Fuel Cell Electric Vehicle Hydrogen Consumption and Battery Cycle Optimization Using Bald Eagle Search Algorithm

Abstract

In this study, the Bald Eagle Search Algorithm performed hydrogen consumption and battery cycle optimization of a fuel cell electric vehicle. To save time and cost, the digital vehicle model created in Matlab/Simulink and validated with real-world driving data is the main platform of the optimization study. The digital vehicle model was run with the minimum and maximum battery charge states determined by the Bald Eagle Search Algorithm, and hydrogen consumption and battery cycle values were obtained. By using the algorithm and digital vehicle model together, hydrogen consumption was minimized and range was increased. It was aimed to extend the life of the parts by considering the battery cycle. At the same time, the number of battery packs was included in the optimization and its effect on consumption was investigated. According to the study results, the total hydrogen consumption of the fuel cell electric vehicle decreased by 57.8% in the hybrid driving condition, 23.3% with two battery packs, and 36.27% with three battery packs in the constant speed driving condition.

1. Introduction

The harsh increase in worldwide energy demand and environmental pollution pushes people to discover new resources, force the more efficient use of existing resources, or force a change in energy use methods [1]. Studies such as conducting bio-based research [2,3], developing wind turbines, or increasing the use of solar energy are being carried out to limit the dependence on coal and oil in the discovery of new resources [4]. To increase resource use efficiency, examples such as research and development facilities to reduce fuel consumption in internal combustion engines, research on energy consumption in public areas [5], applying daylight saving time [6], and using thermal insulators in buildings can be given. The increasing frequency of use of vehicles with electric drive systems compared to internal combustion vehicles in recent years is a good example of a change in the method of energy use. Electric vehicles are quieter, have higher performance, are easier to use, and are more sustainable than internal combustion vehicles. At the same time, the energy cost per unit distance is lower than internal combustion vehicles [7]. By combining high system efficiency with renewable energy sources, sustainable transportation can be achieved on a wide scale. However, besides the several positives of electric vehicles, there are some negatives as well. Among the others, the driving range appears as an anxiety creator of electric vehicle drivers [8]. To solve this problem, researchers propose some solutions such as battery swapping, wireless charging, and Vehicle-to-Vehicle (V2V) platforms [9,10,11]. Apart from range anxiety, another negative phenomenon of electric vehicles is the charge time [12]. The battery charging time is longer than a gasoline tank filling duration [13]. Therefore, charge waiter drivers are planning their route according to charging locations and manage the time on it. To overcome such problems, fuel cell electric vehicles have some advantages. While it takes 5 or 6 h to fully charge a battery in an electric vehicle, it is considered that 600 s may be sufficient to fill hydrogen tanks [14]. The resulting significant time difference shows that fuel cell electric vehicles have the potential to eliminate the energy-filling problem. Similar to the charging time advantage, fuel cell electric vehicles provide good results in terms of driving range. In a study conducted by Gray et al. [15], a significant range advantage of an internal fuel cell electric vehicle compared to a battery electric vehicle is evident. For these reasons, it is important to continue research on fuel cell electric vehicles.

Fuel cell electric vehicles can present a more optimistic picture to the driver than battery electric vehicles. Additionally, there are some technical differences between them. While a battery electric vehicle has types of equipment such as a battery, power electronics, electric motor, and transmission, a fuel cell electric vehicle has elements such as a hydrogen tank, pressure regulator, and fuel cell module in addition to the equipment existing in the battery electric vehicle [16,17]. Most fuel cell electric vehicles include both fuel cell modules and electrical energy storage such as batteries or supercapacitors for long ranges. Since hybrid power systems have multiple power supply components, power management or an optimization strategy is needed for consumption minimization and has long-life components. The result of a well-developed optimization strategy can provide financial savings and ease sustainable transportation. There are many studies in the literature on fuel cell system optimization [18,19,20,21,22]. The general aspect is based on similar contents such as energy and hydrogen consumption minimization, fuel cell and battery lifetime extension, system efficiency increase, and component optimization [23,24,25,26].

Optimization methodologies in the latest studies include some approaches such as neural network (NN) [21], particle swarm algorithm (PSO) [27], genetic algorithm (GA) [28], dynamic programming (DP) [18], sunflower optimization (SFO) [22], and Bald Eagle Search Algorithm (BESA) [29]. The BESA, which is one of the nature-inspired meta-heuristic optimization algorithms [30], is chosen for its superior balance between exploration and exploitation, making it highly effective in navigating complex search spaces. When compared to commonly used algorithms, the BESA offers significant advantages in computation time and convergence speed. Its structured phases allow for the faster identification of optimal solutions with fewer iterations, making it particularly suitable for problems requiring both high precision and computational efficiency [29,31,32,33].

