Optimizing Fuel Economy in Hybrid Electric Vehicles Using the Equivalent Consumption Minimization Strategy Based on the Arithmetic Optimization Algorithm

Abstract

Due to their improved performance and advantages for the environment, fuel cell hybrid electric cars, or FCEVs, have garnered a lot of attention. Establishing an energy management strategy (EMS) for fuel cell electric vehicles (FCEVs) is essential for optimizing power distribution among various energy sources. This method addresses concerns regarding hydrogen utilization and efficiency. The Arithmetic Optimization Algorithm is employed in the proposed energy management system to enhance the strategy of maximizing external energy, leading to decreased hydrogen consumption and increased system efficiency. The performance of the proposed EMS is evaluated using the Federal Test Procedure (FTP-75) to replicate city driving situations and is compared with existing algorithms through a comparison co-simulation. The co-simulation findings indicate that the suggested EMS surpasses current approaches in reducing fuel consumption, potentially decreasing it by 59.28%. The proposed energy management strategy demonstrates an 8.43% improvement in system efficiency. This enhancement may reduce dependence on fossil fuels and mitigate the adverse environmental effects associated with automobile emissions. To assess the feasibility and effectiveness of the proposed EMS, the system is tested within a Processor-in-the-Loop (PIL) co-simulation environment using the C2000 launchxl-f28379d Digital Signal Processing (DSP) board.

1. Introduction

1.1. Research Background

The widespread problem of air pollution caused by internal combustion engine cars has intensified the demand for alternate energy sources in transportation [1,2,3]. Despite the potential of electric vehicles, constraints include their limited range, reduced longevity, and extended charge durations, which impede their extensive acceptance [4,5,6,7]. Proton exchange membrane fuel cells (PEMFCs) present a dependable alternative, with prolonged autonomy and zero greenhouse gas emissions from petrol [8,9]. Despite their advantages, PEMFCs encounter obstacles associated with abrupt power demand surges, resulting in complications such as pressure oscillation and oxygen deficiency, which ultimately reduce cell longevity [10,11]. Electric vehicles offer a promising approach for diminishing carbon emissions in the transportation sector [12]. The fuel cell hybrid electric vehicle (FCEV) is a highly promising technology for the effective reduction of carbon dioxide emissions.

Hydrogen fuel cells (FCs) and energy storage systems (ESSs) work together in FCEV technology to power the electric motor [13]. Energy savings and fuel economy are both improved by FCEV technology [14]. Among FCEV’s numerous advantages are its lack of dependence on fossil fuels, its tiny size, its silent operation, and its excellent performance without polluting emissions [15]. Consequently, electric vehicles (EVs) are anticipated to play a crucial role in future smart grids, contributing to a sustainable transportation sector and a secure environment [16].

Energy storage systems (ESSs), which include supercapacitors and batteries, are responsible for the recovery or delivery of substantial power surges during acceleration or deceleration, while the fuel cell hybrid electric vehicle (FCEV) power system is entirely electric [17]. To address the sluggish performance of fuel cells and the limited longevity of batteries, it is essential to integrate them with a high-capacity energy storage technology, like supercapacitors (SCs), which provide quick response times. Hybridization is crucial for overcoming these limitations and improving overall efficiency [18,19]. Hybridization optimizes the operational environment of the fuel cell system, hence enhancing its overall performance.

In hybrid systems, an energy management strategy (EMS) is essential for allocating load demand among various energy sources to optimize fuel consumption efficiency, while ensuring that the energy sources operate within their designated limits and considering the EMS’s effect on the hybrid power system’s life cycle. Nonetheless, the efficacy of the chosen EMS is the principal concern in this context.

