Accurate and Efficient Energy Management System of Fuel Cell/Battery/Supercapacitor/AC and DC Generators Hybrid Electric Vehicles

Abstract

The development of hybrid electric vehicles (HEVs) is rapidly gaining traction as a viable solution for reducing carbon emissions and improving fuel efficiency. One type of HEV that is gaining significant interest is the fuel cell/battery/supercapacitor HEV (FC/Bat/SC HEV), which combines fuel cell, battery, supercapacitor, AC, and DC generators. These FC/B/SC HEVs are particularly appealing because they excel at efficiently managing energy and cater to a wide range of driving requirements. This study presents a novel approach for exploiting the kinetic energy of a sensorless HEV. The vehicle has a primary fuel cell resource, a supercapacitor, and lithium-ion battery energy storage banks, where each source is connected to a special converter. The obtained hybrid system allows the vehicle to enhance autonomy, support the fuel cell during low production moments, and improve transient and steady-state load requirements. The exploitation of kinetic energy is performed by the DC and AC generators that are linked to the electric vehicle front wheels to transfer the HEV’s wheel rotation into power, contributing to the overall power balance of the vehicle. The energy management system for electric vehicles determines the FC setpoint power through the classical state machine method. At the same time, a robust speed controller-based artificial intelligence algorithm reduces power losses and enhances the supply efficiency for the vehicle. Furthermore, we evaluate the performance of a robust controller with a speed estimator, specifically using the adaptive neuro-fuzzy inference system (ANFIS) and the model reference adaptive system (MRAS) estimator in conjunction with the direct torque control-support vector machine (DTC-SVM), to enhance the torque and speed performance of HEVs. The results demonstrate the feasibility and reliability of the vehicle while utilizing the additional DC and AC generators to extract free kinetic energy, both of which contributed to 28% and 24% of the total power for the vehicle, respectively. This approach leads to a vehicle supply efficiency exceeding 96%, reducing the burden on fuel cells and batteries and resulting in a significant reduction in fuel consumption, which is estimated to range from 25% to 35%.

1. Introduction

In the transportation sector, there has been significant interest in HEVs as a possible approach to enhance energy efficiency and mitigate greenhouse gas emissions [1]. Greenhouse gases, harmful pollutants, and particulate matter resulting from the utilization of fossil fuels are causing severe damage to the environment and pose risks to human well-being, which is of increasing importance. Therefore, it is crucial to promptly replace conventional fuel vehicles with HEVs that can be powered by renewable energy sources [2,3]. By combining different energy storage technologies, HEVs can fulfill the dynamic electrical requirements of the vehicle while avoiding energy losses and maximizing resource efficiency by integrating multiple energy storage systems [4]. This integration allows HEVs to adapt to varying driving circumstances, resulting in better fuel efficiency and lower environmental impact [5]. The integration of multi-energy sources, such as FCs, batteries (Bats), and SCs, has allowed HEVs to achieve optimum power distribution and performance [6].

Efficient energy management systems (EMSs) are critical for achieving the full potential of HEVs, for ensuring the smooth functioning of these numerous sources of energy, for ensuring that there is an efficient energy transfer between the power drive and the wheels, and for increasing the overall efficiency of the vehicle [7]. However, high peak power consumption during acceleration and deceleration periods can degrade the battery life cycle and reduce the EV’s drive range [8]. Indeed, when faced with fluctuating load conditions, fuel cells tend to be less compatible with just the battery in the same system due to their slow response time. As a result, it is common practice to combine fuel cells with secondary energy storage systems as supercapacitors or secondary batteries, which establishes a “hydrogen-electric hybrid energy storage system” for electric vehicles. This integration allows for a more efficient and responsive power delivery [9].

Hybridizing different energy resources and implementing efficient EMSs can address these challenges [10,11]. Using complex algorithms and control methodologies, these systems monitor and regulate the energy transfer between different sources, such as FCs, Bats, and SCs [12]. The EMS guarantees that each energy source performs within its ideal efficiency range by intelligently controlling the power distribution, extending its lifetime, and avoiding loss [13]. Furthermore, the EMS automatically modifies the power distribution depending on the driving circumstances, driver behavior, and real-time energy needs, allowing the vehicle to efficiently run under all situations [14].

Garcia et al. [15] discussed a hybrid system used in the Seville tramway, which combines a fuel cell (FC) and a battery to power the tram. The FC serves as the primary energy source, while the battery acts as a backup source during acceleration, cruising, and energy recovery from braking. The system in the study included four traction induction motor drives and two converters for power conditioning. An EMS was used to control the power flow and manage the energy dissipation during regenerative braking. The study evaluated the hybrid system using the actual driving conditions of the tramway and demonstrated its ability to meet the performance requirements. Khalid [16] presented a comprehensive review of the hybrid storage paradigm, examining recent advances and research developments. The study focused on integrating Bats and SCs in hybrid energy storage systems.

Furthermore, the review discussed the control strategies implemented in different applications. It highlighted the benefits of combining Bat and SC systems and offered valuable insights for the future progress of energy storage technology and its practical use. Suberu et al. [17] discussed three categories of energy storage systems (ESSs) technologies (pumped hydroelectricity storage, Bats, and FCs) for managing the intermittency of renewable energy (RE). HEV energy management systems recharge batteries through regenerative braking and utilize residual energy from FCs in low- and no-load power systems. Batteries function as energy storage units, continuously providing power based on their charging and discharging cycles [18]. However, batteries have a finite lifespan that depends on factors such as operating temperature (around 20 °C), depth of discharge (DoD), and number of cycles. Lead–acid batteries typically last for 1000 cycles, whereas Li-ion batteries can last for 1900 cycles [19]. Li-ion and Ni–MH batteries are lighter and have more energy than lead–acid batteries. Lead–acid batteries are cheaper and quickly respond to current changes [20].

Furthermore, SCs offer a rapid charging capability, which allows for the efficient utilization of regenerative braking. Given their potential as energy storage devices in the near future, various industries are keenly interested in developing SCs using innovative technologies and material designs. Laboratory experiments have shown that SCs can achieve energy densities as high as 300–400 Wh·kg⁻¹; however, it is anticipated that future lithium-based batteries will surpass these values, reaching energy densities in the range of 380–590 Wh·kg⁻¹ [19].

Figure 1 provides a comparison of the power output and energy density among various energy sources and storage media.

