Efficient Power Management Strategy of Electric Vehicles Based Hybrid Renewable Energy

This paper presents a straightforward power management algorithm that supervises the contribution of more than one energy source for charging a vehicle, even if the car is in motion. The system is composed of a wireless charging system, photovoltaic (PV) generator, fuel cell (FC), and a battery system. It also contains a group of power converters associated with each energy resource to make the necessary adaptation between the input and output electrical signals. The boost converter relates to the PV/FC, and the boost–buck converter is connected with the battery pack. In this work, the wireless charging, FC, and PV systems are connected in parallel via a DC/DC converter for feeding the battery bank when the given energy is in excess. Therefore, for each of these elements, the mathematical model is formulated, then the corresponding power management loop is built, which presents the significant contribution of this paper. The efficient power management methodology proposed in this work was verified on Matlab/Simulink platforms. The battery state of charge and the hydrogen consumption obtained results were compared to show the effectiveness of this multi-source system.


Introduction
Nowadays, the carbon dioxide rate has crossed 400 ppm, and it is still rising. Many solutions try to save the environment, and this is by finding some sustainable technologies that help reduce energy consumption or use some other energy resources. The car industry's interest in electrified powertrains is growing due to significantly reducing fuel consumption and harmful transportation emissions. The electrification of this main transport tool was studied as a severe challenge for having an efficient and robust transport tool. Therefore, researchers have not stopped improving in this field, providing many solutions and technical specifications for having a kind of electrified transport tool that is adaptable in use, and is safe and environmentally friendly.
Firstly, some solutions were concentrated on how it is possible using a pure electric vehicle (EV) or a hybrid electric vehicle (HEV). More than synthesis has tested these solutions and proves the advantages and drawbacks of each one. This study provides helpful information regarding the importance of EV or HEV and their problems [1]. These solutions were divided into more than a research field. Some of these studies were concentrated on the central traction part. The objective was to find the best electrical machine that can

Composition of EVs
Hybrid electric vehicles (HEVs) have two or more sources of power onboard the vehicle and/or two or more sources of energy power [18,19]. This vehicle can be categorized into two categories: the first category is the pure EVs, and the second category is HEVs. This model provides electricity with some other source, in which the vehicle could be driven on a battery in an urban/populated area and could turn to the engine outside a city. Further, HEVs can be subdivided into plug-in HEVs (PHEVs) and fuel cell EVs (FCEVs). Thus, EVs may be classified into HEVs, battery-EVs (BEVs), PHEVs, and FCEVs [20]. The illustration of HEVs, addressed in this work, is shown in Figure 1.

Composition of EVs
Hybrid electric vehicles (HEVs) have two or more sources of power onboard the vehicle and/or two or more sources of energy power [18,19]. This vehicle can be categorized into two categories: the first category is the pure EVs, and the second category is HEVs. This model provides electricity with some other source, in which the vehicle could be driven on a battery in an urban/populated area and could turn to the engine outside a city. Further, HEVs can be subdivided into plug-in HEVs (PHEVs) and fuel cell EVs (FCEVs). Thus, EVs may be classified into HEVs, battery-EVs (BEVs), PHEVs, and FCEVs [20]. The illustration of HEVs, addressed in this work, is shown in Figure 1. In the case of a battery charger for HEVs based on fuel cell energy, the amount of energy transferred depends on the energy source and vehicle composition, and the designer has to deal with particular points made by the system: wireless recharging (WR) system, PV generator, battery model, mechanical model, FC, electric motor, and buckboost converter [21]. This paper proposes a multi-source system, and this system consists of FC system, a wireless charging system, a PV generator, and a lithium-ion battery. The system is shown in Figure 2.   In the case of a battery charger for HEVs based on fuel cell energy, the amount of energy transferred depends on the energy source and vehicle composition, and the designer has to deal with particular points made by the system: wireless recharging (WR) system, PV generator, battery model, mechanical model, FC, electric motor, and buck-boost converter [21]. This paper proposes a multi-source system, and this system consists of FC system, a wireless charging system, a PV generator, and a lithium-ion battery. The system is shown in Figure 2.

