The Optimization of PEM Fuel-Cell Operating Parameters with the Design of a Multiport High-Gain DC–DC Converter for Hybrid Electric Vehicle Application

Abstract

The fossil fuel crisis is a major concern across the globe, and fossil fuels are being exhausted day by day. It is essential to promptly change from fossil fuels to renewable energy resources for transportation applications as they make a major contribution to fossil fuel consumption. Among the available energy resources, a fuel cell is the most affordable for transportation applications because of such advantages as moderate operating temperature, high energy density, and scalable size. It is a challenging task to optimize PEMFC operating parameters for the enhancement of performance. This paper provides a detailed study on the optimization of PEMFC operating parameters using a multilayer feed-forward neural network, a genetic algorithm, and the design of a multiport high-gain DC–DC converter for hybrid electric vehicle application, which is capable of handling both a 6 kW PEMFC and an 80 AH 12 V heavy-duty battery. To trace the maximum power from the PEMFC, the most recent SFO-based MPPT control technique is implemented in this research work. Initially, a multilayer feed-forward neural network is trained using a back-propagation algorithm with experimental data. Then, the optimization phase is separately carried out in a neural-power software environment using a genetic algorithm (GA). The simulation study was carried out using the MATLAB/R2022a platform to verify the converter performance along with the SFO-based MPPT controller. To validate the real-time test bench results, a 0.2 kW prototype model was constructed in the laboratory, and the results were verified.

1. Introduction

1.1. Sustainable Development

As the fossil fuel crisis is a common issue across the globe, researchers have been harnessing renewable energy resources. There are two approaches to encouraging sustainable development: one is to optimally utilize existing conventional energy resources in such a way that energy efficiency improves and energy consumption reduces, and the other is to adopt new energy-conversion technologies and their development. Though there are plenty of renewable resources in use, fuel cells have attracted attention in the transportation field because of salient features like low operating temperature, high energy density, quick start-up, and scalable size. The chemical energy that exists inside a fuel cell leads to the production of electricity and hot-water by-products. A fuel cell can be classified into many types based on the electrolyte it uses.

In this research, a PEM fuel cell is used, in which the porous polymer membrane can transfer protons and resist the electron flow. Its salient features make it possible to use it for transportation applications. The construction of hybrid electric vehicles using fuel cells is a challenge for researchers because their output voltage depends on many operating parameters. Therefore, researchers are encouraged to use this technology to optimize the operating parameters and make it economically viable for end-users, promoting sustainable development.

1.2. Literature Review

The operating parameters of a 25 cm² proton-exchange membrane fuel cell were set to improve output power and efficiency. In this study, the researchers considered one design parameter and two operating parameters. The parameters considered were the landing-to-channel ratio, operating temperature, and hydrogen partial pressure. The results revealed that hydrogen partial pressure contributed more than the other two parameters [1]. The effect of different electrode materials used in a PEM fuel-cell electrode was investigated [2]. Three different materials were used in this study, namely aluminum, copper, and steel. In this study, a detailed three-dimensional PEM fuel cell was constructed and simulated using fluid dynamics in the ANSYS ANSYS FLUENT 18.0 software environment. Then, validation of the investigation was carried out by conducting an experimental verification study, and it was reported that the aluminum-based bipolar electrode performed better than the other materials used. A multidimensional optimization study on PEM fuel cells was carried out [3]. A set of parameters was considered for optimization that included efficiency, power density, and oxygen uniformity in the cathode material used. The optimization techniques used in this study were a computational fluid dynamics model, a surrogate model, and, finally, a multi-objective genetic algorithm. The optimized parameters performed better than the other set.

The importance of heating, cooling, and power systems was stressed [4]. The researchers used a modified mayfly optimization-based algorithm to optimize the design specification of a PEM fuel cell. The simulated results were compared against the conventional mayfly algorithm and showed that the proposed optimization-based algorithm could yield better results. There are two ways to improve a PEM fuel cell’s performance: optimizing the operating parameters or optimizing the design specifications [5]. Therefore, it is necessary to optimize the cell dimensions to enhance performance. Bearing that in mind, these researchers optimized the bipolar plate dimension since it is directly related to the water management and thermal management of PEM fuel cells. The results of this study revealed that the square baffled channel could produce more power than bipolar plates of other shapes, as found through the application of an ANFIS-based model.

