology, tested virtually, achieved fuel economy improvements of 4–5% over traditional Rule-Based strategies. Reinforcement learning (RL), derived from ML, and rule-based methods have continuously been key to EMS formulations for PHEVs. Algorithms such as Q-learning, and deep deterministic policy gradient (DDPG) have been used for predicting purposes, training controllers for optimal power distribution, and state prediction, which leads to the design of an EMS. Besides, Mixed-Integer Programming and Gaussian mixture have been utilized for classifying driving conditions and synthesizing strategies. In general, meta-heuristic algorithms are used in EMS formulations. Table 1 presents a summary of methods and algorithms found in the last 5 years.

It is noted from Table 1 that recent approaches to the EMS problem require a combination of several methods and algorithms such that every problem’ stage is solved effectively by an appropriately chosen method. Besides, utilization of convex formulations or solving problems with convex optimization have been explored although rarely used for predictive purposes. Some applications are not closely related to solving or designing an EMS problem for PHEVs, e.g., charging PHEVs via grid consumption reduction [38] using metaheuristic and convex programming for proposing an intelligent railway station. Accurately forecasting electric vehicle charging station (EVCS) power is challenging due to the unpredictable nature of charging behaviors [39]. Nevertheless, EMS optimization objectives are mainly focused on fuel reduction or SOC optimization, variable prediction (speed), and real-time power distribution. The structure of the EMS can be stated in a general manner by identifying the objectives, constraints, and uncertainties.

Table 1. Methods for EMS in PHEVs.

Application	Heuristic Algorithm	Convex Problem	Combination of Algorithms	Type	Findings
SOC optimization or fuel reduction	DDPG [5], DRL [40], DP [41], RL [42,43], DP, NN-based EMS [44], LTV-SMPC and PMP-stochastic MPC [45]	Projected interior point method [3], LQP [45]	DRL, rule-based, DDPG [40], Gaussian mixture model, SDP [41], QL, MPC [42], WF2SLOA [46], C/GMRES, BO [18], LQP, MPC, PMP [45]	Hierarchical EMS [5], Hybrid EMS with torque split between the ICE and ESS [46], MPC EMS with non-linear losses [3]	16.34% of fuel savings [5], fuel economy improvement by 0.55% [40], LTV-SMPC and PMP-SMPC increase fuel economy by 8.79% and 14.42% respectively
Prediction	LSTM [5], Markov chain and LSTM [45]		Power split with NN-based EMS [44]	Speed  [5,40,42]	Prediction of mode and power split 2% higher compared to DP [44]
Real-time power distribution	MPC [5,42], C/GMRES [47]	Polynomial fitting approx. (methodical derivatives) [47]	MPC, RL [42]	Bi-level EMS [42], data-driven calibration [47]	Engine operating time is reduced by up to 2.96% [41]

DDPG: Deep deterministic policy gradient; LSTM: long short-term memory neural network algorithm; DRL: deep reinforcement learning; SDP: stochastic dynamic programming; WF2SLOA: Kernel Wingsuit Flying Search Algorithm and Sea Lion Optimization Algorithm; C/GMRES: Continuation/general minimal residual; BO: Bayesian optimization; LQP: linear quadratic programming problem; PMP: Pontryagin’s minimum principle; LTV-SMPC: linear time-varying stochastic model predictive control.

Table 1. Methods for EMS in PHEVs.

Application	Heuristic Algorithm	Convex Problem	Combination of Algorithms	Type	Findings
SOC optimization or fuel reduction	DDPG [5], DRL [40], DP [41], RL [42,43], DP, NN-based EMS [44], LTV-SMPC and PMP-stochastic MPC [45]	Projected interior point method [3], LQP [45]	DRL, rule-based, DDPG [40], Gaussian mixture model, SDP [41], QL, MPC [42], WF2SLOA [46], C/GMRES, BO [18], LQP, MPC, PMP [45]	Hierarchical EMS [5], Hybrid EMS with torque split between the ICE and ESS [46], MPC EMS with non-linear losses [3]	16.34% of fuel savings [5], fuel economy improvement by 0.55% [40], LTV-SMPC and PMP-SMPC increase fuel economy by 8.79% and 14.42% respectively
Prediction	LSTM [5], Markov chain and LSTM [45]		Power split with NN-based EMS [44]	Speed  [5,40,42]	Prediction of mode and power split 2% higher compared to DP [44]
Real-time power distribution	MPC [5,42], C/GMRES [47]	Polynomial fitting approx. (methodical derivatives) [47]	MPC, RL [42]	Bi-level EMS [42], data-driven calibration [47]	Engine operating time is reduced by up to 2.96% [41]

DDPG: Deep deterministic policy gradient; LSTM: long short-term memory neural network algorithm; DRL: deep reinforcement learning; SDP: stochastic dynamic programming; WF2SLOA: Kernel Wingsuit Flying Search Algorithm and Sea Lion Optimization Algorithm; C/GMRES: Continuation/general minimal residual; BO: Bayesian optimization; LQP: linear quadratic programming problem; PMP: Pontryagin’s minimum principle; LTV-SMPC: linear time-varying stochastic model predictive control.

The EMS formulation requires understanding the problem, i.e., identifying the power train configuration and the power flow among components. Generally, the EMS relies on several concepts regarding power and energy control strategies [31]. Two main modes according to the use of the ESS are charge-depleting mode (CD) and charge-sustaining mode (CS). Besides there are definitions based on the working mode, i.e., all-electric range (AER) or total miles driven after full recharge but before the ICE turns on for the first time, electric vehicle miles (EVM) or distance driven electrically after a full recharge but before reaching CS mode, and charge-depleting range (CDR) which is the distance traveled after a full recharge but before CS mode with ICE assistance.

A rule-based generic formulation of PHEVs is mainly based on the concepts above because the ESS and ICE operational modes are solved during the real-time power distribution to enhance energy efficiency, reduce fuel consumption, and optimize the operation. The concepts are applied to rule-based control strategies that can be expressed in the following example where the ICE on/off state is determined according to the vehicle speed ($v_1<v_2$), torque requirements, and battery’s $SOC$ [48].

$$IC{E}_{on/off}=\left\{\begin{array}{cc}\mathrm{O}\mathrm{f}\mathrm{f},& \mathrm{i}\mathrm{f} v_{PHEV}<v_1,\\ \mathrm{O}\mathrm{n},& \mathrm{i}\mathrm{f} v_{PHEV}>v_2,\\ \mathrm{O}\mathrm{n},& \mathrm{i}\mathrm{f} T_{req}>T_1,\\ \mathrm{O}\mathrm{n},& \mathrm{i}\mathrm{f} SOC<SO{C}_1,\end{array}\right.$$

(1)

Similarly, there are other rules to control power flow, e.g., when the current $SOC$ reaches 10 % (after a CD mode) then the battery is charged to a limit where the battery is not harmed. The EMS problem can be formulated as an optimal control problem. Then, the objective can be written in the following form,

$${\displaystyle \underset{x_i,B}{min}\varphi \left(X\right)}$$

(2)

where $x_i$ is a decision variable or state bounded by upper and lower limits in B, i.e., $b_l\le x_i\le b_u$, and X is the vector of variables (or states). $\varphi \left(X\right)$ represents a cost function. Examples of decision variables are vehicle speed ($v_{PHEV}$) and wheel torque ($T_{PHEV}$), whereas an example of state is the $SOC$ of the battery in the ESS. In the case of fuel consumption minimization, the objective can be written as in the following example,

$$\varphi \left(X\right)={\int }_{t_0}^{t_f}{\dot{m}}_{fuel}(v_{PHEV},T_{PHEV},u\left(t\right),x\left(t\right))dt$$

(3)

In the above example, the cost function is the integral (summation) over a period $t_f-t_0$ of the fuel flow expressed as ${\dot{m}}_{fuel}$ or $\left(\frac{d{m}_{fuel}}{dt}\right)$. $u\left(t\right)=[u_1,u_2]$ are the power split ratios (torque on rear wheels in relation to front wheels), and $x\left(t\right)$ represents the state, battery SOC in this case. Constraints are written based on the operating conditions, the model physics, and any other mathematical relation between decision variables and states. A simple example of a constraint for $SOC$ is [48],

$$\begin{array}{cc}\hfill \dot{x}\left(t\right)& =\frac{dSOC}{dt}\hfill \\ \hfill SOC\left(t_0\right)& =SO{C}_{init}\hfill \\ \hfill SOC\left(t_f\right)& =SO{C}_{final}\hfill \end{array}$$

(4)

where $x\left(t\right)$ is the rate of change in SOC and SOC is defined at the beginning and end of the period. Recalling the cost function $\varphi \left(X\right)$ expressed as the fuel flow in terms of speed, torque, $SOC$ and power split ratios, $\varphi \left(X\right)$ can be expressed as a single objective as in the previous example when the cost function relies on deciding a single optimal value of a cost function. Such simplification can be obtained if the problem allows focusing on the control of a single cost, e.g., fuel consumption. However, real scenarios are commonly multi-objective, i.e., involving several cost functions simultaneously, e.g., efficiency, fuel consumption, torque split, etc. Improvements to more than one cost do not necessarily translate into improvements in others. Therefore, it is necessary to achieve a trade-off. A balance in trade-off can be achieved when improvement in a particular objective is not further motivated without deteriorating other objectives. A trade-off in multi-objective problems is usually determined with the aim of a Pareto front where optimal solutions can be chosen by the designer.