1.2. Literature Review

To attain this objective, numerous EMSs have been documented in the literature. Generally, EMSs can be categorized into optimization- and rule-based systems, as indicated in [20,21]. Rule-based approaches are established on a succession of “IF-THEN” scenarios. This category can be subdivided into two distinct subcategories: deterministic tactics, exemplified by the state machine control (SMC) approach, and the load following energy management strategy (LFS) [22,23]; and intelligent methods, represented by the fuzzy-logic-based EMS [24]. Despite its ease of design and implementation, the performance of this system is limited by the knowledge of the designer [25]. Optimization-based approaches utilize the tools inherent in optimization theory to address the problem at hand. Optimization methods can be classified as either offline (global scale) or online (real-time scale). Offline optimization EMSs involve identifying an optimal control solution for a predetermined situation, such as a speed profile. Various methodologies exist:

• Disciplined optimum control refers to direct approaches.
• Indirect techniques such as Pontryagin’s maximal principle (PMP) [26] and calculus of variations [27] are used.

In [28,29], the authors propose a learning-based model predictive control (L-MPC) energy management system (EMS) for a fuel cell hybrid electric bus (FCHEB), incorporating health-aware control strategies.

Recent research has highlighted the importance of incorporating stochastic elements into EMS design to improve robustness and adaptability. Notably, risk-aware strategies and stochastic modeling approaches such as Monte Carlo simulation and stochastic dynamic programming (SDP) have demonstrated promising results in managing uncertainty effectively [30,31]. These methods enable the EMS to account for probabilistic variations in system inputs and external factors, ultimately enhancing the decision-making reliability in dynamic environments.

In optimization problems, two computational techniques are employed: dynamic programming (DP) [32] and stochastic dynamic programming (SDP) [33]. DP is a technique that recursively addresses a complex problem by breaking it down into smaller subproblems, whereas SDP incorporates uncertainty and randomness into the decision-making process. These methods have been extensively investigated and implemented in a variety of disciplines. These solutions necessitate a thorough comprehension of load profiles, hence requiring substantial data calculations. The objective function value progression determines the selection of online tactics, thereby improving their efficacy and resilience. In this context, the equivalent consumption minimization strategy (ECMS), as delineated in reference [34], is the outcome of the implementation of the optimum control philosophy. Real-time strategies are inherently suboptimal. The PMP technique serves as the foundation for the development and demonstration of the ECMS, as indicated by reference [35], The analogous factor fulfills a comparable function to the co-state in the PMP technique. The employment of ECMS with a fixed co-state may serve as an ideal resolution to the offline optimization issue [36]. The external energy maximization strategy (EEMS), as delineated in the reference [37], endeavors to improve power output by optimizing the utilization of both the supercapacitor (SC) and the battery, thereby resulting in an implicit improvement in the overall system efficacy. Additionally, the FC maintains a constant state with minimal movement, providing power solely in response to demand. The primary sources for addressing transient loads are the battery and the SC. Consequently, this will enhance the system’s efficacy.

Numerous research has validated that the best results can be attained by integrating metaheuristic algorithms (MAs) with online EMSs. These algorithms have gained significant popularity in the field of engineering [38]. An improved variant of the ECMS and EEMS was presented by Hegazy et al. [39]. For optimization, this version implemented the salp swarm algorithm (SSA) and the mine explosion algorithm (MBA).

In the past few years, there has been a significant increase in the use of these algorithms in engineering-related applications [24]. Hegazy et al. [25] enhanced the performance of the ECMS and EEMS in their study by optimizing them with the salp swarm algorithm (SSA) and the mine explosion algorithm (MBA). The SSA and EEMS were integrated to achieve the utmost level of fuel consumption performance and efficiency. Zhao et al. [40] conducted a comparison analysis by employing a variety of metaheuristic optimization methods, such as an artificial bee colony optimization algorithm (EFO) and a whale optimization algorithm (WOA). To further enhance the prediction accuracy of the deep learning model, the authors in [41,42] optimized the structure of the temporal convolutional network (TCN) using the particle swarm optimization (PSO) algorithm, making it more adaptable for state of charge estimation under varying conditions.