The study mentioned above highlighted these technologies’ advantages, disadvantages, and various applications. The study emphasized that ESS selection depends on the performance characteristics and fuel sources, and no single ESS can meet all requirements. Sankarkumar and Natarajan [21] provided an overview of hybrid ESS configurations, EMS techniques, and their performance evaluation in EVs. The study conducted a comparison of performance indicators, including the reduction of battery peak current, power storage during regenerative braking, system design, and voltage fluctuations. Fu et al. [22] presented an EMS for HEVs with FC, Bat, and SC sources. The strategy aimed to enhance energy source lifespan, power performance, and fuel economy. The FC was the primary energy source, while the Bat and SC provided support and storage. The SC managed power fluctuations to reduce the stress on the FC and Bat, while the battery improved hydrogen fuel efficiency. The proposed EMS employed adaptive low-pass filtering for the peak power supply and energy recovery and an equivalent consumption minimization strategy (ECMS) for the optimal power allocation.

Benhammou et al. [23] proposed a hybrid system that combined FCs, SCs, lithium-ion batteries, and DC generators linked to the HEV’s front wheels for additional power generation. An energy management strategy and dual-loop structure optimized the power regulation and efficiency. The results confirmed the system’s feasibility, achieving a 28% contribution from free kinetic energy and reducing the stress on FCs, batteries, and fuel consumption. Li et al. [24] proposed a hybrid powertrain configuration for tramways, which consisted of a proton exchange membrane FC (PEMFC), battery, and SC without a grid connection. An EMS with a power-sharing strategy combining fuzzy logic control (FLC) and Haar wavelet converts (Haar-WT) was proposed to maintain high efficiency and prevent the degradation of the mechanism’s performance. The results showcased that the system efficiently handled the power demand; the PEMFC effectively managed the major positive low-frequency components, the battery alleviated the burden on the PEMFC, and the SC supplied the high-frequency components. The energy management system proposed ensured safe operation, extended the energy source lifetime, and achieved superior energy efficiency compared with other control strategies employed in hybrid tramways. Thounthong et al. [25] presented a hybrid HES that collects a PEMFC, battery, and SC for distributed generation and future FC vehicle applications. The system achieved energy balance through DC bus voltage regulation, with the SC regulating the voltage, the Bat keeping the SC charged, and the FC ensuring that the battery remained charged. The control algorithm utilized three voltage control loops for the different components. The experimental results confirmed the effectiveness of the suggested control principle in regulating the motor drive cycle. Sun et al. [26] addressed the challenges faced by FC HEVs, such as FC durability and power allocation efficiency. A novel energy management strategy based on game theory was introduced to improve operational stability in challenging driving scenarios. The strategy considered the controller and anticipated driving conditions as players in the game, utilizing interval forecasting and a co-evolutionary algorithm to optimize power allocation. This method was evaluated against other strategies in various driving conditions and showed a reduction in hydrogen consumption and FC degradation. The outcomes demonstrated the efficacy of the suggested strategy in improving fuel efficiency and system robustness. Fathabadi [27] presented an innovative FC/Bat/SC hybrid power source for FCHEVs, comprising a 90 kW PEMFC stack as the primary power source complemented by a 19.2 kW Lithium-ion battery and 600 F SC bank as auxiliary energy storage devices. This hybrid power source offers advantages such as a top speed of 161 km/h, acceleration from 0 to 100 km/h in 12.2 s, and a cruising range of 545 km. Jiang et al. [28] optimized the EM and component sizing for FC-EVs to reduce energy consumption and enhance FC durability. The authors introduced a model of a bus equipped with an FC, battery, and SC powertrain. By utilizing a two-dimensional dynamic programming (DP) algorithm, the energy consumption and system degradation were minimized. The study introduced a real-time energy management strategy that relies on the principles of Pontryagin’s 2D Minimal Principle (2DPMP). The simulation results demonstrated the effectiveness of the proposed strategy in minimizing energy consumption and enhancing durability, and it outperformed other strategies. The simultaneous optimization of the component parameters and energy management strategy offers valuable insights for improving energy management and determining appropriate component sizes. Bambang et al. [29] addressed the slow dynamics of FCs as the primary power source in HEVs and proposed supplementing batteries and SCs to overcome this limitation. A feedback control system was developed to regulate the FCs, batteries, and SCs hybrid power system. Three DC–DC converters were used to regulate the output current and voltage of the power sources. The implementation of model predictive control (MPC) technology was employed in this process to generate reference currents for each converter, which were then tracked using hysteresis control. The experimental results demonstrated the feasibility and effectiveness of the control system in regulating the current slope of FCs and batteries and in maintaining the DC bus voltage in accordance with the reference values. Odeim et al. [30] focused on an experimental FC/battery/SC hybrid system with an emphasis on modeling and power management design. The optimized results were validated through experimentation on a test bench featuring an FC system, lithium polymer battery, and SC. Ammar et al. [31] presented a comprehensive review of the optimization of classical direct torque control (DTC) by a DTC-SVM-based robust controller. Ammar et al. [32,33] also provided an overview of the limitation of the classical controller compared with robust ones, and the authors also provided the impact of robust controllers on the system efficiency. Fahassa et al. [34] examined the effect of the ANFIS speed controller in traction systems, where the authors provided an overview of the behavior of this robust controller in the DTC controller. The MRAS algorithm allows for the integration of robust controllers, especially in traction systems, despite its limitations [35].

This study aims to address the limitations of electrical systems in the transportation sector, particularly their limited resources. The objectives are to propose solutions that enhance system autonomy and performance, including extending the autonomy of EVs, reducing stress on Bat and FC resources, exploiting the kinetic free energy of EVs as an additional energy contribution, and implementing a robust database-driven control unit to eliminate the need for speed sensors (MRASs) in the traction system. Additionally, this study focuses on developing robust control strategies for efficient power management.

A powerful and accurate EMS is proposed to ensure the seamless operation of the multiple energy sources in HEVs. This EMS effectively optimizes power allocation and minimizes energy consumption, leading to enhanced overall system efficiency. Furthermore, the study evaluates the performance of a robust controller with a speed estimator, specifically utilizing the ANFIS and model reference adaptive system (MRAS) estimator in conjunction with the direct torque control-support vector machine (DTC-SVM). This integrated control approach aims to enhance the torque and speed performance of HEVs, resulting in improved overall system efficiency and reliability.