Previous studies in the literature include topics such as vehicle component optimization, energy management systems, and parameter optimization. Marghichi et al. [34] benefit from the BESA for a battery state of health estimation. In a methodology comparison, the BESA showed the highest accuracy. Fathy et al. [35] conducted a study on battery parameter estimation using the BESA. They compared the performance of several methods and found that the BESA showed more reliable results. Yuvaraj et al. [36] studied charging distribution in India. They used the BESA to find the best location for charging stations. The chosen methodology resulted in more accuracy. Ghadbane et al. [37] provide a hybrid storage system (battery and supercapacitor) management strategy. The BESA showed superiority in the battery state of charge preserves. Fathy [38] developed an optimization methodology that includes some subsystems, such as photovoltaics, wind turbines, fuel cells, micro turbines, and batteries. During the stages of the optimization process, the developed method structured with the BESA presented the best result values between the specified components. Zaky et al. [29] highlighted the lifetime of fuel cells and researched parameter optimization. The BESA and five different metaheuristic algorithms were used on two different fuel cell systems. Among others, the BESA showed the best results in the optimization of fuel cell systems. Alsaidan et al. [31] provide an optimization strategy for fuel cells with five different algorithms. Three different fuel cell systems were used for the optimization process, and the BESA showed the best result. Yang et al. [32] researched the parameter identification of fuel cells. The BESA showed better performance than the genetic algorithm (GA) to optimize the fuel cell. Youssef et al. [39] utilized the BESA in an energy management system at home. The approach aims to reduce energy consumption while keeping human comfort stable and minimizing the electricity bills and average peak ratio. Rezk et al. [40] researched the best fuel cell characteristic definitions. Among the five different approaches, the BESA made two fuel cell systems with the best parameters. Abaza et al. [41] researched the optimal parameters of a fuel cell system. While the optimization process includes several algorithms, the BESA is the superior algorithm among them. Rezk et al. [42] compared several optimization methodologies for fuel cell performance optimization. The BESA minimized the parameters more effectively. Ferahtia et al. [33] conducted research on energy management optimization of a fuel cell hybrid electric vehicle that has a fuel cell, battery, and supercapacitor. A significant hydrogen consumption reduction was achieved in the New European Driving Cycle (NEDC) and Extra Urban Driving Cycle (EUDC) driving cycles using the BESA.

Studies in the literature make strong contributions to this subject. There are still gaps in the literature on this rapidly developing topic. Energy management systems designed in previous studies are mostly about only hydrogen consumption minimization. Management structures created using real vehicle driving data have also been included in very few studies. Additionally, in the hybrid vehicle architecture, the battery and fuel cell are considered independently. Therefore, this study was conducted to fill the gaps mentioned and to make strong contributions to the literature. In this study, optimization was carried out to minimize hydrogen consumption and the battery cycle in a fuel cell electric vehicle using the BESA. The optimization study was carried out on a digital vehicle model created in a Matlab/Simulink environment to save time and cost, based on a real fuel cell electric vehicle. The digital model has been validated by real-world driving data obtained by driving a real fuel cell electric vehicle. The verified digital model was combined with the BESA in the Matlab Workspace folder. In the main process of optimization, the minimum state of charge (SoC), maximum SoC, hydrogen consumption, and battery cycle values are exchanged between the BESA and the digital vehicle model. Additionally, optimization was repeated for different battery pack numbers. The contribution of this study to the literature includes the simultaneous optimization of hydrogen consumption and the battery cycle in suitable driving cycles of a fuel cell electric vehicle. This study, which includes real-world driving data, also demonstrates the effect of the number of battery packs on hydrogen consumption.

2. Materials and Methods

The methodology followed in the optimization study for the fuel cell electric vehicle includes five sub-stages. In the first stage, the real fuel cell electric vehicle was introduced and technical details were shared. In the second stage, a digital vehicle model was created in Matlab/Simulink to simulate the real vehicle, whose features and operating principles are known. In the third stage, to confirm the operating accuracy of the digital vehicle model, a real road drive was carried out with the real vehicle, and controller area network (CAN) data were recorded. The results obtained by running the same real driving conditions on the digital vehicle model were compared graphically. Additionally, at this stage, the fuel cell was verified with the data shared by the supplier. In the fourth stage, the working principle of the BESA is explained and the limitations taken into account in optimization are stated. To concretely see the effectiveness of the optimization carried out in the fifth stage, different driving conditions were created in the digital model. Driving conditions included constant drive with two and three battery packs and hybrid drive simulating urban driving. Figure 1 shows a summary of the main flow mentioned in general terms.

2.1. Fuel Cell Electric Vehicle

The working principle should be well-defined since this system has a hybrid architecture and two energy sources are working. In this vehicle architecture, the battery is the master energy source of the vehicle, and the fuel cell subsystem works as a battery supplier and range extender. The fuel cell subsystem working conditions depend on the battery SoC level. The user-defined minimum SoC level activates the fuel cell subsystem and forces it to supply power to the battery; The maximum SoC level indicates sufficient energy in the battery and disables the fuel cell subsystem. The real vehicle on which the study is based is a fuel cell hybrid electric bus, and its technical details are shared in

Table 1. Technical specifications of fuel cell electric vehicle.