4. Machine Learning in PHEVs Energy Management

Integrating machine learning (ML) into Energy Management Systems (EMS) represents a strategic advancement to optimize efficiency in the management of energy resources [49]. ML enhances real-time decision-making in energy distribution systems by adapting dynamically to complex patterns. By analyzing extensive sets of historical and real-time data, ML empowers EMS to forecast future energy demands, adapt to variations in renewable energy generation, and optimize resource allocation, promoting more efficient and proactive energy management. Moreover, a diverse range of ML applications exists in EMS. Some critical applications include predictive analytics, load forecasting, demand response, fault detection, energy consumption optimization, and grid optimization, collectively underscoring ML’s transformative potential in advancing EMS capabilities.

Table 2. Energy Management Systems (EMS) using ML.

Application	Objective	References
Predictive Analytics	Anticipating future energy demands Description: ML models analyze historical data to predict energy consumption patterns, helping EMS to manage energy resources proactively.	[50,51,52]
Load Forecasting	Predicting future loads on the energy grid Description: ML algorithms analyze historical load data, weather patterns, and other relevant factors to forecast energy demand accurately.	[53,54]
Demand Response	Modifying energy consumption based on demand signals Description: ML models enable real-time adjustments in energy consumption by predicting demand fluctuations and optimizing load profiles.	[55,56]
Fault Detection and Diagnostics	Identifying and diagnosing faults in energy systems Description: ML algorithms analyze sensor data to detect anomalies or faults in equipment, facilitating preventive maintenance and reducing downtime.	[57,58,59,60]
Energy Consumption Optimization	Optimizing energy consumption patterns for efficiency Description: ML algorithms learn from historical data and user behavior to optimize the operation of devices and systems, reducing overall energy consumption.	[61,62]
Renewable Energy Forecasting	Predicting the output of renewable energy sources Description: ML models use weather data and historical renewable energy production to forecast the output of solar panels, wind turbines, etc., aiding in grid stability.	[61,63]
Battery Management	Optimizing charging and discharging of batteries Description: ML algorithms analyze usage patterns and battery health data to optimize charging and discharging cycles, prolonging battery life and improving efficiency.	[64,65]
Grid Optimization	Enhancing the efficiency and reliability of the energy grid Description: ML models optimize energy distribution, predict grid congestion, and manage grid resources to improve overall system performance.	[54,61,66]
Dynamic Pricing	Adapting energy prices based on real-time demand Description: ML algorithms analyze demand patterns to set dynamic pricing, encouraging users to shift their energy consumption to non-peak hours,	[67,68,69]
Building Energy Management	Optimizing energy use within buildings Description: ML models analyze occupancy patterns, weather data, and building characteristics to optimize heating, ventilation, and air conditioning (HVAC) systems and lighting for energy efficiency.	[66,68]

provides a detailed breakdown of various machine learning (ML) applications in EMS, each aligned with specific objectives. These applications cover a broad spectrum, from predictive analytics for anticipating future energy demands to building energy management for optimizing energy use within structures. For instance, ML models analyze historical data in predictive analytics to foresee consumption patterns, enabling proactive energy resource management. Load forecasting utilizes ML algorithms to predict future loads on the energy grid by analyzing historical load data and relevant factors. Additionally, applications such as demand response, fault detection and diagnostics, and renewable energy forecasting showcase the versatility of ML in optimizing and enhancing the efficiency of energy systems. This comprehensive overview is a foundation for understanding how ML contributes to the multifaceted landscape of EMS applications.

4.1. ML Applications for PHEVs

In automotive innovation, the integration of ML into Energy Management Systems (EMS) plays a pivotal role, particularly in PHEV. This section delves into the multifaceted applications of ML within EMS for PHEVs, showcasing a hierarchical perspective based on their significance and current research trends. From optimizing power distribution to predictive energy management and battery health monitoring, each application is dissected in terms of its importance and rationale. Figure 2 shows a brief perspective on the different applications of PHEV.

4.1.1. Optimized Power Distribution

Regarding machine learning (ML) and its role in optimizing power distribution in hybrid electric vehicles (HEVs), there is a central focus on predictive and adaptive control strategies. ML algorithms adjust the power flow between the engine and electric motors in real time for optimal efficiency and performance. Here, are some examples of how ML excels:

• Data-driven decisions: Unlike rule-based systems, ML models learn from large datasets of driving patterns, road conditions, weather data, and battery characteristics. This enables them to predict future energy needs and adapt power distribution accordingly, rather than relying on pre-defined rules [70].
• Predictive optimization: ML models can anticipate driving conditions like upcoming hills or traffic lights, allowing the EMS to optimize power usage beforehand. This can involve maximizing electric vehicle (EV) propulsion during low-load situations like coasting or regenerative braking to recharge the battery for later use [71].
• Dynamic adjustments: Unlike static algorithms, ML models adapt to continuously changing driving conditions and battery state of charge. They can adjust power distribution in real-time to maintain optimal operating points for the engine and electric motors, reducing emissions and fuel consumption [72].
• Multi-objective optimization: Balancing conflicting objectives like fuel efficiency, emissions, and performance is achieved through algorithms considering various factors simultaneously. ML models can be trained to prioritize these objectives based on driver preferences, environmental conditions, and trip specifics [73].

4.1.2. Predictive Energy Management

Predictive energy management (PEM) is crucial in optimizing power distribution in plug-in hybrid electric vehicles (PHEVs). By leveraging machine learning (ML) algorithms, PEM systems can anticipate future energy demands and dynamically adjust power flow between the engine and electric motors for maximum efficiency and performance [74]. The ML applications in this context would be:

• Predictive Modeling: ML models trained on historical driving patterns, traffic data, and weather forecasts predict future energy needs and road conditions.
• Dynamic Optimization: Based on the predictions, the EMS calculates optimal power distribution strategies to minimize fuel consumption, maximize EV propulsion, and optimize battery usage.
• Real-Time Control: The EMS continuously adjusts the power flow between the engine and electric motors based on the actual driving situation and the updated predictions.

4.1.3. Battery State-of-Health Monitoring

Battery State-of-Health Monitoring (BSHM) is crucial for optimizing energy management in PHEVs. By leveraging ML algorithms, we can gain deeper insights into battery degradation and adjust the EMS accordingly for improved performance, safety, and lifespan [75,76], e.g.,

• Data Collection: Real-time data like voltage, current, temperature, and charging/ discharging cycles are collected from the battery management system (BMS).
• ML Modeling: Trained ML models analyze the features and predict the current BSHM, remaining useful life (RUL), and potential anomalies. Popular techniques include:

  –

  Regression models: Estimate BSHM and RUL based on historical data and operating conditions.

  –

  Time series analysis: Identify patterns and trends in battery data to predict future degradation.

  –

  Anomaly detection: Flag unusual battery behavior that could indicate potential faults.

Figure 3 depicts a PHEV vehicle with its Battery Management System (BMS). The BMS oversees the battery, gathering data from sensors measuring temperature, voltage, and current. These data are processed by the BMS, which employs Machine Learning algorithms to predict the battery’s health status and detect potential anomalies. Additionally, the BMS communicates with a control panel on the vehicle dashboard, displaying readings and relevant alerts for the driver. This diagram illustrates how the BMS integrates Battery State-of-Health Monitoring (BSHM) and Machine Learning to enhance battery monitoring and management, ensuring the safe, efficient, and enduring operation of the PHEV vehicle.

4.1.4. Adaptive Control Strategies

In the realm of PHEVs, optimizing energy management boils down to adaptability. Traditional rule-based systems struggle with ever-changing driving conditions and battery behavior. With ML-powered adaptive control strategies, peak efficiency, and performance are achieved by dynamically adjusting power flow [77]. The main performance characteristics of ML in this context are as follows:

• Real-time Data Input: The EMS ingests a constant stream of data—speed, battery state-of-charge, acceleration, terrain, and even weather.
• ML-based Prediction: Trained ML models analyze this data, forecasting:

  –

  Future energy demand: Predicting how much power the vehicle will need for upcoming hills, traffic lights, or highway stretches.

  –

  Optimal power distribution: Determining the ideal balance between the engine and electric motor to meet those demands while minimizing fuel consumption and maximizing battery life.

• Dynamic Power Flow Adjustment: The EMS continuously tweaks power distribution in real time based on the predictions. This might involve:

  –

  Prioritizing electric propulsion: Utilizing the EV motor during low-load situations, like coasting or city driving, for fuel-free efficiency.

  –

  Engaging the engine strategically: Calling on the ICE for high-power demands like hill climbs or rapid acceleration, ensuring optimal engine operating conditions.

  –

  Adaptive charging/discharging: Optimizing battery charging and discharging cycles based on predicted energy needs and battery health.

4.1.5. Regenerative Braking Optimization

Regenerative braking is a game-changer in HEVs, capturing energy lost during braking and converting it into electricity for the battery. But optimizing this process requires precision, and that is where machine learning (ML) comes in [78]. Let us explore how ML empowers HEVs to maximize energy recovery and efficiency through regenerative braking:

• Real-time Data Acquisition: The EMS gathers data on speed, deceleration, battery SOC, and road conditions.
• ML-based Prediction: Trained ML models analyze this data to predict [79]:

  –

  Regenerative braking potential: Estimating the amount of energy that can be recovered based on vehicle dynamics and road conditions.