The results show that the optimized EEMS with GWO outperforms the ECMS and its optimized variants. In reference [43], an energy management system based on genetic fuzzy was created to improve fuel efficiency. An optimized EMS was proposed using a genetic algorithm, as detailed in reference [44]. This investigation offers an examination of numerous fuel cell electric vehicle (FCEV) configurations. Ghadbane et al. [45] proposed a method for the management of a hybrid storage system that integrated supercapacitors and batteries. The BES exhibited benefits in the preservation of the battery’s state of charge. A salp swarm algorithm was employed to propose an optimized EMS, as detailed in reference [46].

1.3. Motivation and Novelty

The main goals of this research are to reduce hydrogen consumption and improve the electrical efficiency of the power system, leveraging the Arithmetic Optimization Algorithm’s (AOA) innovative design and exceptional performance in solving complex, nonlinear problems [47]. This study marks the initial application of AOA in the field of energy management for FCEVs, where its superior convergence behavior and low computational complexity make it particularly well suited.

The actual implementation of this technology has the potential to enhance the experience of driving electric vehicles by enhancing their range through more efficient fuel usage and increased energy efficiency. The fuel consumption and system efficiency of the proposed EMSs are compared to those of the Zebra Optimization Algorithm (ZOA) [48], as well as the red-tailed hawk algorithm (RTH) [49], COOT-based optimization (COOT) [50], the Walrus Optimization Algorithm (WaOA) [51], the Moth Flame Optimization (MFO) [52], the Artificial Ecosystem-based Optimization (AEO) [53], and the Osprey Optimization Algorithm (OOA) [54].

This study’s principal contribution is the development of an optimized variant of the conventional ECMS, which significantly decreases the consumption of fuel and improves electric performance.

The primary objectives of the present study are listed below:

-

To create a cutting-edge power management system (EMS) for FCEVs that optimizes power distribution, reduces fuel consumption, and maximizes electrical efficiency. The Arithmetic Optimization Algorithm (AOA) is incorporated into the proposed EMS to optimize the external energy maximization strategy (ECMS).

The subsequent divisions of the paper are organized as follows: The FCEV’s architecture, including the mathematical models employed, is delineated in Section 2. The energy management strategy, which encompasses the ECMS and AOA, is further elaborated upon in Section 3. The results and discussion, which comprise the co-simulation results and analysis, are presented in Section 4. The paper is ultimately concluded in Section 5.

2. Architecture for FCEVs

The power of the FCEV is derived from various sources, including a lithium-ion battery, energy storage systems utilizing supercapacitors, and, primarily, a proton exchange membrane fuel cell (PEMFC), as shown in Figure 1. A unidirectional DC/DC boost converter connects the fuel cell to the DC interface. A DC/DC boost converter that can handle both directions connects to the battery. The DC bus is directly linked to the SC. A bidirectional DC/AC converter delivers power to the vehicle’s motor during both traction and braking scenarios, enabling current to flow in either direction between the DC bus and the motor.

2.1. Model for Vehicle Traction

Here is how to determine the traction force based on the physical forces acting on the vehicle’s body: [55].

$$F_t=F_a+F_r+F_{acc}+F_{gr}$$

(1)

The following definitions are assigned to these forces:

$$\left\{\begin{array}{c}{F}_a=0.5 \xi C_d A_f {(v\pm v_w)}^2 \\ F_r=m_v g \mu \\ F_{acc}=\pm k_m m_v{\displaystyle \frac{dv}{dt}} \\ F_{gr}=\pm m_v g \sin \alpha \end{array} \right.$$

(2)

Table 1. Definition of electric vehicle parameters.

Parameter	Description	Unit
v	vehicle’s speed	m/s
vw	wind speed	m/s
$\alpha$	slope angle	rad
mv	vehicle’s mass	Kg
µ	tire’s rolling resistance coefficient	--
Cd	aerodynamic coefficient	--
Γ	air density	Kg/m3
Af	vehicle’s frontal area	m2
g	Earth’s gravitational	m/s2
Fa	aerodynamic force	N
Fr	rolling resistance force	N
Facc	acceleration force	N
Fgr	resistance force	N

represent the electric vehicle parameters definition.