The incorporation of a specialized database and speed estimator into the control system provides a precise foundation for power allocation and resource utilization. The robust controller effectively handles uncertainties and fluctuations in operating conditions, ensuring precise power management and system stability. Furthermore, the speed estimator provides real-time input on the vehicle’s speed, enabling accurate torque management and ensuring smooth and economical operation. Comprehensive simulation tests were conducted on a 30 kW sensorless HEV system to assess the proposed EMS. The simulations employed identical initial conditions and energy management algorithms to accurately compare alternative topologies. Furthermore, the effect of including additional energy sources, such as DC and AC generators, was examined, underlining the need for careful planning to ensure optimum system performance.

One key research gap is addressing the limitations of classical controllers in electrical systems, especially traction systems, which necessitates robust controllers. Additionally, reliance on speed sensors in the control system introduces reliability and cost challenges. To address these gaps, this study explores robust control strategies based on artificial intelligence and explores the use of speed estimators as alternatives to speed sensors.

The novelty of this study is in the evaluation of the performance of adding DC and AC generators to harness the HEV’s kinetic energy. This evaluation improves control robustness, power-sharing efficiency, and system reliability. This study incorporates the use of robust controllers, speed estimators, and advanced control techniques such as ANFIS and MRAS estimators.

The study is structured in the following manner: Section 1 presents the models of the HEVs under study. Section 2 provides an overview of the basic principles and subsystems in HEVs. Section 3, Section 4, Section 5, Section 6 and Section 7 introduce the proposed techniques and topologies and present the results and discussions. Finally, the paper summarizes the study’s findings and provides insights into future perspectives.

2. Description of the Proposed Models

The study examines HEVs with a two-wheel drive configuration, as illustrated in Figure 2. Each HEV topology comprises three energy sources: FC, Bat, and SC. The only difference between the two topologies depicted in Figure 2a,b is the presence of either DC generators (Figure 2a) or AC generators with a gear multiplier on the front wheels.

Specialized converters are employed to maintain a balanced power flow and consistent DC bus voltage in the powertrain. The FC is linked to a DC–DC Boost converter to elevate the output source voltage to 400 V. The battery energy storage system (BESS) and SC are linked with bidirectional converters (DC–DC) to ensure a uniform DC bus voltage (400 V) and power balance in the system.

In the first topology (Figure 2a), the boost converter is responsible for regulating the DC bus voltage and is controlled by the maximum power point tracking (MPPT) algorithm to minimize the low-speed impact. In the second topology (Figure 2b), the output of the AC generators is connected to the AC–DC converters after being linked to an additional DC–DC converter.

The electric motors of the HEV draw power from a power inverter, which is controlled by the sensorless ANFIS DTC-SVM algorithm using an MRAS estimator.

Table 1. The HEV system specifications.

Type	Parameters	Value
HEV	fr	0.0133
	rt (m)	0.32
	cd	0.32
	ρair (kg/m3)	1.109
	A (m2)	2.61
	Drives power (kW)	30
Fuel cell	voltage (v)	200
	MOP and NOP (A, V)	150,200 and 40,200
	Cells number	285
	H2 pressure (bar)	1.5
	Efficiency (%)	55
	Composition: H2O, H2, and O2 (%)	1–99.95, and 21
DC Generator	Ra (Ω)	0.8727
	Power (kW)	3
	La (H)	0.001882
	Tem (N·m)	4.2
AC Generator	Power (kW)	3
	Voltage (V)	320
	Torque (N·m)	4
Battery pack	Capacity	20 Ah
	Voltage (V)	200
	Fully charged (V)	230
SC bank	Rated voltage	200
	Resistance (Ω)	2 × 10−4
	Capacitance (F)	14.6

provides an overview of the HEV’s different parameters and specifications.

Longitudinal vehicle dynamics determine the power demand (P_Load) of an HEV, which is expressed in Equation (1) [36]:

$$P_{Load}=V_0\left(\left(m·g·f_r·\cos (\theta \right)+\frac{1}{2}{\rho }_{air}\times V_0{}^2\times A\times C_d\right)+\left(m·g·\sin (\theta \right)+m·\delta \frac{dv}{dt}))$$

(1)

where V₀ represents the velocity of the EV, m denotes the weight of the EV, $g$ signifies the gravitational acceleration, A represents the frontal area, f_r denotes the rolling resistance coefficient, θ represents the road slope, C_d represents the air coefficient, ${\rho }_{air}$ represents the air density, and Δ denotes the mass conversion factor.

3. Power Hybrid Electric Vehicle Modeling

This section presents a detailed and accurate model of each subsystem of the HEV (control, power, and management), which is essential for comparing the proposed topologies. Table 1 provides the parameters of the HEV, with all topologies having identical initial conditions and parameters.

3.1. Fuel Cell (FC)

The FC is a kind of galvanic cell that transfers chemical energy into electrical energy through an electrochemical reaction, which does not require any mechanical or heat processes; only oxygen is needed to initiate the reaction. The membrane electrode assembly (MEA) is a key component comprising a membrane and two gas diffusion layers [37]. Noble metal catalysts are incorporated into this assembly. Perfluorosulfonic acid membranes such as DuPont’s Nafion membrane are used as membrane materials. These membranes facilitate proton conduction, maintaining a balanced electron transfer and establishing a closed-loop system [38].

A hybrid FC system typically includes a stack and a balance of plant (BoP), which consists of a heat exchanger, air compressor, hydrogen (H₂) tank, cooling system, and humidifier. The electric energy produced by the FC is low-voltage DC, which is used for direct work [39,40]. The main chemical reaction in the thermodynamics of an FC is represented by Equation (2) [36].

2O₂ + 2H₂→2H₂O + Heat + Energy

(2)

where O is oxygen and H is hydrogen. Considering the presence of all losses that result in voltage drop in an FC, the FC voltage can be expressed by Equation (3) [41,42].

$$v_{fc}=V_{nerst}+V_{act}+V_{ahmic}+V_{con}$$

(3)

The FC voltage obtained from the sum of four voltage components, reversible voltage (V_nerst), activation losses voltage (V_act), concentration losses voltage (V_con), and ohmic losses voltage (V_ohmic), are illustrated in Equation (3). The values of these voltage components depend on various factors such as the reactant gases’ temperature, pressure, and flow rate. The used parameters of the FC in this study after dimensioning are given in Table 1.