  –

  Optimal braking force: Determining the ideal balance between regenerative and friction braking to maximize energy recapture while maintaining safe stopping distances.

• Dynamic Braking Control: Based on the predictions, the EMS continuously adjusts the braking force distribution between the electric motor and conventional brakes in real-time [80]. This might involve:

  –

  Prioritizing regenerative braking: Utilizing the electric motor for most of the braking force during low-speed decelerations or gradual stops, maximizing energy recovery.

  –

  Engaging friction brakes strategically: Using conventional brakes only when necessary, such as sudden stops or high-speed decelerations, to supplement regenerative braking and ensure safety.

  –

  Adaptive charging control: Managing the battery’s charging rate to prevent overcharging and optimize battery health.

4.1.6. Energy Harvesting from Environmental Data

Imagine hybrid electric vehicles (HEVs) that utilize regenerative braking and harness energy from the environment itself. This futuristic concept is within reach thanks to machine learning (ML) and its ability to extract valuable insights from environmental data [81]. The potential for miniaturized eco-champions from HEVs can be explored through machine learning as follows:

• Environmental Data Acquisition: Sensors collect real-time data on factors like solar radiation, wind speed, and road vibrations.
• ML-based Energy Prediction: Trained ML models analyze these data to predict:

  –

  Potential energy harvesting opportunities: Identifying periods of strong sunlight, gusts of wind, or rough road conditions where energy recovery could be maximized.

  –

  Optimal harvesting methods: Determining the most efficient way to capture and convert environmental energy into usable electricity for the battery, for example, through solar panels, wind turbines, or piezoelectric materials embedded in the tires.

• Dynamic Power Flow Management: The EMS adjusts power distribution in real-time based on the predictions [82]. This might involve:

  –

  Supplementing regenerative braking: Utilizing environmental energy sources to extend EV range further and reduce reliance on the engine.

  –

  Pre-charging the battery: Harvesting energy during stop-and-go traffic or downhill stretches to prepare for upcoming power demands.

  –

  Boosting acceleration: Providing an extra power kick from environmental energy sources during overtaking maneuvers or uphill climbs.

Figure 4 illustrates the integration of Machine Learning in hybrid electric vehicles to harness energy from the environment. Sensors gather real-time environmental data such as solar radiation and wind speed. These data are analyzed by ML models to identify energy harvesting opportunities and optimal capture methods. The Energy Management System (EMS) adjusts energy distribution based on these predictions, extending vehicle range and reducing fuel consumption.

4.1.7. User Behavior Analysis

Optimizing HEV energy management is not just about technology; it is about understanding the driver. Enter machine learning (ML)-powered user behavior analysis, unlocking a new level of personalization and efficiency in HEVs [83]. The following examples demonstrate how ML can customize power flow based on individual driving habits and styles:

• Data Collection: The EMS gathers data on driving patterns like acceleration, braking, speed, and preferred travel routes. Factors like driver demographics, environmental preferences, and charging habits can also be considered.
• ML-based User Profiling: Trained ML models analyze this data to create a unique profile for each driver, identifying:

  –

  Driving style: Aggressive, cautious, eco-conscious – understanding how a driver typically operates is key [84].

  –

  Predictive energy demand: Anticipating future power needs based on past behavior and planned routes.

  –

  Charging preferences: Optimizing charging schedules and locations based on individual routines and infrastructure access.

• Adaptive Power Flow Management: The EMS personalizes power distribution in real time based on the user profile. This might involve:

  –

  Encouraging eco-friendly driving: Providing feedback and adjustments to promote fuel-efficient behavior.

  –

  Predictive hybrid mode utilization: Seamlessly switching between electric and engine power based on anticipated driving conditions and user preferences [28].

  –

  Innovative charging strategies: Scheduling charging during off-peak hours or utilizing renewable energy sources where available.

4.2. ML Techniques Applied to Apps in PHEVs

In the dynamic landscape of Plug-In Hybrid Electric Vehicles (PHEVs), the fusion of Machine Learning (ML) techniques with Energy Management Systems (EMS) brings forth a transformative paradigm. This section unveils a comprehensive exploration of ML methodologies tailored for specific applications within PHEVs. The ML techniques most used in EMS and that can be applied to PHEVs efficiently are as follows:

• Adaptive EMS Control (AEC): Based on ML predictions, the EMS can adjust charging/discharging patterns, optimize power flow, and activate preventive measures like preheating or cooling to extend battery life and prevent failures.
• Clustering (C): Grouping drivers with similar driving styles based on their data patterns.
• Deep learning (DL): Captures complex relationships between data points like speed, battery temperature, and terrain to predict energy demand and optimize power flow.
• Feature Engineering (FE): Relevant features are extracted from the raw data to capture the battery’s health condition. This might involve calculations like capacity fade rate, internal resistance, and voltage stability.
• Predictive control algorithms (PCA): These algorithms use model-based predictions to calculate optimal power trajectories for the entire trip, further enhancing efficiency.
• Reinforcement learning (RL): Learns optimal power distribution through trial and error in a simulated environment, constantly improving decision-making.
• Support vector machines (SVMs): Classify driving scenarios and predict optimal power distribution strategies based on past driving patterns and environmental data.
• Time Series Analysis (TSA): Identifies patterns and trends in environmental data to predict periods of high energy availability.

Table 3. ML techniques for PHEVs.

Application	ML Techniques	Benefits	References
Optimized Power Distribution	DL, FE, RL, SVM	Enhanced Efficiency Improved performance Enhanced safety	[36,40,85,86,87]
Predictive Energy Management	DL, PCA, RL, SVM	Enhanced fuel economy Improved performance Extended battery life Reduced emissions	[88]
Battery State-of-Health Monitoring	AEC, DL, FE, PCA	Improved battery management Enhanced safety Predictive maintenance Optimized charging strategies	[89,90]
Adaptive Control Strategies	AEC, DL, RL	Fuel Efficiency Breakthrough Performance Boost Battery Life Extension Eco-Friendly Edge	[91,92,93]
Regenerative Braking Optimization	AEC, DL, RL	Fuel Efficiency Triumph Battery Life Extension Enhanced Safety Eco-Friendly	[85,94]
Energy Harvesting from Environmental Data	DL, RL, TSA	Supercharged Efficiency Reduced Emissions Enhanced Performance Resilience to External Factors	[81,82,95]
User Behavior Analysis	C, DL, RL, TSA	Enhanced Efficiency Personalized Driving Experience Environmental Consciousness Improved Infrastructure Utilization	[96,97]

delineates the symbiotic relationship between distinct EMS applications and the ML techniques instrumental in augmenting their efficacy.

The advanced machine learning strategies reviewed in this paper effectively handle the inherent variability and uncertainty in driving conditions through several key mechanisms. By leveraging large datasets and real-time data inputs, these algorithms can dynamically adapt to changing scenarios, ensuring robust performance under diverse driving conditions [98]. Techniques such as reinforcement learning allow the system to continuously learn and optimize its strategies based on real-world feedback, while predictive models anticipate future energy demands and adjust resource allocation accordingly. Additionally, the modular approach of breaking down the problem into interconnected subproblems, each managed by specialized control algorithms, enhances the system’s resilience and adaptability. As processor capabilities advance, these strategies are expected to become even more effective, driving higher efficiencies and more reliable performance in PHEVs across various operational contexts [99].

4.3. Dynamic Adaptation of ML-Based PHEV EMS

Advancements in machine learning (ML) technologies are ushering in a new era for plug-in hybrid electric vehicles (PHEVs), characterized by superior efficiency, enhanced performance, and unprecedented driver personalization [100]. At the heart of this revolution is the remarkable ability of ML algorithms to analyze vast amounts of data, including driving patterns, battery state-of-charge, and real-time vehicle conditions [101,102]. This enables the energy management systems to make informed decisions about power distribution in real time, meticulously optimizing energy usage for maximum efficiency and performance.

Table 4. ML-Powered PHEV EMS Adaptations for Optimal Performance and Efficiency.

Real-Time Condition	ML-Based EMS Adaptation	Contribution to Performance and Efficiency
Battery State-of-Charge (SOC)	- Prioritizes electric motor use during high SOC for maximum electric range. - Seamlessly transitions to engine use as SOC depletes, maintaining performance	- Maximizes electric propulsion for fuel economy. - Ensures smooth power delivery regardless of SOC.
Future Power Demand (Predicted)	- Anticipates high power needs (acceleration, uphill climbs) and engages engine pre-emptively. - Adjusts power distribution based on upcoming traffic conditions (congestion, stop-and-go).	- Maintains responsiveness and power delivery during high demand. - Optimizes engine usage for specific driving situations.
Regenerative Braking Opportunities	- Utilizes regenerative braking more effectively during downhill stretches or traffic stops to capture energy and recharge the battery.	- Maximizes energy recovery and extends electric range. - Reduces reliance on engine for future power needs [103].
Other Real-Time Conditions (Speed, Road Grade)	- Adjusts power distribution based on speed (highway cruising vs. city driving) and road grade (inclines vs. declines).	- Optimizes engine usage for different driving scenarios. - Minimizes unnecessary engine operation on flat or downhill roads [104].

provides a comprehensive overview of how ML empowers the PHEV EMS to become a truly intelligent and adaptive system, unlocking the full potential of PHEVs for sustainable and efficient transportation.