2.2. Hydrogen Consumption Model for FCs

A fuel cell (FC) is an electrochemical device that uses the chemical energy of oxygen and hydrogen to generate electricity. In accordance with [56], the following relationship exists between the FC output current and hydrogen consumption:

$$C_{H_2}{\displaystyle \underset{0}{\overset{t}{\int }}\frac{m_{H_2}{n}_{cell}}{2F}}{i}_{FC}\left(t\right)dt$$

(3)

The variable C_H2 represents the rate at which hydrogen is consumed in (g/s). The variable n_cell represents the number of cells. m_H2 represents the molar mass of hydrogen, which is 2.02 (g/mol). i_FC represents the output current of the fuel cell in amperes (A). F represents the Faraday constant, which is 96,487 coulombs (C).

2.3. Estimation of Battery SOC

The works cited in [57] suggest that the state of charge (SoC) of a battery can be computed in the following way:

$$SOC(t)=SO{C}_i-{\displaystyle \frac{1}{Q}}{\displaystyle \int i_{bat}dt}$$

(4)

where ${SOC}_i$ denotes the initial state of charge of the battery.

3. The Suggested Approach for Energy Management

An effective instantaneous cost-function-based system called the ECMS optimization method was created by [58]. The goal of the ECMS is to reduce fuel usage to a minimum by concurrently reducing the amount of FC hydrogen consumed and the total equivalent fuel from other sources to regulate the battery’s SOC within a certain range with a fine included objective function. Figure 2 illustrates the ECMS scheme.

The Optimization Algorithm’s goal is to identify the optimal X = [P_fc,α,P_bat].ΔT in order to minimize the cost function F, which shows the battery and FC’s equivalent consumption: [58].

$$F=\left[P_{fc}+\alpha P_{batt}\right].\Delta T$$

(5)

as long as P_load = P_fc + P_bat are same.

The energy levels of the battery and supercapacitor are directly proportional to the equivalent fuel consumption, which is then multiplied by a penalty factor (α).

The empirical presentation of the equivalence factor is as follows [27,59,60]:

$$\alpha =1-2\mu {\displaystyle \frac{\left(SO{C}_{bat}-\frac{SO{C}_u+SO{C}_l}{2}\right)}{SO{C}_u+SO{C}_l}}$$

(6)

where μ is the equilibrium coefficient of SOC, and SOC_l and SOC_u are the lower and upper SOCs of the battery.

The constraints that have been taken into account are as follows:

$$\begin{array}{l}{P}_{f{c}_{\min }}\le P_{fc}\le P_{f{c}_{\max }}\\ P_{ba{t}_{\min }}\le P_{bat}\le P_{ba{t}_{\max }}\\ 0\le \alpha \le 2\end{array}$$

(7)

The aims to increase efficiency, prolong the life of batteries and supercapacitors, and reduce fuel consumption are the driving forces for the development of the energy management strategy.

Arithmetic Optimization Algorithm

The AOA updates solutions using arithmetic operators such as addition, subtraction, multiplication, and division. The user employs the arithmetic operators to traverse the search space, and uses the addition and subtraction operators to exploit it [47]. As stated in Equation (8), the accelerated mathematical optimizer (MOA) is the control parameter that helps to maintain a balance between intensification and diversification in the search space [47].

$$M_{OA}(t)={\displaystyle \frac{C-Iter}{M-Iter}}$$

(8)

In this formula, C-Iter and M-Iter are the current and total number of iterations.

The diversification of the search space relies on multiplication and division factors, allowing for a wide distribution of the generated values in accordance with Equation (9) when the condition (rand > M_OA) is satisfied, with rand being a randomly generated number.

$$x_i^{(t)}=\left\{\begin{array}{l}best\left(x^{(t)}\right)÷\left(M_{OP}+\epsilon \right)\left(U_B-L_B\right)\mu +LB r_2<0.5\\ best\left(x^{(t)}\right)\times \left(M_{OP}+\epsilon \right)\left(U_B-L_B\right)\mu +LB else\end{array}\right\}$$

(9)

