# Design and experimental validation of a robust and real-time power management strategy and control system for a hybrid electric vehicle

R Achdad, M A Mossadak, Abdelhamid Rabhi, A Chebak, A Hadjaissa, H Midavaine

► To cite this version:

R Achdad, M A Mossadak, Abdelhamid Rabhi, A Chebak, A Hadjaissa, et al.. Design and experimental validation of a robust and real-time power management strategy and control system for a hybrid electric vehicle. Journal of Energy Storage, 2026, 148, 10.1016/j.est.2025.120288. hal-05445131

HAL Id: hal-05445131

https://hal.science/hal-05445131v1

Submitted on 6 Jan 2026

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
<figure><img src="image_2.png" /></figure>

Research papers

# Design and experimental validation of a robust and real-time power management strategy and control system for a hybrid electric vehicle☆

R. Achdad<sup>a,●,*</sup>, M.A. Mossadak<sup>a,b</sup>, A. Rabhi<sup>a</sup>, A. Chebak<sup>b</sup>, A. Hadjaissa<sup>c</sup>, H. Midavaine<sup>a</sup>

## ARTICLE INFO

**Keywords:**

Frequency-decoupling
Electric vehicle
Hybrid system
Supercapacitor
Fuzzy-logic
Fuel cell
Battery

## ABSTRACT

Hybrid energy storage systems combining fuel cells, batteries, and supercapacitors are gaining significant attention for electric vehicle applications due to their ability to enhance efficiency and durability. This paper presents a new energy management strategy for a multi-source electric vehicle system integrating a fuel cell, a lithium-ion battery, and a supercapacitor. Each source plays a distinct role based on its power and energy characteristics, enabling optimal power distribution. The proposed strategy employs frequency decomposition, fuzzy logic and deterministic rules to optimize power sharing, ensuring system stability, enhanced efficiency, and extended component lifespan. The fuel cell supplies steady power, while the battery regulates the DC bus voltage and provides intermediate power support. The supercapacitor manages high-frequency transient power demands, mitigating stress on the fuel cell and battery. Real-time simulations and experimental validation on a hybrid storage system test bench demonstrate the effectiveness of the proposed strategy under Worldwide Harmonized Light Vehicles Test Procedure and Artemis driving cycles. The results confirm stable DC bus voltage regulation, accurate current tracking, and improved energy efficiency, with the supercapacitor effectively absorbing transient power fluctuations. The findings highlight the potential of hybrid energy management in fuel cell-based electric vehicles, contributing to improved system longevity and overall performance.

# 1. Introduction

## 1.1. Background

The increasing concerns regarding global warming, air pollution caused by toxic emissions from internal combustion engines, and the depletion of fossil fuel reserves have driven the automotive industry toward alternative energy sources such as Fuel Cells (FCs) and electrochemical batteries [1,2].

Hybrid Electric Vehicles (HEVs) integrate multiple energy sources to enhance efficiency and performance. Among them, Fuel Cell Hybrid Electric Vehicles (FCHEVs) use an FC as the primary power source, while secondary energy storage systems, such as lithium-ion batteries and Supercapacitors (SCs), complement the power demand [3]. The Proton Exchange Membrane Fuel Cell (PEMFC) is widely employed in FCHEVs due to its low-temperature and low-pressure operating conditions [4,5].

Lithium-ion batteries, known for their high energy and power density and low self-discharge rate, dominate HEVs and Electric Vehicles

(EVs). Additionally, they enable energy recovery through regenerative braking, improving overall efficiency [6]. However, PEMFCs have a slow dynamic response, which may lead to power shortages during high-demand conditions. To address this issue, SCs are integrated alongside batteries to handle rapid power fluctuations, ensuring system stability and efficiency [7]. With high power density and fast charge-discharge capabilities. SCs serve as an ideal complement to FCs and batteries [8]. Given the distinct characteristics of PEMFCs, batteries, and SCs in power delivery and energy storage, an Energy Management Strategy (EMS) is essential to ensure efficient power distribution within the embedded sources [9].

## 1.2. Literature survey

Beyond powertrain-level control, recent reviews address the broader system-level management of zero-emission mobility. Kumar et al. [10] survey smart energy-management frameworks for EVs participating in

<footnote><sup>a</sup> Modelling, Information and Systems (MIS) Laboratory, Picardie Jules Verne University, Amiens, 80000, France</footnote>

<footnote><sup>b</sup> Green Tech Institute, Mohammed VI Polytechnic University, Ben Guerir, 43150, Morocco</footnote>

<footnote><sup>c</sup> LACoSERE Laboratory, Amar Telidji University, BP 37G, Ghardaia Road, 03000, Laghouat, Algeria</footnote>

<footnote>☆ This document is the results of the research project as part of the V3EA project funded by the National Research Agency in France.</footnote>

<footnote>* Corresponding author.
E-mail address: reda.achdad@gmail.com (R. Achdad).</footnote>
X2V/V2X services, covering multi-objective control, predictive strategies, and grid-interaction mechanisms. Complementing these system-level perspectives. Munsi et al. [11] provide a comprehensive review of rule-based, optimization-based, and learning-based EMS and control approaches for EVs, HEVs, and PHEVs, outlining their strengths, limitations, and their relevance for future intelligent and emission-free transportation systems. In parallel, recent studies have highlighted the importance of intelligent and data-driven methods in electric transportation. For example, Ahmed et al. [12] review the computational challenges and advanced ML/RL-based solutions for routing, charging planning, and energy management in green charging networks, further underscoring the growing relevance of cognitive control strategies in zero-emission mobility.

Several energy management strategies, whether online or offline, have been proposed in the literature to effectively distribute power between FCs, batteries, and SCs in HEVs [8,13]. Rule-based EMS methods are frequently utilized due to their simplicity, low computational burden, and real-time implementation capability [4,6,14]. For instance, [15] proposed an optimal rule-based control strategy employing direct transcription. In [16] an adaptive supervisory control was adopted for power management in fuel cell-battery hybrid city buses. Authors in [17] proposed a power management control strategy ensuring continuous power supply while effectively managing dynamic load variations. To further improve system performance, researchers have introduced low-pass filter-based approaches that allocate low-frequency components of the power demand to the FC and high-frequency transient loads to the SC, thereby mitigating rapid fluctuations and enhancing FC durability [4,5]. A recent study in [13] proposed a fuzzy logic-based EMS for FC hybrid trucks, optimizing FC power demand based on real-time driver input and State Of Charge (SOC) monitoring. This approach reduced hydrogen consumption by 24.8% while maintaining battery's SOC stability, demonstrating the effectiveness of rule-based fuzzy control strategies in fuel economy improvement. Although rule-based methods provide simplicity, they often face challenges in adapting dynamically to unpredictable driving conditions.

Optimization-based EMS approaches aim to minimize hydrogen consumption while maintaining optimal energy efficiency. These strategies often employ mathematical models and control algorithms to achieve near-optimal power distribution. Dynamic programming, Equivalent Consumption Minimization Strategy (ECMS), and Pontryagin's minimum principle (PMP) are among the most prominent. Authors in [18] introduced an optimal control strategy using classical minimum principles, providing optimal power management solutions. Similarly, in [19] compared an operation mode switching method with ECMS, highlighting ECMS's advantages in fuel economy and durability. However, the necessity for a priori knowledge of driving cycles limits real-time applicability. Combining rule-based and optimization-based methods has shown promising results in balancing computational efficiency and power distribution performance. For instance, genetic algorithm (GA)-optimized fuzzy logic EMS was explored in [8], demonstrating improved hydrogen economy while maintaining stable power distribution.

Recent work has increasingly focused on improving the robustness and reliability of control strategies for multi-source FCHEVs, particularly under uncertainties and component degradations. Maaruf and al. [20] introduce a fault-tolerant control strategy for FC, battery and supercapacitor HEVs, combining a fractional-order sliding-mode controller with an RBF-neural network to handle sensor faults and parametric uncertainties. The method achieves robust current tracking and DC-bus regulation. In [21], a current-sharing control method is proposed for a fuel-cell, battery and supercapacitor HEV, combining a simple LPF-based energy management scheme with a passivity-based control structure to regulate source currents and stabilize the DC-bus voltage. Their approach ensures stable current allocation among the three

sources and provides asymptotic stability through an energy-function formulation.

Fuzzy Logic, have gained significant attention for their adaptability, robustness, and capability to handle system nonlinearities without comprehensive mathematical modeling. The fuzzy logic-based strategies presented in [22,23] have significantly improved the performance of FC hybrid vehicles. Similarly, the studies in [24,25] demonstrated enhancements in fuel economy and system performance in FC/SC hybrid power systems using fuzzy logic due to its inherent flexibility and adaptability. In [26], a multi-stage fuzzy EMS was developed to enhance FC health by mitigating transient power fluctuations. This approach integrates a transition-based switching mechanism that compensates for the sluggish response of FCs and reduces power ripples in HEVs. Frequency decoupling-based EMSs have also widely used because of their ability to effectively manage energy sources by splitting the required power into different frequency ranges. For instance, a wavelet transform-based frequency decomposition technique was introduced in [5], where a fuzzy control method was used to assign low-frequency power demands to the FC and high-frequency components to the SC. This method demonstrated a 7.94% reduction in hydrogen consumption compared to the conventional ECMS. A hierarchical EMS integrating fuzzy logic and state regulation was introduced in [27], where a low-pass filter was employed to manage high-frequency power fluctuations, ensuring smooth energy transitions between the battery and SC. Another approach involves integrating fuzzy logic control with optimization techniques to improve power-sharing accuracy. In [6], a fuzzy logic-based EMS was developed to dynamically balance power distribution, achieving a 29% reduction in hydrogen consumption. Similarly, a hybrid fuzzy-optimization EMS was proposed in [7], where an adaptive frequency-based power allocation method was used to split power flow and extend battery SOC. An additional rule-based optimization EMS was introduced in [28], leveraging PMP to balance fuel economy and power source durability. By incorporating a FC power variation limiting factor, this approach mitigates rapid power changes, thus improving the lifespan of both the FC and battery.