3.2. Li-Ion ESS

Lithium-ion (Li-ion) batteries have gained popularity as energy storage units due to their excellent energy density and efficiency, and they have found widespread use in various industries [43,44]. Their desirable properties have made them an attractive option for traction systems [35]. The simulation tool SimPowerSystems (SPS MATLAB 9.7 R2019b) uses a mathematical representation of the battery, specifically a modified Shepherd curve-fitting model. This model includes voltage polarization as an additional element in the battery discharge voltage equation. By incorporating this aspect, the model highlights the impact of the battery’s state of charge (SoC) on its overall performance [45]. To ensure consistent outcomes in the simulation, the computation of the polarization resistance relies on a filtered battery current rather than the direct measurement of the battery current. This approach is implemented to maintain reliability and accuracy in the simulation results. Figure 3 provides a schematic to simplify the battery energy storage system (BESS) model [46].

3.3. DC Generator

A permanent magnet DC generator (PMDCG) is an apparatus that transforms mechanical energy into direct current electrical energy. Instead of using rotor windings, permanent magnets are employed, eliminating the requirement for an independent DC power source, slip rings, or contact brushes. PMDC generators can be integrated with various systems, such as turbines [47], diesel generators [48], and hybrid vehicles [23]. They are not restricted to any specific working environment and can be used in wind turbines and water turbines. The primary application of PMDCGs is to harness the kinetic energy of EVs, similar to how wind energy is harnessed.

Equation (4) depicts the model of a PMDCG [49]. The DC generator parameters are listed in Table 1.

$$\left\{\begin{array}{c}{V}_a=E-R_a\times I_a\hfill \\ P_a=V_a\times I_a\hfill \end{array}\right.$$

(4)

where V_a is the output voltage, E is the electromotive force, R_a is the resistor, I_a is the current DC generator, and P_a is the output power.

Figure 4 shows the PMDCG connected to the EV wheel.

Typically, commercial models of DC generators have a high weight-to-power ratio and require special working environments, particularly those with high nominal speeds [50].

3.4. AC Generator

A permanent magnet synchronous generator (PMSG) is an AC generator composed of a stator and rotor, where a permanent magnet rather than a coil creates the excitation field. The term “synchronous” signifies that the rotor and magnetic field rotate at an identical speed, as the magnetic field is generated by a permanent magnet mechanism that is mounted on the shaft [51]. Equation (5) represents the model of the PMSG.

$$\left\{\begin{array}{c}d{i}_d=-\frac{R_s}{l_s}{i}_d+p\times i_q\times \Omega +\frac{1}{l_s}{u}_d\hfill \\ d{i}_q=-\frac{R_s}{l_s}{i}_q-p\times i_d\times \Omega -\frac{p{\Phi }_f}{l_s}\Omega +\frac{1}{l_s}{u}_q\hfill \\ d\Omega =\frac{p{\Phi }_f}{j}{i}_q-\frac{f}{j}\Omega -\frac{1}{j}{c}_r\hfill \\ d\theta =\Omega \hfill \end{array}\right.$$

(5)

where i_d represents the current along the d-axis, i_q represents the current along the q-axis, R_s represents the stator resistor, p represents the pole number, Ω represents the speed, l_s represents the stator inductor, u_d represents the voltage along the d-axis, u_q represents the voltage along the q-axis, ϕ_f represents the flux, and c_r represents the torque from the resistor. The PMSG generates electromagnetic power P_e, which is given by Equation (6), neglecting copper loss (i.e., assuming that the stator resistance Rs equals zero) [52,53].

$$P_E=U_d{i}_d+U_q{i}_q$$

(6)

Typically, AC generators using PMSGs are widely used in industry due to their affordability, performance, and ease of diagnostics. However, integrating AC generators in HEVs faces the challenge of weight, which requires special construction to achieve the desired performance. Figure 5 illustrates the connection between the wheel of the electric vehicle and the AC generator. The basic concept of using AC generators in HEVs is similar to wind energy [54].

3.5. Supercapacitor (SC)

The SC, also known as an ultracapacitor, is an energy storage device that is characterized by a considerably higher capacitance value compared with traditional capacitors, albeit with lower voltage restrictions. It has the capability to store energy at a volume efficiency that is 10 to 100 times greater per unit volume, delivering power much faster than Li-ion batteries and lasting many more life cycles than other energy storage units, such as batteries [55].

Due to their quick response time, SCs are extensively employed in HEV applications that require fast charge/discharge cycles, including for regenerative braking, short-term energy storage, and for providing quick startup power. The SoC of SC and current can be described by Equation (7) [56,57], where V_max is the maximum voltage of the SC, V_min is the minimum output voltage, V_sc is the voltage across the capacitor, and R_sc is the equivalent resistance.

$$\begin{gathered} V_{sc}=SoC\left(V_{max}-V_{min}\right)+V_{min} \\ I=\frac{v_{dc}-\sqrt{v_{dc}^2-4R_{sc}{P}_{sc}}}{2R_{sc}} \end{gathered}$$

(7)

where V_sc is the SC voltage, SoC is the SC state of charge, V is the maximal and minimal voltage, I is the SC current, V_dc is the DC voltage, R_sc is the SC resistor, and P_sc is the SC power.

3.6. DC–DC Bi-Directional Converter

DC–DC bidirectional converters are linked to the system’s energy storage units that are depicted in Figure 2. Equation (8) describes the bidirectional buck–boost converter mathematic model [58].

$$\left\{\begin{array}{c}\frac{d{i}_{in}}{n}=\frac{-u{v}_{dc}}{L}-\frac{-r_L{i}_{in}}{L}+\frac{v_{in}}{L}\hfill \\ \frac{d{v}_{dc}}{dt}=\frac{u{i}_{in}}{C}+\frac{-P_{EV}}{C\times v_{dc}}\hfill \end{array}\right.$$

(8)

where i_in, v_dc, v_in, P_EV, L, and C are the input current, DC voltage, input voltage, EVs energy, converter inductor, and converter capacitor, respectively.

3.7. DC–DC Boost Converter

In Figure 1, the FC, DC generator, and AC generator outputs are linked to boost converters (DC/DC) to provide a common DC voltage of 400 V. The boost converters are modeled by Equation (9) [59,60].

$$\left\{\begin{array}{c}\frac{d{i}_{in}}{n}=\frac{-\left(1-u\right)v_{dc}}{L_{Boost}}+\frac{v_{in}}{L_{Boost}}\hfill \\ \frac{d{v}_{dc}}{dt}=\frac{\left(1-u\right)i_{in}}{C_{Boost}}+\frac{-v_{dc}}{R \times C_{Boost}}\hfill \end{array}\right.$$

(9)

where i_in, C_Boost, V_in, R, L_Boost, and V_dC represent the input current, converter capacitor, input voltage, load resistor, boost inductor, and DC bus voltage, respectively.