In this context, x denotes the solution, UB and LB denote the upper and lower bounds of the solutions, ε and μ are constants, best (x) represents the global optimal solution, r₂ signifies a randomly generated number, and the probability of the mathematical optimizer (MOP) serves as a scaling parameter that facilitates exploration, estimated via Equation (10), where α represents a constant.

$$M_{OP}(t)=1-{\displaystyle \frac{C-Ite{r}^{1/\alpha }}{M-Ite{r}^{1/\alpha }}}$$

(10)

Addition and subtraction operations are utilized to reduce the search space owing to the high density of solutions generated and applied for a specific situation (rand > M_Op). Equation (11) delineates the updating method during exploitation, with r₃ being a random variable.

$$x_i^{(t)}=\left\{\begin{array}{l}best\left(x^{(t)}\right)-\left(\left(M_{OP}\right)\left(\left(U_B-L_B\right)\mu +LB\right) \right) r_3<0.5\\ best\left(x^{(t)}\right)+\left(\left(M_{OP}\right)\left(U_B-L_B\right)\mu +LB\right) else\end{array}\right\}$$

(11)

The complete AOA procedure is outlined in the flowchart shown in Figure 3.

4. Implementation of Control Algorithms Using the PIL Technique

The Processor-in-the-Loop (PIL) co-simulation technique enables the validation and verification of control algorithms by deploying the generated code onto an embedded processor and executing it in a real-time environment. In this study, the PIL co-simulation is conducted using the C2000 LaunchXL-F28379D DSP board, ensuring that the control algorithms operate under realistic conditions. During the simulation process, the implemented algorithm is interfaced with a computer running the physical system model. This setup facilitates a comprehensive evaluation of system performance, allowing for the assessment and optimization of key parameters such as storage capacity, code efficiency, and execution time.

As illustrated in Figure 4, the PIL prototyping follows a structured approach where the power system’s power components are simulated within the MATLAB/Simulink environment using a predefined simulation time. Throughout each simulation step, the C2000 LaunchXL-F28379D DSP board receives control signals from the computer, executes the corresponding control algorithms, and transmits the generated control commands back to the computer. This iterative process forms a continuous PIL co-simulation cycle, ensuring real-time synchronization between the computer and the DSP board via serial communication. By leveraging this co-simulation framework, the accuracy, efficiency, and robustness of the proposed control strategy can be thoroughly assessed and refined before practical implementation.

5. Findings and Discussion

The C2000 LaunchXL-F28379D DSP board and the Matlab/Simulink environment were used to make a co-simulation model and test and confirm how well each strategy worked, offering a safe and cost-effective way to refine control algorithms. While PIL allows testing on real DSP hardware with virtual power components, it cannot fully capture real-world complexities. Sim power system elements were used to represent all of the components, including converters and sources. We evaluated the performance of the EMS under investigation on the Driving Cycle FTP-75. Figure 5 illustrates the motor power and speed profiles of both FTP-75s.

The co-simulations were conducted with identical parameters for both the battery and the supercapacitor. The supercapacitor was operating at 270 V, and the battery was at 70% state of charge (SoC). Figure 6 and Figure 7 illustrate the consumption of hydrogen. In comparison to the alternatives under consideration, these figures illustrate that the proposed method can reduce the consumption rate and hydrogen consumption.

In comparison to the alternatives, the proposed method had the potential to reduce the consumption and use of hydrogen.

The results from the several ESMs that were considered are shown in

Table 2. Comparative study of a number of acknowledged EMSs.

EMS	Consumed H2 (g)	Efficiency (%)	Final SOC	H2 Saving (%)	Efficiency Increase (%)	Decrease in SoC (%)	Performance Index (%)
AOA	31.6	57.31	42.1	0	0	0	0
ZOA	40.1	55.75	49.85	21.2	1.56	7.75	15.01
RTH	43.01	55.49	52.52	26.53	1.82	10.42	17.93
COOT	44.56	54.92	53.74	29.08	3.57	11.64	21.01
WaOA	49.89	54.51	57.79	36.6	2.8	15.69	23.71
MFO	51.67	54.37	59.2	38.84	2.49	17.1	24.3
AEO	62.48	55.67	66.41	49.42	1.64	24.31	26.75
OOA	77.6	48.88	73.37	59.28	8.43	31.27	36.44

. After comparing the two, it became clear that the AOA built on the ECMS was superior. Using the AOA based on the ECMS reduced the total quantity of hydrogen consumed from 73.37 g (when using the OOA-ECMS) to 31.6 g.