### 1.3. Main contribution

In [6], an EMS based on fuzzy logic was validated on a Hardware-In-the-Loop (HIL) test bench. Although this approach reduced hydrogen consumption, the figures indicate that the FC current exhibits significant fluctuations during the EUDC scenario, which in turn affects both its lifespan and efficiency. In [4], a novel energy management system for a FC hybrid system is proposed using fuzzy logic combined with frequency decoupling. While the strategy's structure is promising, the power distribution between the sources could be further optimized to keep the battery's state of charge within its desired range. Moreover, the proposed strategy was only validated through simulation on Matlab/Simulink. In [29], an online EMS based on a power-frequency approach is introduced. A low-pass filter is used to compute the required FC power; however, the EMS is validated solely via simulation and HIL. The study in [5] presents a frequency decoupling and fuzzy logic based EMS for FCHEVs. The frequency decomposition in this work is based on the HARR wavelet transform, a method known for its delay during processing, making it unsuitable for real-time management [30]. The results show that the delay caused by the wavelet-based frequency decomposition leads to a misalignment between the FC output and the load demand, resulting in the supercapacitor directly absorbing the FC's power. Additionally, the FC power fluctuations are high and even greater than those of the battery, which negatively impacts its lifespan.

From the literature on frequency-based power-splitting approaches for FC/Battery/SC electric vehicles, real-time experimental validation is rarely performed, and the results are limited by a lack of rigorous and comprehensive analysis. In this context, this paper proposes the following contributions:
* A new energy management strategy is developed based on the combination of fuzzy logic, frequency decoupling, and deterministic rules that leverages the distinct characteristics of the energy sources to reduce stress on the FC and battery, while addressing power sharing between sources and the load and considering the SOC of both the battery and the supercapacitor.

* A FC emulator is used in this work to reproduce the behavior and characteristics of an actual FC, while a traction emulator replicates the power consumption and delivery of an EV under the WLTP and Artemis driving scenarios.

* A comprehensive experimental test bench is established. The experimental results demonstrate the relevance of the proposed strategy and the effectiveness of the control system across the selected scenarios. In particular, the results underscore the benefits of frequency decomposition, clearly illustrating how each energy source responds to the load demand in accordance with the requirements set by the proposed strategy.

## 1.4. Paper organization

The paper is structured as follows. In Section 2, we introduce the mathematical modeling of the different components of the hybrid system ranging from the energy storage system, which integrates boost and bidirectional buck-boost DC/DC converters, to the EV dynamics. Section 3 details the proposed power management strategy, while Section 4 outlines the design of the PI controller. Experimental results validating the energy management system are discussed in Section 5. Finally, Section 6 concludes the paper and suggests potential directions for future work.

## 2. Hybrid electric vehicle system description and modeling

The architecture of the HEVs is depicted in Fig. 1, it comprises two main subsystems:

- A Hybrid Energy Storage System (HESS) incorporating two bidirectional buck-boost DC/DC converters and a boost DC/DC converter, connected to three different energy sources: FC, battery, and supercapacitor. The FC serves as the primary energy source, providing sustained power to ensure an extended driving range. In contrast, the battery and the supercapacitor function as auxiliary sources, effectively handling abrupt load variations by delivering transient or peak power demands and recovering energy during braking phases.

- The DC bus, in turn, is connected to a DC/AC inverter that drives the vehicle's traction motor. Ideally, the HESS should exhibit high power density, long operational lifespan, and high efficiency. It is important to note that the power inverter and electric motor are not included in this study; instead, they are modeled as a controllable current source, as illustrated in Fig. 4. This section addresses system modeling, including the mathematical models of the lithium-ion battery, the ultracapacitor, the vehicle dynamics, and the averaged state-space models of the bidirectional buck-boost and boost DC/DC converters.

### 2.1. Vehicle dynamic modeling

The vehicle dynamic model describes the longitudinal motion of the vehicle by considering key forces acting on it, including aerodynamic drag, rolling resistance, gravitational forces on inclines, and traction forces. The vehicle's motion is governed by Newton's second law, expressed as [31]:

$$F_{tr} - F_{res} = m \cdot a \quad (1)$$

where $F_{tr}$ represents the traction force generated by the drivetrain, $F_{res}$ includes all opposing forces (aerodynamic drag, rolling resistance,

<figure><img src="image_3.png" /><figcaption>Fig. 1. FCHEV structure.</figcaption></figure>

and gravitational forces), $m$ is the vehicle's mass, and $a$ is the vehicle's acceleration. The total resistance force $F_{res}$ can be detailed as [14]:

$$ 
\begin{aligned}
F_{res} &= F_{aero} + F_{roll} + F_{grav} \\
&= \frac{1}{2} \rho C_d A v^2 + C_r m g \cos(\theta) + m g \sin(\theta)
\end{aligned} 
\quad (2) $$

where $F_{aero}$ represents aerodynamic drag, with $\rho$ being air density, $C_d$ the drag coefficient, $A$ the frontal area, and $v$ the vehicle speed. $F_{roll}$ represents rolling resistance, where $C_r$ is the rolling resistance coefficient, $g$ is gravitational acceleration, and $\theta$ is the road slope. $F_{grav}$ accounts for gravitational forces on inclines. The model provides a basis for estimating power demands under various driving conditions, which is essential for energy management in hybrid EV systems. The required electric power $P_{trac}$ to drive a vehicle at a given speed $V$ can be expressed as [14]:

$$P_{elec} = F_{trac} \cdot V \quad (3)$$

### 2.2. Fuel cell model

The output voltage of the FC, $V_{fc}$ can be empirically estimated using Eq. (4), which incorporates the effects of activation, ohmic, and concentration losses, as depicted in Fig. 2 [8].

$$V_{fc} = N (E_{Nernst} - V_{act} - V_{ohm} - V_{con}) \quad (4)$$

where $N$ is the number of cells, $E_{Nernst}$ denotes the thermodynamically reversible voltage, $V_{act}$ represents activation losses, $V_{ohm}$ refers to ohmic losses, and $V_{con}$ reflects concentration losses [8]. The efficiency of the PEMFC system is expressed as the ratio of the net electrical power output, $P_{NET}$ to the total energy content of the supplied hydrogen fuel, $P_{H_2}$, defined as [8]:

$$ 
\begin{aligned}
\eta_{fc} &= \frac{P_{NET}}{P_{H_2}} = \frac{P_{fc} - P_{AUX}}{H HV \cdot \dot{n}_{H_2}} = \frac{V_{fc} i_{fc} - P_{AUX}}{H HV \cdot \frac{N i_{fc}}{2F}}
\end{aligned} 
\quad (5) $$

The auxiliary power consumption, $P_{AUX}$, encompasses the air processing and thermal management systems. The FC current is denoted by $i_{fc}$, while $H HV$ represents the higher heating value of hydrogen ($\approx 285.83$ kJ/mol). The hydrogen consumption is determined as follows [8]:

$$m_{H_2} = \int_{0}^{t} \dot{m}_{H_2} dt = \int_{0}^{t} \frac{N i_{fc}}{2 F \eta_{fc}} \cdot M_{H_2} dt \quad (6)$$

where $\dot{m}_{H_2}$ denotes the hydrogen consumption rate, $F$ is Faraday's constant, and $M_{H_2}$ represents the molar mass of hydrogen (2.02 g/mol).
<figure><img src="image_4.png" /><figcaption>Fig. 2. Energetic representation of PEMFC system.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 3. Lithium-ion battery model.</figcaption></figure>

## 2.3. Lithium-ion battery model

This study employs a generic lithium-ion battery model, selected for its simplicity and integration within the MATLAB/Simulink library. As depicted in Fig. 3.

The adopted model consists of a controlled voltage source $E_0$ connected in series with an internal resistance $R_{int}$. The model simulates both charge and discharge cycles according to the following dynamics [26]:

$$V_{bat\_ch} = E_0 - K \cdot \frac{Q}{0.1Q + it} \cdot i^* - K \cdot \frac{Q}{Q - it} \cdot it + A \cdot e^{-B \cdot it} \quad (7)$$

$$V_{bat\_disch} = E_0 - K \cdot \frac{Q}{Q - it} \cdot i^* - K \cdot \frac{Q}{Q - it} \cdot it + A \cdot e^{-B \cdot it} \quad (8)$$

where $V_{bat}$ denotes the battery voltage (V), $V_{OC}$ represents the open-circuit voltage (V), $K$ is the polarization constant (V/Ah), $Q$ corresponds to the maximum battery capacity (Ah), $i$ is the instantaneous battery current (A), $A$ represents the exponential voltage (V), $B$ is the exponential capacity coefficient ($Ah^{-1}$), and $i^*$ denotes the filtered current used to capture the low-frequency dynamics of the battery (A), $it$ is the extracted capacity (Ah).

The real-time estimation of the battery's State of Charge, denoted as $SOC_t$, is determined using the Coulomb counting method, as presented in Eq. (9). In this approach, $SOC_{t0}$ indicates the initial state of charge, while $i_b$ represents the charge or discharge current. For simplicity, losses during the charging and discharging processes are neglected in the calculation [32].

$$SOC_t = SOC_{t0} - \frac{1}{3600Q_{bat}} \int_{t_0}^{t} i_b dt \quad (9)$$

## 2.4. Supercapacitor model

The intermediate energy storage system under consideration consists of two supercapacitor modules connected in series. Each module is characterized by a nominal voltage of 16 V and is itself an assembly of six elementary supercapacitors connected in series. To accurately represent the behavior of SCs during transient operation, it is necessary to employ a model that captures the rapid charge and discharge cycles. Therefore, a simple two-branch R-C model inspired by the works presented in [33] is used.