The optimal design of PEM fuel cells has been investigated [6]. The design variables included both design parameters and operating parameters. They employed a Box–Behnken model for numerical calculations. Then, a regression model constructed via the RSM method was analyzed using the NDRG-II algorithm (non-dominated ranking genetic algorithm), and the results revealed that the proposed optimization method offered better design parameters. A novel sunflower optimization technique to select the optimized operating parameters was implemented [7]. This method was purely based on a PEMFC circuit-based model, which reduced the SSE (sum of square error) of the actual value and the estimated value. The results obtained using this model were compared against seagull optimization, shuffled frog-leaping optimization, and multiverse optimization methods and showed that the proposed method yielded better results than the other three methods.

A suitable combination of parameters of nano-coolants to maximize the performance of PEM fuel cells, such as relative humidity, thermal conductivity, and empirical coefficients, has been investigated [8]. The optimal combination was identified using a genetic algorithm. The performance of the PEM fuel cells was improved when the nano-coolant was added with an optimized thermal conductivity value. An Elman Neural Network for selecting the suitable parameters of a PEM fuel cell has been proposed [9]. After the identification of suitable parameters for PEM fuel cells, the researchers used combined algorithms, including TLBO and DE, to optimize the parameter selection. After the implementation of this method, the fuel cell could operate efficiently on the maximum output voltage and output power.

PEM fuel-cell parameters have been analyzed using a novel optimization technique called the deer-hunting optimization algorithm [7]. The operating conditions of the PEM fuel cell were analyzed under different fuel pressure conditions. The proposed optimization yielded a very fast convergence with reduced weight function when applied to a convolution neural network. The proposed optimization performed better than other conventional methods used in the state of the art. The operating conditions of the proton-exchange membrane fuel cell were optimized using the Tuguchi method, in which many operating parameters, such as operating temperature, electrode inlets, and the fuel flow channel parameters, were considered [10].

The COSMOL multiphysics environment was used to optimize the operating parameters. A novel optimization technique known as the chaos-embedded PSO algorithm was proposed for the first time to determine the unknown parameters of PEMFC [11]. A new objective function was formulated and yielded a better convergence rate. It is worth mentioning that the proposed objective function yielded the minimum error in finding the global maximum value. The polarization curve of PEMFC in which maximum performance was obtained was important [12]. The researchers used the real-time operating data of 50 cm² using a data analytical model of one-dimensional size. Here, the results were validated with real-time data, and a good agreement was found between analytical data results and real-time polarization curve data. There were 2% and 3% error deviations in obtaining maximum and minimum power between simulation and real-time experimental results, respectively.

An accurate modeling of PEMFC performance analysis is inevitable [13]. Therefore, researchers proposed the whale optimization technique, which was aimed to increase the accuracy of the predicted model and reduce the error between simulated results and data obtained from the polarization curve. After simulation and real-time data validation, it was obvious that the proposed model could perform well. The performance of PEMFC was not only altered by the operating parameters but also influenced by the material used in the electrode [2]. From that perspective, researchers analyzed the performance of PEM fuel cells with electrodes made from Cu, Al, and stainless-steel material alloys. The simulation analysis was carried out using CFD-ANSYS software, and then the results were validated through experimental work. The polarization curve obtained from this work showed the effectiveness of the material used in the electrode.

The hybrid electric vehicle is usually fed from multiple sources like solar PV and fuel cells with a battery backup. There are multiple converters adopted in the vehicle to handle different sources, which leads to many difficulties like bulk in size, occupying more space, complex control circuits, etc. To overcome these practical difficulties, a multiport DC–DC converter, which handles two input sources effectively, has been proposed in the literature [14,15,16,17,18,19]. There was power-quality improvement for a grid-connected PEMFC in which modified pelican optimization was used to generate a switching pulse to the buck converter [20]. A multiport DC–DC converter has been shown to be capable of handling clean energy resources [21]. This multiport converter could integrate with three energy resources along with a battery, and the output was isolated from the source. A novel meta-heuristic technique, known as converged collective animal behavior optimization for PEMFC operating parameters, has been proposed [22]. Pulse generation for high-voltage converters using SiC-MOSFET switches has been implemented [23].