Parameter	Specification
Gross vehicle weight	18,000–20,000 kg
Vehicle length	10–14 m
Vehicle front area	7–8 m2
Drag coefficient	0.6–0.8
Tire radius	0.4–0.5 m
Transmission ratio	20–23
Maximum motor power	200–300 kW
Maximum motor torque	800–1000 Nm
Motor type	In-wheel hub PMSM
Battery capacity	25–30 kWh
Fuel cell type	Proton Exchange Membrane
Fuel cell maximum power	70 kW
Hydrogen tank capacity	1500–1700 L

.

The fuel cell power supply–SoC level relationship between the maximum and minimum SoC level in the operating principle before vehicle optimization is shared in Figure 2.

2.2. Digital Vehicle Model

To provide time and cost advantages in the optimization study, a digital model of the real fuel cell electric vehicle was structured in Matlab/Simulink. The digital vehicle model was examined in two areas: the vehicle and fuel cell. While on the vehicle side, there are concepts such as speed, acceleration, torque, power, and energy consumption, on the fuel cell side there are variables such as SoC, current demand, temperature, voltage, and power. Operations between the inputs given in the digital vehicle model and the desired outputs can be carried out with some basic equations.

Equations (1)–(10) describe the basic calculations performed in the digital vehicle model. Equations (1)–(5) show the basic resistance forces acting on a vehicle, which are also shown in Figure 3, while Equations (6)–(8) reveal the required motor power calculations. Equations (9)–(10) show the data obtained in the required motor power calculation and the required energy and charge rate calculations. Among the parameters in Equations (1)–(5), $\mathsf{\rho }$ is the air density, A is the vehicle front surface area, V_v is the vehicle speed, C_d is the drag coefficient, m is the vehicle mass, g is the gravitational acceleration, C_rr is the wheel rolling resistance coefficient, $\propto$ is the road slope angle, and F_resistance is the total force that the vehicle faces while driving.

$${\mathrm{F}}_{\mathrm{a}\mathrm{e}\mathrm{r}\mathrm{o}}={\displaystyle \frac{1}{2}}\mathsf{\rho }\mathrm{A}{\mathrm{V}}_{\mathrm{v}}^2{\mathrm{C}}_{\mathrm{d}}$$

(1)

$${\mathrm{F}}_{\mathrm{r}\mathrm{r}}=\mathrm{mg}{\mathrm{C}}_{\mathrm{r}\mathrm{r}}cos(\propto )$$

(2)

$${\mathrm{F}}_{\mathrm{g}\mathrm{r}}=\mathrm{mg}sin(\propto )$$

(3)

$${\mathrm{F}}_{\mathrm{i}}=\mathrm{m}\mathrm{a}$$

(4)

$${\mathrm{F}}_{\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}}={\mathrm{F}}_{\mathrm{a}\mathrm{e}\mathrm{r}\mathrm{o}}+{\mathrm{F}}_{\mathrm{r}\mathrm{r}}+{\mathrm{F}}_{\mathrm{g}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{e}}+{\mathrm{F}}_{\mathrm{i}}$$

(5)

Among the parameters in Equations (6)–(10), M_w represents the wheel torque, i_tr is the total transmission ratio, ${\mathsf{\eta }}_{\mathrm{t}\mathrm{r}}$ is the power transmission efficiency, w_m is the motor angular speed, and P_m is the motor power. E_battery is the total energy in the battery, E_cons is drawn energy from the battery, and V_nominal is the nominal voltage in the battery.

$${\mathrm{M}}_{\mathrm{w}}={\mathrm{F}}_{\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}}\ast {\mathrm{r}}_{\mathrm{w}}$$

(6)

$${\mathrm{M}}_{\mathrm{m}}={\displaystyle \frac{{\mathrm{M}}_{\mathrm{w}}}{{\mathrm{i}}_{\mathrm{t}\mathrm{r}}}}\ast {\mathsf{\eta }}_{\mathrm{t}\mathrm{r}}$$

(7)

$${{\mathrm{P}}_{\mathrm{m}}=\mathrm{M}}_{\mathrm{m}}\ast {\mathrm{w}}_{\mathrm{m}}$$

(8)

$${\mathrm{E}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}}=\left({\int }_0^{\mathrm{t}}{\mathrm{P}}_{\mathrm{m}}\mathrm{d}\mathrm{t}\right){\displaystyle \frac{1}{3600}}$$