4.4. ML Challenges in PHEVs

In the pursuit of enhancing Plug-In Hybrid Electric Vehicles (PHEVs) through Machine Learning (ML), various applications face intricate challenges. From optimizing power distribution to predicting energy demand and adapting control strategies, each facet encounters distinct hurdles that demand sophisticated ML approaches. This section succinctly explores these challenges, recognizing their significance in realizing the full potential of ML in advancing the efficiency and sustainability of PHEVs. An analysis follows, presenting several challenges that PHEVs must confront in their journey toward seamless integration with ML technologies. Figure 5 shows an overview of the difficulties in PHEV in each ML application.

Table 5. Meaning of the challenges of ML applications for PHEV.

Challenges	Description
Data acquisition and processing	Integrating diverse real-time data sources and efficiently processing them for accurate predictions remains challenging.
Computational power	Implementing complex ML models in real-time requires robust onboard computing systems, which can add cost and complexity.
Battery modeling	Accurately predicting battery behavior under varying conditions is crucial for optimal PEM performance and requires continuous research.
Human-machine interaction	Integrating driver preferences and feedback into the PEM system can further personalize the driving experience and optimize energy usage.
Model explainability and interpretability	Ensuring transparency in ML predictions is crucial for trust and acceptance in safety-critical applications like battery management.
Limited training data	Obtaining diverse and high-quality battery data remains challenging for accurate ML model training [64].
Continuous model adaptation	Batteries degrade over time, and operating conditions vary, requiring constant model updates and retraining for reliable predictions.
Integrating ML with existing BMS	Efficient and seamless integration of ML algorithms with existing Battery Management System (BMS) hardware and software infrastructure is necessary for practical implementation.
Sensor Accuracy and Reliability	Precise braking control relies on accurate sensor data, requiring continuous sensor technology and calibration improvement.
Driver Behavior Adaptation	Integrating driver preferences and adapting braking behavior accordingly can further personalize the driving experience and optimize energy recovery.
Predictive Traffic Flow Integration	Anticipating upcoming traffic lights and congestion can further optimize braking strategies and energy recuperation.
Supercharged Efficiency	Harvesting even modest amounts of environmental energy can significantly improve overall fuel economy and extend EV range.
Reduced Emissions	Decreased reliance on the engine translates to lower emissions, promoting a cleaner environment.
Enhanced Performance	Access to additional power sources can boost acceleration and responsiveness, making HEVs even more competitive with conventional vehicles.
Resilience to External Factors	By diversifying energy sources, HEVs become less dependent on fuel availability and infrastructure, increasing their adaptability.
Privacy Concerns	Balancing personalization with user privacy requires careful data anonymization and ethical considerations.
Acceptance and User Education	Encouraging drivers to trust and actively participate in the system requires open communication and education.
Continuous Learning and Adaptation	ML models must constantly learn and evolve to adapt to changing driving habits and preferences.
Integration with Third-Party Services	Connecting the EMS with smart grids, weather data, and traffic information can enhance predictive capabilities and personalization.

outlines the challenges of implementing ML in PHEVs and their implications in these technologies. This brief analysis offers a detailed understanding of specific obstacles and their significance in PHEVs [105,106,107].

4.5. Future of PHEV Energy Management with ML

The realm of PHEV energy management systems (EMS) has witnessed a significant transformation due to advancements in machine learning (ML) technologies. Here, are some key advancements with profound impacts and their practical implications for future vehicle designs:

Table 6. Future techniques of PHEV Energy Management with ML.

Technique	Impact	Practical Implications
Deep Learning for Enhanced Prediction	Deep learning algorithms like convolutional neural networks (CNNs) can analyze vast amounts of driving data, including traffic patterns, weather conditions, and driver behavior. This enables highly accurate predictions of future energy demands, allowing the EMS to optimize power distribution for maximum efficiency and performance.	Future PHEVs will leverage deep learning for proactive energy management. The EMS can anticipate upcoming hills and adjust power distribution accordingly, maximizing electric propulsion and minimizing fuel consumption. Additionally, driver behavior can be factored in, tailoring power delivery based on individual driving styles [108].
Reinforcement Learning for Adaptive Control	Reinforcement learning (RL) allows the EMS to learn optimal control strategies through trial and error in a simulated environment. This enables continuous adaptation to diverse driving conditions and driver behavior, optimizing power distribution in real-time for maximum efficiency.	Future PHEVs will benefit from RL algorithms that dynamically adjust powertrain operation. The EMS can learn from each driving experience, continuously refining its strategies to achieve optimal fuel economy and performance in various scenarios. Additionally, RL can personalize the driving experience by adapting to individual preferences for power delivery [109,110].
Improved Battery Modeling for Longevity and Efficiency	ML is facilitating the development of more accurate battery models that consider factors like temperature, aging, and charging/discharging patterns. This enables the EMS to optimize charging cycles and power distribution, maximizing battery life and overall system efficiency.	Future PHEVs will have more intelligent battery management systems thanks to improved ML models. The EMS can predict battery health and remaining useful life, allowing for preventive maintenance and extending battery lifespan. Additionally, charging strategies can be adjusted to minimize stress on the battery, further enhancing its longevity [111].

highlights the significant impact of machine learning advancements on PHEV EMS. However, these advancements also necessitate further developments in vehicle design to fully unlock their potential. Here, are some key considerations:

• Hardware Advancements: As ML algorithms become more sophisticated, their computational demands increase. Faster on-board processors will be essential to handle these demands in real-time. This may involve the integration of dedicated hardware accelerators or more powerful central processing units (CPUs) specifically designed for efficient machine learning tasks within vehicles.
• Sensor Fusion: The effectiveness of ML algorithms heavily relies on the quality and richness of data they are trained on. Integrating diverse sensors beyond traditional ones can provide a more comprehensive picture of the driving environment and vehicle operation. Cameras, Lidar (Light Detection and Ranging) systems, and weather data can be valuable sources of information for ML models, allowing them to make more accurate predictions and optimize power distribution even further.
• Connectivity and Cloud-based Learning: PHEVs equipped with robust connectivity features can leverage cloud-based platforms for training ML models. By utilizing vast datasets collected from multiple vehicles operating in diverse conditions, these models can continuously learn and improve their performance. This collaborative learning approach can lead to more efficient and adaptable EMS strategies across the entire PHEV fleet.

5. Optimization in Plug-in Hybrid Electric Vehicles Energy Management

This section aims to answer the research question, “What optimization techniques have been employed in the design of Energy Management Systems for Plug-in Hybrid Electric Vehicles (PHEV), and how do they contribute to enhancing overall vehicle performance and efficiency?”

In this context, it is necessary to have a view of the classification of the existing optimization techniques, which are divided into three main groups: 1. Deterministic; 2. Heuristic; 3. Artificial Intelligence. Deterministic and heuristic optimization methods represent two contrasting approaches to solving optimization problems. Deterministic optimization, grounded in certainty, aims to find the optimal solution under well-defined and known conditions, assuming precise knowledge of all input parameters. This approach typically employs systematic and exhaustive search algorithms to explore the solution space [112]. In contrast, heuristic optimization embraces flexibility and acknowledges the uncertainty inherent in real-world problems. While heuristic methods do not guarantee optimality, they prioritize efficiency and practicality, offering good solutions within a reasonable time frame. Heuristic algorithms use approximation and shortcut strategies to navigate complex solution spaces, making them particularly suitable for large-scale or NP-hard problems where finding an exact solution is computationally challenging [113]. Examples of deterministic methods include linear programming and dynamic programming, while genetic algorithms and simulated annealing are instances of heuristic optimization techniques. Artificial Intelligence-based optimization techniques leverage advanced computational models to mimic human intelligence and learning capabilities. Machine Learning (ML) algorithms, Neural Networks, and Deep Learning techniques fall under the AI umbrella for optimization. These approaches excel in adapting to complex and dynamic problem spaces, learning from data, and iteratively improving solutions over time. The choice between these approaches depends on the nature of the optimization problem, the availability of information, and the computational resources at hand.

5.1. Deterministic Optimization Studies

Deterministic optimization helps in finding an optimal global solution, offering theoretical guarantees that the solution is the global best indeed. To achieve global optimum, deterministic optimization follows a given set of steps that exploit particular attributes of the problem. Deterministic optimization comprises two sets of algorithm classes called complete and rigorous. Complete algorithms reach global optimum within an indefinitely long execution time. However, it is possible to stop around a local best in a finite time by accepting a predefined tolerance. On the other hand, rigorous algorithms find global optimum in a finite execution time considering predefined tolerance.

Deterministic optimization algorithms can solve convex and non-convex problems. On one hand, convex optimization problems can be linear and non-linear. On the other hand, non-convex optimization problems can be classified into discrete problems and continuous problems. A convex optimization problem is a problem where objectives and constraints are convex functions (feasible set); convexity is a mathematical property that needs to be satisfied by each function such that solution search can be approachable by exploiting convexity, e.g., convexity requires that functions are continuous, but this is not the only feature to comply with. On the contrary, non-convex problems break the convexity, e.g., a problem becomes non-convex by the existence of integer or binary variables (there is no continuity between integer values).

5.1.1. Convex Optimization

Convex optimization holds a large family of problems with a predefined hierarchy; from higher to lower levels there is semidefinite programming (SDP), second-order cone programming (SOCP), quadratic programming (QP), and linear programming (LP). For instance, LP is a special case of QP, i.e., QP encompasses LP; similarly, SOCP encompasses QP, etc.

