Minimization Hydrogen Management Strategy Using the Red‐Tailed Hawk Algorithm for Hybrid Storage Electric Vehicles

Abstract

Hybrid electric vehicles (HEVs) utilizing fuel cells (FCs), batteries, and supercapacitors (SCs) necessitate sophisticated energy management systems (EMSs) to optimize hydrogen utilization and improve efficiency. Conventional techniques, including proportional–integral (PI) control, state machine control strategy (SMCS), and the equivalent consumption minimization strategy (ECMS), have difficulties in sustaining optimal performance under dynamic loads because of their fixed or slowly adjusting parameters. This work introduces an improved energy consumption control system (ECMS) coupled with the red‐tailed hawk (RTH) optimization method for real‐time and adaptive power control. The RTH algorithm dynamically modifies the ECMS equivalency factor to enhance the equilibrium between the hydrogen economy and the battery state of charge (SOC). Simulation outcomes under the FTP‐75 driving cycle indicate that the proposed ECMS‐RTH decreases hydrogen consumption by 61.6% and enhances total system efficiency by 21.47% relative to traditional ECMS, while ensuring the battery SOC remains within safe parameters. The method surpasses contemporary metaheuristic techniques, including bald eagle search (BES), white shark optimizer (WSO), manta ray foraging optimization (MRFO), and cuckoo search (CS). The findings validate the efficacy of the ECMS‐RTH technique as an adaptive real‐time energy management framework for HEV applications. Future endeavors will encompass hardware‐in‐the‐loop validation and scalability studies of many microgrids.

1. Introduction

It is crucial to decrease greenhouse gas emissions and environmental impact and rely more on renewable energies (REs) than fossil fuels [1, 2]. It is imperative that storage devices can be installed with RE. They can be installed in hybrid, fuel cell (FC), battery, or supercapacitor (SC) systems. FC transforms chemical reactions into DC power, and it became well-known because of its small size and insignificant environmental impact [3]. FCs have been widely used in trains, airplanes, and electric vehicles (EVs) in recent decades. FC encounters limited applications due to its low power density and sluggish performance under varying loads. As a result, adding SC or batteries to create a hybrid system can improve FC’s performance.

Energy management systems (EMSs) are categorized into two groups in the literature [4, 5]: rule-based EMSs and optimization-based EMSs, as shown in Figure 1. There are two categories of rule-based EMSs: fuzzy [6, 7] and deterministic [8, 9], which include look-up tables, filter-based control [9], wavelet transform [10, 11], and state machine control (SMC) [12, 13]. Real-time optimization (RTO) [14] and global optimization (GO) EMSs [15] are the other two categories wherein optimization-based EMSs are included. External energy maximization strategies (EEMSs) [16] and equivalent consumption minimization strategies (ECMSs) [17] are two examples of RTO EMSs that focus on fuel consumption without taking the power grid’s overall performance into account.

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One of the most popular EMSs for managing microgrids is the SMC approach [18]. It primarily depends on the established roles and the condition of the system. The strategy’s primary concern is measurement accuracy, which means that changes in load and unpredictability in renewable power output could lower the system’s efficiency. Due to their many benefits, fuzzy logic control (FLC)-based intelligent management techniques have been applied extensively [19]. However, the primary disadvantages of this approach are the reliance on preexisting knowledge, the designer’s experience, the intricate adjustment of the type and parameters of the membership function (usually through trial and error), and the challenge of selecting the best ruleset.

Because of their higher immediate performance, RTO provides high performance. These tactics are commonly used in applications involving EVs. One of the common RTO EMSs is the equivalent consumption based on the ECMS [20]. The ECMS minimizes immediate fuel consumption by reducing the fuel usage of the FC and the battery bank’s comparable fuel consumption. This is done by applying a cost function that quantifies the battery bank’s equivalent hydrogen consumption using an equivalent factor. Nonetheless, the minimization accuracy might be impacted by the corresponding component.

In [21], the direction predictions optimal foraging optimization algorithm (OFA/DP) has been proposed for the EEMS strategy for unmanned aerial vehicle (UAV) applications. The presented OFA/DP-based EEMS proved superior performance over rule-based, FLC, ECMS, and conventional optimization algorithms. Another method has been presented in [22] based on Pontryagin’s minimum principle (PMP) EMS for FC-EVs with minimizing the consumed hydrogen. An optimized neural network (NN)-based driving cycle recognizer is employed in the algorithm. However, the presented OFA/DP-based EEMS and PMP-EMS strategies do not consider the hybrid energy storage systems. In addition, the PMP-EMS depends on the quality of the trained NN for recognizing the driving cycles, which increases the complexity of the system.