(9)

$$\mathrm{S}\mathrm{o}\mathrm{C}=\left({\displaystyle \frac{{\mathrm{E}}_{\mathrm{b}\mathrm{a}\mathrm{t}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{y}}-{\mathrm{E}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}}}{{\mathrm{V}}_{\mathrm{n}\mathrm{o}\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{l}}}}\right){\displaystyle \frac{1}{3600{\mathrm{E}}_{\mathrm{b}\mathrm{a}\mathrm{t}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{y}}}}100$$

(10)

There are basic empirical formulas expressing the operation of the fuel cell in the literature [43,44,45,46,47,48,49]. The operating principle of the system is similar to the vehicle’s basic equations. The net voltage output of the fuel cell is obtained after subtracting the loss voltages from the reference voltage value. In this study, the calculations for the fuel cell used in the digital vehicle model are given in Equations (11)–(20). Among the empirical formulas created for the fuel cell, Equation (11) expresses the voltage value created per cell, Equation (12) expresses the fundamental voltage value in the system excluding losses, Equation (13) expresses the voltage drop due to activation loss, Equation (14) expresses the ohmic voltage loss, and Equation (16) declares the concentration voltage loss. Equation (17) is the total voltage produced in the fuel cell stack, Equations (18) and (19) are the flow equations of the anode and cathode, and Equation (20) is the cathode water flow equation.

Equation (11) is the voltage per cell in the fuel cell stack.

$${\mathrm{V}}_{\mathrm{c}\mathrm{e}\mathrm{l}\mathrm{l}}={\mathrm{V}}_{\mathrm{n}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{t}}-{\mathrm{V}}_{\mathrm{a}\mathrm{c}\mathrm{t}}-{\mathrm{V}}_{\mathrm{o}\mathrm{h}\mathrm{m}}-{\mathrm{V}}_{\mathrm{c}\mathrm{o}\mathrm{n}}$$

(11)

Equation (12) is the Nernst voltage that includes T as the cell temperature, F as the Faraday constant, R as the gas constant, and P_H2, P_O2, and P_H2O are hydrogen, oxygen, and vapor pressures, respectively.

$${\mathrm{V}}_{\mathrm{n}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{t}}=1.229-0.85\ast {10}^{-3}\ast \left(\mathrm{T}-298.15\right)+{\displaystyle \frac{\mathrm{R}\ast \mathrm{T}}{2\ast \mathrm{F}}}\ast \ln \left({\displaystyle \frac{{\mathrm{P}}_{{\mathrm{H}}_2}\ast {\mathrm{P}}_{{\mathrm{O}}_2}^{0.5}}{{\mathrm{P}}_{{\mathrm{H}}_2\mathrm{O}}}}\right)$$

(12)

Equation (13) is the activation loss voltage, also expressed by the Tafel equation [50], occurring in low current regions. In related parameters, n is the cell number and $\mathsf{\alpha }$ is the charge coefficient. The rest of the parameters can be extracted from the Tafel equation in the related reference.

$${\mathrm{V}}_{\mathrm{a}\mathrm{c}\mathrm{t}}=-{\displaystyle \frac{\mathrm{R}\ast \mathrm{T}}{\mathrm{n}\ast \mathsf{\alpha }\ast \mathrm{F}}}\ast \ln \left({\displaystyle \frac{\mathrm{l}}{{\mathrm{l}}_0}}\right)$$

(13)

Equation (14) is the ohmic loss occurring in the continuous operating region. In the ohmic loss, I is the instant current and ${\mathrm{R}}_{\mathrm{m}\mathrm{e}\mathrm{m}}$ is the membrane resistance.

$${\mathrm{V}}_{\mathrm{o}\mathrm{h}\mathrm{m}}=\mathrm{I}\ast {\mathrm{R}}_{\mathrm{m}\mathrm{e}\mathrm{m}}$$

(14)

Equation (15) is the membrane resistance expression used in the ohmic loss calculation. Tm is the membrane thickness, and $\mathsf{\sigma }$ is the conductivity value of the membrane.

$${\mathrm{R}}_{\mathrm{m}\mathrm{e}\mathrm{m}}={\displaystyle \frac{{\mathrm{t}}_{\mathrm{m}}}{\mathsf{\sigma }}}$$

(15)

Equation (16) is the concentration loss in high current regions.

$${\mathrm{V}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}}=\left(1.1\ast {10}^{-4}-12\ast {10}^{-6}\ast \left(\mathrm{T}-273\right)\right)\ast {\mathrm{e}}^{8\ast {10}^{-3}\ast \mathrm{I}}$$

(16)

Equation (17) is the total voltage produced from cells connected in series in the fuel cell stack. V_cell is the produced voltage in a cell.

$${\mathrm{V}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{c}\mathrm{k}}={\mathrm{V}}_{\mathrm{c}\mathrm{e}\mathrm{l}\mathrm{l}}\ast {\mathrm{N}}_{\mathrm{c}\mathrm{e}\mathrm{l}\mathrm{l}}$$

(17)