Linear problems can be solved with LP optimization. The mathematical model of the problem, objective, and constraints must be represented by linear relationships, that is, a linear objective function subject to linear equalities and linear inequality constraints, as written in Equation (5).

$$\begin{array}{c}\hfill \underset{x_i,B}{min}\varphi \left(c^{T}X\right)\\ \hfill subjecttoAX\le b,\\ \hfill A_{eq}X=b_{eq}\end{array}$$

(5)

$c^T$, b, $b_{eq}$ are given vectors and A and $A_{eq}$ are given matrices. The inequality and equality constraints specify a convex polytope over which the objective function is optimized. In the case of multi-objective optimization, a linear objective function can also represent the linear combination of cost functions where the elements of $c^T$ correspond to the weights for each cost function, thus, multiple objectives can be expressed as a single objective (changing weights could result in a different optimal). Real problems can rarely be expressed directly into linear problems, in most cases, formulations are non-linear and non-convex. Nevertheless, approximation to linear problems via linearization is commonly applied although accuracy and uncertainties must be observed when obtaining an optimal solution.

Non-linear problems can be convex; thus, these types of problems can be solved by convex optimization techniques mentioned earlier. QP aims to solve a problem where there is a quadratic function in the objective while the rest of the constraints are linear. An example of a quadratic objective is an error defined as a least square function, which is the starting point of the cost function in most control problems. SOCP has constraints in the form of a second-order cone that can be embedded in the cone of positive semidefinite matrices, i.e., a constraint of this type is equivalent to a linear matrix inequality (LMI). Some contemporary methods such as interior-point methods, cutting-plane methods, and sub-gradient methods, among others, have been used in convex optimization.

5.1.2. Non-Convex optimization

As stated earlier, the presence of integer and binary variables breaks convexity and problems become non-convex and discrete. Whenever the problem can be modeled linearly, it can be solved with Integer Programming (IP) or Mixed Integer Linear Programming methods (MILP). In IP problems, all variables are integers, e.g., yes/no selections, tap position in transformers, etc., while MILP have real (non-integer) and integer variables. These methods provide convergence to global optimum at the cost of losing accuracy when linear approximations are performed. Some instances of MILP problems are intractable, so heuristic methods are part of the solver.

In the case of non-convex non-linear problems with real variables only, non-convex optimization can be utilized. The selection of a solver depends on the purpose of the optimization, the mathematical properties of the problem, and the experience of the designer. Non-convex optimization problems are hard to solve because of the risk of falling into a local optimum (not necessarily the global optimum), encountering saddle points, flat regions, and widely varying curvature. There cannot be a general algorithm to solve all problems efficiently. One example of non-convex problems is the neural networks (NN). Neural networks comprise a series of universal function approximations that may have symmetric configurations, but symmetry is not a feature of convex functions. Some methods for non-convex problems include stochastic gradient descent, deep learning, and other heuristic methods. At this point, it is convenient to explore the heuristic optimization studies.

5.2. Heuristic Optimization Studies

Over the past two decades, there has been a surge in the popularity of heuristic optimization techniques for addressing complex, multimodal, high-dimensional, and nonlinear energy management problems. This surge is attributed to their ease of implementation, adaptability to diverse optimization challenges, and robust search capabilities that facilitate the attainment of effective global optima. While various metaheuristic optimization techniques exist, they can be categorized into four main groups, as illustrated in Figure 6.

In order to clarify the different applications of each heuristic optimization technique in the context of EMS, the

Table 7. Heuristic optimization techniques applied in EMS.

Optimization Technique	References	Application	Findings
Evolutionary algorithm	[114,115,116,117,118,119]	Battery State-of-Health Monitoring	Frequent sbtartup, shutdown, and rapid load changes that can diminish fuel cell lifespan using GA
	[120,121]	Battery State-of-Health Monitoring considering hierarchical strategy	Frequent startup, shutdown, and rapid load changes that can diminish fuel cell lifespan using GA
	[4,122,123,124]	Real-time maximization of energy utilization	Optimum storage energy using GA
	[125]	Intelligent energy management strategy of hybrid energy storage system for electric vehicle	Pattern recognition used for EM using GA
	[126,127]	Design strategy for a plug-in HEV with HESS	Model prediction and rule-based energy management using GA
	[7,8,10,128,129]	Optimized Power Distribution	Enhancement in GA combining other algorithms such as Biogeography-Based Optimizer, Clonal Flower Pollination [8,128], Fuzzy Harmony Search [129], Mutated Differential Evolution [10], and Imperialist Competitive Algorithm [7].
Swarm Intelligence	[130]	Regenerative Braking Optimization	Optimal EM strategy incorporating PSO and fuzzy logic
	[126,131,132,133,134,135,136,137]	Battery State-of-Health Monitoring	Approach to efficiently distribute engine and motor power, enhance engine efficiency, and mitigate battery damage using PSO
Physics based	[138]	Battery State-of-Health Monitoring	Minimize the average operating cost, encompassing manufacturing cost and system end-of-life timing using simulated annealing
	[139,140]	Real-time maximization of energy utilization	Novel approach for velocity planning and EM of intelligent PHEVs using Whale Optimization Algorithm
	[141]	Control parameters in a plug-in Hybrid Electric Vehicle	Substantial fuel economy improvements using modified PSO
	[142]	Maximization of energy utilization	Cooperative optimal power split method for a cluster of intelligent electric vehicles equipped with battery/ supercapacitor hybrid using modified PSO
	[143,144]	Design strategy for range extended EV	An approach for EM control parameters using modified PSO
Fuzzy logic	[115,145,146,147,148,149,150,151]	Optimized Power Distribution	An approach for enhancing overall vehicle performance using fuzzy logic combined neural network

is presented:

5.2.1. Evolutionary Algorithms (EAs)

The first group encompasses evolutionary algorithms (EAs), grounded in the principles of natural evolution. Notably, the Genetic Algorithm (GA) has emerged as the most widely adopted within this category, initially proposed by Holland in 1992 [131]. Drawing inspiration from Darwin’s evolution theory, GA orchestrates the evolution of a population, through crossover, and mutation processes, ensuring the progression towards the best solution in each iteration (next generation). The genetic algorithm commences with the “Selection”, also termed the “Encoding of a Chromosome” [132]. In this initial phase, multiple chromosomes are generated, each representing a candidate solution expressed as a binary string in relation to the objective function. Subsequently, two parents are chosen through a normalized evaluation of the objective function, incorporating random number generation (similar to a roulette wheel). The ensuing step is “Crossover” [132], where two children are derived from the parents. This involves merging a segment of the string from the first parent with a corresponding part of the second parent, and vice versa. If the children’s probability of crossover is met, they proceed to the subsequent stage; otherwise, the parents are retained. The subsequent “Mutation” [132] step involves the probability of altering genes (variables pertaining to the objective function) to mitigate the risk of local optima. Finally, the algorithm incorporates “Elitism” [132], selecting a specific number of top-performing individuals based on fitness. These elite individuals transition directly to the next generation without modification, serving to safeguard superior solutions and sustain consistency within the population, thereby preventing the loss of highly fit individuals. An insightful depiction of the genetic algorithm is provided in Figure 7.

A comprehensive compilation of advanced algorithms based on GA with applications in the field of EV energy management can be found in recent studies. For instance, Ref. [114] explores the application of proton exchange membrane fuel cells in automobiles as an efficient, emission-free, and low-noise alternative to traditional internal combustion engines. Given the focus on improving the lifespan of fuel cells, the research concentrates on the design of an energy management strategy for a fuel cell hybrid electric vehicle where the fuel cell serves as the main power source and a battery functions as the auxiliary power source. The paper introduces a novel algorithm, namely Neural Network Optimized by Genetic Algorithm, which addresses the challenge of frequent startup, shutdown, and rapid load changes that can diminish fuel cell lifespan. Another relevant study on this field appears in [115] that focuses on the crucial role of energy management strategy in optimizing the energy control of electric vehicles. The study introduces a novel approach, presenting a GA-optimized fuzzy control energy management strategy for a hybrid energy storage system in electric vehicles. The methodology involves a systematic experiment characterizing lithium-ion batteries and ultracapacitors at various temperatures, establishing accurate models, and analyzing their performances. The GA is then employed to optimize the fuzzy membership function, aiming to minimize energy loss. The paper concludes that the GA-optimized strategy outperforms non-optimized approaches, demonstrating better performance. To validate the method’s robustness, experiments are conducted at different ambient temperatures (10 °C, 25 °C, 40 °C), showing an increase in the energy economy of electric vehicles by 2.6%, 2.4%, and 3.3% at 10 °C, 25 °C, and 40 °C, respectively. From the perspective of an energy management system (EMS) in plug-in hybrid electric vehicles (PHEV) to overcome limitations posed by battery performance, authors in [133] propose a hybrid EM system for a series-parallel PHEV integrates a rule-based control strategy with a GA-based optimization technique to enhance battery utilization. The results indicate that the GA optimization successfully meets set sub-targets in the fitness function, demonstrating the effectiveness of the proposed technique. Comparisons with a rule-based control strategy highlight significant improvements in hydrocarbon (HC) and NOx emissions achieved by the proposed EMS. Similar studies can be found in [120,121] with the difference that it incorporates an adaptive hierarchical strategy. Other GA applications in the field of study include real-time maximization of energy utilization by coordinating the battery energy and fuel consumption [134,135,136,137], intelligent energy management strategy of hybrid energy storage system for electric vehicles based on driving pattern recognition [152], and enhanced designed strategy for a plug-in HEV with HESS [138,139]. A comprehensive review on this field can be found in [116,117,118,119], which aims to underscore the importance of energy management strategies and optimization for fuel cell-driven HEVs. Against the backdrop of environmental challenges and fossil energy shortages, the goal is to emphasize that the hybrid system’s output performance significantly influences the fuel cell’s lifespan. Ultimately, the papers seek to contribute insights for improving energy utilization efficiency and extending fuel cell life in the context of energy management optimization. It is noteworthy to highlight that within the realm of study, various sophisticated Evolutionary Algorithm (EA) optimization techniques have been employed, encompassing methods such as Biogeography-Based Optimizer, Clonal Flower Pollination [140,141], Fuzzy Harmony Search [142], Mutated Differential Evolution [143], and Imperialist Competitive Algorithm [144]. Despite their potential, it is worth acknowledging that these algorithms are not widely recognized or extensively documented in the existing literature, particularly in applications beyond the scope of this research. This limited visibility may contribute to their relatively lower popularity within the broader research community.