Composition of EVs
Hybrid electric vehicles (HEVs) have two or more sources of power onboard the vehicle and/or two or more sources of energy power [18,19]. This vehicle can be categorized into two categories: the first category is the pure EVs, and the second category is HEVs. This model provides electricity with some other source, in which the vehicle could be driven on a battery in an urban/populated area and could turn to the engine outside a city. Further, HEVs can be subdivided into plug-in HEVs (PHEVs) and fuel cell EVs (FCEVs). Thus, EVs may be classified into HEVs, battery-EVs (BEVs), PHEVs, and FCEVs [20]. The illustration of HEVs, addressed in this work, is shown in Figure 1. In the case of a battery charger for HEVs based on fuel cell energy, the amount of energy transferred depends on the energy source and vehicle composition, and the designer has to deal with particular points made by the system: wireless recharging (WR) system, PV generator, battery model, mechanical model, FC, electric motor, and buckboost converter [21]. This paper proposes a multi-source system, and this system consists of FC system, a wireless charging system, a PV generator, and a lithium-ion battery. The system is shown in Figure 2.

The Vehicle Model
The comportment of a moving vehicle is determined by all the forces acting on it in that direction. Figure 3 illustrates the forces acting on the vehicle [22]. The tractive force F t in the contact area between the tires of the drive wheels and the road surface thrusts the vehicle forward [23]. The torque from the power plant produces it and then transfers it through the transmission to the driving wheels. When the vehicle is mobile, there is resistance that attempts to stop its movement.

The Vehicle Model
The comportment of a moving vehicle is determined by all the forces acting on it in that direction. Figure 3 illustrates the forces acting on the vehicle [22]. The tractive force Ft in the contact area between the tires of the drive wheels and the road surface thrusts the vehicle forward [23]. The torque from the power plant produces it and then transfers it through the transmission to the driving wheels. When the vehicle is mobile, there is resistance that attempts to stop its movement.

Tractive Force
The mechanical model of the vehicle must make it possible to calculate the power necessary to propel the latter according to its characteristics, speed, and acceleration. To calculate the power required to move the vehicle forward, we apply the fundamental principle of dynamics [24,25].
The force is equivalent to the aerodynamic drag force and is given by: where is the air density, v is the vehicle speed, is the frontal vehicle area, and is the aerodynamic drag coefficient.
The rolling resistance force of the wheels on the ground ( ) is given by the formula: where is the rolling resistance coefficient, g denotes the acceleration due to gravity, ang denotes the angle, and mv is the vehicle mass.
The gravitational force ( ) depends on the road slope and is given as: The traction force expression ( ) is represented as: The mechanical power ( ) required to move the vehicle forward is equal to the product of the traction force and the speed, thus:

Tractive Force
The mechanical model of the vehicle must make it possible to calculate the power necessary to propel the latter according to its characteristics, speed, and acceleration. To calculate the power required to move the vehicle forward, we apply the fundamental principle of dynamics [24,25].
The force F aero is equivalent to the aerodynamic drag force and is given by: where ρ air is the air density, v is the vehicle speed, A f is the frontal vehicle area, and C d is the aerodynamic drag coefficient.
The rolling resistance force of the wheels on the ground F r f is given by the formula: where C r is the rolling resistance coefficient, g denotes the acceleration due to gravity, ang denotes the angle, and m v is the vehicle mass.
The gravitational force F slope depends on the road slope and is given as: The traction force expression (F t ) is represented as: The mechanical power (P m ) required to move the vehicle forward is equal to the product of the traction force and the speed, thus: According to Equation (6), the load torque is given by: F r is the total force and r is the tire radius.