Equation (18) includes the expressions for anode flow. V_a is the anode volume, ${\mathrm{m}}_{{\mathrm{H}}_2}$ is the hydrogen flow rate, and k_a is the flow constant for the anode.

$$\begin{array}{c}{\displaystyle \frac{{\mathrm{V}}_{\mathrm{a}}}{\mathrm{R}\ast \mathrm{T}}}{\displaystyle \frac{\mathrm{d}{\mathrm{P}}_{{\mathrm{H}}_2}}{\mathrm{d}\mathrm{t}}}={\mathrm{m}}_{{\mathrm{H}}_2-\mathrm{i}}-{\mathrm{m}}_{{\mathrm{H}}_2-\mathrm{o}}-{\displaystyle \frac{1}{4\ast \mathrm{F}}}\\ {\mathrm{m}}_{{\mathrm{H}}_2}={\mathrm{k}}_{\mathrm{a}}\ast ({\mathrm{P}}_{{\mathrm{H}}_2}-{\mathrm{P}}_{\mathrm{a}\mathrm{m}\mathrm{b}})\end{array}$$

(18)

Equation (19) has the fundamental explanations for cathode flow. V_c is the cathode volume, m_O2 is the oxygen flow rate, and k_c is the flow constant for the cathode.

$$\begin{array}{c}{\displaystyle \frac{{\mathrm{V}}_{\mathrm{c}}}{\mathrm{R}\ast \mathrm{T}}}{\displaystyle \frac{\mathrm{d}{\mathrm{P}}_{{\mathrm{O}}_2}}{\mathrm{d}\mathrm{t}}}={\mathrm{m}}_{{\mathrm{O}}_2-\mathrm{i}}-{\mathrm{m}}_{{\mathrm{O}}_2-\mathrm{o}}-{\displaystyle \frac{1}{4\ast \mathrm{F}}}\\ {\mathrm{m}}_{{\mathrm{O}}_2}={\mathrm{k}}_c\ast ({\mathrm{P}}_{{\mathrm{O}}_2}-{\mathrm{P}}_{\mathrm{a}\mathrm{m}\mathrm{b}})\end{array}$$

(19)

Equation (20) is the expression of the cathode water.

$${\displaystyle \frac{{\mathrm{V}}_{\mathrm{c}}}{\mathrm{R}\ast \mathrm{T}}}{\displaystyle \frac{\mathrm{d}{\mathrm{P}}_{{\mathrm{H}}_2\mathrm{O}-\mathrm{C}}}{\mathrm{d}\mathrm{t}}}={\mathrm{m}}_{{\mathrm{H}}_2\mathrm{O}-\mathrm{i}\mathrm{c}}-{\mathrm{m}}_{{\mathrm{H}}_2\mathrm{O}-\mathrm{o}\mathrm{c}}-{\displaystyle \frac{1}{2\ast \mathrm{F}}}$$

(20)

The polarization curve in Figure 4 expresses the main loss behavior during the working stage of a fuel cell [51]. At low currents, the activation loss due to the barrier that must be overcome for the reaction to begin is dominant. Ohmic loss, which occurs due to the resistance encountered by ions moving in the electrolyte and electrons moving in the external circuit, is constantly effective. At high currents, concentration loss is more dominant due to inefficiency and an insufficient diffusion rate on the electrode surface. In Figure 4, the dominance regions of the loss types are shown for an easier understanding of the expressions in Equations (13), (14) and (16).

Two subsystems were taken into account in the operating logic of the virtual fuel cell electric vehicle model. In the resulting fuel cell electric vehicle model, the vehicle side consumes the energy stored in the battery by consuming energy while driving, and the fuel cell side replaces the consumed energy according to the battery charge state. The general operating scheme of the fuel cell vehicle model is shown in Figure 5.

2.3. Data-Driven Validation

The created digital vehicle model was used in an optimization study. The accuracy of the study is largely limited by the ability of the digital model to provide accurate results. For this reason, a driving test was carried out with the fuel cell electric vehicle, the features of which were mentioned before, and CAN-bus data were recorded using the method shown in the flowchart of the study. The data obtained from the test drive were converted into meaningful data to be used in the validation study of the digital model. In the verification study, the vehicle and the fuel cell were evaluated separately to demonstrate the operating accuracy of the two separate subsystems.

The real fuel cell electric vehicle is used in urban driving conditions with frequent stop-and-go traffic and has a relatively low average speed. For this reason, one of the most critical points on the vehicle side of the verification study of the digital model is that the values occurring during rapid start-up can be seen with sufficient accuracy in the digital environment. Therefore, to verify the vehicle side in the digital model, a sudden start was made under real driving conditions and the vehicle was accelerated to full speed. A moment of the real driving and data recording setup can be seen in Figure 6.