5.2.2. Swarm Intelligence (SI)

Swarm Intelligence (SI) optimization stands as an innovative and powerful paradigm inspired by nature’s complex, collective behaviors observed in social organisms. Rooted in the principles of self-organization and decentralized decision-making, SI draws inspiration from the collaborative strategies employed by swarms, flocks, and colonies to solve complex problems efficiently. This burgeoning field has garnered significant attention across various scientific disciplines for its ability to address intricate optimization challenges that traditional methods find daunting [153].

The essence of SI lies in mimicking the cooperative behaviors observed in social insects, birds, and even bacteria, where groups of relatively simple individuals interact locally to achieve global optimization. The collective intelligence emerging from these interactions enables the swarm to adapt, learn, and navigate through complex solution spaces, which are linked to the memory and communication features within the swarm [153]. Memory refers to the ability of individual agents within the swarm to retain information about their past experiences or the global best solutions encountered during the optimization process. This memory feature allows the swarm to adapt and learn from its exploration of the solution space. This historical knowledge guides the swarm toward regions of the solution space that have previously shown promise, enhancing the efficiency of the optimization process [153]. Following with communication, it lies at the heart of SI, fostering interaction and collaboration among individual agents within the swarm. Inspired by the communication mechanisms found in social organisms, SI algorithms leverage decentralized interactions to exchange information about potential solutions. This collaborative exchange allows the swarm to collectively converge toward optimal solutions by sharing insights about promising regions in the search space. Communication in SI not only facilitates the dissemination of valuable information but also aids in the coordination of swarm movements, contributing to the emergence of intelligent, collective behavior [153].

In a broad overview, the SI algorithm unfolds through three primary phases. Commencing with the “Initialization” stage, particles assume distinct positions, embodying candidate solutions for the objective function. Subsequently, the “Memory and Communication” stage ensues, during which particles establish their local best and global best positions by virtue of a speed function. Finally, the algorithm progresses to the “Update Positions” phase, wherein each particle assesses its current position against a new one, adjusting its movement based on the superior position. This iterative process persists until predefined stopping criteria are met [113]. Figure 8 provides a visual representation of this general algorithm for swarm intelligence, illustrating the orchestrated interplay between initialization, memory and communication, and position updates. It is noteworthy to highlight that, based on the outlined algorithm, various adaptations and iterations of SI algorithms have emerged. For instance, Ant Colony Optimization utilizes a form of memory in the pheromones deposited by ants. The cumulative pheromone concentrations act as a memory mechanism, influencing the likelihood of other ants selecting the same paths, thereby improving the overall efficiency of the swarm. Another illustrative example is found in the Grey Wolf Optimizer, which emulates the leadership hierarchy and hunting dynamics of grey wolves in nature. In this context, the “Initialization” phase mirrors the hunting initiation, the “Memory and Communication” phase replicates the collaborative search for prey, and the “Update Positions” stage corresponds to the strategic attack on prey. These adaptations showcase the versatility of SI algorithms, each tailored to emulate specific natural behaviors and problem-solving strategies.

Applications of SI algorithms in PHEV Energy Management are vast in the literature. For instance, ref. [154] introduces a dual planetary gear hybrid electric vehicle, establishing speed and torque relationships using a lever analogy. It focuses on optimizing transmission efficiency by analyzing the impact of engine speed ratios. An optimal energy management strategy is proposed, incorporating PSO and fuzzy control algorithm for engine torque control. Simulation results using AVL/Cruise and MATLAB/Simulink R2016a platforms show that the strategy optimizes engine operation, maintains the battery state of charge, and reduces overall vehicle fuel consumption by 10.26%. Other applications can be found in [155], which presents a hybrid electric vehicle with an internal combustion engine and motor, addressing issues of limited electric vehicle range and slow charging. An energy management strategy, utilizing a PSO algorithm, is proposed to efficiently distribute engine and motor power, enhance engine efficiency, and mitigate battery damage. The strategy focuses on reducing energy consumption and excessive battery discharge. Results, validated under the Worldwide Light-Duty Test Cycle (WLTC) and the New European Driving Cycle (NEDC) test cycles, indicate a 7.7% reduction in overall fuel consumption under WLTC and a 9.8% reduction under NEDC after optimization. Similar studies can be found in [138,145,146,147,148,149,150]. Additional applications showcase their adaptability to complex scenarios. One such instance involves the development of an optimal sizing methodology for hybrid electric vehicles, incorporating ultracapacitors and fuel cells (FC) alongside battery units (BU). This innovative approach leverages the Butterfly Optimization algorithm coupled with the quantum wave concept, enhancing the exploration of the search space more effectively [121]. This methodology contributes to the efficient determination of hybrid energy source sizes, emphasizing advancements in energy storage technologies. Furthermore, SI algorithms prove valuable in optimizing the mode division strategy for series-parallel plug-in hybrid electric vehicles. A study introduces a rule design method that combines K-means clustering with an improved Artificial Bee Colony algorithm [151]. This hybrid approach ensures a robust strategy for mode division, considering the dynamic nature of real-world driving conditions. The integration of clustering and improved bee colony algorithms demonstrates the versatility of SI techniques in refining complex decision-making processes, contributing to the overall efficiency and performance of plug-in hybrid electric vehicles. These applications exemplify the diverse and sophisticated ways SI algorithms contribute to advancing the field of Plug-in Hybrid Electric Vehicle Energy Management.

The utilization of SI has proven to be a promising and versatile approach. The reviewed literature showcases the efficacy of SI algorithms, such as Particle Swarm Optimization (PSO), Butterfly Optimization, and Artificial Bee Colony, in addressing the complex challenges associated with optimizing engine operation, transmission efficiency, and battery management in hybrid vehicles. Notably, these algorithms contribute to achieving substantial reductions in overall vehicle fuel consumption, demonstrating their practical impact on enhancing the sustainability and efficiency of PHEVs. The applications extend beyond traditional optimization methods, incorporating quantum-inspired concepts and innovative approaches such as optimal sizing methodologies for hybrid energy sources. As the field of PHEV Energy Management continues to evolve, SI algorithms offer valuable tools for researchers and practitioners alike, providing robust solutions to intricate optimization challenges. The amalgamation of nature-inspired algorithms with cutting-edge technologies reflects a promising trajectory for the future development and refinement of energy-efficient and environmentally friendly hybrid electric vehicles.

5.2.3. Physics Based (PB)

PB optimization algorithms represent a distinctive class of optimization techniques inspired by the fundamental principles of physics and natural phenomena. These algorithms draw inspiration from the dynamic behavior observed in physical systems to design efficient and robust optimization strategies. By leveraging analogies to physical processes, such as the laws of motion, thermodynamics, or electromagnetic interactions, these algorithms seek to emulate the optimization capabilities exhibited by natural systems. The underlying philosophy of PB optimization lies in translating the governing principles of physical systems into mathematical models that guide the search for optimal solutions in complex problem spaces. Unlike traditional optimization methods that may rely on mathematical heuristics or evolutionary principles, physics-based algorithms introduce a unique perspective, often embodying principles like energy minimization, force interactions, or equilibrium conditions. The key characteristics of PB optimization algorithms are the following:

• Analogous Modelling: Physics-based optimization algorithms often construct analogies between optimization problems and physical systems, translating problem-specific constraints and objectives into analogous physical concepts.
• Dynamic Evolution: Inspired by the dynamic nature of physical systems, these algorithms often incorporate iterative processes that simulate the evolution of a system towards equilibrium or optimal states. Therefore, PB algorithms sometimes are combined with SI algorithms, which results in a robust optimization technique.
• Global Exploration: Physics-based algorithms may exhibit characteristics conducive to global exploration of the solution space, mimicking the natural tendency of physical systems to seek equilibrium states.
• Energy Concepts: Concepts related to energy minimization or conservation are frequently integrated into these algorithms, contributing to the efficient exploration of solution spaces.