1.3. Main Contribution to This Research

To trace the optimum power from a practical source, the converter is designed with an SFO-based MPPT controller. The output port of the DC–DC converter drives the BLDC motor through three phase inverters, as shown in Figure 1. A smooth mode transition is an inherent feature of the proposed DC–DC converter.

• The fuel cell is the most obvious choice of power source for sustainable transportation applications as it does not pollute the environment, offers high energy density, noise-free operations, etc. This research deals with the optimization of fuel-cell operating parameters, and based on that, a multiport high-gain DC–DC converter is designed for electric vehicle applications.
• To contribute to sustainable development, we worked on the PEM fuel-cell field because it is challenging to obtain constant output voltage at all times. It is necessary to optimize the operating parameters. In this context, a deep-learning neural network has been developed and trained to optimize the significant parameters.
• Regulating the DC power when it is used in electric vehicle applications is another challenge. A multiport high-gain DC–DC converter is designed along with an SFO-MPPT controller, and the performance of the power converter was experimentally validated. We hope these two objectives and their outcomes will be helpful for future researchers to work on the PEM fuel-cell field, therefore contributing to sustainable development in the transportation field.

2. Modeling of Input Sources

2.1. Physical Model of PEMFC

The electrochemistry modeling of fuel cells is more effective and advantageous than the thermodynamics model. Though the thermodynamics model has been used by researchers for theoretical performance analysis, the rate at which reactant reacts to produce electricity cannot be analyzed. Moreover, the electrochemistry model can be used to predict the loss that occurs during the chemical reaction. With that aspect in mind, the following section elucidates the electrochemical modeling of PEM fuel cells. Figure 2a shows the construction of PEMFC, and Figure 2b shows the equivalent circuit model of PEMFC.

From Figure 2b, the operating voltage of the PEM fuel cell can be written as

$$V_{o/p}=V_{ideal}-V_{act(a+c)}-V_{mass(a+c)}-V_{ohm}$$

(1)

$$V_{ideal}=-(\frac{G}{2F}+\frac{RT}{2F}\ln \frac{P_{H_{2O}}}{P_{O_2\sqrt{P_{H_2}}}})$$

(2)

a—anode, c—cathode, G—Gibbs constant, F—Faraday’s constant, R—gas constant, T—operating temperature in K, $P_{H_2}$—hydrogen pressure, P_O2—oxygen pressure, P_H2O—water pressure.

$$V_{act(a+c)}=\frac{RT}{\alpha F}\mathrm{l}\mathrm{n}\left(\frac{i_d}{i_r}\right)$$

(3)

α—coefficient of charge transfer, i_d—current density and i_r—current density corresponding to reaction exchange, i_L—limiting current density

$$V_{mass(a+c)}=\frac{RT}{\alpha F}(\frac{\mathsf{\alpha }+1}{\mathsf{\alpha }})\mathrm{l}\mathrm{n}(1-\frac{i_L}{i_d})$$

(4)

$$V_{ohm}=i{R}_{(a+c)}$$

(5)

R_(a+c)—resistance of anode and cathode. From the modeling of the PEM fuel cell, it is obvious that the operating parameters like temperature, fuel supply pressure, air supply pressure, fuel flow rate, and airflow rate decide the output voltage of the PEM fuel cell at any cost.

2.2. Physical Model of the Battery

The physical model of a lead-acid battery is depicted in Figure 3a. To understand the electrical behavior of any battery, it is essential to obtain a mathematical model of the battery. Three models of the batteries have been given in the literature [24,25], namely the equivalent circuit model, electrochemical model, and data-driven model. The equivalent circuit model (ECM) is considered to be an obvious choice because it gives good accuracy without complexity. It consists of purely electrical components like controlled voltage sources, resistors, and capacitors. Second-order ECM is a well-proven model for accuracy without complexity. It consists of one controlled voltage source representing the State of Charge (SoC) and series resistance connected with two parallel RC branches, as depicted in Figure 3b. The charging and discharging behavior of the battery can be understood by a mathematical model of the battery, as given below.