Figure 7 shows the comparison of the results obtained from the vehicle side validation study on the fuel cell electric vehicle digital model. Figure 7a shows the instant speeds between the data of the real and digital vehicle models, Figure 7b shows the instant motor power, Figure 7c shows the current drawn and Figure 7d shows the instant motor torque. In the graphs of the comparison study of the four basic parameters required for energy consumption in an electric vehicle, black lines show the digital model response, and red lines show the values of the CAN-bus data record taken from the real vehicle. In this part of the study, while the real vehicle has drawn 1.540 Ah from the battery, this value was 1.624 Ah in the digital vehicle model. According to the resulting consumption values, there is an acceptable difference of 5.17% between the real vehicle and the digital model.

A similar approach to the vehicle verification test was adopted in determining the operating accuracy of the fuel cell. At this stage, the current, voltage, and power values shared by the fuel cell supplier in the real vehicle were taken as references. By giving current demand to the fuel cell digital model, total voltage and power values were taken and comparison graphs were created. In the resulting comparison graphs, the power and voltage responses of the fuel cell digital model in response to current demand were largely similar to the values shared by the supplier. For this reason, it has been observed that the fuel cell digital model works with sufficient accuracy for the optimization study. The benchmark graphs resulting from the verification study are shared in Figure 8.

2.4. Optimization Assessment Cycles

The optimization algorithm detects the optimal minimum and maximum SoC values at which the fuel cell is activated and deactivated and reports it to the digital vehicle model. The digital vehicle model runs the driving profile according to the SoC values determined by the algorithm and displays the hydrogen consumption and the number of battery charging cycles. To see the effect of the optimization algorithm concretely, comparable values before and after optimization are needed.

Before the optimization, the fuel cell module was activated at 50% and disabled at 85%, depending on the SoC. The algorithm effect comparison study was carried out in two stages. In the first stage, called “constant drive”, driving the vehicle on a flat road at a constant speed of 70 km/h for 7200 s was simulated. The SoC values of the digital model before and after optimization, the amount of hydrogen consumed in constant drive, and the number of battery charging cycles were obtained.

The second stage aims to see the optimal SoC values of the vehicle under frequent stop-and-go driving and passenger-load conditions and to determine the optimization improvement rate. For this, SORT [52] by The International Association of Public Transport (UITP) [53] was used. SORT types, namely, SORT-1 represents heavy urban, SORT-2 is easy urban, and SORT-3 is easy suburban, were combined in the same driving profile and called “hybrid drive”, and different traffic behaviors were desired to be seen in a single drive. The velocity profile of the combined SORT types is seen in Figure 9.

In the digital vehicle model, running is started with 100% SoC. For the SoC value to drop to the minimum SoC value and activate the fuel cell, sufficient energy consumption must be made on the vehicle side. During the control, it was seen that the SORT combination profile given in Figure 9 was not sufficient for the fuel cell to be activated. Therefore, the combination created was repeated 15 times and the final version of the 8114 s hybrid drive profile was obtained, as shown in Figure 10. Since hybrid drive simulates real urban driving conditions, it was studied according to the fully loaded condition of the vehicle.

2.5. The BESA

In a study conducted by Alsattar et al. [30], the BESA, a meta-heuristic optimization technique that simulates the hunting behavior of the North American bird of prey, the bald eagle, was introduced. Thanks to their superior vision, bald eagles can locate their prey from very far away. They are in search of suitable trees for food and nesting in their habitats. While searching for food in an ocean, hunting behaviors are divided into three categories: selecting, searching, and swooping. These behaviors can be seen in Figure 11. An eagle in the selection phase heads towards the area where the prey is most abundant, and in the search phase, it starts looking for prey in the selected area. The basic concept of the BESA is to mimic bald eagle behaviors while flying and fishing.

2.5.1. Selection Phase

Bald eagles in the selection phase find and choose the best hunting area based on the amount of food for which they can search. Equation (21) represents this behavior.

$${\mathrm{P}}_{\mathrm{n}\mathrm{e}\mathrm{w},\mathrm{i}}={\mathrm{P}}_{\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t}}+\mathsf{\alpha }\ast \mathrm{r}({\mathrm{P}}_{\mathrm{a}\mathrm{v}\mathrm{e}}-{\mathrm{P}}_{\mathrm{i}})$$

(21)

Here, r is an arbitrary value between 0 and 1, and α takes a value between 1.5 and 2 to handle changes in position. The eagle searches several different nearby areas to select an area based on the information available. P_best refers to the search area that eagles choose based on the best position they discover during their search. The pre-selected search region is surrounded by spots that the eagles search randomly, and P_mean suggests that these eagles use all the information from previous regions. The preliminary data obtained from the random search are multiplied by α to calculate their current movements. This procedure randomly changes each search position [30,54].