Common examples of PB optimization algorithms include Simulated Annealing, which is inspired by the annealing process in metallurgy, this algorithm simulates the gradual cooling of a material to minimize defects; molecular dynamics optimization, which employs concepts from molecular dynamics simulations, this approach models optimization problems as dynamic systems of interacting particles, each representing a potential solution; Electromagnetism-Like Optimization, which is inspired by the principles of electromagnetism, EMO models optimization problems as charged particles interacting through electromagnetic forces to converge towards optimal solutions; Quantum Particle Swarm Optimization that introduces quantum-inspired concepts to enhance the exploration and exploitation capabilities of the traditional PSO algorithm. This hybrid approach aims to leverage the principles of quantum mechanics, such as superposition and entanglement, to provide a more robust and efficient optimization technique. Independently of the PB optimization algorithms, most of them follow the pseudocode presented in Figure 9.

Simulated Annealing, a prominent PB optimization algorithm, emulates the physical process of heating a material and gradually cooling it to minimize system energy. In the context of [156], simulated annealing is applied to minimize the average operating cost, encompassing manufacturing cost and system end-of-life timing. Another noteworthy PB algorithm employed in this field is the Whale Optimization Algorithm, drawing inspiration from the bubble-net hunting strategy of humpback whales. This algorithm replicates the collaborative behavior of whales in encircling and trapping prey. The literature features several studies leveraging whale optimization, as evidenced in [157,158], showcasing its versatility and effectiveness in diverse optimization scenarios. The fusion of PB algorithms with SI often results in a robust optimizer. A noteworthy instance is found in [159], where authors propose an enhanced Particle Swarm Optimization (PSO) by incorporating the “PI method” and “turning direction” to modify the inertia weight. This refined algorithm is deployed to optimize control parameters in a plug-in Hybrid Electric Vehicle (HEV) with ultracapacitors. The outcomes reveal substantial fuel economy improvements, achieving a fuel-saving rate of 9.20% in the urban section, 6.40% in the roadway section, and 5.40% in the freeway section. A parallel optimization approach is observed in [160], focusing on a cooperative optimal power split method for a cluster of intelligent electric vehicles equipped with battery/supercapacitor hybrid energy storage systems. The synergy of improved PSO using PB algorithms extends to various applications, encompassing powertrain energy management [122,161], energy storage sizing, and power-splitting optimization for plug-in hybrid electric vehicles [4]. Additionally, it extends to thermal management control for the hybrid electric energy system of electric vehicles, as illustrated in [123]. This confluence proves instrumental in addressing multifaceted challenges and enhancing the efficiency of diverse systems within the realm of electric vehicles.

5.2.4. Fuzzy Logic (FL)

Fuzzy Logic, a robust computational paradigm, plays a crucial role in optimizing energy management systems and control strategies within the domain of power split HEVs. A significant application is in optimizing the control strategies that dictate the power distribution between the internal combustion engine and the electric motor. Fuzzy logic enables the creation of adaptive and intelligent control rules, responding dynamically to various driving conditions such as traffic patterns, road inclinations, and driver behavior. The linguistic rules inherent in fuzzy logic systems facilitate a more human-like decision-making process, enhancing the optimization of the power split in HEVs [124]. Adaptive energy management is another key area where fuzzy logic shines. By employing fuzzy sets and linguistic variables, adaptive energy management systems can adjust parameters in real time. This adaptability proves instrumental in optimizing energy usage under diverse driving scenarios, contributing significantly to improved fuel efficiency and overall vehicle performance. The flexibility of fuzzy logic systems allows for intuitive adjustments, accommodating imprecise or uncertain information and ensuring that the power split aligns with the current energy demands and constraints [124].

Designing and implementing a fuzzy logic system involves a systematic process. The first steps include “Variables Identification”. Each variable is then characterized by linguistic terms through the definition of membership functions, indicating the degree of membership to each fuzzy set. The subsequent creation of a rule base captures the expert or data-driven relationships between input and output variables. The inference system, encompassing methods like Mamdani or Sugeno models, combines these rules and membership functions to derive fuzzy outputs from fuzzy inputs. “Fuzzification converts” crisp input values into fuzzy sets, and rule evaluation determines the firing strength of each rule. The aggregation step combines the results of all rules, leading to a combined fuzzy output. “Defuzzification” then converts this aggregated fuzzy output into a crisp value, providing a clear and actionable result. System validation, optimization, and implementation follow, ensuring the effectiveness and robustness of the fuzzy logic system. Continuous testing and iteration refine the system, reflecting the iterative nature of designing and deploying fuzzy logic solutions [125]. Figure 10 delivers a comprehensive representation of the overarching fuzzy logic framework, elucidating the sequential steps involved in the intricate fuzzy logic process.

Fusing fuzzy logic with neural networks in the domain of energy management control represents a powerful and versatile paradigm, demonstrating profound implications across various applications. This synergistic approach leverages the interpretability of fuzzy logic alongside the learning capabilities of neural networks, creating a control system that adapts to dynamic energy scenarios, particularly in the context of power split HEVs. Fuzzy logic, renowned for its rule-based decision-making and linguistic variable interpretation, forms the foundational layer of the control strategy. This component ensures transparency and human-understandable decision rules, facilitating expert validation. On the other hand, neural networks contribute advanced learning mechanisms, enabling the system to glean insights from historical and real-time data, continually optimizing the fuzzy logic rules for enhanced adaptability.

The literature, as encapsulated in references [71,126,127,128,136,162,163,164,165], underscores the wide-ranging applications and empirical validations of this combined approach. These references likely detail specific instances where the fuzzy logic and neural network synergy has been applied successfully, showcasing its effectiveness in optimizing energy distribution, improving fuel efficiency, and enhancing overall vehicle performance. These applications could span diverse scenarios, including variations in driving conditions, load demands, and component efficiencies. The vastness of applications, as presented in the referenced literature, further validates the robustness and versatility of the proposed control strategy. Whether in optimizing power split HEVs or other hybrid energy systems, the combined fuzzy logic and neural network approach emerges as a transformative solution for achieving adaptive and efficient energy management control. In your exploration of this topic, consider delving into specific examples or findings from the cited literature to illustrate this control strategy’s practical impact and relevance in real-world energy management scenarios.

Fuzzy logic stands out as a valuable and interpretable tool within energy management control. Its rule-based decision-making, linguistic variable interpretation, and transparency make it particularly well-suited for applications in optimizing energy distribution, as evidenced in the area of study. However, it is essential to acknowledge that while fuzzy logic excels in energy management control, its utility may be somewhat limited to this specific domain. The strength of fuzzy logic lies in its ability to provide human-understandable decision rules, ensuring that control strategies are transparent and interpretable. This attribute is especially beneficial in energy management scenarios, where the need for expert validation and comprehensibility is paramount. The adaptability of fuzzy logic, coupled with its capacity for real-time optimization, contributes significantly to improving fuel efficiency and overall system performance. Nevertheless, it is crucial to recognize that the application scope of fuzzy logic might not extend seamlessly beyond the realm of energy management control. Other optimization problems or decision-making contexts may require more advanced computational approaches, such as hybrid systems combining fuzzy logic with neural networks or other artificial intelligence techniques. In essence, while fuzzy logic serves as a robust solution for energy management control, its effectiveness may be context-dependent. Acknowledging its limitations outside this domain encourages researchers and practitioners to explore complementary methodologies and hybrid approaches to address a broader spectrum of challenges in diverse fields. The continued exploration and integration of advanced computational techniques, such as the combination of fuzzy logic with neural networks, promise to push the boundaries of optimization and decision-making in various complex systems.

5.3. Optimization Techniques for PHEV EMS with Real-Time Constraints

Selecting the most effective optimization technique for a PHEV’s energy management system (EMS) hinges on striking a critical balance between several key factors. This analysis will compare various optimization techniques commonly employed in PHEVs, evaluating their performance based on four crucial metrics [166,167]:

• Computational Efficiency: Real-time applications demand fast decision-making. Techniques like rule-based control and Model Predictive Control (MPC) with a short prediction horizon are prime contenders in this category.
• Scalability: The ability to handle increasing system complexity is vital. Dynamic Programming (DP), for instance, struggles with intricate PHEV models, whereas techniques like Equivalent Consumption Minimization (ECMS) and Reinforcement Learning (RL) demonstrate better adaptability.
• Solution Quality: The ideal technique should effectively balance fuel efficiency, battery life, and performance. DP and MPC have the potential to deliver globally optimal solutions, while ECMS and RL strive for well-rounded approximations.
• Real-Time Suitability: Techniques that offer rapid computation and adaptation are best suited for real-time implementation. Rule-based control, ECMS, and MPC with limited prediction horizons generally excel in this area.

Table 8. Comparison of Optimization Techniques for PHEV EMS with Real-Time Constraints.

Technique	Description	Limitation	Computational Efficiency	Scalability	Solution Quality	Real-Time Suitability
Rule-based Control	Pre-defined rules govern power distribution based on factors like battery SOC, speed, and driver demand.	Can be inflexible and may not adapt well to unforeseen conditions. May not achieve optimal efficiency or performance.	High	High	Moderate	High
Dynamic Programming	Breaks down the optimization problem into smaller sub-problems, finding the optimal solution for each stage.	Computationally expensive for real-time applications, especially with long prediction horizons.	Low	Low	High	Low
Equivalent Consumption Minimization (ECMS)	A rule-based approach that approximates optimal control by minimizing a weighted sum of fuel consumption and equivalent electric energy consumption.	Requires careful tuning of weighting factors to achieve desired results.	Moderate	Moderate	High	Moderate
Model Predictive Control (MPC)	Uses a model of the PHEV to predict future behavior and optimizes power distribution over a finite time horizon	Computational cost depends on model complexity and prediction horizon.	Low (online)	Moderate	High	Moderate
Reinforcement Learning (RL)	Learns optimal control strategies through trial and error in a simulated environment or real-time experience.	Requires training time and can be computationally expensive.	Moderate	High	High (learning- based)	Moderate (learning required)

will provide a detailed comparison of these optimization techniques, highlighting their strengths and weaknesses in each of these crucial aspects. This comparison will empower you to make an informed decision when selecting the most suitable optimization technique for your specific PHEV EMS application [168].