The evolution of the voltage across the terminals of the supercapacitor module can be expressed as:

$$ \begin{aligned} V_{sc}(t) &= N_{s,sc} \times U_{sc} = N_{s,sc} (V_1 + R_{sc1} i_{sc}) \\ &= N_{s,sc} \left( V_1 + R_{sc1} \frac{I_{sc}}{N_{p,sc}} \right) \end{aligned} \quad (10) $$

where $U_{sc}$ represents the voltage across a single SC cell, $V_1$ corresponds to the voltage across the first capacitor in the SC module, and $R_{sc1}$ denotes the first resistor in the SC equivalent circuit. The variable $i_{sc}$ indicates the current flowing through a single SC cell, while $I_{sc}$ refers to the input current to the SC module. $N_{s,sc}$ represents the number of SC cells connected in series within the module, and $N_{p,sc}$ the number of cells connected in parallel within the module. The SOC equation is expressed as follows [33]:

$$SOC_t = SOC_{t0} - \frac{1}{3600C_{sc}} \int_{t_0}^{t} i_{sc} dt \quad (11)$$

where $C_{sc}$ and $i_{sc}$ represent the supercapacitor's capacitance and the charge/discharge current, respectively.

## 2.5. Converters modeling

Effective energy flow management between the HESS and the traction emulator requires precise control of the associated converters. The FC is connected to the DC bus via a unidirectional boost DC/DC converter, while both the battery and the SC are connected in parallel to the DC bus through two bidirectional DC/DC converters. This configuration facilitates independent control over the charging and discharging processes of the three HESS components, based on the operating modes defined by the EMS. The mathematical modeling of each converter is detailed in the following sections.

### 2.5.1. Fuel cell boost converter model

The mathematical representation of the DC/DC boost converter, based on the average switching model, is described by Eqs. (12),(13) and (14) [6]:

$$\frac{di_{fc}}{dt} = -\frac{R_1}{L_1} i_{fc} + \frac{1}{L_1} v_{fc} - \frac{1-d_1}{L_1} V_{bus} \quad (12)$$

$$\frac{dV_{bus}}{dt} = \frac{1-d_1}{C_{bus}} i_{fc} - \frac{1-d_1}{C_{bus}} i_{bus} \quad (13)$$

$$i_{d_{fc}} = (1 - d_1) i_{fc} \quad (14)$$

where, $i_{fc}$ and $v_{fc}$ represent the FC current and voltage, respectively, $d_1$ refers to the duty cycle, $V_{bus}$ corresponds to the output voltage of DC bus, and $i_{d_{fc}}$ represents the output current of the boost converter.

### 2.5.2. Battery bidirectional converter model

Two distinct operating modes can be identified for the battery system: charging mode and discharging mode. To manage the bidirectional energy flow, a DC/DC bidirectional converter with two switches, $S_3$ and $S_4$, is employed.

In discharge mode, when the battery supplies energy to the load ($I_{B\_ref} > 0$), switch $S_3$ remains OFF, while switch $S_4$ can be in either position. Conversely, in charging mode, when excess energy is available
for storage ($I_{B\_ref} < 0$), switch $S_4$ is OFF, and $S_3$ can be in any state. The mathematical model representing the system dynamics during both charging and discharging modes is described by the following equations [7]:

$$ \frac{di_{bat}}{dt} = \frac{v_{bat}}{L_2} - \frac{R_2}{L_2}i_{bat} - d_{bat}\frac{V_{bus}}{L_2} \quad (15) $$

$$ \frac{dV_{bus}}{dt} = d_{bat}\frac{i_{bat}}{C_{bus}} - \frac{i_{s2}}{C_{bus}} \quad (16) $$

$$ i_{d_{bat}} = d_{bat}i_{bat} \quad (17) $$

with

$$ d_{bat} = \begin{cases} 1 - d_2 & \text{if } I_{B\_r e f} > 0 \\ d_2 & \text{if } I_{B\_r e f} < 0 \end{cases} \quad (18) $$

where, $v_{bat}$ and $i_{bat}$ represent the battery voltage and current, respectively, while $d_{bat}$ denotes the average control input of the converter, and $i_{d_{bat}}$ corresponds to the converter's output current.

### 2.5.3. SC bidirectional converter model

The charging and discharging processes of supercapacitors are comparable to those of batteries. Therefore, the corresponding characteristic equations are derived as follows [7]:

$$ \frac{di_{sc}}{dt} = \frac{v_{sc}}{L_3} - \frac{R_3}{L_3}i_{sc} - d_{sc}\frac{V_{bus}}{L_3} \quad (19) $$

with

$$ d_{sc} = \begin{cases} 1 - d_3 & \text{if } I_{sc\_r e f} > 0 \\ d_3 & \text{if } I_{sc\_r e f} < 0 \end{cases} \quad (20) $$

$$ i_{d_{sc}} = d_{sc}i_{sc} \quad (21) $$

where, $v_{sc}$ and $i_{sc}$ denote the supercapacitor voltage and current, respectively, $d_{sc}$ represents the converter's average control input, and $i_{d_{sc}}$ refers to the converter's output current.

## 2.6. Global system modeling

The circuit diagram of the overall power conversion system is illustrated in Fig. 4. The next step involves developing a comprehensive system model that integrates the FC Boost Converter, as well as the bidirectional converters for the battery and SC. By applying Kirchhoff's Current Law (KCL) to the DC bus, the following equations are derived [6]:

$$ i_{bus} = i_{d_{fc}} + i_{d_{bat}} + i_{d_{sc}} \quad (22) $$

where $i_{bus}$ represents the load current.

$$ \frac{dV_{bus}}{dt} = \frac{1 - d_1}{C_{bus}}i_{fc} + d_{bat}\frac{i_{bat}}{C_{bus}} + d_{sc}\frac{i_{sc}}{C_{bus}} - \frac{i_{bus}}{C_{bus}} \quad (23) $$

# 3. Energy management strategy

## 3.1. Power source characteristics

The studied system is a multi-source EV equipped with three energy sources: a FC, a battery, and a SC. Each source exhibits distinct characteristics and functionalities. According to the Ragone diagram depicted in Fig. 6, the FC is characterized by a high energy density, making it suitable for providing sustained power over long durations. However, its low power density limits its ability to address rapid power transients, necessitating its integration with auxiliary sources capable of delivering high instantaneous power and absorbing transient fluctuations.

The lithium-ion battery offers a relatively high energy density and can supply sufficient power for applications such as vehicle acceleration. Nevertheless, its response time is slower compared to SCs, which are highly efficient in delivering instantaneous power surges needed for rapid acceleration and regenerative braking. However, SCs are limited by their low energy density, restricting their ability to sustain energy over extended periods.

## 3.2. Real-time energy management strategy

It is worth noting that the combination of frequency decoupling and fuzzy logic offers several practical advantages for real-time hybrid energy management. Frequency decomposition enables a clean separation of low, mid, and high-frequency power components, allowing each source to operate within its optimal dynamic bandwidth and thereby reducing stress on the fuel cell and the battery. The fuzzy layer provides a low-complexity decision mechanism that handles SOC constraints and transient load variations without requiring prediction models or computationally intensive optimization. This structure is therefore particularly suitable for embedded implementation, where deterministic execution and robustness to measurement noise are essential. These features motivate the choice of this EMS architecture for the experimental platform used in this work.

As illustrated in Fig. 5. The primary objective of frequency decoupling in the proposed EMS is to balance the power distribution among the various energy sources within a hierarchical structure. Initially, the reference power for the FC is generated using fuzzy logic based on two inputs: the real-time power demand of the vehicle and the SOC of the battery. The output power from the fuzzy logic controller is then passed through a low-pass filter to mitigate rapid peak currents, which could lead to electrode degradation in the FC.

The battery is responsible for regulating the DC bus voltage via a cascade control loop. A low-pass filter is integrated between the inner current control loop and the outer voltage regulation loop, ensuring that the current reference is smoothed. This filtering reduces sharp current variations, promoting a more gradual response from the battery and extending its lifespan. The high-frequency components of the filtered power, which correspond to significant current peaks, are handled by the SC, a device well suited for fast and high-current variations.

The power contribution of the SC is adjusted based on its SOC using deterministic rules, as detailed in Algorithm 2. The operational limitations and dynamic behavior of the SC are analogous to those of an electrolytic capacitor. Consequently, the SC primarily operates during transient conditions, where its average current must remain zero in steady-state scenarios. This strategy enables the SC to rapidly deliver or absorb energy in response to dynamic variations in load demands, thereby improving system stability and operational efficiency.

### 3.2.1. Fuzzy rule-based strategy unit

A fuzzy logic-based EMS is proposed to generate the reference current for the FC, which is determined by the load demands and the SOC of the battery. To obtain the optimal output decisions, the inputs are first fuzzified. In this step, each crisp numerical input is converted into a linguistic variable using the information contained in the knowledge base. The degree of membership of an input to its corresponding linguistic classes is described using triangular and trapezoidal membership functions, which define the operating domains of the inputs. These functions are given by:

$$ \operatorname{trian}(x, a, b, c) = \begin{cases} 0, & x \le a, \\ \frac{x-a}{b-a}, & a \le x \le b, \\ \frac{c-x}{c-b}, & b \le x \le c, \\ 0, & x \ge c, \end{cases} \quad (24) $$

$$ \operatorname{trap}(x, a, b, c, d) = \begin{cases} 0, & x \le a, \\ \frac{x-a}{b-a}, & a \le x \le b, \\ 1, & b \le x \le c, \\ \frac{d-x}{d-c}, & c \le x \le d, \\ 0, & x \ge d. \end{cases} \quad (25) $$
<figure><img src="image_6.png" /><figcaption>Fig. 4. Hybrid energy storage EV architecture.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 5. Proposed EMS architecture.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 6. Ragone diagram.</figcaption></figure>

In the proposed fuzzy decision layer, the crisp output is obtained from the aggregated fuzzy set using the centroid method, expressed as:

$$y^* = \frac{\int_{Y} y \mu_{\text{agg}}(y) dy}{\int_{Y} \mu_{\text{agg}}(y) dy} \qquad (26)$$

where $\mu_{\text{agg}}(y)$ denotes the aggregated membership function resulting from the activation of all fuzzy rules, Y is the domain of the output

variable, and $y^*$ represents the defuzzified control action. This method ensures smooth and stable transitions, which is essential for real-time energy management.