2.5.2. Search Phase

Bald eagles in the search phase look for prey within the chosen area and move in a spiral to speed up the search. Equation (22) mathematically expresses the best position for attack.

$${\mathrm{P}}_{\mathrm{i},\mathrm{n}\mathrm{e}\mathrm{w}}={\mathrm{P}}_{\mathrm{i}}+\mathrm{y}\left(\mathrm{i}\right)\ast \left({\mathrm{P}}_{\mathrm{i}}-{\mathrm{P}}_{\mathrm{i}+1}\right)+\mathrm{x}\left(\mathrm{i}\right)\ast ({\mathrm{P}}_{\mathrm{i}}-{\mathrm{P}}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}})$$

(22)

$$\mathrm{x}\left(\mathrm{i}\right)={\displaystyle \frac{\mathrm{x}\mathrm{r}\left(\mathrm{i}\right)}{\max \left(\right|\mathrm{x}\mathrm{r}\left|\right)}},\mathrm{y}\left(\mathrm{i}\right)={\displaystyle \frac{\mathrm{y}\mathrm{r}\left(\mathrm{i}\right)}{\max \left(\right|\mathrm{y}\mathrm{r}\left|\right)}}$$

(23)

$$\mathrm{x}\mathrm{r}\left(\mathrm{i}\right)=\mathrm{r}\left(\mathrm{i}\right)\ast \sin \left(\mathsf{\theta }\left(\mathrm{i}\right)\right),\mathrm{y}\mathrm{r}\left(\mathrm{i}\right)=\mathrm{r}\left(\mathrm{i}\right)\ast \mathrm{c}\mathrm{o}\mathrm{s}\left(\mathsf{\theta }\left(\mathrm{i}\right)\right)$$

(24)

$$\begin{gathered} \mathsf{\theta }\left(\mathrm{i}\right)=\mathsf{\beta }\ast \pi \ast \mathrm{rand}\dots \\ \mathrm{r}\left(\mathrm{i}\right)=\mathsf{\theta }\left(\mathrm{i}\right)+\mathrm{R}\ast \mathrm{rand}\dots \end{gathered}$$

(25)

The $\mathsf{\beta }$ parameter determines the corner between the point search at the center point by taking a value between 5 and 10, and the R parameter determines the number of search cycles by taking a value between 0.5 and 2.

2.5.3. Swooping Phase

During the attack phase, eagles attack the target they have reduced. All eagles move toward the best position for prey. Equation (26) shows this behavior mathematically.

$$\begin{gathered} {\mathrm{P}}_{\mathrm{i},\mathrm{n}\mathrm{e}\mathrm{w}}=\mathrm{rand}\ast {\mathrm{P}}_{\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t}}+{\mathrm{x}}_1\left(\mathrm{i}\right)\ast \left({\mathrm{P}}_{\mathrm{i}}-{\mathrm{c}}_1\ast {\mathrm{P}}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}\right)+{\mathrm{y}}_1\left(\mathrm{i}\right)\ast \left({\mathrm{P}}_{\mathrm{i}}-{\mathrm{c}}_2\ast {\mathrm{P}}_{\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t}}\right) \\ {\mathrm{c}}_1,{\mathrm{c}}_2\in [1,2] \end{gathered}$$

(26)

$$x_1\left(\mathrm{i}\right)={\displaystyle \frac{\mathrm{x}\mathrm{r}\left(\mathrm{i}\right)}{\max \left(\right|\mathrm{x}\mathrm{r}\left|\right)}},y_1\left(\mathrm{i}\right)={\displaystyle \frac{\mathrm{y}\mathrm{r}\left(\mathrm{i}\right)}{\max \left(\right|\mathrm{y}\mathrm{r}\left|\right)}}$$

(27)

$$\mathrm{r}\left(\mathrm{i}\right)=\mathrm{r}\left(\mathrm{i}\right)\ast \sinh \left[\left(\mathsf{\theta }\left(\mathrm{i}\right)\right)\right],\mathrm{y}\mathrm{r}\left(\mathrm{i}\right)=\mathrm{r}\left(\mathrm{i}\right)\ast \cosh \left[\left(\mathsf{\theta }\left(\mathrm{i}\right)\right)\right]$$

(28)

$$\mathsf{\theta }\left(\mathrm{i}\right)=\mathsf{\beta }\ast \pi \ast \mathrm{rand},\mathrm{r}\left(\mathrm{i}\right)=\mathsf{\theta }\left(\mathrm{i}\right)$$

(29)

Figure 12 shows the main components of the BESA, including the selection, search, and swooping stages.

The fitness function can be seen in Equation (30). The weighted sum of hydrogen consumption and battery cycle is the main target to be minimized in the optimization study. The minimum and maximum SoC values are set to ensure the least hydrogen consumption with the minimum number of cycles. Here, the weighted coefficients used to determine the total fitness value are φ1 and φ2, respectively.

$$\mathrm{F}\mathrm{i}\mathrm{t}\mathrm{n}\mathrm{e}\mathrm{s}\mathrm{s}=\mathsf{\phi }1\ast \mathrm{battery}\mathrm{cycle}+\mathsf{\phi }2\ast \mathrm{hydrogen}\mathrm{consumption}$$

(30)

Minimum and maximum SoC values are the parameters that must be obtained for optimal hydrogen consumption. The number of variables is set to two. In the initial phase, minimum and maximum SoC values are randomly assigned. For these initial values, the digital vehicle model in Simulink is run and the objective function is calculated with Equation (30). The flow diagram of the BESA can be seen in Figure 13.