The mathematical modeling of the battery is derived as follows:

The terminal voltage of the battery is expressed as

$$V_b=V_{oc}-I_b{R}_o-V_{\left(RC\right)1}-V_{\left(RC\right)2}$$

(6)

The current flowing through the battery is written as

$$I_b=\frac{V_{\left(RC\right)1}}{R_1}+C_1\dot{V_1}=\frac{V_{\left(RC\right)2}}{R_2}+C_2\dot{V_2}$$

(7)

The voltage across each pair of RC parallels is expressed as

$$V_{\left(RC\right)1}=\left(\frac{Q}{C_1}+I_b{R}_1\right)e^{\left(-\frac{t}{R_1{C}_1}\right)}-I_b{R}_o$$

(8)

$$V_{\left(RC\right)2}=\left(\frac{Q}{C_2}+I_b{R}_2\right)e^{\left(-\frac{t}{R_2{C}_2}\right)}-I_b{R}_o$$

(9)

For the RC parallel branch, the voltage and current are related as follows:

$$\dot{V_1}=-\frac{V_{\left(RC\right)1}}{R_1{C}_1}+\frac{I_b}{C_1}$$

(10)

$$\dot{V_2}=-\frac{V_{\left(RC\right)2}}{R_2{C}_2}+\frac{I_b}{C_2}$$

(11)

Here, V_b—voltage across the battery, I_b—current through the battery, V_(RC)1, V_(RC)2—voltage across the parallel branch RC, Q—usable capacity of the battery, V_oc—voltage across the open circuit in the battery.

3. Optimization of PEMFC Operating Parameters

The modeling of PEMFC using design and operating parameters has been reviewed, and it is concluded that numerous parameters influence the output voltage of the system [26], but their contribution towards deciding the output voltage must be analyzed using machine learning for better understanding. In this experimental work, there are five parameters, namely system temperature, fuel supply pressure, air supply pressure, fuel flow rate, and airflow rate, which vary from minimum value to maximum value as given in

Table 1. The range of PEMFC operating parameters.

System Parameter	Max. Value	Min. Value
System temperature	358 K	298 K
Fuel supply pressure	2 bar	1 bar
Air supply pressure	1.5 bar	0.5 bar
Fuel flow rate	23.46 lpm	12.2 lpm
Airflow rate	4615 lpm	2400 lpm
Output voltage	25.63 V	17.06 V
Output current	1094.91 W	485.01 W

, and the corresponding output voltages and output powers are noted. To analyze the most significant factor, a certain number of parameter experiments must be conducted. Therefore, here, three levels are considered for five factors, which results in 243 data points obtained from experiments. The interaction of other parameters with the most significant factors vs. output parameters is shown in Figure 4. The importance of the parameters is analyzed using statistical analysis, and its results are depicted in Figure 5. It is found that the operating temperature is the most significant factor, whereas the airflow rate is the least significant factor among the five parameters.

3.1. Multilayer Feed-Forward Neural Network

To optimize the input parameters of a 6 kW PEMFC, a simple multilayer feed-forward neural network is taken in which one input layer with five nodes, two hidden layers with five nodes each, and one output layer with two nodes are set in the proposed network as shown in Figure 6. The relationship between input and output of the hidden layer is expressed as

$$h_{{in}_j}=b_{oj}^{hid}+\sum _{i=1}^n{x}_i{v}_{i_i}$$

(12)

The net output of the hidden layer is obtained by applying the sigmoid activation function, and the input and output of the layer is expressed as

$${ O}_{{in}_k}=b_{ok}^{Out}+\sum _{j=1}^n{h}_j{w}_{j_k}$$

(13)

The net output is obtained from the output layer by applying a linear activation function. The network is trained using an incremental back-propagation algorithm with 80% input data. During each iteration, the bias and weight are updated in the hidden and output layers using the following equation.

$${ v}_{ij\left(next\right)}=v_{ij\left(pre\right)}+∆v_{ij }$$

(14)

$${ w}_{jk\left(next\right)}=w_{jk\left(pre\right)}+∆w_{jk}$$

(15)

$${ b}_{oj\left(next\right)}^{hidd}=b_{oj\left(pre\right)}^{hidd}+∆b_{oj}^{hidd}$$

(16)

$${ b}_{ok\left(next\right)}^{Out}=b_{ok\left(pre\right)}^{Out}+∆b_{ok}^{Out}$$

(17)

h_inj and O_ink are the inputs of the hidden and output layers. b_oj and b_ok are the bias terms in the hidden and output layer. V_ij and w_jk are the connection weights of the hidden and output layers.