The system consists of two inputs and one output, governed by 36 fuzzy rules, as outlined in Table 1. The input $I_{\text{Load}}$ and the output $I_{\text{FC}}$ are normalized to the ranges [-1, 1] and [0, 1], respectively. Appropriate gain factors are introduced to scale these quantities according to the power levels of the load and the fuel cell. The inputs, outputs, and their respective membership functions are defined and implemented as follows:

• Input 1: Battery state of charge

This parameter has been incorporated to maintain the battery's SOC within a range of 0.4 to 0.9. The rules have been designed to enable the FC to increasingly support the load power demand as the battery discharges, even recharging the battery with the FC when its SOC reaches a critically low level. The SOC of the battery is divided into five membership functions: Very Low (VL), Low (L), Medium (M), High (H), and Very High (VH), as illustrated in Fig. 7(a).

• Input 2: Load current The output from the vehicle's power sources is determined by the load current, which has been classified into seven membership functions: Negative High (NH), Negative Medium (NM), Negative Low (NL), Zero (Z), Positive
<table><caption>**Table 1**
FC-EMS fuzzy rules.</caption><thead><tr><th></th><th colspan="7">I<sub>bus</sub></th></tr><tr><th></th><th>NH</th><th>NM</th><th>NL</th><th>Z</th><th>PL</th><th>PM</th><th>PH</th></tr></thead><tbody><tr><th>VL</th><td>VL</td><td>VL</td><td>VL</td><td>VL</td><td>M</td><td>Max</td><td>Max</td></tr><tr><th>L</th><td>VL</td><td>VL</td><td>VL</td><td>VL</td><td>M</td><td>H</td><td>Max</td></tr><tr><th>M</th><td>VL</td><td>VL</td><td>VL</td><td>VL</td><td>L</td><td>M</td><td>M</td></tr><tr><th>H</th><td>VL</td><td>VL</td><td>VL</td><td>VL</td><td>VL</td><td>L</td><td>M</td></tr><tr><th>VH</th><td>Z</td><td>Z</td><td>Z</td><td>Z</td><td>Z</td><td>Z</td><td>Z</td></tr></tbody></table>

<figure><img src="image_9.png" /><figcaption>**Fig. 7.** MFs of the fuzzy logic strategy inputs and output variables.</figcaption></figure>

Low (PL), Positive Medium (PM), and Positive High (PH), as depicted in Fig. 7(b).

### Output: Fuel cell reference current

The output reference current is defined by five membership functions: Very Low (VL), Low (L), Medium (M), High (H), and Maximum (Max), as illustrated in Fig. 7(c). The default Mamdani-type inference method is employed in this study. The 36 rules formulated for this fuzzy logic strategy are detailed in Table 1.

Regarding the fuzzy rule base presented in Table 1, the design follows the principle that the fuel cell operates primarily as a quasi-steady energy source. In particular, limiting the fuel cell output when the battery state of charge is high aims to avoid unnecessary fuel cell operation and excess power generation. Under high battery SOC conditions, additional fuel cell power would mainly result in inefficient

battery charging or increased auxiliary losses, while the battery is already capable of meeting the load demand. Conversely, increasing the fuel cell contribution at low battery SOC helps restore the battery to an appropriate operating range and improves the overall energy balance of the system.

### 3.2.2. Frequency-decoupling based energy management strategy unit

The proposed power management strategy is based on the frequency decomposition of the power demand into low- and high-frequency components. Two low-pass filters (LPFs) with distinct cutoff frequencies ($f_{c1}$, $f_{c2}$) are designed. The first-order low-pass filter was selected as a deliberate compromise between simplicity, robustness, and physical relevance. A first-order filter provides a smooth separation between slow and fast power components while avoiding phase lag amplification and implementation complexity associated with higher-order filters. Since the objective of the filter is not sharp frequency discrimination but rather the extraction of the slow power trend to be assigned to the fuel cell, a first-order structure was found sufficient and well suited for real-time implementation. The first LPF (LPF-1) is utilized to extract the lowest frequency component of the fuel cell reference current ($I_{FC,ref}$), which is supplied to the boost converter connected to the FC. The second LPF (LPF-2) is applied to determine the faster dynamic response of the battery reference current ($I_{bat,ref}$), which is managed by the bidirectional DC/DC converter of the battery. The remaining high-frequency power component, filtered out by both LPFs, is handled by the SC. The LPF block is modeled as a first-order low-pass filter with a cutoff frequency defined by [34].

$$H(s) = \frac{1}{\tau s + 1}, \quad \tau = \frac{1}{2\pi f_c} \qquad (27)$$

Some studies in the literature have proposed adaptive methods for tuning the filter's cutoff frequency based on the state of charge of the energy sources and consumptions [27,35]. However, the cutoff frequency should primarily be determined by the dynamic characteristics of the power demand, which are inherently tied to the driving profile. In real-time applications, accurately predicting the driving profile remains a challenge.

In this work, The cutoff frequencies were determined through a quantitative methodology combining the spectral characteristics of the WLTP and Artemis driving cycles with the inherent dynamic bandwidth of the fuel cell, battery, and supercapacitor.

The cutoff frequencies were determined through a quantitative methodology combining the spectral characteristics of the WLTP and Artemis driving cycles with the inherent dynamic bandwidth of the fuel cell, battery, and supercapacitor. The cutoff frequencies were determined through a quantitative methodology combining the spectral characteristics of the WLTP and Artemis driving cycles with the inherent dynamic bandwidth of the fuel cell, battery, and supercapacitor.

Fig. 8 shows that over 90% of the WLTP energy and 80%-90% of the Artemis energy lie below 0.15-0.2 Hz, with dominant components in the 0.07-0.10 Hz range. This leads to a clear separation of the load dynamics into slow (< 0.05 Hz), medium (0.05-0.2 Hz), and fast (> 0.2 Hz) frequency domains.

Due to its electrochemical and air-supply dynamics, the fuel cell can only track slow variations, which limits its effective bandwidth to frequencies below approximately 0.05 Hz [36]. The battery is suited for medium-frequency dynamics [37], whereas the supercapacitor inherently handles fast fluctuations.

By combining the slow-frequency content of the driving cycles with the usable bandwidths of the fuel cell and the battery, the admissible interval for the filters can be defined as follows:

$$f_{c,FC_{[exp]}} \in [0.01, 0.05] \text{ Hz}, \quad f_{c,Bat_{[exp]}} \in [0.05, 0.2] \text{ Hz} \qquad (28)$$

Several candidate values within these intervals were evaluated experimentally. The final cutoff frequencies were selected as the best compromise between DC-bus voltage ripple, fuel-cell dynamic loading,
<figure><img src="image_10.png" /><figcaption>Fig. 8. Power spectral density of the chosen driven cycles.</figcaption></figure>

battery RMS current, and proper allocation of fast dynamics to the supercapacitor. The values used in the experimental validation are:

$$f_{c,fc} = 0.032 \text{ Hz}, \quad f_{c,Bat} = 0.1273 \text{ Hz} \qquad (29)$$

The reference current of the FC, generated at the output of the fuzzy logic block, is then filtered by the LPF-1 filter, which decomposes the current into low-frequency and high-frequency components as follows:

$$I_{Fc\_ref} = H_1(s) \cdot I_{Fc} \qquad (30)$$

$$I_{Fc\_exc} = I_{Fc} - I_{Fc\_ref} \qquad (31)$$

where $H_1(s)$ represents the transfer function of LPF-1, $I_{Fc}$ is the input current of LPF-1, $I_{Fc\_ref}$ denotes the low frequency current reference for the FC, and $I_{Fc\_exc}$ corresponds to the high-frequency current component to be delivered by the SC.

Similarly, for the battery, LPF-2 is employed to separate the low and high frequency components of the battery current, which are derived from the DC bus voltage control loop. These currents are defined as follows:

$$I_{Bat\_ref} = H_2(s) \cdot I_{Bat} \qquad (32)$$

$$I_{Bat\_exc} = I_{Bat} - I_{Bat\_ref} \qquad (33)$$

where $H_2(s)$ represents the transfer function of LPF-2, $I_{Bat\_ref}$ denotes the low-frequency current reference, and $I_{Bat\_exc}$ corresponds to the high-frequency current component to be delivered by the SC.

Due to their slow dynamic response, the FC and battery are unable to instantly supply high-frequency current components ($I_{Fc\_exc}$ and $I_{Bat\_exc}$). Fortunately, the SC, with its high power density and rapid response capability, is integrated into the system to compensate for load fluctuations and absorb the high-frequency currents that the FC and battery cannot handle. As a result, the reference current for the SC based on high-frequency components can be determined as follows:

$$I_{Sc} = I_{Fc\_exc} + I_{Bat\_exc} \qquad (34)$$

Similar to the battery, a SOC regulation algorithm is implemented to maintain the SC's SOC within predefined limits.