Electrical Motor
The permanent magnet synchronous motor (PMSM) dynamic properties can be described by a set of nonlinear differential equations relating the stator and rotor currents and voltages with the mechanical quantities; torque, speed, and angular position [26][27][28]. After implementing Park transformation, the voltage expressions in the (d, q) axis are presented in Equation (8): where v d , v q , i d , i q , L d , L q are the direct and the quadrature voltages, currents, and stator inductances, respectively. Additionally, ω m denotes the mechanical speed of the electrical motor, and λ m denotes the permanent magnet flux linkage. R s is the stator resistance.
The electromechanical torque (T e ) can be represented as follows: where λ d = L d .i d + λ m and λ q = L q .i q . For the non-salient poles PMSM model, L d = L q = L s , then the modified torque expression becomes: The electromechanical motor equation is formulated as: where T l , P m and J denote the load torque, the number of poles, and the rotor inertia coefficient, respectively. The inverter voltage vector ( → V S ) is given in (12): In this work, a PMSM of a maximum power of 50 kW was used. The parameters of this electric motor are summarized in Table 1.

Battery Model
As the recharge system is employed to charge a battery pack, it is essential to recognize the mathematical battery model. The best performances can be found for the lithium model, and its detailed function can be visualized in [29,30]. In (13), we show the battery output voltage, referred to as (V batt/cell ) by one cell. Thus, the voltage expression depends on the (V oc ), which is the open-circuit voltage. R st and C st , which represent the resistance and capacitance of the electromagnetic short-term double-layer properties, respectively, and R lt and C lt , which represent the resistances and capacitances of the electro-chemical long-time-interval mass transport effects. As it can be discharged or charged, I st could be either positive or negative.
where R batt and I b denote the ohmic resistance and load current of the cell, respectively. The battery pack voltage V batt relies on the number of series (N sbatt ) and parallel (N pbatt ) cells used. Equation (14) formulates both V batt and R batt in terms of N sbatt and N pbatt .
where R o denotes the charging or discharging battery cell resistance. The state of charge (SOC) of the battery can be expressed as a function of time as given in Equation (15) [31].
where W denotes the charge/discharge coefficient, and N b means the battery self-discharge.

Buck-Boost Converter
The battery is the main energy source connected to a two-quadrant DC/DC converter in this phase. This phenomenon is necessary as the storage system may have two different signs, positive or negative, allowing both directions to transfer energy. This converter has two roles-voltage elevation and minimization. A buck-boost DC converter assures this. The DC/DC converter comprises two IGBT transistors (S 1 and S 2 ) and a coil (L) connected, as illustrated in Figure 4.

Buck-Boost Converter
The battery is the main energy source connected to a two-quadrant DC/DC converter in this phase. This phenomenon is necessary as the storage system may have two different signs, positive or negative, allowing both directions to transfer energy. This converter has two roles-voltage elevation and minimization. A buck-boost DC converter assures this. The DC/DC converter comprises two IGBT transistors (S1 and S2) and a coil (L) connected, as illustrated in Figure 4. Steady-state converter analysis, the bidirectional converter works in boost when the switch S 1 and the diode D 2 are in conduction. In this case, the battery is discharged, and the current of the inductor i L is positive. The mathematical model of the converter in boost mode is given by the differential system Equation (16).
The bidirectional converter works in the buck mode when the switch S 2 and the diode D 1 are in conduction. In this case, the battery charges and i L is negative. The mathematical model of the converter in buck mode is given by the differential system Equation (17).
A binary variable Y is defined to represent the operating mode. Thus: where i Lre f denotes the reference current to control S 1 and S 2 . Hence, the converter (buck-boost) model can be obtained by: The control signal of the buck-boost converter, u 12 , is defined and expressed by Equation (20).
Therefore, the system of equations becomes: The DC bus of the system is modeled by a filter capacitor and is expressed in (22):

Hybrid Recharge System
This recharge system utilizes three kinds of energy sources: the wireless recharge model, PV panels, and FC generators. Therefore, modeling each of these facilities is essential to introduce this hybrid recharge tool clearly.