A linear activation function is used in the output layer to obtain the net output. The learning rate of the network is 0.8, with 0.8 as momentum, and it is trained until the root mean square error (RMSE) reaches 0.01. It takes 13 min with 10,320 iterations for learning. After successful completion of learning, it is tested with the remaining 20% of input data. The results have been stored for optimization.

3.2. Optimization of PEMFC Operating Parameters Using the Genetic Algorithm

The genetic algorithm (GA) is a meta-heuristic optimization technique that imitates the natural process of Darwin’s principle of evolution. The conventional optimization process suffered from local optimum and failed to provide accurate results, whereas GA is a global search optimization algorithm and is implemented in the following sequence of processes: selection, cross-over, and mutation. The first step in GA is to generate parental chromosomes with population size P. Each chromosome is represented as

$$P=\{X_1,X_2,X_3\dots X_n\}$$

(18)

Here, n is the number of individual chromosomes in the population size.

Each chromosome in the population is an N-dimensional vector and can be represented as

$$a_m<x_m<b_m$$

(19)

Here, a_m and b_m are the lower and upper limits of variables to be optimized, and x_m is the total number taken into account for optimization. The parent generation chromosomes are evaluated at the end of each generation with its fitness function f(X_n). After that, the cross-over process begins. Two new offspring, X_p and X_q, are produced from two random parents, X_r and X_s, and the process of cross-mating is limited by the cross-mate rate r.

$$x_{p,i}=\left(1-r\right)x_{ri}+r{x}_{si}$$

(20)

$$x_{q,i}=\left(1-r\right)x_{si}+r{x}_{ri}$$

(21)

The population size doubles at the end of the cross-over process. Then, chromosomes with high fitness values are selected among the doubled population. The mating process begins with reliable genetic diversity with a probability of 0.1. This process is repeated with newly generated chromosomes as parental chromosomes until a satisfied fitness value is attained or the required number of iterations is reached. The optimization phase is separately carried out in a neural-power software environment. The genetic algorithm is used with population size = 30, cross-over rate = 0.8, and mutation rate = 0.1 to optimize the results obtained from a multilayer feed-forward neural network. It takes less than a minute with 20,501 iterations to yield the optimized result. The maximum output voltage and power are obtained when the input parameters are set as follows: system temperature = 328 K, fuel supply pressure = 1.9998894 bar, air supply pressure = 1.4995502 bar, fuel flow rate = 19.490219 lpm, and airflow rate = 4613.4466 lpm.

4. The Multiport High-Gain DC–DC Converter

The proposed DC–DC converter consists of two input ports and one output port, as depicted in Figure 7. One input port is fed with a polymer-exchange membrane fuel cell, and the second input port is connected to a battery. There are three active switches used in the proposed converter, namely M1, M2, and AS, in which main switch M1 is operated when the fuel cell is sufficient to supply the load, and M2 is operated when the fuel cell is drained off and shut down for fuel filling. An auxiliary switch AS is operated when the fuel cell and battery are together enough to meet the demand. The load RL is supplied from the output capacitor Co. The mode of operation of the proposed converter is detailed as follows:

During Mode I operation, the fuel cell alone is sufficient to supply load, the switch M1 is turned on, and the diodes D2 and D3 cause the source inductance Ls to become charged, as shown in Figure 8. The load RL is supplied from the output capacitor Co. The steady-state equations of this mode are given below.

$$V_{FC}=L\frac{d{i}_s}{dt}+V_{Co}$$

(22)

When main switch M1 is in the OFF condition, VFC becomes zero, and the inductor Ls supplies load, as shown in the key waveforms in Figure 11a.

$$V_{Co}=-L\frac{d{i}_s}{dt}$$

(23)

During Mode II operation, hydrogen fuel is completely drained off, and it looks for a new hydrogen cylinder. In this case, the battery comes into action to drive the load. The active switch M2 is turned on during Mode II, as depicted in Figure 9a. When the main switch M2 is in the OFF condition, both diodes D1 and D2 come into conduction, as depicted in Figure 9b. When the main switch M2 is in the OFF condition, the source inductance supplies the load. The key waveforms are shown in Figure 11b.

$$V_{batt}=L\frac{d{i}_s}{dt}+V_{Co}$$

(24)

In this particular mode, both the battery and fuel cell are operated simultaneously since they are supposed to meet the demand together. In this case, all three switches, M1, M2, and AS, come into action, during which the source inductance absorbs energy from both the battery and fuel cell, as shown in Figure 10. When all three switches are in the OFF condition, diodes D1 and D2 come into action. The key waveforms are shown in Figure 11c.

$$V_{batt}+V_{FC}=L\frac{d{i}_s}{dt}+V_{Co}$$

(25)

Figure 10. Mode III operation (a) M1 and M2 are turned ON; (b) Both M1 and M2 are turned OFF.