6. Challenges and Future Directions

The integration of ML and optimization in PHEVs involve advanced system modeling and control strategies. It has been found that a modular design methodology incorporating more than two advanced methods and algorithms elevates the accuracy and effectiveness of the EMS proposed, enhancing ESS dynamics, and providing optimal configuration solutions for different user types. Deep Reinforcement Learning (DRL), Model-based Q-learning, and Particle Swarm Optimization (PSO) have recently been explored by researchers to generate EMS for PHEVS. The need for DRL comes from the fact that EMS requires integration of computer vision such that visual information captured is being used as a state input for a continuous DRL model to synthesize EMS strategies [8], where a fuel consumption reduction of 4.3% to 8.8% has been obtained compared to non-aided computer vision DP. With the increasing computational burden and the limited time during real-time executions and practical implementations, optimization may be difficult to achieve. In the following sections, the challenges in designing an EMS for PHEVs are presented in a format where the reader can acknowledge current limitations that might be explored in future research directions.

6.1. Towards More Intelligence

DRL has gained momentum in the EMS for PHEVs arena. The EMS problem has emerged from an isolated vehicle-only system to a crucial component of a larger Intelligent Transportation System (ITS) under the Smart Grid (SG) scenario in Smart Cities (SC). The emerging technology for creating a more decentralized, intelligent energy paradigm is DL and DRL. Decentralizing the functional components of an EMS system is achieved by integrating cloud services that allow the existence of optimized services for a real-time EMS, as in the case of PHEV buses in [129] where an MPC-based EMS is combined with a cloud-enabled speed profile optimizer and vehicle speed predictor.

Besides DRL, with the rapid development of artificial intelligence and computing technology, learning algorithms have been gradually applied to the design of EMS and have recently become a novel research hotspot. Learning algorithms have been implemented in terms of Reinforcement Learning Algorithms (RL), and DL. However, research is directing efforts towards reducing time execution in real-time applications and lightening software implementation when using computer vision. In fact, the uncertainty and low convergence speed of DRL methods impede direct application to real-world scenarios [10]. With the increasing dimension of the control problem, the learning stage is heavily burdened, hence, optimization potential is reduced [40]. It has also been found that implementation of DRL in non-linear systems poses challenges in mapping complexities for control signal outputs, that is, there is an inherent difficulty in implementing DRL with physical constraints [7].

6.2. Challenges

Some challenges in the design of EMS for PHEVs are described below.

• Data and Modeling Accuracy: Obtaining accurate and representative data for training ML models is a hurdle, as driving conditions and user behaviors vary widely. Additionally, the complexity of the PHEV system poses a challenge for developing accurate models.
• Computer capabilities: Real-time implementation of optimization algorithms is constrained by computational limitations, impacting their responsiveness in dynamic driving environments. Moreover, the uncertainties associated with external factors, such as traffic conditions and weather, pose challenges for predictive modeling and optimization strategies.
• Addressing real-time operation conditions: Presents a significant challenge due to the dynamic and uncertain nature of driving conditions and powertrain operation. Real-time operation conditions refer to the need for the EMS to make rapid and accurate decisions in response to changing factors such as vehicle speed, road grade, traffic conditions, driver behavior, and power demand.
• Managing battery SOC: The SOC represents the amount of energy stored in the battery, and effective management of SOC is crucial for maximizing vehicle performance, extending battery life, and optimizing fuel economy. Managing SOC involves dynamic fluctuations of operating conditions, trade-offs between performance and battery health, uncertainty in driving patterns, modeling and control complexity, and integration with vehicle dynamics.

Addressing these challenges is crucial for enhancing the effectiveness of ML and optimization techniques in real-world EMS applications for PHEVs. The application ML and Optimization in EMS for Plug-In Hybrid Electric Vehicles PHEVs faces several challenges in real-world scenarios.

Traditional convex optimization techniques may not be suitable for real-time applications due to their computational complexity and time-consuming nature, although can be part of EMS subproblems such as the examples in MPC implementations. ML, such as DRL and other online learning algorithms, offer promising solutions by enabling the EMS to learn from past experiences and adapt its control strategy in real-time; however, limitations in obtaining an optimum may be restricted due to the dimensionality of the problem and the learning burden. Ensuring the reliability and robustness of ML-based control algorithms in real-world driving scenarios is challenging. PHEVs operate in highly dynamic and uncertain environments, where unexpected events such as sudden changes in traffic conditions or road obstacles can occur. ML models need to be trained on a large, diverse, and representative dataset to generalize well to unseen situations and mitigate the risk of catastrophic failures.

Fluctuations in battery state-of-charge are difficult to handle, especially because they depend on various factors including the energy management of the battery itself and the real-time vehicle conditions. Various innovative approaches have been developed. For instance, an improved deep learning-based velocity prediction control EMS uses feature engineering and LSTM velocity prediction to prolong battery life and optimize power allocation online [169]. Other approaches focus on using data-driven fault prediction models to monitor battery performance and predict potential issues [170]. Data-driven regression model utilizing ML has been developed to predict the state of charge of a battery with high accuracy, enhancing the monitoring and control of battery fluctuations [171]. Nevertheless, challenges remain in fully leveraging the potential of ML in battery research, needing further initiatives in academia and industry [172]. These strategies showcase the ability of ML-based EMS to dynamically respond to changing battery conditions and enhance overall system efficiency in real-time scenarios.

6.3. Future Vision for EMS

The future vision for Energy Management Systems in Plug-in Hybrid Electric Vehicles includes innovative strategies aimed at boosting efficiency. These may leverage learning algorithms, which could prove more effective even under heavy processing loads, potentially incorporating computer vision technology. Nevertheless, it is compelling that reliability and security comply and surpass the current standards such that any issue is resolved within the critical time, that is, no decision-making must take more than the time required to update control signals and maintain the system safe. In this matter, it is expected that the configuration of EMS continues integrating several processes implemented with different algorithms according to the complexity and reliability of the system.

Due to the stringent reliability constraints and the limitation for decision-making in real-time EMS implementations, a potential area of research for the design of an EMS may be the use of techniques based on multiparametric programming (MP) [173]. MP has indeed been used in some MPC implementations for process manufacturing [130]; its main idea relies on the parametrization of optimization problems into functions that can be evaluated, similarly to the lookup table task. Hence, this can be simpler and faster to evaluate than solving a full optimization problem online. Depending on the nature of the problem, MP can feature integer variables (MP is known to be an MP mixed-integer programming problem MP-MIP), and if constraints are affine, MP could become an MP mixed integer linear, quadratic, or non-linear programming problem.

Because the EMS is in nature a control system of a non-linear non-convex system in most cases where determining what happens in every scenario with algebraic mathematics could be cumbersome due to the high dimensionality of the problem, researchers have explored the utilization of Linear Temporal Logic (LTL) and Signal Temporal Logic (STL) as a mathematical language that could better describe the conditions under which an action is executed [174]. LTL is a formal language used to specify and reason about temporal properties of reactive systems. A reactive system is a type of computer system that continuously interacts with its environment, reacts to external stimuli, and produces output based on those interactions, just as an EMS is desired to behave in PHEVs. LTL has been used in controller synthesis in power system applications [175] and automata research [176].

EMS will require extended computational capabilities because it will be integrated into other control systems such as computer vision and real-time power and energy split between power sources onboard. The inclusion of new techniques will depend on an appropriate problem division into subproblems such that each stage is effectively solved within stringent constraints. Moreover, the replacement of the ICE with other renewable or green power sources will provide new challenges to resemble traditional car dynamics to current drivers and customers.

7. Conclusions

The present paper explores Machine Learning and Optimization in Energy Management Systems for Plug-In Hybrid Electric Vehicles (PHEVs). The integration of learning algorithms in this domain has gained significant momentum, particularly in addressing more complex problems that involve computer vision and larger dimensional datasets. These advancements have enabled EMS to enhance their predictive capabilities and optimize energy distribution more effectively. Optimization techniques, in particular, have proven to be highly effective when time constraints are managed efficiently, which is especially critical for real-time applications. The combination of ML and optimization has shown promise in improving the overall efficiency and performance of PHEVs, offering a substantial leap beyond traditional methods.

Looking forward, it is anticipated that learning algorithms will benefit from the continual advancements in processor capabilities, enabling even more sophisticated analyses and faster computations. The future trend suggests breaking down the overarching problem into several interconnected subproblems, each addressed with specialized control algorithms. This modular approach is expected to achieve higher efficiencies and more robust solutions. Additionally, the ongoing development of ML frameworks and optimization techniques will likely result in more adaptive and resilient EMS for PHEVs, paving the way for smarter and more sustainable transportation solutions.