### Algorithm 1 Rule-based power sharing

1: if $I_{bus} < 0$ then

2: $I_{Fc\_exc} = I_{bus}$

3: else if ($I_{Fc\_ref} - I_{bus} > 0$) and ($I_{bus} > 0$) then

4: $I_{Fc\_exc} = 0$

5: else

6: $I_{Fc\_exc} = I_{bus} - I_{Fc\_ref}$

7: end if

### Algorithm 2 Supercapacitor's SOC regulation

1: $\alpha = 4 \times \frac{|SOC_{Sc}(t) - SOC_{Scmin}|}{SOC_{Scmin}}$

2: if ($0.4 \le SOC_{Sc} \le 0.5$) and ($I_{Sc} > 0$) then

3: $I_{Sc\_ref} = \alpha \times I_{Sc}$

4: else if ($SOC_{Sc} < 0.4$) and ($I_{Sc} > 0$) or ($SOC_{Sc} > 0.9$) and ($I_{Sc} < 0$) then

5: $I_{Sc\_ref} = 0$

6: else

7: $I_{Sc\_ref} = I_{Sc}$

8: end if

### 3.2.3. Power sharing and SOC regulation algorithms

In the proposed EMS architecture, deterministic rules and fuzzy logic operate in a complementary manner to ensure both constraint satisfaction and smooth power sharing. The deterministic rules encode the strict operational limits of the energy sources, such as SOC boundaries, maximum allowable currents, and protection constraints for the fuel cell and the battery.

These rules act as hard constraints that must always be satisfied, regardless of the operating conditions. In contrast, the fuzzy logic layer generates soft decisions that regulate the distribution of intermediate-frequency power flows and smooth transitions between sources based on SOC levels and power deviations.

The fuzzy controller therefore operates within the feasible region defined by the deterministic rules. This hierarchical interplay ensures that safety-critical limitations are always respected while maintaining flexible, continuous, and real-time power allocation among the fuel cell, battery, and supercapacitor.

As an illustration of this complementary role, the fuzzy logic layer is specifically designed to maintain the FC power at a very low level (VL) without fully shutting it down when the vehicle demand is low and the battery SOC is high ($SOC_{bat} = V H$).

This behavior prevents premature degradation of the fuel cell, which can result from frequent start/stop cycles, insufficient warm-up periods, and operation away from the optimal temperature range. By ensuring that the FC remains active at a minimal level while still respecting the deterministic constraints, the EMS contributes to improved system longevity and more reliable energy-source coordination.

To prevent energy transfer from the FC to the SC, we have implemented a controller based on Algorithm 1, which enforces a zero reference current $I_{Fc\_exc}=0$ during phases where the FC's power output exceeds the vehicle's power demand. This mechanism also ensures that the energy delivered by the FC during braking phases is not entirely absorbed by the SC. Instead, the strategy prioritizes battery charging from the FC, as the proportion of power supplied by the FC is primarily determined by the battery's SOC. Except during acceleration phases, where both the battery and FC contribute to the required power due to their higher energy densities, the strategy favors battery charging under steady-state conditions. Not to mention that the battery is responsible for maintaining the voltage at the DC bus.
<figure><img src="image_11.png" /><figcaption>Fig. 9. PI voltage control diagram.</figcaption></figure>

On the other hand, thanks to frequency decomposition, the high-power transients generated by the motor during braking phases are predominantly absorbed by the SC. Once the battery reaches its maximum charge, the FC is deactivated, and the vehicle operates solely using the battery and SC as energy sources.

The SOC regulator for the supercapacitor depicted in Algorithm 2 is implemented to maintain the SOC within predefined limits. Once a certain threshold is reached, the power supplied by the SC is progressively limited as the SOC decreases, incorporating a tuning parameter $\alpha$.

Moreover, if the SOC of the SC reaches its upper or lower bound, a disconnection action is executed, and the device remains idle until the next charging or discharging cycle, respectively.

A lower SOC limit of 40% was imposed on the supercapacitor to avoid deep discharge. This threshold preserves sufficient voltage margin for stable DC/DC converter operation, limits current stress and efficiency degradation at low voltages, and mitigates excessive thermal and aging effects in the capacitor. In the hybrid FC/battery/SC architecture, maintaining this reserve also ensures that the SC can reliably buffer high-frequency load fluctuations, thereby protecting the battery from rapid current transients and contributing to overall system reliability.

## 4. Design of PI controller

The primary objective of the PI controllers is to regulate the DC bus voltage, manage the currents of the HESS, and ensure overall system stability under dynamic and sudden power variations.

The bidirectional converter connected to the battery is controlled using a cascaded control loop to mitigate the effects of the non-minimum phase zero. The outer loop, characterized by a slower dynamic response, regulates the voltage and generates the battery reference current $I_{bat\_ref}$ for the inner current control loop. This hierarchical control structure ensures that each loop operates efficiently within its respective bandwidth, thereby minimizing interference and enhancing system stability.

The transfer functions are given in (35), (36), (37) and (38):

$$F_1(s) = \frac{\tilde{I}_{fc}(s)}{\tilde{d}_1(s)} = \frac{2 \cdot V_{bus}}{R \cdot (1 - d_1)^2} \frac{1 + \frac{R \cdot C_{bus}}{2} s}{1 + \frac{L_1}{R \cdot (1 - d_1)^2} s + \frac{L_1 \cdot C_{bus}}{(1 - d_1)^2} s^2} \quad (35)$$

$$F_2(s) = \frac{\tilde{V}_{bus}(s)}{\tilde{I}_{bat}(s)} = \frac{R \cdot (1 - d_{bat})}{2} \frac{\left(1 - \frac{L_2}{R \cdot (1 - d_{bat})^2} s\right)}{1 + \frac{R \cdot C_{bus}}{2} s} \quad (36)$$

$$F_3(s) = \frac{\tilde{I}_{bat}(s)}{\tilde{d}_{bat}(s)} = \frac{2 \cdot V_{bus}}{R \cdot (1 - d_{bat})^2} \frac{1 + \frac{R \cdot C_{bus}}{2} s}{1 + \frac{L_2}{R \cdot (1 - d_{bat})^2} s + \frac{L_2 \cdot C_{bus}}{(1 - d_{bat})^2} s^2} \quad (37)$$

$$F_4(s) = \frac{\tilde{I}_{sc}(s)}{\tilde{d}_{sc}(s)} = \frac{2 \cdot V_{bus}}{R \cdot (1 - d_{sc})^2} \frac{1 + \frac{R \cdot C_{bus}}{2} s}{1 + \frac{L_3}{R \cdot (1 - d_{sc})^2} s + \frac{L_3 \cdot C_{bus}}{(1 - d_{sc})^2} s^2} \quad (38)$$

For the design of all PI controllers, it is essential to derive analytical expressions that define the relationship between each control variable, as referenced in [38]. Each converter is modeled using distinct control variables duty cycles ($d_1$, $d_{bat}$, $d_{sc}$) and input currents ($I_{fc}$, $I_{bat}$ and $I_{sc}$). These models are then integrated into the overall control scheme, as illustrated in Figs. 9 and 10.

<figure><img src="image_12.png" /><figcaption>Fig. 10. PI currents control diagram.</figcaption></figure>

<table><caption>Table 2
Test bunch specifications.</caption><thead><tr><th>HESS parameters</th><th>Value</th></tr></thead><tbody><tr><td colspan="2"><strong>Fuel cell emulator</strong></td></tr><tr><td>Stack voltage</td><td>V<sub>fc</sub> = [15, 25] V</td></tr><tr><td>Power output</td><td>P<sub>fc</sub> = 250 W</td></tr><tr><td>Number of Cells</td><td>N = 24</td></tr><tr><td>Max current</td><td>I<sub>max</sub> = 18.36 A</td></tr><tr><td colspan="2"><strong>Li-ion Batteries</strong></td></tr><tr><td>Nominal/charge voltage</td><td>V<sub>bat</sub> = 12.8/14.6 V</td></tr><tr><td>Capacity</td><td>Q<sub>bat</sub> = 12 Ah</td></tr><tr><td colspan="2"><strong>Supercapacitor</strong></td></tr><tr><td>Number of cells</td><td>N<sub>sc</sub> = 6</td></tr><tr><td>Rated voltage</td><td>V<sub>SC</sub> = 16 V</td></tr><tr><td>Rated capacitance</td><td>C<sub>SC</sub> = 500 F</td></tr><tr><td colspan="2"><strong>Other Components of the Test Bench</strong></td></tr><tr><td>Emulator-battery</td><td>V<sub>bat-emu</sub> = 12 V</td></tr><tr><td>Capacity</td><td>Q<sub>bat-emu</sub> = 80 Ah</td></tr><tr><td>Dc bus capacitor</td><td>C<sub>bus</sub> = 1.1 mF</td></tr><tr><td>Resistance</td><td>R = 240 Ω</td></tr><tr><td>Inductances</td><td>L<sub>1</sub>, L<sub>2</sub>, L<sub>3</sub> = 1 mH</td></tr></tbody></table>

To fine-tune the PI voltage and current controller outlined in Eqs. (39), (40) we employed the SISOTOOL graphical tool in MATLAB. By inputting the transfer functions $F(s)$, considering the phase and gain margin, settling-time and overshoot.

$$PI_{\_Voltage}(s) = 0.059 \cdot \frac{(s + 1413)}{s} \quad (39)$$

$$PI_{\_Current}(s) = 0.8 \cdot \frac{(s + 12.5)}{s} \quad (40)$$

## 5. Experimental results and discussion

### 5.1. Test bench setup, and system description

An experimental test bench is built in MIS laboratory of Amiens, in order to assess the developed FL-FD EMS and converters control for the studied HESS. The setup is composed of:

* Fuel cell emulator.

* Batteries.

* Supercapacitors.

* Three Bi-directional DC/DC converters.

* Boost DC-DC converter.

* Voltage and current sensors.

* DC power supply.

* dSPACE MicrolabBox 1202.

* ControlDesk software.