Based on two-dimensional optimization techniques, Jiang et al. [23] proposed energy management in addition to component sizing for a hybrid powertrain, including FC/battery/SC. The suggested approach significantly lowers FC and battery deterioration and energy usage. For DC microgrids with hybrid photovoltaic (PV), FC, and battery, Han et al. [24] presented an EMS based on two levels: device and system control levels. In [25], an EMS for a car driven by FC was provided in a way that can lead to reducing the amount of gasoline used by the primary source. Kamel et al. [26] introduced a management strategy using a proportional–integral (PI) controller. Reducing the consumed hydrogen was set as the goal by Kamel et al. [26], with battery state of charge (SOC) and FC current being the variables to be assessed. Additionally, the proposed controller was contrasted with the traditional SMC and FL techniques. In [27], an EMS was introduced as part of PV/FC/battery/SC to decrease hydrogen consumption by FC and calculate battery SOC. The FL and SMC represent the main parts of the suggested strategy. A rule-based EMS and mathematical model for a hybrid FC/SC/wind was presented by Kadri et al. [28]. A method for controlling the energy of DC MG with the help of several states of operation was described by Han et al. [12]. PV, FC, and battery are the components of the built MG. Sikkabut et al. [29] have described a nonlinear flatness FL-based EMS used in a hybrid system of PV, FC, and SC. Batteries have been added to a hybrid system using PV/FC, and a control mechanism has been implemented to optimize energy management among the various sources [30]. The contributions of the work can be summarized in the following manner:

• •

  An enhanced ECMS is suggested based on modifying the original algorithm by including an improved metaheuristic algorithm to achieve the minimization process. The conventional minimization process is replaced with a robust metaheuristic optimization algorithm, leading to a decrease in consumed hydrogen.

• •

  A new application process is proposed for the recent red-tailed hawk (RTH) to improve the overall ECMS performance index. The proposed method ensures the powerful operation of the RTH method in microgrid applications. This RTH has proved its superior performance for a large number of engineering applications, from parameter identification to control optimization, due to its updating mechanism based on three optimization levels. This feature enhanced its exploration and exploitation functions, enhancing its performance. For these reasons, the RTH has been chosen.

• •

  Detailed comparisons are provided in the paper from the EMS side-related performance indices, in addition to the optimization algorithm-side performance metrics. The proposed ECMS-based RTH is compared with the conventional PI control strategy, SMC strategy (SMCS), and ECMS methodologies. Moreover, RTH is compared with recent optimization algorithms, such as manta ray foraging optimization (MRFO), bald eagle search (BES) optimization, white shark optimizer (WSO), and cuckoo search (CS).

The rest of the work is given as follows: Section 2 presents detailed models of various MG components. The conventional EMS methods are explained in Section 3. Section 4 presents the proposed RTH-based ECMS methods. The main results associated with discussions are discussed in Section 5. Section 6 lastly gives the conclusions of the work.

2. Model of System Components

2.1. FC Model

PEMFCs use chemical reactions to help the movement of electrons to generate power. These procedures fall into two primary categories: reduction, in which electrons are taken in, and oxidation, in which they are released. The electrolyte in PEMFCs is an acid-based polymer membrane, and the chemical processes that generate electricity occur at the electrodes [31]. Using the newly proposed energy management method to optimize hydrogen consumption leads to better economic operation of the microgrid system and higher system efficiency. Incorporating PEMFC provides an economic and dispatchable energy storage system for better electrical energy management in the microgrid system. The chemical reaction at the level of the anode and cathode responsible for producing the electrical energy is presented as follows: 1 $\begin{array}{}{\text{H}}_2\to 22{\text{H}}^{+}+e^{-}\left(\text{at\hspace{0.17em}anode}\right),\end{array}$ 2 $\begin{array}{}442{\text{H}}^{+}+e^{-}+{\text{O}}_2\to {\text{H}}_2\text{O}\left(\text{at\hspace{0.17em}cathode}\right).\end{array}$

While the equations of the output voltage are provided as follows: 3 $\begin{array}{}A=\frac{\text{RT}}{z\alpha F},\end{array}$ 4 $\begin{array}{}{E}_{\text{oc}}=E_n{K}_c,\end{array}$ 5 $\begin{array}{}{i}_o=\frac{zFk\left(P_{{\text{H}}_2}+P_{{\text{O}}_2}\right)}{\text{RH}}{e}^{\frac{-\Delta G}{\text{RT}}},\end{array}$ 6 $\begin{array}{}{U}_{f{\text{O}}_2}=\frac{n_{{\text{O}}_2}^r}{n_{{\text{O}}_2}^{\text{in\hspace{0.17em}}}}=\frac{6000{\text{RTN}}_{\text{ifc}}}{2zF{P}_{\text{air\hspace{0.17em}}}{V}_{\text{lmpa}}y\mathrm{\%}},\end{array}$ 7 $\begin{array}{}{U}_{f{\text{H}}_2}=\frac{n_{{\text{H}}_2}^r}{n_{{\text{H}}_2}^{\text{in}}}=\frac{6000{\text{RTN}}_{\text{ifc}}}{zF{P}_{\text{fuel\hspace{0.17em}}}{V}_{\text{lmpf}}x\mathrm{\%}},\end{array}$ where R denotes the gas constant, and K_c is the voltage constant. T denotes the temperature; F denotes the Faraday constant. ΔG is the activation energy barrier. H is the Planck’s constant. k is the Boltzmann constant. $P_{{\text{O}}_2}$and $P_{{\text{H}}_2}$ are oxygen pressure and hydrogen pressure, respectively. E_n is the Nernst voltage. P_air is the air absolute pressure. N is the number of cells. V_lmpa is the flow rate of air, and V_lmpf is the flow rate of fuel. The Nernst voltage is defined by the following relations [32]: 8 $\begin{array}{}{E}_{\text{n\hspace{0.17em}}}=1.229-\left(T-298.15\right)\frac{-44.43}{zF}+\frac{-\text{RT}}{zF}\ln \left(P_{{\text{H}}_2}{P}_{{\text{O}}_2}^{\frac{1}{2}}\right),\text{\hspace{0.17em}when\hspace{0.17em}}T\le 100°\text{C},\end{array}$ 9 $\begin{array}{}{E}_{\text{n\hspace{0.17em}}}=1.229100-\left(T-298.15\right)\frac{-44.43}{zF}+\frac{-RT}{zF}\ln \left(\frac{P_{{\text{H}}_2}{P}_{{\text{O}}_2}^{\frac{1}{2}}}{P_{{\text{H}}_2\text{O}}}\right),\text{\hspace{0.17em}when\hspace{0.17em}}T>°\text{C}.\end{array}$