4. Sensorless ANFIS DTC SVM

An ANFIS controller can learn and map a system’s input and output signals [61]. As ANFIS is independent of the system model, it uses the given data (output/input) and selected membership. ANFIS controllers are effective in nonlinear systems, combining fuzzy logic and neural network (NN) adjustments [62,63]. Fuzzy rules use the input data from the artificial neural network (ANN) that is trained and from the NN formation sets to determine the output [64,65]. DTC-SVM utilizes three proportional-integral (PI) controllers to generate reference torque and voltage values (d/q) to control the switches using the SVM technique [66].

The speed estimator based on MRAS utilizes the motor’s current and voltage to generate the adjustable and reference flux models. The input to the control unit is obtained by comparing the adaptive and adjustable results to reduce the error between them and obtain the speed estimator value. In the ANFIS DTC-SVM approach, the PI controllers are replaced by an ANFIS controller. This method utilizes two PI controllers and an additional ANFIS controller that is integrated with the SVM algorithm. The design mode of the sensorless ANFIS DTC-SVM is illustrated in Figure 6 [35].

4.1. Space Vector Modulation (SVM)

The utilization of the space vector modulation (SVM) technique enables the modulation of reference voltage components, which in turn generates the control signals for the inverter. Figure 7 illustrates the three surrounding vectors for each sector. The duration of application for each vector is determined through vector calculations, while the remaining time is allocated for the application of the null vector. Equation (10) is used to determine the duration of vectors T₁ and T₂ [67,68].

$$\left\{\begin{array}{c}{T}_1=\frac{T_s}{2.v_{DC}}\left(\sqrt{6}{v}_{\beta s}{}^{*}-\sqrt{2}{v}_{\alpha s}{}^{*}\right)\hfill \\ T_2=\sqrt{2}\frac{T_s}{v_{DC}}{v}_{\alpha s}{}^{*}\hfill \end{array}\right.$$

(10)

V_αs $v_{\alpha s}{}^{*}$ and $v_{\beta s}{}^{*}$ represent the reference voltage vectors, T₁ and T₂ denote their respective durations, T_s represents the sampling time, and $v_{DC}$ represents the DC bus voltage. Equation (11) expresses the duty cycle calculation based on the SVM algorithm for the first sector, where T_a, T_b, and T_c represent the respective duty cycles.

$$\left\{\begin{array}{c}{T}_a=\frac{T_s-T_1-T_2}{2}\hfill \\ T_b=T_a+T_1\hfill \\ T_c=T_b+T_2\hfill \end{array}\right.$$

(11)

Figure 7 illustrates the voltage positions and first sector duty cycle, while

Table 2. Cycles of SVM outputs.

Sector	1	2	3	4	5	6
Sa	Tb	Ta	Ta	Tc	Tb	Tc
Sb	Ta	Tc	Tb	Tb	Tc	Ta
Sc	Tc	Tb	Tc	Ta	Ta	Tb

provides the states of each switch calculated based on the SVM unit.

4.2. ANFIS Controller

The ANFIS controller, which is illustrated in Figure 8, is an artificial intelligence approach that integrates neural networks and the Takagi–Sugeno fuzzy inference system. By utilizing a dataset of observations, this approach constructs a fuzzy inference system comprising input–output pairs [69]. The structure includes two inputs (error and its derivative), ANN layers, and one output (control signal u).

The mean-square error (MSE) is used in conjunction with the outputs of the working database to determine the membership function that represents the model’s best option for selecting the membership function. The task of choosing a suitable membership function for the fuzzification of input data poses a significant challenge that needs to be effectively addressed [70].

The influence of the membership function’s shape on a particular fuzzy inference system is the result of the form of the membership function. The fuzzy membership function can take on a variety of shapes, including Gaussian, trapezoidal, and triangular shapes, among others. It is assumed that the selection of the most appropriate type of membership function will lead to optimal prediction accuracy and desired outcomes. On the other hand, selecting the membership function that is best suited for a particular fuzzy model has been exposed to a significant amount of ambiguity [70].

The if/then rules can be derived using Equation (12) [71,72]:

$$R_n=If{M}_{1n}\left(e\right) and M_{2n}\left(e\right), then f=P_{n}e\left(t\right)+q_n\mathsf{\Delta }e\left(t\right)+r_n$$

(12)

where ‘n’ represents the rule number; M_1n and M_2n represent membership functions of fuzzy P_n; q_n, and r_n are the parameters of the nth rule; and e(t) and Δe(t) denote the error and its derivative. The computation of the degrees of membership functions is dependent on the input variable, which serves as the fundamental step of fuzzification. Each layer node is computed using Equation (13), where a_n, b_n, and c_n are set parameters. Layer 2 denotes the inference layer, where w_n (second layer outputs) is computed using Equation (14). Layer 3 is the normalization layer, which can be calculated from previous layers, as shown in Equation (15).

$$M_{1n}=\frac{1}{1+{\left[\frac{x-c_n}{a_n}\right]}^{bn}}$$

(13)

$$w_n=M_{1n}\left(e\right)\times M_{2n}\left(\Delta e\right)$$

(14)

$${\tilde{\omega }}_n=\frac{w_n}{{{\displaystyle \sum }}_n{w}_n}$$

(15)

In the ANFIS model, the fourth layer utilizes the input values that are generated by the preceding layer (layer 3). The nodes in this layer can be mathematically represented by Equation (16), where p, q, and r represent the set parameters and u signifies the control signal.

$${\tilde{\omega }}_{n}u={\tilde{\omega }}_n\left(P_{n}e\left(t\right)+q_n\Delta e\left(t\right)+r_n\right)$$

(16)

Layer 5 is the output layer, which sums up all of the previous node output signals to defuzzify the consequent part of the rules [73].

$${{\displaystyle \sum }}_n{\widetilde{(\omega }}_{n}u)=\frac{{{\displaystyle \sum }}_n{w}_{n}u}{{{\displaystyle \sum }}_n{w}_n}$$

(17)

Figure 9 illustrates the membership inputs of the ANFIS controller used in the sensorless ANFIS DCT-SVM.

4.3. Electromagnetic Torque and Flux Estimators

In DTC-SVM, the calculation of the flux components is illustrated by Equation (18) [74]:

$$\left\{\begin{array}{c}{\phi }_{\alpha s}={{\displaystyle \int }}_0^t\left(V_{\alpha s}-R_s{i}_{\alpha s}\right)dt\hfill \\ {\phi }_{\beta s}={{\displaystyle \int }}_0^t\left(V_{\beta s}-R_s{i}_{\beta s}\right)dt\hfill \end{array}\right.$$

(18)

where φ_αβs is the stator flux components in (α, β) farm, V_αβs is the stator voltage components, I_αβs is the stator current components, and R_s is the stator resistor.