The parameters of the system components are summarized in Table 2.
<figure><img src="image_13.png" /><figcaption>Fig. 11. Fuel cell voltage and power curves at 70 °C.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Fig. 12. Block diagram of the fuel cell emulator.</figcaption></figure>

### 5.1.1. PEM fuel cell emulator based on a buck converter

The PEMFC emulator was developed in this related work [39], the purpose of the emulator is to deliver the electrical properties of the FC model, interfaces with the system through a DC/DC converter, which supplies the voltage and power behavior dictated by the simulated FC model in response to the load current.

The FC model is developed to simulate the electrical characteristics of PEMFC with a power rating of 250 W and a 24-cells stack. Its output voltage varies between 15 V and 25 V. Fig. 11 presents the characteristic curve of the FC at an operating temperature of 70 °C.

During tests, the multicellular converter is powered by a 43 V constant DC voltage supply. The DC bus current serves as input to the real-time FC model, with a current sensor transmitting the instantaneous current value via dSPACE. The converter controller utilizes the predicted real-time FC stack voltage model as a reference to emulate the physical behavior of the stack, including its output voltage as depicted in Fig. 12.

### 5.1.2. Traction emulator

The controllable current source used to emulate the traction subsystem consists of a battery, an inductor, and a DC-DC converter. During the traction phases of the WLTP/Artemis driving scenarios, the battery absorbs traction power by charging, while it supplies current during braking phases. The emulator is regulated by a current controller to accurately track the reference current, which is derived from the speed profile of the driving cycles.

### 5.1.3. Adopted driving cycles

To validate the applicability of the proposed framework in real-world scenarios, various driving cycles are considered, including the Artemis Urban and the Worldwide Harmonized Light Vehicles Test Procedure class 2 (WLTP-class 2). The WLTP-class 2 cycle is selected

for this study as it closely represents real driving behavior, incorporating numerous speed fluctuations across low, medium, and high-speed ranges. Meanwhile, the Artemis Urban cycle is particularly relevant for assessing fluctuations in urban environments, making it well-suited for testing the frequency decoupling strategy. The velocity and current load profiles corresponding to each driving cycle are illustrated in Fig. 14. It should be noted that:

* The road slope is neglected due to the absence of parameters in the adopted driving cycles [40].

* The current load profiles are adjusted to comply with hardware limitations, with a maximum current of 15 A.

## 5.2. Driving cycles results

Experiments were conducted on a hybrid storage system test bench using the topology depicted in Fig. 13 to evaluate the performance of the proposed strategy and control. For both scenarios, the tests were carried out under the following conditions: a sampling time of 0.001s and a transistor switching frequency of 20 kHz.

The tracking of the FC, battery, and SC currents to their respective reference values ($I_{FC\_ref}$, $I_{Bat\_ref}$, and $I_{Sc\_ref}$) is illustrated in Figs. 18 and 21. These figures provide a comprehensive evaluation of the PI controller's performance across WLTP and Artemis driving cycles.

Zoomed-in views within the figures reveal that the reference tracking for all three sources remains highly accurate, despite the abrupt variations inherent to the transient nature of the selected driving profiles. This is further corroborated by the Root Mean Square Error (RMSE) values presented in Table 3, where a lower RMSE indicates higher accuracy, ranging from 0.03 to 0.09 for both the WLTP and Artemis scenarios. However, a more pronounced ripple is observed during near-zero-current phases, which can be attributed to the discontinuous conduction mode of the power converters.

DC bus voltage regulation under WLTP-class 2 and Artemis Urban is depicted in Figs. 15 and 20. The plots demonstrate that the controller effectively maintained the DC bus voltage at its 26 V reference, ensuring accurate tracking throughout the driving cycles, even under high-fluctuation power loads. The controller's performance, evaluated using RMSE, is presented in Table 3. For WLTP, the RMSE is 0.096, with a voltage variation ranging from 25.2 V to 26.6 V. For Artemis Urban, the RMSE is 0.144, with a voltage variation between 24.6 V and 27.3 V.

Fig. 16 illustrates the evolution of the SOC of the battery and SC throughout the WLTP scenario, with an initial SOC estimated at 70%. The battery discharges to 59.95%, while the supercapacitor reaches 62.46%. The SOC curve of the supercapacitor exhibits more abrupt variations compared to the battery, due to its high solicitation during this scenario, as dictated by the energy management strategy. Additionally, the lower energy capacity ($Q_{sc}$) of the supercapacitor leads to more pronounced SOC fluctuations.

Figs. 17 and 26 illustrate the real-time performance and response of the emulator compared to the mathematical model. The PEMFC stack model generates a voltage reference based on the current load. The converter output voltage closely follows this reference signal (PEMFC stack voltage), ensuring that the (Current/Voltage) points remain within the polarization curve region. This enables the emulator to accurately replicate the fuel cell behavior with high fidelity. Fig. 19 shows the hydrogen consumption of the fuel cell during the WLTP and Artemis scenarios, calculated using Eq. (6). Given that these scenarios are scaled down due to test bench limitations, the reported consumption is therefore proportional to the power delivered by the fuel cell. Accordingly, a consumption of $7.6 \times 10^{-4}$ kg is observed for the WLTP scenario, while the Artemis scenario records a consumption of $3.06 \times 10^{-4}$ kg. Fig. 24 illustrates the role of the strategy in real-time management and distribution of power among the three sources ($P_{bat}$, $P_{fe}$, and $P_{sc}$) to
<figure><img src="image_15.png" /><figcaption>**Fig. 13.** Experimental setup, (1) FC-emulator, (2) Li-ion batteries, (3) Supercapacitor, (4) DC-DC converters, (5) voltage and current sensors, (6) Traction emulator, (7) dSPACE MicrolabBox, (8) ControlDesk interface.</figcaption></figure>

meet the load demand ($P_{load}$) according to the WLTP scenario. Two zoomed-in windows, from 470 s to 590 s and from 1040 s to 1250 s, were added to provide a more detailed analysis of the sources' dynamic response.

The yellow curve ($P_{fc}$), representing the power supplied by the fuel cell, exhibits a stable and smooth profile, even during sudden variations in ($P_{load}$). This stability is ensured by the low-pass filter (LPF-1) and a fuzzy logic-based management system, preventing fluctuating operations that could accelerate its degradation. Consequently, the adopted strategy improves the lifespan, efficiency and thermal management of the fuel cell while reducing energy losses.

The blue curve ($P_{bat}$) represents the power supplied by the battery. Its reference is determined by the DC bus voltage regulation loop, ensuring that the voltage remains at the reference value. To achieve this, the battery injects or absorbs current into the DC bus. This reference current is filtered using the (LPF-2) filter to obtain a smoother and more stable response compared to that of the supercapacitor. This battery behavior extends the battery's lifespan, improves its efficiency, and reduces risks related to heat and electrochemical reactions.

The orange curve ($P_{sc}$) represents the power supplied by the supercapacitor. Its reference corresponds to the high-frequency component of the load power demand, previously filtered by LPF-1 and LPF-2. The results show that the load transients, corresponding to acceleration

<table><caption>**Table 3**
PI control performance.</caption><thead><tr><th>PI controller</th><th>Battery current (A)</th><th>Fuel cell current (A)</th><th>Supercapacitor current (A)</th><th>DC bus voltage (V)</th></tr></thead><tbody><tr><td>WLTP-C2 (RMSE)</td><td>0.05319</td><td>0.03513</td><td>0.09354</td><td>0.09691</td></tr><tr><td>ARTEMIS (RMSE)</td><td>0.08993</td><td>0.03777</td><td>0.09029</td><td>0.14472</td></tr></tbody></table>

and braking phases, are effectively absorbed by the supercapacitor, as required by the proposed strategy.

Fig. 25 illustrates the evolution of the SOC of the battery and supercapacitor throughout the Artemis Urban scenario, starting with an initial SOC of 70%. The battery discharges to 68.84%, while the supercapacitor reaches 74.07%. As shown in Fig. 8, the WLTP cycle compared to the Artemis Urban driving cycle includes more braking phases. As a result, the supercapacitor charges more frequently, while the battery experiences less discharge.

Fig. 27 illustrates the real-time power distribution among the three sources ($P_{bat}$, $P_{fc}$, and $P_{sc}$) to meet the load demand ($P_{load}$) under the Artemis-urban scenario. Two zoomed-in windows, from 310 s to
<figure><img src="image_16.png" /><figcaption>(a) WLTP class 2 driving cycle</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>(b) Artemis Urban driving cycle</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>**Fig. 15.** DC bus voltage under Artemis.</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>**Fig. 16.** Sc-Battery State of Charge under WLTP.</figcaption></figure>

430 s and from 750 s to 820 s, have been added to provide a more detailed analysis of the sources' dynamic response. The power supplied by the fuel cell ($P_{fc}$) operates in a stable regime throughout the scenario, delivering a low current (VL-L) during low load phases due to the high state of charge of the battery. The power supplied by the battery varies very smoothly, leaving the major power transients to

<figure><img src="image_20.png" /><figcaption>**Fig. 17.** Emulation validation on the FC mathematical polarization curve model under WLTP.</figcaption></figure>

the supercapacitor. As shown in the curve, the power delivered by the supercapacitor closely follows the shape of the load power demand curve (notably the same sawtooth pattern), thereby improving the system's dynamic performance, extending the lifespan of both the fuel cell and the battery, and enhancing the overall energy efficiency of the system.

Figs. 22 and 23 illustrate the current fluctuation over time for the three sources across both scenarios.