The hydrogen (H₂) partial pressure, oxygen (O₂) partial pressure, and water vapor (H₂O) can be estimated using the following equations [33]: 10 $\begin{array}{}{P}_{{\text{H}}_2}=\left(1-U_{f{\text{H}}_2}\right)x\mathrm{\%}{P}_{\text{fuel\hspace{0.17em}}},\end{array}$ 11 $\begin{array}{}{P}_{{\text{H}}_2\text{O}}=\left(W+2y\mathrm{\%}{U}_{f{\text{O}}_2}\right)P_{\text{air}},\end{array}$ 12 $\begin{array}{}{P}_{{\text{O}}_2}=\left(1-U_{{\text{fO}}_2}\right)y\mathrm{\%}{P}_{\text{air}},\end{array}$ where W represents the water vapor level.

2.2. Lithium-Ion Battery Model

The discharging battery voltage (V_{Bat_dis}) and the charging battery voltage (V_{Bat_ch}) are calculated using the following relations [34–36]: 13 $\begin{array}{}{V}_{\text{Bat}-\text{dis}}=E0-\text{R}\cdot i_{\text{Bat}}-K\cdot \frac{Q}{Q-\text{it}}\cdot \left(i_{\text{Bat}F}+\text{it}\right)+A\cdot \exp \left(-B\cdot \text{it}\right),\end{array}$ 14 $\begin{array}{}\text{it}={\int }_0^t{i}_{\text{Bat}}dt,\end{array}$ 15 $\begin{array}{}{V}_{\text{Bat}-\text{ch}}=E0-R\cdot i_{\text{Bat}}-K\cdot Q\cdot \left(\frac{i_{\text{Bat}F}}{\text{it}+0.1\cdot Q}+\frac{\text{it}}{Q-\text{it}}\right)+A\cdot \exp \left(-B\cdot \text{it}\right),\end{array}$ where E₀ is the battery’s OCV, R represents the internal resistance, i_Bat is the battery’s charging/discharging current, K is the voltage due to polarization, Q is the battery’s capacity, i_BatF is the filtered battery current, A is the amplitude related to the exponential zone, and B represents the reciprocal of the time constant.

The SOC is defined by Ma et al. [35] as follows: 16 $\begin{array}{}\text{SOC}={\text{SOC}}_0-\frac{\text{it}}{Q},\end{array}$ where SOC₀ is the battery’s initial charge level, and i_Bat is the battery current.

2.3. SC Model

The SC has a higher energy storage capacity compared to the electrostatic capacitor. The SC model is based on the Stern model. It integrates the Helmholtz and Gouy–Chapman models. The capacitance of the SC is represented as follows [37]: 17 $\begin{array}{}C={\left[\frac{1}{C_H}+\frac{1}{C_{\text{GC}}}\right]}^{-1},\end{array}$ 18 $\begin{array}{}{C}_H=\frac{N_e\in {\varepsilon }_0{A}_i}{d},\end{array}$ 19 $\begin{array}{}{C}_{\text{GC}}=\frac{{\text{FQ}}_C}{2N_e\text{RT}}\sinh \left(\frac{Q_c}{N_e^2{A}_i\sqrt{8\text{RT}\in {\varepsilon }_{0}C}}\right),\end{array}$ where N_e is the number of electrode layers, C denotes the molar concentration, ∈ is the permittivity, and Q_c is the cell electric charge. The total capacitance of SC is defined by Equation (24) [38, 39]: 20 $\begin{array}{}{C}_T=\frac{N_p}{N_s}\cdot C,\end{array}$ where N_s and N_p denote the series and parallel cells, respectively. The SC voltage is expressed as [39] 21 $\begin{array}{}{V}_{\text{sc}}=\frac{N_s{Q}_{T}d}{N_p{N}_e\in {\varepsilon }_0{A}_i}+\frac{2N_e{N}_s\text{RT}}{F}\text{arsinh}\left(\frac{Q_T}{N_p{N}_e^2\in {\varepsilon }_0{A}_i\sqrt{8\text{RT}\in {\varepsilon }_{0}C}}-i_{\text{sc}}\cdot R_{\text{sc}}\right),\end{array}$ 22 $\begin{array}{}{Q}_T=\int i_{sc}dt.\end{array}$

2.4. DC Voltage Regulation

The control of battery system converters for all EMSs achieves the control of DC-bus voltage. As demonstrated in Figure 2, the voltage regulator involves a traditional PI-based controller. The principal difference among various studied EMSs depends on how the FC reference power is obtained.