Figure 10. Mode III operation (a) M1 and M2 are turned ON; (b) Both M1 and M2 are turned OFF.

Figure 11. (a) Key waveform of Mode I operation; (b) Key waveform of Mode II operation; (c) Key waveform of Mode III operation.

Figure 11. (a) Key waveform of Mode I operation; (b) Key waveform of Mode II operation; (c) Key waveform of Mode III operation.

5. Voltage Conversion Ratio

It is assumed that the inductance is sufficient to supply load continuously, and all semiconductor devices used in the converter are ideal. According to the voltage–time balance equation, the voltage applied across inductance over the period of time in Mode I can be expressed as

$$V_{out}\left(1-\left(M_{S1}+M_{S2}\right)\right)={(V}_{FC}-V_{out})M_{S1}+{(V}_{batt}-V_{out})M_{S2}$$

(26)

On simplifying the expression (26), the output voltage can be expressed as

$$V_{out}=V_{FC}{M}_{S1}+V_{batt}{M}_{S2}$$

(27)

Similarly, the voltage–time balance equation for the source inductance Ls for Mode II can be written as

$${(V}_{FC}+V_{batt})M_{S3}={(-V}_{FC}+V_{out})M_{S1}+{(-V}_{batt}+V_{out})M_{S2}$$

(28)

On simplifying the expression (29), the output voltage can be expressed as

$$V_{out}\left(2-\left(M_{S1}+M_{S2}\right)\right)=V_{FC}{M}_{S1}+V_{batt}{M}_{S2}$$

(29)

$$V_{out}=\frac{V_{FC}{M}_{S1}+V_{batt}{M}_{S2}}{\left(2-\left(M_{S1}+M_{S2}\right)\right)}$$

(30)

Assuming V_FC and V_batt are equal for the ideal case (V_FC = V_batt = V_in), the voltage conversion ratio can be generalized as

$$G=\frac{V_{out}}{V_{in}}=\frac{M_{S1}+M_{S2}}{\left(2-\left(M_{S1}+M_{S2}\right)\right)}$$

(31)

6. SFO Algorithm

The sunflower optimization (SFO) algorithm has recently been introduced into the engineering era to solve non-linear problems. It imitates the orientation process of sunflowers towards the Sun to obtain maximum solar irradiance for the whole day. It is a well-known global search optimization technique rather than a local search optimization one. Sunflower fertilization happens during the orientation of the sunflower towards the Sun to produce the next generation of sunflowers. For simplicity, it is assumed that one pollen comes from the sunflower during the fertilization process. The sunflower inverse square law relates solar irradiance intensity and power from the Sun, as denoted below.

$${\mathrm{I}}_{\mathrm{S}\mathrm{R}}=\frac{{\mathrm{P}}_{\mathrm{s}\mathrm{u}\mathrm{n}}}{4\mathsf{\pi }{\mathrm{r}}^2}$$

(32)

where ${\mathrm{I}}_{\mathrm{S}\mathrm{R}}$—represents intensity of solar radiation, ${\mathrm{P}}_{\mathrm{s}\mathrm{u}\mathrm{n}}$—represents Sun power, and r—distance between Sun and sunflower. The alignment of the sunflower towards the Sun is based on the following expression.

$${\mathrm{D}}_{\mathrm{j}}=\frac{{\mathrm{S}}^{\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t}}-{\mathrm{S}}_{\mathrm{j}}}{‖{\mathrm{S}}^{\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t}}-{\mathrm{S}}_{\mathrm{j}}‖}$$

(33)

where S^best—represents the best solution, and S_j—jth iteration solution. The movement of the Sun in each step of the iteration is denoted as follows.