Wireless Power Transfer Model
The wireless charging device enables electrical energy to be transferred to the battery. An equivalent installation of the EV wireless charging device is shown in Figure 5a. The static model of the charger system with one receiver coil was studied in this section. In Figure 5b, a simplified representation of this inductive power transfer method is shown. V S (secondary voltage) and V P (primary voltage) represent this inductive power transfer's output and input voltages (IPT).
The reflected impedance from the secondary to the primary is represented by: denotes the oscillation angular frequency (rad/s). Additionally, Zp and Zs denote the primary and secondary impedances.
depends on the selected compensation topology. The current Is flows through the secondary winding is represented as follows: The voltages across the primary and secondary windings are introduced as follows: The primary and secondary resonant frequencies are identical and given by: The power expressions ( and ) of the primary and secondary sides are expressed as follows: The power provided by the wireless charging system is proportional to the vehicle's speed. This conclusion was previously proved in [31]. A wireless charging system of a maximum power of 8-10 kW is used in this work. The other parameters of the wireless charging system are summarized in Table 2. The mutual inductance (M) is related to the magnetic coupling coefficient (k WR ) as follows, where L p and L s denote the primary and secondary inductances.
The reflected impedance from the secondary to the primary is represented by: ω denotes the oscillation angular frequency (rad/s). Additionally, Z p and Z s denote the primary and secondary impedances. Z s depends on the selected compensation topology. The current I s flows through the secondary winding is represented as follows: The voltages across the primary and secondary windings are introduced as follows: The primary and secondary resonant frequencies are identical and given by: Sustainability 2021, 13, 7351 9 of 20 The power expressions (P p and P s ) of the primary and secondary sides are expressed as follows: P p = V p I p = jωL p I p − jωMI s I p P s = V s I s = jωMI p − jωL s I s I s (28) The power provided by the wireless charging system is proportional to the vehicle's speed. This conclusion was previously proved in [31]. A wireless charging system of a maximum power of 8-10 kW is used in this work. The other parameters of the wireless charging system are summarized in Table 2.

PV Generator Model
The solar cell is an electrical component used in some application requirements, such as an EV to transform solar energy into electricity to produce the electrical energy requirements. Many authors have suggested various models for modeling solar cells [32,33]. Figure 6 shows the single-diode model used to model the solar cell [34].

PV Generator Model
The solar cell is an electrical component used in some application requirements, such as an EV to transform solar energy into electricity to produce the electrical energy requirements. Many authors have suggested various models for modeling solar cells [32,33]. Figure 6 shows the single-diode model used to model the solar cell [34]. The current is given by The current ℎ (PV cell's current) can be evaluated as: The current I c is given by The current I ph (PV cell's current) can be evaluated as: With I rs current can be approximately obtained as: Finally, the current I c can be given by The model of a PV generator depends on the number of parallel and series cells, N p and N s . Finally, the PV generator current can be given by: The parallel and series resistance (R p and Rs) values are not be considered in this model, i.e., R p = ∞ and R s = 0. Thus:

FC Generator Model
The FC uses air and hydrogen as fuel sources. Equation (35) shows the rates of conversion between the hydrogen U f H 2 and the oxygen U f O 2 . Figure 7 shows the FC proton exchange membrane (PEM) [35].
Finally, the current can be given by The model of a PV generator depends on the number of parallel and series cells, and . Finally, the PV generator current can be given by: The parallel and series resistance (Rp and Rs) values are not be considered in this model, i.e., Rp = ∞ and Rs = 0. Thus:

FC Generator Model
The FC uses air and hydrogen as fuel sources. Equation (35) shows the rates of conversion between the hydrogen 2 and the oxygen 2 . Figure 7 shows the FC proton exchange membrane (PEM) [35]. The partial pressures of the hydrogen 2 , oxygen 2 and products water vapor defined by the parameters applied to block B, are expressed by the following equations [36]: The partial pressures of the hydrogen P H 2 , oxygen P O 2 and products water vapor defined by the parameters applied to block B, are expressed by the following equations [36]: where x denotes the hydrogen in the fuel (%) and y represents the oxygen in the oxidant (%).
When T ≤ 100 • C When T > 100 • C Then, from the Nernst voltage (E n ) and the partial pressures of gases, the exchange current (i 0 ) and the values of the circuit voltage (E oc ) can be calculated as given in the following equations: Equation (41) expresses the Tafel slope model.
Using the polarization curve at nominal operation conditions and some additional parameters, such as the stack efficiency, supply pressures, composition of fuel and air, and temperatures, the nominal rates of conversion gases can be estimated as it is in Equation (42).
60,000 * R * T nom * N * I nom 2 * z * F * P airnom * V I pm(air)nom * 0.21 (42) The voltage source (E) can be given by where i fc is the FC current (A), R fc is the internal resistance (Ω), N is the cells number, and T d is the response time.
The expressions in Table 3 are used to calculate the detailed model parameters. The corresponding expression represents each variable. Table 3. FC variables and their expressions.
Where V fc is the voltage of the FC (V), P fuel is the pressure of fuel (atm), and P air is the pressure of air (atm). K c is the voltage of nominal operation conditions (V), z is the moving electrons, k is the Boltzmann's constant, and h is a constant (6.626 × 10 −34 Js).

The Proposed Power Management Strategy
When the vehicle is in a garage or a covered parking place, the solar radiation cannot give the necessary power for starting the vehicle. Therefore, the battery/ultracapacitor is used for moving the vehicle. On the other hand, the battery charging method needs many technologies, solutions, or sources for quick recharge and increasing vehicle autonomy when it is on the highway [37]. Therefore, it is mandatory to control and supervise the different recharge solutions for improving the global efficiency of the battery [38].
An easy power management algorithm is built to show how to control the three used energy sources for charging the EV. The PV generator cannot be efficient only in particular weather conditions and vehicle positions, different from the dark zones or when the sunshine is covered. Therefore, the PV generator system is absent in this control algorithm when the vehicle starts from the stop position as a garage or covered parking. Even if the vehicle starts from a sunshine zone, the PV generator cannot collaborate by feeding the vehicle with the necessary energy, as its given power, not enough. Therefore, when the EV starts, the battery is used as the primary energy source. Next, if the EV is in motion, more than one case can occur, and this is related to the acceleration given ratio. Even the acceleration factor is high; the FC generator will contribute by the maximum as possible. Additionally, it is crucial to indicate that the wireless recharge method will decrease its contribution even the vehicle speed increase. The case of deceleration is also taken into account in this algorithm, and the idea is to shut down the FC generator. Therefore, based only on the wireless recharge method by percentage and according to the vehicle speed. The proposed algorithm is shown in Algorithm 1. if (acceleration ratio is between 0 and 0.4%) -

Results and Discussion
The simulation steps were carried out, and the results obtained are presented and discussed. A detailed discussion regarding the efficiency of this multiple recharge tool is introduced. However, it is necessary to mention that the presented results were obtained in the condition supposing each of these three-recharge systems is stable and running in the stationary mode. If one of these systems is not stable, the proposed solution will have difficulty, and the overall running system will need an adaptable control tool. The stability analysis and effects of each of these recharge tools are discussed in [39][40][41]. From the other side, investigation of the stability factors for each of these elements and on the global re-charge performance will be treated in our future endeavors.

Simulated Drive Cycle
The different simulation conditions were carried on after implementing the mathematical models on the Matlab/Simulink platform. The simulation time is calculated to have 300 m distance as a road. On this trajectory, there are 150 coils, and the distance between two coils is 1.5 m. Figure 8 shows this arrangement. On the other side, the car simulation model comprises 256 PV cells, which provide 6 kW electrical power in the best climatic conditions. The initial SOC of the battery is set to 65%.