The computation of the stator flux magnitude and electromagnetic torque can be expressed using the following equation [53]:

$$\left\{\begin{array}{c}\parallel {\phi }_s\parallel =\sqrt{{\phi }_{\alpha s}{}^2+{\phi }_{\beta s}{}^2}\hfill \\ T_{em}=P\left({\phi }_{\alpha s}·i_{\beta s}-{\phi }_{\beta s}·i_{\alpha s}\right)\hfill \end{array}\right.$$

(19)

where T_em represents the electromagnetic torque and P denotes the number of pole pairs.

4.4. MRAS Estimator-Based Rotor Flux

The MRAS-based rotor flux is a common method for velocity estimation in the field of speed estimation, and it is obtained by using voltage and current expressions [74]. The MRAS estimator comprises three fundamental components, namely an adjustable model, a speed adaptation mechanism (AM), and a reference model (RM) [75]. The AM determines the rotor speed by eliminating the error between the reference and adjustable models [76]. In contrast to the adaptive model, the adaptation mechanism in a closed-loop fashion utilizes the speed as the output variable, which is simultaneously employed within the adaptive model. The reference model, on the other hand, is independent of the calculated speed value. Figure 10 illustrates the MRAS-based rotor flux model used in this study.

The detailed relations referenced in Figure 10 are presented in Equation (20). Where:

$$\left\{\begin{array}{c}{T}_r=\frac{L_r}{R_r}\hfill \\ \delta =1-\frac{L_m^2}{L_s{L}_r}\hfill \end{array}\right.$$

(20)

where ϕαs and ϕβs denote the stator and rotor flux, respectively; $v_{\alpha s}$ and $v_{\beta s}$ denote the stator voltage in the αβ reference; R_s and R_r represent the stator and rotor resistors, respectively; and L_m, L_s, and L_r denote the mutual, stator, and rotor inductances, respectively. The stator current in the αβ reference is denoted as iαs and i_βs. The symbol (^) indicates the estimation, and Ω_est represents the estimated speed. The error between the reference and adjustable models is represented by o.

4.5. Electronics Differential (ED)

The ED algorithm ensures that HEVs with multiple drives can operate seamlessly on different road conditions, such as straight roads, bends, and ramps. The algorithm achieves this by generating a reference speed based on the EV’s dimensions and the angle of deviation to ensure that the EV maintains balance. However, the ED algorithm is complicated due to the nonlinearity of the EV dynamics [77,78]. Equation (21) calculates the reference speeds of the drives generated by the ED.

$$\left\{\begin{array}{c}{W}_{r1}*=C_{red}\times W*\times \left(1-\frac{d_w \times tan(\delta )}{2L}\right)\hfill \\ W_{r2}*=C_{red}\times W*\times \left(1+\frac{d_w \times tan(\delta )}{2L}\right)\hfill \end{array}\right.$$

(21)

where C_red, W*, d_w, Δ, and L represent the gear coefficient, HEV width, angle of turn, speed, and EV length, respectively.

5. SM-Based EMS

SM is a fundamental energy management technique of operating under specific conditions and rules. Each rule or state of an EMS is defined based on heuristic or prior empirical knowledge. The usage of SM control is a simple and well-established rule-based method. However, the effectiveness of this technique relies heavily on the designer’s understanding of how each component of the system works. This approach is illustrated in more detail in Figure 11, which presents the algorithm for a fuel-cell HEV. The calculation of the fuel reference power relies on various factors, including the battery state of charge and the powers of the load and generators. FC has the flexibility to operate in either load-following mode (LF) or load-leveling mode (LL), adapting to the specific power requirements [79].

Figure 11 depicts the state machine EMS algorithm. In this system, the EMS algorithm ensures a delicate equilibrium between fuel consumption and the SoC of the battery, maintaining it within the optimal range of 10–90%. This prevents any potential issues of overcharging or undercharging the battery, thus preserving its lifespan. Consequently, this approach enables a fair and accurate performance comparison between the two topologies [80].

6. Simulation Results and Discussion

This section presents an overview and analysis of the main findings derived from MATLAB simulations.

Table 3. The initial conditions parameters.

PI Controller Gains	PI-Based-EMS	DC–DC Boost Converter	DC–DC BDCs		DTC-SVM
			Outer Voltage Loop	Inner Current Loop	Torque Control	Flux Control
Ki	10	142.8	50,000	500	200	4000
Kp	500	1.5	15,000	15,000	18	250

and

Table 4. The proposed speed schedule for the HEV.

State	Period	Explanation
1	(0,40)	90 km/h is the HEV reference speed, and the HEV climbed an 11° slope from 20 s to 30 s
2	(40,70)	The vehicle’s speed is 60 km/h and detoured to the right at 30° with the same speed.
3	(70,90)	The HEV runs at 90 km/h, applying the slope of 12° from 80 s to 90 s.
4	(90,125)	The HEV’s Speed dropped to 60 km/h with a ramp of 12° from 100 s to 110 s.
5	(125,130)	The vehicle stopped during this period.

outline the parameters of the EV model and the operational scenario employed for the sensorless HEV simulation tests. The analysis of the simulation results examines the influence of the EV’s kinetic energy on the dynamics of the sensorless HEV when utilizing both DC and AC generators. The outcomes are presented separately, covering aspects such as the speed estimation and control, power balance system, battery energy storage system BESS, and FC stress using the two proposed topologies. Additionally, the results encompass the bus voltage stability with SC compensation, power losses (ΔP), fuel consumption with SoC in each topology, efficiencies, and errors in controllable variables.