$${\mathrm{d}}_{\mathrm{j}}=\mathsf{\delta }\times {\mathrm{P}}_{\mathrm{j}}\left(‖{\mathrm{S}}_{\mathrm{j}}+{\mathrm{S}}_{\mathrm{j}-1}‖\right)\times ‖{\mathrm{S}}_{\mathrm{j}}+{\mathrm{S}}_{\mathrm{j}-1}‖$$

(34)

where $\mathsf{\delta }$—the inertial displacement, and ${\mathrm{P}}_{\mathrm{j}}\left(‖{\mathrm{S}}_{\mathrm{j}}+{\mathrm{S}}_{\mathrm{j}-1}‖\right)$—the probability of pollination. To limit the control parameter within the control range, the following mathematical expression is followed.

$${\mathrm{d}}_{\mathrm{m}\mathrm{a}\mathrm{x}\mathrm{l}\mathrm{i}\mathrm{m}}=\frac{‖{\mathrm{S}}_{\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathrm{S}}_{\mathrm{m}\mathrm{i}\mathrm{n}}‖}{2\mathrm{j}}$$

(35)

where S_max and S_min are the maximum and minimum values of the solution, and j is the population size. The minimization of the cost function is updated for each iteration by following the below expression.

$${\mathrm{S}}_{\mathrm{j}+1}={\mathrm{S}}_{\mathrm{j}}+({\mathrm{d}}_{\mathrm{j}}\ast {\mathrm{D}}_{\mathrm{j}})$$

(36)

where ${\mathrm{S}}_{\mathrm{j}+1}$ is the new sunflower orientation, ${\mathrm{S}}_{\mathrm{j}}$ is the current position of the sunflower.

7. Simulation Results

The proposed converter is constructed using the following components listed in

Table 2. The proposed converter components.

S. No	Components Used	Symbol	Rating
1.	Power switch	M1, M2	5 A
2.	Auxiliary switch	As	2 A
3.	Diodes	D1, D2, D3	5 A
4.	Source inductor	Ls	300 µH
5.	Output capacitor	Co	230 µF (electrolytic)
6.	Load resistance	RL	100 Ω

. Both the simulation and experimental setup are constructed using the same components as given below. To analyze the results, an extensive simulation analysis has been carried out using the MATLAB/R2002a platform. In this section, a detailed analysis of the mode of operation and mode transition is clearly elucidated.

7.1. PEMFC Is Meeting the Demand Alone

A 6 kW 45 V PEM fuel cell is taken for this study. This stack contains 65 cells connected in series with nominal operating points of 133 A nominal current and 45 V open-circuit voltage, respectively. The nominal stack efficiency of this converter is around 46%. The nominal composition of hydrogen, oxygen, and water present in the air is taken in a ratio of 99:21:1. During Mode I, the fuel cell is able to meet the demand alone. As the fuel cell is fully supplied from hydrogen fuel, it can produce 45 V in the ideal case, and the same voltage is stepped up to 220 V by the proposed converter during the optimum power extraction conditions with the help of the SFO-based control technique. The duty cycle is maintained as 0.5, and the corresponding inductor current waveform is depicted in Figure 12.

7.2. Battery Is Meeting the Demand Alone

In this mode, the battery takes over demand when the fuel for PEMFC is completely exhausted. A 24 V 80 AH heavy-duty lead-acid battery is taken as the source. The charging voltage of each cell is 2.2 V/cell under high temperature, and it is 245 V/cell under low temperature. Since heat dissipation is a major concern for hybrid electric vehicle applications, it is calculated as 0.45 W/cell for 80 AH. For a long battery life-span, the ripple content must be less than 5 A. The duration of this mode must be minimal since the battery rating is low for the sake of advantages to the hybrid vehicle. The duty cycle is maintained at 0.6, which can give the output voltage of 120 V, while the input voltage supplied from the battery is 24 V. The corresponding inductor current waveform is shown in Figure 13.

7.3. Both Sources Are Meeting Demand Together

This mode comes into action when the PEMFC’s fuel is partially exhausted, it is in need of fuel filling, and the lead-acid battery is partially full enough to supply the demand. During this Mode III, both the switches, M1 and M2, are turned ON for the duty cycle of 0.5 and 0.6, respectively, which in turn conduct the auxiliary switch AS for the duty cycle of 0.1, as shown in the figure. Both input voltages (45 V, 24 V) are stepped up to 345 V, as depicted in the figure. The duration of this mode is greater than Mode II and less than Mode I. The inductor current waveform is presented in Figure 14.