For the optimization study to be completed successfully, the constraint and success target must be determined. In this study, a separate classification was made for minimum and maximum SoC values to determine the optimal SoC range. However, regardless of the driving cycle, the consumed hydrogen mass and battery cycle constraints are given in Equation (31).

The limitations are as follows:

20 < SoC_min < 49
50 < SoC_max < 80
SoC_min < SoC _(t) < SoC_max
H₂ < 10
BC < 5

(31)

Figure 14 shows the interaction between the BESA and the digital vehicle model created in Simulink.

3. Results

In the optimization study carried out using the BESA on a fuel cell electric vehicle, the optimal minimum and maximum SoC values that would minimize the total hydrogen consumption and battery cycle were determined. Two driving conditions were considered in the study: constant drive and hybrid drive. Since the optimization study also included the battery cycle status, the effect of the number of battery packs was also included. The results obtained can be considered as two groups: constant drive with two and three battery packs, and hybrid drive. In each result group, the hydrogen consumption amount and battery cycle values before and after optimization were shared and the saving rates were stated. Additionally, the SoC behavior graphs obtained from the digital vehicle model operated according to optimal SoC values and the power conditions of the fuel cell, battery, and motor were also shared.

The BESA in the combination of constant drive with two battery packs revealed the optimization result in 33,186 s. According to this combination, the optimal minimum SoC was determined as 20% and the maximum SoC was determined as 60%. With optimal SoC values, hydrogen consumption was 7.729 kg and battery cycle was two. Before optimization, hydrogen consumption was 9.638 kg, and the battery cycle was three. According to this result, a total improvement of 23% was achieved. Optimal minimum and maximum SoC values for three battery packs were found as 20% and 62%, respectively. The optimization process resulted in 32,325 s. Hydrogen consumption was 6.144 kg and the battery cycle was one with the optimal SoC, while hydrogen consumption was 9.132 kg and the battery cycle was two before optimization. The improvement for three battery packs was calculated as 36.27%.

Figure 15 shows the SoC behavior in constant driving. Figure 15a shows the SoC behavior before optimization with two battery packs, Figure 15b shows after optimization with two battery packs, Figure 15c shows before optimization with three battery packs, and Figure 15d shows after optimization with three battery packs.

Figure 16 shows the power behavior during constant drive with two and three battery packs. Figure 16a shows the behavior before optimization with two battery packs, Figure 16b shows the behavior after optimization with two battery packs, Figure 16c shows the behavior before optimization with three battery packs, Figure 16d shows the behavior after optimization with three battery packs. In the graphs, the black color is the power requested by the motor, the red color is the response of the battery, and blue is the power provided by the fuel cell when it is turned on and off. It is obvious that the battery cycles have been reduced after optimization and a decrease in the number of cycles can be achieved by increasing the number of battery packs.

In hybrid drive, the defined optimal minimum SoC was 25% and the maximum SoC was 51% within 36,124 s. While hydrogen consumption was 3.641 kg and the battery cycle was two before optimization, hydrogen consumption decreased to 1.378 kg and the battery cycle to one after optimization. According to these results, a total improvement of 57.8% was achieved. The SoC graphs before and after optimization are shared in Figure 17.

The power behaviors in the hybrid drive are shown in Figure 18. Figure 18a shows the power behavior before optimization, while Figure 18b shows the after optimization. Since this driving condition had frequent stop-and-go conditions, the motor power demand and battery power response made the graph noisy. However, the switching on and off interval of the fuel cell can be seen in blue.

4. Conclusions

In this study, the optimization of the sum of hydrogen consumption and battery cycle for a fuel cell electric vehicle was carried out with the help of the BESA. Since both of the outputs taken into consideration in the study are valuable, a global optimization perspective was adopted. According to the study results, hydrogen consumption was decreased by 57.8% in the hybrid driving condition, 23.3% with two battery packs, and 36.27% with three battery packs in the constant speed driving condition.

The most important output obtained from this study is given below.

• The number of battery packs has a slight impact on optimal SoC ratios.
• An increase in the number of battery packs reduces hydrogen consumption.
• As the number of battery packs increases, the effectiveness of the optimization algorithm also increases.
• Increasing the optimal SoC range causes excessive hydrogen consumption while decreasing it causes excessive battery usage.
• The energy recovered through regenerative braking reduces hydrogen consumption.

The findings of the study are not limited to these and will be supported by experimental data in future studies. The optimization strategy will also be repeated in the fuel cell-dominant vehicle architecture.