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3. Conventional Energy Management Strategies

The targeted objectives of EMS are the assurance of three main criteria, including low consumed hydrogen, high efficiency, and an average value of battery SOC. This is attained by controlling the power-sharing among system components using EMS. The following subsection explains the principles of conventional EMS using PI control strategy, SMCS, ECMS, and optimized ECMS.

3.1. PI Control

In this method, as explained in Figure 3, the battery SOC has been regulated by a PI and produced battery power. The battery power is detached from the load demand to find the FC reference power. If battery SOC exceeds a specific threshold, the FC power is kept low, and the battery offers full capacity. The FC delivers the required load if the SOC is lower than the threshold.

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3.2. State Machine-Based Control Strategy

SMCS is applied in different stages of operations, as explained in Table 1. As displayed in Figure 4, the FC power is attained using the battery SOC and load demand. Next, the obtained FC power is used to get the FC reference current. The drawback of SMCS is the need for a hysteresis controller when switching between stages, which significantly affects EMS response to changes in the demanded load.

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Table 1 Main rules of SMCS.

Battery SoC	Stat	The net power (Pnet)	FC power ($P_{\text{FC}}^{\text{ref}}$)
High SoC > SoCmax	1	$P_{\text{net}}\le P_{\text{FC}}^{\min }$	$P_{\text{FC}}^{\text{ref}}=P_{\text{FC}}^{\min }$
2	$P_{\text{FC}}^{\min }<P_{\text{net}}<P_{\text{FC}}^{\max }$	$P_{\text{FC}}^{\text{ref}}=P_{\text{net}}$
3	$P_{\text{net}}\ge P_{\text{FC}}^{\max }$	$P_{\text{FC}}^{\text{ref}}=P_{\text{FC}}^{\max }$
Normal SoCmin < SoC < SoCmax	4	$P_{\text{net}}<P_{\text{FC}}^{\min }$	$P_{\text{FC}}^{\text{ref}}=P_{\text{FC}}^{\min }$
5	$P_{\text{FC}}^{\min }<P_{\text{net}}<P_{\text{FC}}^{\text{opt}}$	$P_{\text{FC}}^{\text{ref}}=P_{\text{FC}}^{\text{opt}}$
6	$P_{\text{FC}}^{\text{opt}}<P_{\text{net}}{P}_{\text{FC}}^{\max }$	$P_{\text{FC}}^{\text{ref}}=P_{\text{net}}$
7	$P_{\text{net}}\ge P_{\text{FC}}^{\max }$	$P_{\text{FC}}^{\text{ref}}=P_{\text{FC}}^{\max }$
Low SoC < SoCmin	8	$P_{\text{net}}<P_{\text{FC}}^{\min }$	$P_{\text{FC}}^{\text{ref}}=P_{\text{net}}+P_{\text{Batt}}^{\text{char}}$
9	$P_{\text{FC}}^{\min }<P_{\text{net}}<P_{\text{FC}}^{\text{opt}}$	$P_{\text{FC}}^{\text{ref}}=\max \left\{P_{\text{net}}+P_{\text{Batt}}^{\text{char}},P_{\text{FC}}^{\text{opt}}\right\}$
10	$P_{\text{FC}}^{\text{opt}}<P_{\text{net}}$	$P_{\text{FC}}^{\text{ref}}=P_{\text{net}}+P_{\text{Batt}}^{\text{char}}$
11	$P_{\text{net}}\ge P_{\text{FC}}^{\max }$	$P_{\text{FC}}^{\text{ref}}=P_{\text{FC}}^{\max }$

SoC_max and SoC_min are the battery SoC boundaries, and $P_{\text{fc}}^{\min },P_{\text{fc}}^{\text{opt}}$, and $P_{\text{fc}}^{\max }$ are the minimum, optimum, and maximum FC power, respectively.

3.3. Equivalent Consumption-Based Minimization Strategy

The aim of ECMS is to attain the lowest consumed hydrogen by minimizing consumed fuel in FCs and the needed equivalent fuels to keep the battery’s SOC. A variable factor of equivalence, which relies upon the battery’s SOC, is utilized. Also, to make ECMS less sensitive to the SOC balancing coefficient (μ), an equivalence factor is involved in the designed cost function for the optimization process. Therefore, at different values for μ, the optimum value is obtained for the equivalence factor. Figure 5 shows the ECMS scheme. The system optimization problem is mathematically formulated as follows.

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The objective function (F) aims to minimize total equivalent consumption (C). It may be formulated by the following equation [40]: 23 $\begin{array}{}F=\min \left(C\right)=\min \left(C_{\text{FC}}+\alpha C_{\text{Bat}}\right)=\min \left(C_{\text{FC}}+\alpha \frac{P_{\text{Bat}}}{H_L}\right),\end{array}$ where C_FC is the consumed fuel by the FC, C_Bat is the consumed fuel by the battery, α is the equivalent consumption factor, P_Bat is the battery power, and H_L is the fuel’s low heat value. This objective function (F) has the following equality constraints: 24 $\begin{array}{}{P}_{\text{net}}=P_{\text{FC}}+P_{\text{Bat}},\end{array}$ 25 $\begin{array}{}\alpha =12-\mu \frac{\text{SOC}-0.5\left({\text{SOC}}_{\max }+{\text{SOC}}_{\min }\right)}{{\text{SOC}}_{\max }+{\text{SOC}}_{\min }}.\end{array}$