7.4. Performance of SFO Controller

To verify the effectiveness of the SFO control technique in tracing maximum power from PEMFC, the operating temperature is taken as a variable parameter, as discussed in Section 3. The variation in operating temperature is as follows: 54.84 °C for the first 0.3 s, 24.85 °C for the next 0.3 s, and 84.85 °C for the next 0.3 s. During this variation in temperature, the SFO controller is supposed to generate dynamic pulses to the switches to extract high power from PEMFC. The power-tracing capability is checked against the ANN controller and variable step-size FLC-based controller, as shown in Figure 15. The proposed SFO-based controller can yield better power-tracing capability compared with the other two controllers in terms of maximum power traced and transient parameters.

8. Experimental Results

To validate the simulation results on a real-time test bench, a 0.2 kW hardware prototype was constructed in the laboratory using the hardware components listed in Table 2. The entire experimental arrangement is shown in Figure 16. A 2 kW PEMFC and 80 AH 24 V Exide-made heavy-duty lead-acid battery are used as the sources for a multiport high-gain DC–DC converter.

During Mode I, the fuel-cell voltage is stepped up to 215.6 V, and its corresponding inductor waveform is shown in Figure 17a. During Mode II, the battery voltage is stepped up to 115.6 V, and its corresponding inductor current waveform is depicted in Figure 17b. When both these sources supply demand, the corresponding output voltage is stepped up to 339.8 V, and its inductor current waveform is given in Figure 17c. The output power is measured across the load resistance 1 kΩ by adjusting from its minimum value to maximum value using the Tektronix SMU 2450 power-quality analyzer. It should be noted that the maximum power conversion efficiency is 95.12% for a 105 W load, as given in Figure 18. The various losses contributing to overall loss are measured using the same analyzer and shown in Figure 19. The performance comparison of the proposed converter is made against the state of the art, as listed in

Table 3. The performance comparison.

S. No	Reference No	Circuit Components				Peak Power Conversion η (%)	No of Ports
		No of Switches (M)	No of Diodes (D)	No of Capacitors (C)	No of Inductors (L)
1	[14]	2	2	3	2	98.41	4
2	[15]	5	9	7	9	98.12	2
3	[16]	3	4	2	1	94.80	3
4	[17]	2	2	3	2	95.13	2
5	[18]	2	8	3	5	Not reported	2
6	[19]	4	3	5	5	98.1	3
7	Proposed converter	3	3	1	1	95.12	3

. It is observed that the proposed converter can handle more than one source with a minimum number of circuit components and yield a maximum conversion efficiency.

9. Conclusions

In this research, the optimization of 6 kW PEMFC operating parameters was carried out using a neural-power software environment. The operating parameters varied, and the corresponding output voltage and output power were measured experimentally. This dataset was used for training a multilayer feed-forward neural network, and then the results obtained after testing were optimized using a genetic algorithm. It was worth mentioning that the operating temperature was the most significant parameter in deciding the performance of PEMFC. This inference led to the design of the MPPT controller, which extracts optimum power from PEMFC under variable temperatures. A multiport high-gain DC–DC converter was designed to handle two sources, namely 6 kW PEMFC and an 80 AH 24 V heavy-duty battery with a smooth transition. A meta-heuristic algorithm called an SFO-based controller was designed to obtain optimum output power from PEMFC under dynamic operating temperature. The performance of the DC–DC converter, along with the SFO-based MPPT control technique, was tested using MATLAB/R2022a software environment. To validate the real-time test bench results, a 0.2 kW DC–DC converter was designed in the laboratory, and the results were compared against the literature. Future researchers may use advanced artificial intelligence (AI) techniques to optimize the operating parameters and design a Hardware In Loop (HIL)-based operating condition management system for hybrid electric vehicle applications.

Highlights of this research work:

• The PEMFC operating parameters were optimized, and it was experimentally proven that the operating temperature is the most significant factor.
• A multiport high-gain DC–DC converter can effectively handle PEMFC and batteries with inherent smooth mode transition.
• The SFO-based MPPT control technique outperforms ANN and variable fuzzy-based controllers under dynamic operating temperature conditions.
• The maximum conversion efficiency of a multiport high-gain DC–DC converter is 95.12%, with fewer components used in the converter.