During the WLTP scenario, the fuel cell current distribution shows that the majority of points (1166 points) fall between +0.1 and -0.1 A s⁻¹, with the largest current variation per second reaching values of +0.3 A s⁻¹ and -0.5 A s⁻¹. The battery current distribution is more spread out, with 646 points within the range of +0.1 and -0.1 A s⁻¹, while its highest current variation per second reaches values of +1 A s⁻¹ and -1.3 A s⁻¹. As for the supercapacitor, its current variation over time shows the lowest concentration of points in the center compared to the other two sources, with a total of 395 points between -0.1 and 0.1 A s⁻¹. The maximum fluctuation reaches values ranging from -2.9 A s⁻¹ to 2.4 A s⁻¹.

In the Artemis scenario, most points fall within a variation range of -0.1 to 0.1 A s⁻¹, with a total of 615 points for the fuel cell, 397 points for the battery, and 258 points for the supercapacitor. The highest current fluctuation in the fuel cell reaches ±0.5 A s⁻¹, while for the battery, the largest variations recorded are -2.9 A s⁻¹ and 2.1 A s⁻¹. For the supercapacitor, the highest fluctuations reach -5.2 A s⁻¹ and 4.7 A s⁻¹.

This study highlights that the lowest current variation belongs to the fuel cell, demonstrating the contribution of the proposed strategy in enhancing its lifespan. The highest variations are handled by the supercapacitor, which effectively fulfills its role in the system. This results in a well-balanced system with complementary energy sources, ensuring fast dynamics, extended autonomy, and improved efficiency.

### 5.3. Very low state of charge case

Fig. 28 presents the simulation results obtained under critical state of charge conditions of both the supercapacitor and the battery, with the objective of assessing the robustness of the proposed energy management strategy under non-nominal operating conditions. As shown in Fig. 28(c), the initial state of charge is set to 38.8% for the supercapacitor and 50% for the battery. Under these conditions, the proposed strategy enforces the following operating behavior. The supercapacitor is prevented from delivering current during traction phases as long as its state of charge remains below the 40% threshold, while it is recharged during braking phases through regenerative energy recovery. Meanwhile, the battery is charged both by the fuel cell and regenerative braking, and during acceleration phases it absorbs power transients, allowing the fuel cell to continue operating in an efficient and quasi-steady regime.
<figure><img src="image_21.png" /><figcaption>Fig. 18. Current plots under WLTP.</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>Fig. 19. Estimated H2 consumption.</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>Fig. 20. DC bus voltage under WLTP.</figcaption></figure>

Over the 500 s simulation horizon, the state of charge of both storage elements progressively increases toward their nominal operating ranges. Specifically, the supercapacitor SOC rises from 38.8% to 42.4%, while the battery SOC increases from 50% to 53.4%, demonstrating the capability of the proposed strategy to recover from low-SOC conditions.

Fig. 28(b) shows that the DC bus voltage is correctly regulated at its reference value of 48 V throughout the scenario, despite variations in the load current $I_{bus}$, confirming the robustness of the voltage control under constrained operating conditions.

Finally, Fig. 28(a) illustrates the power-sharing behavior among the sources in the low-SOC case. The fuel cell delivers a higher share of power to simultaneously meet the load demand and recharge the

battery. The magnitude of the surplus current supplied by the fuel cell is inversely proportional to the battery SOC, decreasing as the battery approaches higher charge levels. The battery effectively manages power transients, thereby reducing dynamic stress on the fuel cell and contributing to lifespan preservation. The supercapacitor absorbs regenerative power peaks but does not supply current during traction phases when its SOC is below 40%, thus avoiding deep discharge.

The proposed strategy is designed to handle extreme driving conditions, the frequency decomposition approach ensures that energy demands are distributed based on the dynamic characteristics of each source. During prolonged uphill driving, where sustained high power is required, the fuel cell supplies the baseline power demand, while the battery provides additional support to handle the increased load and the supercapacitor addresses fast transients and short bursts of power. Deterministic rules ensure that the supercapacitor is never discharged to less than 40%, enabling the source to absorb energy during sudden braking and ensure high power demand during prolonged uphill driving. In the worst-case scenario, when the supercapacitor's state of charge drops to 40%, the battery is required to compensate for the energy deficit. This represents a limitation of the proposed strategy, as under such unfavorable conditions, the battery is temporarily pushed beyond its optimal operating range. However, this situation does not affect the fuel cell's operation.

In the other hand, the proposed EMS algorithm was deployed on a dSPACE MicroLabBox platform interfaced with an i7-based host PC. Despite the capabilities of the hardware, the computation involves only simple frequency decomposition, a compact fuzzy rule-base, and deterministic logic, resulting in a negligible CPU load and short execution times well below the loop-cycle constraints. This illustrates that the strategy is not only conceptually efficient but also fully compatible with embedded real-time controllers. In particular:

* the absence of large optimization problems or predictive horizons avoids unpredictable computation delays,

* the rule-based fuzzy decision logic ensures deterministic, fast, and stable command generation, even under rapid load fluctuations,

* the architecture can therefore be ported to automotive-grade Electronic Control Units (ECUs) with limited computation and memory resources, supporting practical implementation in real-world FC/battery/SC hybrid systems.
<figure><img src="image_24.png" /><figcaption>Fig. 21. Current plots under Artemis.</figcaption></figure>

<figure><img src="image_25.png" /><figcaption>Fig. 22. Currents fluctuation under WLTP.</figcaption></figure>

<figure><img src="image_26.png" /><figcaption>Fig. 23. Currents fluctuation under Artemis.</figcaption></figure>

## 6. Conclusion

This study assessed the performance of a real-time energy management strategy for a multi-source electric vehicle combining a fuel cell, a lithium-ion battery, and a supercapacitor. The hybrid strategy, based on frequency decomposition, fuzzy logic, and deterministic constraints, enabled coordinated power sharing while enhancing system stability and source protection. Experimental validation using WLTP-Class 2 and Artemis urban driving cycles demonstrated the practical feasibility of the approach. Quantitative results confirm the effectiveness of the proposed method:

* the DC bus voltage was regulated around 26 V with minimal deviation;

* the PI current controllers achieved accurate tracking with low RMSE values across all scenarios,

* the supercapacitor absorbed fast power transients, reducing high-frequency oscillations on the battery and fuel cell,

* the fuel cell operated predominantly within low-frequency regions, avoiding rapid load variations known to accelerate degradation.

Hydrogen consumption trends followed the power-demand profile as expected, while the SOC evolution of the battery and supercapacitor confirmed their complementary roles in supporting mid- and high-frequency dynamics. These results collectively indicate improved energy efficiency, reduced stress on the fuel cell and battery, and enhanced robustness during dynamic operation.

Overall, the proposed strategy demonstrates strong potential for real-time implementation in fuel-cell-based electric vehicles, offering a balance between computational simplicity and effective power distribution.
<figure><img src="image_27.png" /><figcaption>Fig. 24. Power plots under WLTP. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_28.png" /><figcaption>Fig. 25. Sc-Battery Stat of Charge under Artemis.</figcaption></figure>

<figure><img src="image_29.png" /><figcaption>Fig. 26. Emulation validation on the FC mathematical polarization curve model under Artemis.</figcaption></figure>

Future work will focus on the development of adaptive control strategies to account for temperature variations and long-term aging effects of the energy sources. In practical operation, temperature changes and component aging significantly affect key parameters such as internal resistance, available power capability, efficiency, and dynamic response of the battery, supercapacitor, and fuel cell. Neglecting these effects may lead to suboptimal power sharing and reduced robustness over the system lifetime.

To address this, online estimation techniques will be investigated to identify temperature and aging-dependent parameters, including internal resistance, state of health, and effective energy capacity. These estimated parameters can be incorporated into adaptive control laws that dynamically adjust cutoff frequencies, controller gains, and fuzzy rule thresholds. For instance, as battery aging increases internal resistance, the adaptive controller may reduce its allocation of high-frequency power components and shift a larger share of fast dynamics toward the supercapacitor or fuel cell, when feasible. Similarly, temperature aware adaptation can prevent excessive current stress under low temperature conditions by modifying power-sharing priorities.

### CRediT authorship contribution statement

**R. Achdad:** Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Resources, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. **M.A. Mossadak:** Writing – original draft, Validation, Software, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation. **A. Rabhi:** Writing – review & editing, Visualization, Validation, Supervision, Software, Resources, Project administration, Investigation, Formal analysis, Conceptualization. **A. Chebak:** Writing – review & editing, Visualization, Validation, Project administration, Data curation, Conceptualization. **A. Hadjaissa:** Writing – review & editing, Visualization, Validation, Supervision, Software, Investigation, Funding acquisition, Formal analysis, Data curation. **H. Midavaine:** Validation, Supervision, Software, Resources, Investigation, Funding acquisition, Data curation.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Data availability

Data will be made available on request.
<figure><img src="image_30.png" /><figcaption>Fig. 27. Power plots under Artemis.</figcaption></figure>

<figure><img src="image_31.png" /><figcaption>Fig. 28. Simulation results under critical SOC conditions.</figcaption></figure>

References

[1] Mohsen Kandidayeni, Alvaro Omar Macias Fernandez, Arash Khalatbarisoltani, Loic Boulon, Sousso Kelouwani, Hicham Chaoui, An online energy management strategy for a fuel cell/battery vehicle considering the driving pattern and performance drift impacts, IEEE Trans. Veh. Technol. 68 (12) (2019) 11427-11438.

[2] Andrew Chapman, Kenshi Itaoka, Hadi Farabi-Asl, Yasumasa Fujii, Masaru Nakahara, Societal penetration of hydrogen into the future energy system: Impacts of policy, technology and carbon targets, Int. J. Hydrog. Energy 45 (7) (2020) 3883-3898.

[3] Hajer Marzougui, Ameni Kadri, Jean Philippe Martin, Mansour Amari, Serge Pierfederici, Faouzi Bacha, Implementation of energy management strategy of hybrid power source for electrical vehicle, Energy Convers. Manage. 195 (2019) 830-843.