Within the following boundary conditions [41] 26 $\begin{array}{}\frac{1}{\text{HL}}\le \alpha \le \frac{{\eta }_{\text{inv}}{\eta }_{\text{batt}}}{\text{HL}{\eta }_m},\end{array}$ 27 $\begin{array}{}{P_{\text{Bat}}}^{\min }\le P_{\text{Bat}}\le {P_{\text{Bat}}}^{\max },\end{array}$ 28 $\begin{array}{}{\text{SOC}}_{\min }\le \text{SOC}\le {\text{SOC}}_{\max },\end{array}$ 29 $\begin{array}{}{P_{\text{FC}}}^{\min }\le P_{\text{FC}}\le {P_{\text{FC}}}^{\max }.\end{array}$

To implement classical ECMS, a Simulink-based S-function using the «fmincon» function in the MATLAB software is employed to solve the formulated optimization problem.

4. The Optimized ECMS-RTH

The common EMSs, such as PI control strategy, SMCS, and ECMS, cannot simultaneously achieve high efficiency and low hydrogen consumption while operating battery SOC within the safe region. The PI control strategy is the best option for minimum consumed hydrogen, followed by SMCS and ECMS. For overall efficiency, SMCS is better than the PI control strategy and ECMS. Moreover, ECMS is the best option for a good average battery SOC, followed by SMCS and PI control strategies. Therefore, the current work aims to propose a novel integration between common classical ECMS and the RTH algorithm to boost the overall performance index. Therefore, the «fmincon» function inside classical ECMS has been replaced by the RTH algorithm, as explained in Figure 6.

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The optimization process of RTH contains three main hunting phases: first, the high-soaring phase; then, the low-soaring phase, and, lastly, the swooping phase. One can think of the initialization procedure as the basic step that any SI optimizer must take. The primary solutions are produced as follows: 30 $\begin{array}{}{x}_i^d=L_i^d+\left(U_i^d-L_i^d\right)\times r_i^d,\end{array}$ where x represents the initial value for the i^th solution, d denotes the dimension, L is the lower limit, U is the upper limit, and r is a random value. After initialization, the solutions are supplied to the cost function to determine the average value and estimate the global location. Then, the three previously mentioned techniques can be updated repeatedly.

• 1. High soaring: As it searches for the ideal spot, the RTH soars high into the sky but far away from its target. This can be represented mathematically as follows:

31 $\begin{array}{}x\left(k\right)=x_G+\left(x_{\text{av}}-x\left(k-1\right)\right)\cdot \text{Levy}\left(\text{Dim}\right)\cdot \text{TF}\left(k\right),\end{array}$ where x(k) is the location, and x_G denotes the global-best location. TF(k) is the transition factor. The distribution of Levy may be represented mathematically according to the following equations: 32 $\begin{array}{}\text{Levy}\left(\text{Dim}\right)=C_1\frac{r_1\cdot \sigma }{{\left|r_2\right|}^{{C_2}^{-1}}},\end{array}$ 33 $\begin{array}{}\sigma =\left(\frac{\Gamma \left(1+C_2\right)\cdot \sin \left(\frac{\pi C_2}{2}\right)}{\Gamma \left(\frac{1+C_2}{2}\right)\cdot C_2\cdot 2^{\left(\frac{1-C_2}{2}\right)}}\right),\end{array}$ where C₁ is a constant; Dim is the dimension; C₂ is a constant; r₁ and r₂ are arbitrary values. 34 $\begin{array}{}\text{TF}\left(k\right)=1+\sin \left(2.5+\left(\frac{k}{T_m}\right)\right),\end{array}$ where T_m is the maximum number of iterations.

• 2. Low-soaring phase: The hawk flies near the prey in a spiral movement to surround it. The model of such a stage is formulated as

35 $\begin{array}{}x\left(k+1\right)=x_G+\left(x\left(k\right)+y\left(k\right)\right)\cdot T_s\left(k\right),\end{array}$ 36 $\begin{array}{}{T}_s\left(k\right)=x\left(k\right)-x_{\text{av}},\end{array}$ 37 $\begin{array}{}\begin{array}{c}\left\{\begin{array}{c}x\left(k\right)=A\left(k\right)\cdot \sin \left(\theta \left(k\right)\right)\\ y\left(k\right)=A\left(k\right)\cdot \cos \left(\theta \left(k\right)\right)\end{array}\right.\left\{\begin{array}{c}A\left(k\right)=A_0\cdot \left(g-\frac{k}{T_m}\right).r_1\\ \theta \left(k\right)=\varnothing \cdot \left(1-\frac{k}{T_m}\right).r_1\end{array}\right.\left\{\begin{array}{c}x\left(k\right)=\frac{x\left(k\right)}{\max \left|x\left(k\right)\right|}\\ y\left(k\right)=\frac{y\left(k\right)}{\max \left|y\left(k\right)\right|}\end{array}\right.\end{array},\end{array}$ where ∅ represents angle gain, r₁ is an arbitrary value, and g denotes a controlling factor ranging between 1 and 2.