Results and Discussion
The simulation steps were carried out, and the results obtained are presented and discussed. A detailed discussion regarding the efficiency of this multiple recharge tool is introduced. However, it is necessary to mention that the presented results were obtained in the condition supposing each of these three-recharge systems is stable and running in the stationary mode. If one of these systems is not stable, the proposed solution will have difficulty, and the overall running system will need an adaptable control tool. The stability analysis and effects of each of these recharge tools are discussed in [39][40][41]. From the other side, investigation of the stability factors for each of these elements and on the global recharge performance will be treated in our future endeavors.

Simulated Drive Cycle
The different simulation conditions were carried on after implementing the mathematical models on the Matlab/Simulink platform. The simulation time is calculated to have 300 m distance as a road. On this trajectory, there are 150 coils, and the distance between two coils is 1.5 m. Figure 8 shows this arrangement. On the other side, the car simulation model comprises 256 PV cells, which provide 6 kW electrical power in the best climatic conditions. The initial SOC of the battery is set to 65%. Values of the vehicle parameters and the electric motor used in the simulation are listed in Table 4. In the different simulation steps, more than one parameter should be supervised and evaluated for calculating the efficiency of the power management algorithm. Essentially, Values of the vehicle parameters and the electric motor used in the simulation are listed in Table 4. In the different simulation steps, more than one parameter should be supervised and evaluated for calculating the efficiency of the power management algorithm. Essentially, the instant battery voltage, the battery state of charge, the instant battery current, the battery capacitor, and more need to be sensed and evaluated. These parameters must be supervised for the measured vehicle speed and according to the given acceleration form. However, it is mandatory to oversee the energy flow of the different recharge sources and inspect the global energy management reaction. Figure 9 shows the given driving cycle and the corresponding vehicle speed. It should be mentioned that the drive cycle form was applied for simulating a city road condition.
Sustainability 2021, 13, x FOR PEER REVIEW 14 of 20 the instant battery voltage, the battery state of charge, the instant battery current, the battery capacitor, and more need to be sensed and evaluated. These parameters must be supervised for the measured vehicle speed and according to the given acceleration form. However, it is mandatory to oversee the energy flow of the different recharge sources and inspect the global energy management reaction. Figure 9 shows the given driving cycle and the corresponding vehicle speed. It should be mentioned that the drive cycle form was applied for simulating a city road condition. According to the drive cycle, the profitability of the hybrid system can be verified, especially with supervising the battery's SOC. The forms of power delivered by the studied source are illustrated in Figure 10a-e for the power provided by the PV generator, wireless charging, FC generator, consumed power by the electric motor, and the battery power, respectively. According to the drive cycle, the profitability of the hybrid system can be verified, especially with supervising the battery's SOC. The forms of power delivered by the studied source are illustrated in Figure 10a-e for the power provided by the PV generator, wireless charging, FC generator, consumed power by the electric motor, and the battery power, respectively.
The implemented hybrid device provides enough power to drive the engine and charge the battery simultaneously, especially for low speeds, and this is shown in Figure 10e, between the instants 4 s and 8 s, where the given battery power is the minimum. Figure 11 shows the SOC of the used battery. From the obtained results, it is possible to understand that the hybrid system runs perfectly, as indicated by the power management algorithm. Furthermore, to check the robustness of the hybrid system, a sudden shift in the rotational speed at t = 2 s, t = 4 s, and t = 8 s is made. The results obtained validate the hypothesis proposed. We note that even the induction motor's rotation speed varies, holding the flux steady. This figure shows that the SOC rate increases during weak acceleration, although the vehicle is in motion, and the same during the stop phase. Figure 12 shows the dynamics of the consumption of hydrogen. It is clear that the hydrogen consumption rate is closely related to the power delivery by PV and WR systems. We note that the proposed hybrid system has contributed to saving a significant amount of hydrogen.