[4] Hoai-An Trinh, Hoai-Vu-Anh Truong, Kyoung-Kwan Ahn, Energy management strategy for fuel cell hybrid power system using fuzzy logic and frequency decoupling methods, in: International Conference on Mechatronics Technology, ICMT, 2021, pp. 1-6.

[5] Fazhan Tao, Longlong Zhu, Zhumu Fu, Pengju Si, Lifan Sun, Frequency decoupling-based energy management strategy for fuel cell/battery/ultracapacitor hybrid vehicle using fuzzy control method, IEEE Access 8 (2020) 166491-166504.
[6] Aqeel Ur Rahman, Syeda Shafia Zehra, Iftikhar Ahmad, Hammad Armghan, Fuzzy supertwisting sliding mode-based energy management and control of hybrid energy storage system in electric vehicle considering fuel economy, J. Energy Storage 37 (2021) 102468.

[7] Mohammed Benzaouia, Bekkay Hajji, Abdelhamid Rabhi, Soufyane Benzaouia, Adel Mellit, Real-time super twisting algorithm based fuzzy logic dynamic power management strategy for hybrid power generation system, J. Energy Storage 65 (2023) 107316.

[8] Hai-Bo Yuan, Wen-Jiang Zou, Seunghun Jung, Young-Bae Kim, Optimized rule-based energy management for a polymer electrolyte membrane fuel cell/battery hybrid power system using a genetic algorithm, Int. J. Hydrog. Energy 47 (2022) 7932-7948.

[9] Majid Zandi, Alireza Payman, Jean-Philippe Martin, Serge Pierfederici, Bernard Davat, Farid Meibody-Tabar, Energy management of a fuel cell/supercapacitor/battery power source for electric vehicular applications, IEEE Trans. Veh. Technol. 60 (2011) 433-443.

[10] Gokula Manikandan Senthil Kumar, Xinman Guo, Shijie Zhou, Haojie Luo, Qi Wu, Yulin Liu, Zhenyu Dou, Kai Pan, Yang Xu, Hongxing Yang, Sunliang Cao, State-of-the-art review of smart energy management systems for supporting zero-emission electric vehicles with X2V and V2X interactions, Renew. Sustain. Energy Rev. 208 (2025) 115050.

[11] Md. Shahin Munsi, Hicham Chaoui, Energy management systems for electric vehicles: A comprehensive review of technologies and trends, IEEE Access 12 (2024) 60385-60403.

[12] Ijaz Ahmed, Muhammad Maaruf, Amjad Ali, Mohammad AlMuhaini, Muhammad Khalid, A review on challenges and future of green charging networks for zero emission electric transportation, Energy Convers. Manag.: X 25 (2025) 100867.

[13] Benchang Jin, Liyan Zhang, Qihong Chen, Zhichao Fu, Energy management strategy of fuzzy logic control for fuel cell truck, Energy Rep. 9 (2023) 247-255.

[14] Mohammed Amine Mossadak, Ahmed Chebak, Nada Ouahabi, Abdelhafid AIT Elmahjoub, Real-time power management strategy of battery/supercapacitor hybrid energy storage system for electric vehicle, Lect. Notes Electr. Eng. 954 (2023) 559-569.

[15] Laura V. Perez, Elvio Angel Pilotta, Optimal power split in a hybrid electric vehicle using direct transcription of an optimal control problem, Math. Comput. Simulation 79 (6) (2009) 1959-1970.

[16] Liangfei Xu, Jianqiu Li, Jianfeng Hua, Xiangjun Li, Minggao Ouyang, Adaptive supervisory control strategy of a fuel cell/battery-powered city bus, J. Power Sources 194 (1) (2009) 360-368.

[17] Youcef Belkhier, Adel Oubelaid, Rabindra Nath Shaw, Hybrid power management and control of fuel cells-battery energy storage system in hybrid electric vehicle under three different modes, Energy Storage 6 (2023).

[18] Mehdi Ansarey, Masoud Shariat Panahi, Hussein Ziarati, Mohammad Mahjoob, Optimal energy management in a dual-storage fuel-cell hybrid vehicle using multi-dimensional dynamic programming, J. Power Sources 250 (2014) 359-371.

[19] Wenbin Zhang, Jianqiu Li, Liangfei Xu, Minggao Ouyang, Optimization for a fuel cell/battery/capacity tram with equivalent consumption minimization strategy, Energy Convers. Manage. 134 (2017) 59-69.

[20] Muhammad Maaruf, Sami El-Ferik, Neural learning fault-tolerant control of fuel cell-battery-ultracapacitor-based hybrid electric vehicle, J. Energy Storage 98 (2024) 112892.

[21] Muhammad Maaruf, Georgios Konstantinou, Muhammad Khalid, Current sharing control method for fuel cell hybrid electric vehicles, in: 2022 IEEE PES 14th Asia-Pacific Power and Energy Engineering Conference, APPEC, 2022, pp. 1-5.

[22] Dawei Gao, Zhenhua Jin, Qingchun Lu, Energy management strategy based on fuzzy logic for a fuel cell hybrid bus, J. Power Sources 185 (1) (2008) 311-317.

[23] Chun-Yan Li, G.P. Liu, Optimal fuzzy power control and management of fuel cell/battery hybrid vehicles, J. Power Sources 192 (2) (2009) 525-533.

[24] Yavuz Eren, Ozan Erdinc, Haluk Gorgun, Mehmet Uzunoglu, Bulent Vural, A fuzzy logic based supervisory controller for an FC/UC hybrid vehicular power system, Int. J. Hydrog. Energy 34 (20) (2009) 8681-8694.

[25] Saman Ahmadi, Seyed Mohamad Taghi Bathaee, Amir H. Hosseinpour, Improving fuel economy and performance of a fuel-cell hybrid electric vehicle (fuel-cell, battery, and ultra-capacitor) using optimized energy management strategy, Energy Convers. Manage. 160 (2018) 74-84.

[26] Adel Oubelaid, Nima Khosravi, Youcef Belkhier, Nabil Taib, Toufik Rekioua. Health-conscious energy management strategy for battery/fuel cell electric vehicles considering power sources dynamics, J. Energy Storage 68 (2023) 107676.

[27] Xiaorui Jia, Mi Zhao, A hierarchical energy control strategy for hybrid electric vehicle with fuel cell/battery/ultracapacitor combining fuzzy controller and status regulator, Electronics 12 (2023) 3428.

[28] Ke Song, Xiaodi Wang, Feiqiang Li, Marco Sorrentino, Bailin Zheng, Pontryagin's minimum principle-based real-time energy management strategy for fuel cell hybrid electric vehicle considering both fuel economy and power source durability, Energy 205 (2020) 118064.

[29] Abderrezak Badji, Djaffar Ould Abdeslam, Djafar Chabane, Nacereddine Benamrouche, Real-time implementation of improved power frequency approach based energy management of fuel cell electric vehicle considering storage limitations, Energy 249 (2022) 123743.

[30] Miguel Robayo, Real-time Energy Management System of Battery-Supercapacitor in Electric vehicles (Ph.D. thesis), University of Exeter, Exeter, England, 2023.

[31] Mohammed-Amine Mossadak, Ahmed Chebak, Nada Ouahabi, Abdelhamid Rabhi, Abdelhafid Ait Elmahjoub, A novel hybrid PI-backstepping cascade controller for battery-supercapacitor electric vehicles considering various driving cycles scenarios, IET Power Electron. 17 (9) (2024) 1089-1105.

[32] Yuejiu Zheng, Wenkai Gao, Minggao Ouyang, Languang Lu, Long Zhou, Xuebing Han, State-of-charge inconsistency estimation of lithium-ion battery pack using mean-difference model and extended Kalman filter, J. Power Sources 383 (2018) 50-58.

[33] Maria C. Argyrou, Paul Christodoulides, Christos C. Marouchos, Soteris A. Kalogirou, Hybrid battery-supercapacitor mathematical modeling for PV application using matlab/simulink, in: 2018 53rd International Universities Power Engineering Conference, UPEC, 2018, pp. 1-6.

[34] Jamila Snoussi, Seifeddine Ben Elghali, Mohamed Benbouzid, Mohamed Faouzi Mimouni, Optimal sizing of energy storage systems using frequency-separation-based energy management for fuel cell hybrid electric vehicles, IEEE Trans. Veh. Technol. 67 (10) (2018) 9337-9346.

[35] Hongzhe Li, Jinsong Kang, Cheng Li, Energy management strategy based on reinforcement learning and frequency decoupling for fuel cell hybrid powertrain, Energies 17 (8) (2024).

[36] Jay T. Pukrushpan, Anna G. Stefanopoulou, Huei Peng, Control of Fuel Cell Power Systems: Principles, Modeling, Analysis and Feedback Design, Springer Science & Business Media, 2004.

[37] Mehrdad Ehsani, Yimin Gao, Stefano Longo, Kambiz Ebrahimi, Modern Electric, Hybrid Electric, and Fuel Cell Vehicles, third ed., CRC Press, 2018.

[38] Faruk Yalcin, Uğur Arifoğlu, İrfan Yazici, Kenan Erin, A robust single phase inverter based on buck-boost converter through an efficient hybrid control, IET Power Electron. 13 (2020).

[39] Soufiane Gahgouhi, Aboubakeur Hadjaissa, Khaled Ameur, Abdelhamid Rabhi, Mechri Kious, A novel fuzzy-PI-based control for PEM fuel cell emulator based on a buck converter, Energy Syst. (2024).

[40] Abdoulaye Pam, Alan Bouscayrol, Philippe Fiani, Fabien Faval, Philippe Barrade, Integration of the road slope in the optimization of the energy management strategy of a parallel HEV, IFAC-PapersOnLine 52 (5) (2019) 28-33, 9th IFAC Symposium on Advances in Automotive Control AAC 2019.