To evaluate the performance of the proposed EMS, two key metrics were considered: efficiency improvement and hydrogen savings. These metrics were calculated relative to a baseline EMS method—specifically, the AOA-ECMS—which served as a reference for comparison.

Hydrogen saving was calculated using:

$$H_2 Saving\left(\%\right)={\displaystyle \frac{Consumed H_2(MA)-Consumed H_2(AOA)}{Consumed H_2(MA)}}\times 100$$

(12)

where the Consumed H₂ (MA) is the hydrogen consumption value per metaheuristic algorithm.

Efficiency was defined as:

$$Efficiency Increase \left(\%\right)=Efficiency (AOA)-Efficiency (MA)$$

(13)

Decrease in SoC:

$$Decrease in SoC \left(\%\right)=Final SOC (MA)-Final SOC (AOA)$$

(14)

Performance index:

$$Performance Index=H_2 Saving+Efficiency Increase-Decrease in SoC$$

(15)

In the final analysis, the ECMS-based AOA showed significant improvements over other control systems, including ZOA, RTH, COOT, WaOA, MFO, AEO, and OOA. At first, the AOA system that relied on ECMS showed significant reductions in hydrogen consumption. When compared to ZOA, RTH, COOT, WaOA, MFO, AEO, and OOA, the decline was 21.2%, 26.53%, 29.08, 36.6%, 38.84, 49.42%, and 59.28%, respectively. Reducing hydrogen consumption and maximizing resource utilization were both achieved by the recommended ECMS-based technique. In addition, applying the ECMS-based AOA technique significantly improved the system’s efficiency. The ZOA had an efficiency enhancement of 1.56%, an RTH of 1.82%, a COOT of 3.57%, a WaOA of 2.8%, an MFO of 2.49%, an AEO of 1.64, and an OOA of 8.43%. More cost-effective and environmentally beneficial hydrogen-powered systems could be generated using the ECMS-based AOA method, as shown by the efficiency gains. There were benefits to the ECMS-based AOA approach, but the downsides with respect to the battery’s SoC must be carefully considered. Compared to the ZOA strategy, the state of charge (SoC) decreased by 7.75%; compared to the RTH strategy, by 10.42%; compared to the COOT strategy, by 11.64%; compared to the WaOA strategy, by 15.69%; compared to the MFO strategy, by 24.31%; compared to the AEO strategy, by 24.31%; and compared to the OOA strategy, by 31.27%. Investigating the reduction in SoC may be vital, because it may affect the stability and performance of a hydrogen-based system in the long run. Significant progress was made in analyzing the comprehensive performance index using the AOA technique that is based on the ECMS. In comparison to the ZOA, RTH, COOT, WaOA, MFO, AEO, and OOA, the corresponding improvement percentages were 15.01%, 17.93%, 21.01%, 23.71%, 24.3%, 26.75%, and 36.44%.

The findings from the FTP-75 driving cycle, as reported in reference [61], provide additional evidence of HHO’s excellence.

Table 3. Evaluation of several EMSs with respect to their quality [61].