Hybrid System Efficiency
Based on this case of deceleration and brake mode, each recharge method was tested, and its energetic contribution can be evaluated. The best choice can be related to the combination between FC, PV, and WR. However, as the difference is not enough, the fundamental energy efficiency cannot be evaluated unless the PV weight system is correctly studied. It is demonstrated that with the new PV cells technology [42], the extra weight on the vehicle will be relatively affected. Therefore, one can conclude that the benefit of this renewable energy source is assured. However, it is also essential to indicate that the vehicle speed factor significantly influences the energetic performance as demonstrated in [2][3][4][5], which shows that PV cells and WR will contribute by 100% on a deceleration mode.
Finally, the efficiency of each recharge system can be summarized as presented in Table 5, in which this table classifies these recharge tools according to their energetic gain for the same road conditions. According to the drive cycle, the profitability of the hybrid system can be verified, especially with supervising the battery's SOC. The forms of power delivered by the studied source are illustrated in Figure 10a-e for the power provided by the PV generator, wireless charging, FC generator, consumed power by the electric motor, and the battery power, respectively. The implemented hybrid device provides enough power to drive the engine and charge the battery simultaneously, especially for low speeds, and this is shown in Figure  10e, between the instants 4 s and 8 s, where the given battery power is the minimum. Figure 11 shows the SOC of the used battery. From the obtained results, it is possible to understand that the hybrid system runs perfectly, as indicated by the power management algorithm. Furthermore, to check the robustness of the hybrid system, a sudden shift in the rotational speed at t = 2 s, t = 4 s, and t = 8 s is made. The results obtained validate the hypothesis proposed. We note that even the induction motor's rotation speed varies, holding the flux steady. This figure shows that the SOC rate increases during weak acceleration, although the vehicle is in motion, and the same during the stop phase. Figure 12 shows the dynamics of the consumption of hydrogen. It is clear that the  holding the flux steady. This figure shows that the SOC rate increases during weak acceleration, although the vehicle is in motion, and the same during the stop phase. Figure 12 shows the dynamics of the consumption of hydrogen. It is clear that the hydrogen consumption rate is closely related to the power delivery by PV and WR systems. We note that the proposed hybrid system has contributed to saving a significant amount of hydrogen.  Based on this case of deceleration and brake mode, each recharge method was tested, and its energetic contribution can be evaluated. The best choice can be related to the combination between FC, PV, and WR. However, as the difference is not enough, the fundamental energy efficiency cannot be evaluated unless the PV weight system is correctly studied. It is demonstrated that with the new PV cells technology [42], the extra weight on the vehicle will be relatively affected. Therefore, one can conclude that the benefit of this renewable energy source is assured. However, it is also essential to indicate that the  Based on this case of deceleration and brake mode, each recharge method was tested, and its energetic contribution can be evaluated. The best choice can be related to the combination between FC, PV, and WR. However, as the difference is not enough, the fundamental energy efficiency cannot be evaluated unless the PV weight system is correctly studied. It is demonstrated that with the new PV cells technology [42], the extra weight on the vehicle will be relatively affected. Therefore, one can conclude that the benefit of

Conclusions
This section ends the article after this report by outlining the key points and the main contribution of this study. Therefore, after providing all of the necessary equations for constructing a hybrid electric vehicle with a multi-charged source and displaying all of the internal models for the three studied recharge tools, a global model is designed and applied on the MATLAB Simulink tool to provide input on energy performance. The findings demonstrate that all of the designed models are operating well, and the power management control loop has been tested for the simulation test conditions. Statistics show that using this multi-recharge tool improves vehicle power performance and increases vehicle autonomy. However, some flaws in this analysis can be seen in terms of the weight of the PV recharge method and its global input on the real energetic gain. These flaws will only be fully evaluated if a thorough analysis of the PV weight system is conducted, which is why this issue is one of the work's future endeavors.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to their large size.