Figure 12 presents the performance analysis of the sensorless ANFIS DTC-SVM system using the MRAS speed estimator. The diagram includes various components, such as reference speed, measured speed, and estimated speed, which is displayed in Figure 12A for each motor. Upon closer inspection (ZOOM), it becomes apparent that all speeds are nearly identical, with the errors being less than 0.06 km/h. Figure 12B,C exhibit the speed error (control) and estimation error under different scenarios. These scenarios involve the hybrid electric vehicle (HEV) traversing various paths with fluctuating speed values, encountering ramps and taking detours at different times. The setpoint speed for the wheels is generated by the ED (exact differentiator), which is effectively regulated by the robust ANFIS controller. In Figure 12D, the electromagnetic torque of the motors is depicted, closely following the reference torque with a slight ripple of ±0.51 N·m for each wheel. Furthermore, Figure 12E demonstrates the effectiveness of the control strategy as the vehicle encounters ramps at specific intervals during the simulation, namely between 20–30, 80–90, and 100–110 s. The plot reveals that the control strategy efficiently handles these situations. In Figure 12F, the stator current is depicted, appearing smooth without any noticeable waves. At the start time, the initial current was 137 A, and it varies based on the load. The reliability of the control strategy is further demonstrated in Figure 12H, where the speed estimator and robust controller maintain the flux’s shape by regulating the nominal value of the flux and preserving the smooth circular shape of the flux compound ring with a diameter of 0.8 (wb). This regulation remains unaffected by load changes, as depicted in Figure 12G.

The power balance, which is controlled by the SM-EMS for the proposed topologies in the HEV system, is depicted in Figure 13. The diagram provides an overview of the power distribution from four different sources: FC, batteries, SC, and DC generators in the first topology, as well as AC generators in the second topology. By including both types of generators, the goal is to showcase the influence of kinetic energy on the energy management of the HEV.

The FC acts as the primary power source for the hybrid electric vehicle (HEV) and operates in parallel with the battery and supercapacitor to manage any excessive loads. In the reference scenario (without generators), the battery energy storage system (BESS) and FC supply 9 kW and 4 kW of power to the EV in 0–40 s intervals. However, the inclusion of generators reduces the power provided by the BESS to 6 kW and the power supplied by the FC to 3 kW instead of their original values.

Between 40 and 70 s, the impact of utilizing kinetic energy becomes apparent as the power generated by the BESS and FC in the proposed topologies is lower than the classical topology. From 70 to 125 s, utilizing the HEV’s kinetic energy further contributes to a reduction in the power output of the FC and BESS throughout the entire duration.

In general, the kinetic energy of the HEV contributes around 22% of its power when AC generators are used and approximately 24% when DC generators are employed during specific intervals. These contributions result in a decrease in power production from the BESS and FC. These findings have significant implications for stress analysis and fuel consumption, which will be discussed in detail in the subsequent results.

The behavior of the battery FC under the proposed topologies is illustrated in Figure 14. Figure 14A presents the energy production of the FC in each topology. In the basic topology (without generators), the FC generated an average energy of 4 kW. However, the utilization of kinetic energy led to a reduction in FC energy production, with a decrease of 35% when DC generators were used and 25% when AC generators were employed. Additionally, the incorporation of generators decreased the power generated from the battery, having a reduction of 29% when using DC generators and 22% when using AC generators, as depicted in Figure 14B.

Moreover, it is important to note that the reduction in power output from these sources contributed to decreased stress on them, as shown in Figure 14C,D. The use of DC generators led to a 10% reduction in the FC stress and a 20% reduction in the battery stress compared with the basic HEV scenario. Similarly, AC generators reduced the FC stress by 7% and the battery stress by 17%.

Figure 14E presents the fuel indicator of the proposed topologies. In the basic topology, the average fuel consumption was estimated to be 26 (SI). However, incorporating DC generators resulted in a 40% reduction in fuel consumption, while AC generators led to a 25% reduction in fuel consumption.

Furthermore, Figure 14F illustrates the SoC of the BESS in all proposed topologies. The use of both DC and AC generators led to a decrease in the BESS’s SoC, extending the lifespan of both the battery and the overall system.

Figure 15 illustrates the stability of the EV system. The first subfigure shows the DC bus voltage for each topology. All of the systems exhibit stability and closely track the reference voltage of 400 V without any overshoot, as depicted in Figure 15A. The response times of each topology are within acceptable limits, with a response time of 0.02 s when DC and AC generators are utilized and 0.04 s when the topologies are without generators. The DC voltage in the basic topology displays smoother behavior than the proposed topologies, with a ripple of only ±0.02 V. The sudden fluctuations observed at 80 s (Figure 15B) and 90 s (Figure 15C) are a result of the rapid variations in speed, application of ramps, or detours. These fluctuations trigger the intervention of the SC, as shown in Figure 15D and in the ZOOM view (Figure 15E,F), to ensure the required power and bus voltage stability. During ramp application, the SC intervention power at 80 s is 0.6 kW in the basic topology, 0.2 kW in the topology with DC generators, and 1.4 kW in the AC topology. At the end of the ramp, synchronized with a speed decrease at 90 s, the SC intervention is 0.5 kW in the basic and DC generator topologies and 0.8 kW in the AC topology. As a result, the hybrid electric vehicle (HEV) system remains stable throughout the simulation across all topologies. In accordance with the law of power conservation, power balance naturally incurs some losses. These losses primarily stem from energy losses within the system, as depicted in Figure 15G. While adding generators introduces some losses, these losses are negligible compared with the overall energy gain. Adding extra energy leads to losses that are proportionate to the total energy amount.

Key Performance Indexes (KPIs)

Figure 16 illustrates the main performance indicators of the system, including the MAE, root-mean-square error (RMSE) of the DC bus voltage, power losses, and supply efficiency. It also displays the mechanical parameters of the HEV speed and torque. Comparing Figure 16A, which represents the basic HEV scenario, with the utilization of the EV’s kinetic energy through additional generators (AC and DC) shown in Figure 16B, we observe an improvement in the stability of the bus voltage. The average error is reduced to 0.0017 V, and the additional harvested energy contributes to smooth power exchange among the HEV resources while maintaining a stable supply voltage.

In terms of the overall power efficiency, Figure 16B clearly demonstrates the difference between the basic HEV scenario and the scenarios where the EV’s kinetic energy is exploited using additional generators. Taking into account the number of power converters involved, the inclusion of additional DC–DC and DC–AC converters for the generators leads to extra power losses. Consequently, there is an approximately 2% increase in power losses compared with the basic scenario. The basic HEV scenario exhibits the highest power efficiency of 97.5%, which corresponds to the lowest power loss of 817 W. However, when exploiting the energy from the AC and DC generators, the system’s power efficiency decreases by about 0.51% and 0.82%, respectively.