• 3. Stooping and swooping stage: The hawk suddenly lowers its body to strike its prey, which is recognized by being in the optimal location during the low soaring. The model of such a stage is mathematically represented in the following way:

38 $\begin{array}{}x\left(k\right)=\alpha \left(t\right)\cdot x_G+x\left(k\right)\cdot T_{s1}\left(k\right)+y\left(t\right)\cdot T_{s2}\left(k\right).\end{array}$

The steps’ sizes can be obtained according to 39 $\begin{array}{}{T}_{s1}\left(k\right)=x\left(\text{k}\right)-\text{TF}\left(k\right)\cdot x_{\text{av}},\end{array}$ 40 $\begin{array}{}{T}_{s2}\left(k\right)=G\left(k\right)\cdot x\left(k\right)-\text{TF}\left(k\right)\cdot x_G,\end{array}$ where α and G are the accelerating and gravitational parameters. 41 $\begin{array}{}\alpha \left(k\right)={\sin }^2\cdot \left(2.5-\frac{k}{T_m}\right),\end{array}$ 42 $\begin{array}{}G\left(k\right)=2\cdot \left(1-\frac{k}{T_m}\right).\end{array}$

Integration of the RTH algorithm in the ECMS framework enables dynamic and adaptive modification of the equivalency factor (α), crucial for real-time fuel–battery energy trade-off. Heuristic rules often enforce or adjust α in conventional ECMS, limiting responsiveness to fluctuations in demand. However, the RTH’s three hunting stages boost flexibility. In the high-soaring phase, the optimizer explores an extensive search space to determine α values that minimize instantaneous hydrogen consumption under various load situations. The low-soaring phase refines options in potential regions, enabling smoother α adjustment with changes in SOC or load demand. During the stooping and swooping phase, the RTH conducts a local search around the global optimum, guaranteeing rapid convergence to the most energy-efficient α value for each sampling interval. Hierarchical search behavior matches ECMS’s physical control needs, where the equivalence factor must respond swiftly yet steadily to transient driving circumstances. Thus, the RTH-enhanced ECMS improves hydrogen efficiency and system stability without human retuning or control rules.

The suggested ECMS–RTH energy management method integrates the RTH optimizer into the ECMS loop, as shown in Figure 7. The flow diagram shows the evolution of processes, from driving-cycle inputs and constraints to the RTH algorithm’s dynamic tuning of the equivalence factor (α) and computation of optimal FC reference power and system component power distribution.

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5. Results and Discussion

Through DC/DC converters, the connection between the FC and battery system is made using DC/AC converter systems. This enables complete control over the FC/battery current in addition to the DC bus voltage and voltage conversion (from the low-side to the high-side voltage and vice versa). While the battery-side power conversion system comprises one boost converter (for the discharging phase) and one buck-based converter (for the charging phase), the FC system is connected with a boost converter. The battery system should be ideally charged and discharged using a bidirectional DC converter to increase the system’s power density.

To guarantee identical conditions for comparison, the simulations are conducted at identical operating primary conditions for both battery and SC systems. The battery SOC and SC voltage are 65% and 270 V, respectively. The performance metric is the summation of the increased rate of efficiency, decreased rate of hydrogen consumed, and increased rate of battery SOC. The hybrid FC/BS/SC DC power system topology is shown in Figure 8. The FC’s purpose is to balance the load demand’s net power average. In the meantime, the load can be supported by the battery and SC during periods of continuous and transient highest demand, respectively. The lithium-ion battery’s rated capacity and nominal voltage are 40 Ah and 48 V, respectively. The SC’s rated voltage and capacitance are 291.6 V and 15.6 F, respectively, while its beginning voltage and operating temperature are 270 V and 25°C, respectively.

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The battery is initially charged at 65%, and the response time equals 20 s. The considered 12.5 kW PEMFC consists of 65 series-connected cells. One important distinction between the EMS is the technique used to determine the PEMFC reference power. Together with two DC converters, one for charging (1.2 kW buck converter) and one for discharging (4 kW boost converter). These converters provide current limiting and output voltage regulation as well. Finally, a 15 kVA, 270 V DC input, 200 V AC, 400 Hz inverter system is used by the system. The system’s parameters are listed in Table 2.

Table 2 System’s parameters.

Component	Parameters
PEMFC	Capacity 12.5 kW	Rated voltage 65 V	Number of cells 65
Battery	Capacity 40 Ah	Rated voltage 48 V	Initial SOC 65%
SC	Capacity 15.6 F	Rated voltage 291.6 V	Initial voltage 270 V
Inverter	Max power 15 kVA	DC voltage 270 V	AC voltage 200 V	Frequency 400 Hz

The suggested enhanced ECMS-based RTH decreases a PEMFC-integrated hybrid system’s hydrogen consumption. The currents control the output, the FC, and the battery. The common ECMS, SMCS, PI, and optimized ECMS-based MRFO, BES, CS, and WSO are contrasted with the optimized ECMS-based RTH. All the optimizers are set with the same optimization parameters (population size = 5, max iteration = 100), while the specific parameters of each used algorithm are listed in Table 3.

Table 3 Optimizers’ parameters.

Optimizer	Parameters
RTH	A = 15	R0 = 0.5	R = 1.5
BES	lm = 2	a = 10	R = 1.5
WSO	fmax = 0.75	fmin = 0.07	tau = 4.11	pmax = 1.5	pmin = 0.5	a0 = 6.25	a1 = 100	a2 = 0.0005
MRFO	Somersault factor (S) = 2
CS	Discovery rate = 0.25	Tolerance = 1 × 10−5

The hybrid EV’s (HEV) power demand is determined by the FTP-75 standard driving cycle, which offers a realistic urban driving profile with variable speed, acceleration, and idling periods. The vehicle dynamics model calculates the instantaneous load power (P_load) by considering the vehicle mass parameters, aerodynamic drag, rolling resistance, and traction force. This power demand is the reference input for all energy management strategies that have been tested (PI, SMCS, ECMS, and ECMS-RTH).