EMS	Consumed H2 (g)	Efficiency (%)	Final SOC	H2 Saving (%)	Efficiency Increase (%)	Decrease in SoC (%)	Performance Index (%)
HHO	44.78	55.04	58.21	29.43	2.72	16.11	16.05
PSO	59.1	48.7	62.93	46.53	8.61	20.83	34.31
MRFO	63.61	47.17	64.42	50.32	10.11	22.32	38.11

shows that the AOA system that used the ECMS significantly reduced the amount of hydrogen that was used. In comparison to HHO, the decline was 29.43%, while it was 48.7% compared to PSO, and 47.17 percent compared to MRFO. In addition, applying the ECMS-based AOA technique significantly improved the system’s efficiency. The efficiency improved, compared to the HHO, by 2.72%, the PSO by 8.61%, and the MRFO by 10.11%. When compared to the HHO method, the PSO strategy, and the MRFO strategy, the state of charge (SoC) dropped by 16.11%, 20.83%, and 22.32%, respectively. Significant progress was made in analyzing the comprehensive performance index using the AO technique that was based on the ECMS. The percentage of improvement relative to the HHO was 16.05%, relative to PSO was 34.31%, and relative to MRFO was 38.11%.

The battery was only used to store extra energy for usage when the FC’s performance declined, as Figure 8 illustrates. The sluggish dynamics of the FC performed the majority of the work. It could take a long time before FC reached its potential production. The system’s dependability was enhanced since the battery could discharge its stored energy during periods of high demand or power deficiency. However, by using an SC, which can store and quickly release electrical energy, the fast load variations could be reduced.

In Figure 9, you can see the obtained FC voltage data from different control techniques. The suggested approach used the FC with modest dynamics, which was different from the other techniques.

Because of this choice, the fuel cell was in a condition of prolonged well-being, which would have increased its efficiency, longevity, and cost-effectiveness.

The superconducting circuit (SC) voltage is shown in Figure 10. The voltage fluctuations were caused by changes in the ability of the DC bus to absorb and dissipate power. With an equilibrium of supply and demand, the voltage was 270 V. And yet, in order to meet the immediate power demands, the SC voltage quickly dropped when the load was suddenly changed.

Figure 11 shows the battery voltage. The proposed method that was based on the AOA caused the battery voltage to show large fluctuations. The reason behind this was that the battery system was specifically engineered to protect the fuel cell system and significantly reduce voltage fluctuations. Consequently, as seen in the figure that follows, the amplitude of voltage variations increased.

The proposed EMS showed significant improvements, reducing fuel consumption by up to 59.28% and increasing system efficiency by 8.43% in simulations. While these results were promising, they were based on idealized conditions and required real-world testing for validation.

6. Conclusions

This research introduces an innovative method for energy management in a hybrid fuel cell electric car. The main benefit of this research is the energy management system it develops, which uses the Arithmetic Optimization Algorithm and a revised variant of the equivalent consumption minimization strategy (ECMS). This innovative approach is designed to improve the overall performance, efficiency, and efficacy of fuel cell electric vehicles’ HPS.

The EMS is assessed utilizing ZOA, RTH, COOT, WaOA, MFO, AEO, and OOA. This study evaluates the efficacy of fuel efficiency and electrical systems. The findings demonstrate that the suggested energy management system (EMS) effectively decreases fuel consumption by 73.37%. Furthermore, there is an 8.43 % increase in overall efficiency. Significant progress is also achieved in terms of the comprehensive performance index, which shows an improvement of 36.44%. The aim of this research is to reduce fuel consumption and improve the efficiency of the power system. The researchers plan to investigate the complex problem of multi-optimization in future studies, stemming from the intricate properties of the battery’s state of charge (SoC). Furthermore, evaluating power losses is essential for improving system efficiency.

The principal limitation of the suggested technique is in its capacity for real-time implementation.

In order to minimize the objective function more efficiently, the optimizer requires a very efficient calculator. Nonetheless, developments in processing technology present a prospective resolution to this difficulty in the imminent future.

Future work will involve Hardware-in-the-Loop (HIL) testing or physical prototypes for more comprehensive validation.

To enhance the practical relevance and robustness of the proposed EMS, future studies will evaluate the system using additional standard driving cycles (Urban Dynamometer Driving Schedule (UDDS), Worldwide Harmonized Light Vehicles Test Procedure (WLTP), and New European Driving Cycle (NEDC)) and incorporate real-world driving data from commercial HEVs. This will help validate performance under dynamic conditions and support real-world implementation.