Despite the additional power losses and the slight impact on the HEV power efficiency, the benefits of utilizing the free kinetic energy from the DC and AC generators outweigh these drawbacks. The energy extracted from the generators contributes 28% and 24% of the total EV power, respectively. As a result, the stress on the FC and battery resources are reduced, preventing the deep discharge of their stored energy (SoC/Fuel), extending the HEV’s autonomy, and improving power supply reliability. By analyzing the mechanical variables of the HEV, specifically the speed and load torque in Figure 16C,D, the additional harvested energy is shown to have a minimal influence on speed and torque control. The errors in the speed and torque of the HEV remain within acceptable thresholds. For a rated speed of 150 km/h and a rated motor torque of 100 Nm, the RMSE for speed and torque is approximately 0.5% and 0.6%, respectively, whereas the MAE is 0.18% and 0.25%, respectively, relative to their rated values. Figure 16E illustrates the primary effects of incorporating additional resources on the fuel cell (FC), specifically on fuel consumption and stress levels.

In the basic topology, the fuel consumption was measured at 25.85 (IPM) with a corresponding stress level of 39%; however, the introduction of extra resources, namely AC generators, resulted in a reduction in fuel consumption down to 19.3 (IPM) and a decrease in stress down to 32.7%. On the other hand, the second topology utilizing DC generators further lowered fuel consumption down to 15.6 (IPM) and reduced stress down to 28.4%. The optimization ratio achieved in this case was approximately 7% and 10% for fuel consumption and stress reduction, respectively.

Table 5. Examining the performance indexes of HEVs based on the proposed contributions for comparison.

	HEV Scenarios	DC Generators	AC Generators	Basic HEV
Criteria
		DC Bus voltage (V)
Response time (s)		0.002	0.002	0.004
RMSE (%)/MAE (%)		0.0017/0
Efficiency (%)		96.7	97	97.5
		Battery
BESS stress (%)		43.4	47.5	64.9
SoC (%)		60.1–59.68	60.1–59.64	60.1–59.56
${\Delta }_{\mathrm{SoC}} \left(\%\right)$		0.42	0.46	0.54
		Fuel Cell
Fuel consumption (IPM))		15.6	19.3	25.85
FC stress (%)		28.4	32.7	39
		Load power
Load supply losses	RMSE (W)	835	833	817
	MAE (W)	316	307	255
		HEV Speed
Measured speed	RMSE (%)	0.4
	MAE (%)	0.17
Estimated speed	RMSE (%)	0.48
	MAE (%)	0.17
		HEV Torque
Torque	RMSE (%)	0.59
	MAE (%)	0.24

provides a summary of the prominent outcomes derived from the preceding analysis, presenting the statistical discoveries pertaining to the performance measures of the suggested configurations.

Table 6. Overview of recent studies on resource utilization in HEVs.

References	Energy		EMSs	Controller		Analysis Type	Comments
	Resources	Efficiency		Speed	Power
Soumeur et al. [36], (2020)	-BESS -FC -SC	<85	-PI-EMS -SM-EMS -FLC-EMS -FD-EMS	DTC-SVM	PIs	Simulation: MATLAB/Simulink	Despite the diverse range of energy management systems, the study’s reliance on only three sources implies limited independence and overall efficiency.
Gasbaoui et al. [81], (2017)	FC	<75	/	DTC-SVM	PIs	Simulation: MATLAB/Simulink	“Adopting a single feeding source may reduce the efficiency and independence of the system, but it often results in lower costs compared to multi-source systems.”
Mantriota et al. [82], (2021)	BESS	<90	/	Optimization process	optimization process	Simulation: MATLAB/Simulink	The application of optimization systems has a significant impact on the system’s efficiency. Still, the issue of relying solely on a single power source remains one of the challenges in improving electric transportation autonomy.
Ruan et al. [83], (2017)	-BESS -SC	<86	/	Multi-speed DCTs	PIs	Simulation: MATLAB/Simulink	Enhancing battery integration with a fast storage system positively impacts system transmission, particularly in transient systems and energy recovery. However, the system’s limitations necessitate including additional energy sources.
Huma et al. [84], (2021)	BESS SC	<80	Supervisory control	/	Buckstepping	Simulation: MATLAB/Simulink	Enhancing battery integration with a fast storage system positively impacts system transmission, particularly in transient systems and energy recovery. However, the system’s limitations necessitate including additional energy sources.
Current study	BESS FC SC AC generators DC generators	>96	SM-EMS	Sensorless ANFIS DTC-SVM	PIs and MPPT	Simulation: MATLAB/Simulink	Adopting multiple energy sources in the same system has a significant impact on system efficiency. It contributes to enhancing the autonomy of transportation means, particularly when considering the growing challenges in harnessing alternative energy. However, the issue of system cost remains relative.

provides a summary and compilation of important criteria, including the technology, renewable energy source, and electrical characteristics, as extracted from other research papers and compared with the findings of this study.

7. Conclusions

This study aimed to compare the integration performances of DC and AC generators in 2WD HEVs, focusing on harnessing the vehicle’s kinetic energy and implementing a reliable sensorless control system for EV motors. Various topologies for utilizing the kinetic energy of a two-wheel drive EV were evaluated and compared against a basic topology without generators. Additionally, an EMS was developed to optimize fuel usage and maintain the charge of the BESS during EV operations.

Simulations were conducted on 30 kW sensorless HEV systems with consistent initial conditions and EMSs. The stability of the energy and mechanical systems in all of the studied topologies confirmed the effectiveness of the control strategy while highlighting the potential negative impact of adding generators on the overall system performance.

The proposed topologies demonstrated the ability to harness free energy, thereby reducing the stress on the FC and BESS by 10% and 21%, respectively, with the use of DC generators; the stress was reduced by 6% and 17%, respectively, with the use of AC generators. This reduction in stress extended the lifespan of these resources significantly. Furthermore, the additional DC and AC generators contributed to fuel consumption reduction, resulting in cost savings and preserving hydrogen resources. The utilization of HEV kinetic energy also increased the EV’s autonomy and running duration without compromising system efficiency ratios. The efficiency ratios remained above 97%, indicating that the energy loss was not significant considering that the total power contribution was between 24% and 28%.

The combination of the robust controller, which relied on a specialized database, and the speed estimator yielded excellent results. The speed estimation error was below 0.5%, while the torque error was below 0.6%. These results ensured smooth speed and torque profiles, further enhancing the system’s overall performance. In conclusion, the satisfactory energy responses achieved using the classical PI controller for the DC converters provide motivation to explore the adoption of robust controllers in future applications. Additionally, experimental validation of the proposed HEV system is necessary to gain valuable insights and further improve its performance. These future perspectives will contribute to advancing the field of HEV technology and facilitating its practical implementation.