Figures 9 and 10 show the hydrogen consumption in liters per minute (lpm) and g, respectively. Table 4 and Figure 11 show the comparative results between the various ESMs under consideration. The results confirmed that the suggested ECMS-based RTH is better than other studied strategies. The consumed hydrogen is reduced from 80.48 (by classical ECMS) to 30.91 g using the ECMS-based RTH.

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Table 4 Performance comparison among considered strategies.

EMS	H2 (g)	η (%)	SOC (%)	Decrease in H2%	Increase in η (%)	Decrease in SOC (%)	Performance index (%)
SMCS	58.62	53.14	63.08	47.28	11.84	16.16	42.95
PI	56.12	54.75	60.5	44.93	8.54	12.59	40.88
ECMS	80.48	48.92	67.34	61.6	21.47	21.47	61.59
RTH	30.91	59.42	52.88	0	0	0	0
BES	39.98	56.74	56.15	22.7	4.74	5.82	21.62
WSO	59.89	48.26	63.12	48.39	23.14	16.22	55.3
MRFO	64.9	46.74	63.12	52.38	27.15	16.22	63.3
CS	45.6	54.53	58.51	32.22	8.98	9.62	31.58

Overall, in comparison with SMCS, PI, ECMS, BES, WSO, MRFO, and CS, respectively, the amount of hydrogen consumed decreased by 47.28%, 44.93%, 61.6%, 22.7%, 48.39%, 52.38%, and 32.22% while utilizing the suggested ECMS-based RTH. The ECMS-based RTH raised efficiency from 48.92% (using the original ECMS) to 59.42%. Furthermore, compared to SMCS, PI, ECMS, BES, WSO, MRFO, and CS, respectively, the efficiency was raised by 11.84%, 8.54%, 21.47%, 4.74%, 23.14%, 27.15%, and 8.98% while employing the suggested ECMS-based RTH. Regretfully, in contrast to SMCS, PI, ECMS, BES, WSO, MRFO, and CS, employing ECMS-based RTH reduced the average battery SOC by 16.16%, 12.59%, 21.47%, 5.82%, 16.22%, 16.22%, and 9.62%. Last but not least, the performance index rose in relation to SMCS, PI, ECMS, BES, WSO, MRFO, and CS by 42.95%, 40.88%, 61.59%, 21.62%, 55.3%, 63.3%, and 31.58%, respectively. The RTH provided better results due to its updating mechanism of the current optimization variables, where this mechanism needs a small number of iterations to achieve the optimal or sub-optimal solutions (the best possible solutions) for each sampling time.

The suggested ECMS–RTH outperforms the other techniques (PI, SMCS, ECMS, BES, WSO, MRFO, and CS) in reducing hydrogen consumption and improving system efficiency. Table 4 shows that the proposed ECMS–RTH utilized 61.6% less hydrogen than traditional ECMS, from 80.48 to 30.91 g. By dynamically adapting the equivalency factor using the RTH’s exploration–exploitation process, the FC’s operating point is constantly tuned near its maximum efficiency zone. ECMS system efficiency rose from 48.92% to 59.42% with the suggested technique, a 21.47% improvement. Due to its three-stage search structure (high soaring, low soaring, and stooping), the RTH algorithm converged faster (within 100 iterations) and had lower objective function variations than metaheuristic-based EMSs like BES, MRFO, WSO, and CS. These stages enable early global exploration and precise local exploitation around the optimum in subsequent iterations.

The 21.47% drop in average battery SOC relative to ECMS reveals a basic trade-off: the optimization prioritizes hydrogen consumption and system efficiency, which deepens battery drain. The battery SOC stayed under the safety limit (SOC_min = 40%) throughout the FTP-75 cycle, assuring operational dependability. The total performance index—which includes hydrogen saving, efficiency gain, and SOC penalty—is 61.59% higher than the conventional ECMS, indicating that the RTH-based EMS balances energy distribution across FC, battery, and SC components.

A comprehensive assessment of all tactics shows that the ECMS–RTH strategy is most adaptable. The PI controller and SMCS are easier to design and behave well in transients, but they fail to optimize energy sharing during rapid load fluctuations, increasing hydrogen usage. Conventional ECMS improves fuel efficiency but requires real-time equivalency factor retuning. Integrating the RTH algorithm solves this problem by autonomously modifying the equivalency factor based on immediate load and SOC data, balancing hydrogen efficiency and energy usage. Compared to contemporary bio-inspired optimizers like BES, MRFO, WSO, and CS, the RTH-based EMS has lower hydrogen consumption, higher efficiency, and better computational stability and convergence speed. The ECMS-RTH is a potential real-time energy management system for HEV microgrids, with stronger performance indices and more adaptation to dynamic driving circumstances.

Figures 12 and 13 show the power distribution among FC, battery, SC, and SOC of the battery using optimized ECMS-based RTH. The SC’s power is not considered through the optimization problem, as the DC bus voltage regulation is made through battery converter systems. Once the SC is discharged, it is recharged again with equal energy from the battery. Consequently, the total energy of connected loads is shared only among FC and battery systems over the given loading cycle. Figure 14 shows the SC voltage with different EMSs.

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Despite the ECMS-RTH’s greater efficiency, the average battery SOC diminished by 21.47% relative to traditional ECMS. Subsequent iterations will limit SOC dynamics to guarantee enduring dependability.

6. Conclusion

This study suggests a novel approach for managing electrical energy in hybrid microgrid systems, comprising FC, battery, and SC applications in electric car technology. The suggested approach addresses the drawbacks of the most widely used PI control technique, the ECMS, and the SMCS. The main goal of the suggested approach is to integrate traditional ECMS with the RTH algorithm to raise the overall performance index. The obtained results are compared with the PI control strategy, SMCS, and ECMS, as well as regression optimization algorithms, such as BES optimization, WSO, MRFO, and CS, to showcase the superiority of the suggested ECMS-based RTH. The outcomes proved the superior performance of the suggested ECMS based on the RTH method. The main findings of the paper are summarized as follows:

• •

  The ECMS-based RTH reduces the consumed hydrogen fuel from 80.48 (using traditional ECMS) to 30.91 g.

• •

  Overall, using the recommended ECMS-based RTH resulted in a decrease in hydrogen consumption by 47.28%, 44.93%, 61.6%, 22.7%, 48.39%, 52.38%, and 32.22% compared to SMCS, PI, ECMS, BES, WSO, MRFO, and CS, respectively.

• •

  The ECMS-based RTH increased the efficiency from 48.92% (using the original ECMS) to 59.42%.

• •

  Overall, using the recommended ECMS-based RTH increased the efficiency by 11.84%, 8.54%, 21.47%, 4.74%, 23.14%, 27.15%, and 8.98% as compared to SMCS, PI, ECMS, BES, WSO, MRFO, and CS, respectively.

• •

  Unfortunately, using ECMS-based RTH decreased the average battery SOC by 16.16%, 12.59%, 21.47%, 5.82%, 16.22%, 16.22%, and 9.62% compared to SMCS, PI, ECMS, BES, WSO, MRFO, and CS.

• •

  Lastly, the performance index increased by 42.95%, 40.88%, 61.59%, 21.62%, 55.3%, 63.3%, and 31.58% with respect to SMCS, PI, ECMS, BES, WSO, MRFO, and CS, respectively.

The proposed ECMS-based RTH method can reduce hydrogen consumption and improve the performance index and efficiency of the microgrid system. Nevertheless, future research can address the management of battery SOCs and integrate them into the optimization process under physical testing conditions (HIL or PHIL) by utilizing emulators like Opal-RT systems. Furthermore, the present investigation is restricted to simulation analysis. Despite the fact that the RTH optimizer converges within 100 iterations (~0.45 s per iteration), additional enhancements are necessary to guarantee full real-time performance in embedded vehicle controllers. These computational aspects will also be addressed in future work, which will also expand validation to include large-scale microgrid configurations and multiple driving cycles. In addition, interoperating AI algorithms within the optimization process can significantly enhance performance by providing transient and steady-state performance enhancement and assisting the system’s state of health in real-time. Future work includes the scalability of the RTH algorithm with multi-microgrid systems and larger power system structures. In addition, modified versions of the RTH algorithm can be developed to provide more advantages to the system, followed by hardware implementation of the developed method. Moreover, future research will extend validation under UDDS, NEDC, and high-speed cycles to verify adaptability.

Nomenclature

• PEMFC:
• Proton exchange membrane fuel cell
• SC:
• Supercapacitor
• BS/Bat:
• Battery system
• EV:
• Electric vehicle
• EMS:
• Energy management strategy
• ECMS:
• Equivalent consumption minimization strategy
• SMCS:
• State machine control strategy
• SOC:
• Battery’s state of charge (%)
• η:
• Efficiency (%)
• P_Bat:
• Battery ower (W)
• P_FC:
• Fuel cell power (W)
• P_Load:
• Load power (W)
• P_SC:
• Supercapacitor power (W)
• C_FC:
• Fuel consumption by fuel cell (g)
• C_Bat:
• Equivalent fuel consumption by battery (g)
• A:
• Equivalence factor (ECMS weight coefficient)
• HL:
• Lower heating value of hydrogen (J/kg)
• E₀:
• Battery’s OCV (V)
• i_Bat:
• Battery current (A)
• R:
• Internal resistance (Ω)
• Q:
• Battery capacity (Ah)
• T:
• Operating temperature (K)
• F:
• Faraday constant (96,485 C/mol)
• R_gas:
• Universal gas constant (J/mol·K)
• P_H2, P_O2:
• Partial pressure of hydrogen, oxygen (Pa)
• C:
• Total equivalent hydrogen consumption (g).

Data Availability Statement

Data are available upon reasonable request from the corresponding author.

Conflicts of Interest

The authors declare no conflicts of interest.

Funding

The authors extended their appreciation to Prince Sattam bin Abdulaziz University for funding this research work through the project number (PSAU/2025/01/32231).

Acknowledgments

The authors extended their appreciation to Prince Sattam bin Abdulaziz University for funding this research work through the project number (PSAU/2025/01/32231).

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