Design and development of different adaptive MPPT controllers for renewable energy systems: a comprehensive analysis

Abstract

As of now, all over the world is focusing on the Electric Vehicle (EV) technology because its features are low environmental pollution, less maitainence cost required, high robustness, and good dynamic response. Also, the EVs work continuously until the input fuel is provided to the fuel stack. Here, a Proton Exchange Membrane Fuel Cell (PEMFC) is used as an input source to the electric vehicle system because of its merits fast startup, and quick response. However, the PEMFC gives nonlinear voltage versus current characteristics. As a result, the extraction of maximum power from the fuel stack is very difficult. The main aim of this work is to study different Maximum Power Point Tracking Techniques (MPPT) for the DC-DC converter-fed PEMFC system. The studied MPPT controllers are Adjusted Step Value of Perturb & Observe (ASV with P&O), Adaptive Step Size with Incremental Conductance (ASS with IC), Radial Basis Functional Network (RBFN), Incremental Step-Fuzzy Logic Controller (IS with FLC), Continuous Step Variation based Particle Swarm Optimization (CSV with PSO), and Adaptive Step Value-Cuckoo Search Algorithm (ASV with CSA). The selected MPPT controllers’ comprehensive study has been in terms of maximum power extraction, tracking speed of the MPP, settling time of the fuel stack output voltage, oscillations across the MPP, and design complexity. From the comprehensive performance results of the hybrid MPPT controllers, the ASV with CSA technique gives superior performance when equated to the other MPPT controllers.

Introduction

As of now, the nonrenewable energy sources utilization kept on reducing because of their drawbacks are more implementation costs, excessive environmental pollution, and heavy damage to human health, wildlife, and habitat loss¹. Also, nonrenewable energy sources require a high catchment area for the installation and release the greenhouse gasses². So, most of the automotive industries are working on the development of various renewable energy systems. The most popularly used renewable energy systems are wind, solar, tidal, hydropower, and geothermal energy³. In wind power generation systems, the kinetic energy of the wind blades is converted into an electrical power supply by using the Permanent Magnet Synchronous Generator (PMSG). After collecting the electricity from the PMSG, the power converters are utilized for the conversion of direct power supply into alternative power supply. In addition, the transformer is included with power converters for enhancing the voltage profile of the grid. The features of wind power systems are very low operating cost, clean energy, effective utilization of land space, and creating more jobs for human beings⁴. The drawbacks of wind systems are noise pollution, intermittent, high environmental impact, and suitable only at remote locations. The demerits of wind power production systems are limited by utilizing the solar energy source⁵.

The solar cells convert the sunlight photo energy into useful electrical power. Every cell gives only 0.78–0.95 V which is not useful for local load applications⁶. So, the solar cells are integrated in parallel and series sequence to improve the supply power rating of the solar system. The working nature of solar cells is quite equal to the P-N diode operation. The features of solar systems are diverse applications, reduced electricity bills, less maitainence cost, plus ease of maintenance⁷. The drawbacks of this power generation system are weather dependent, needs a high catchment area for installation, and its working performance depends on environmental pollution. So, the above drawbacks of solar, and wind energy systems are limited by using fuel cell technology⁸. A fuel stack is a device that transfers chemical energy into an electrical power supply by the use of electrochemical reactions. In the fuel cell, the oxygen and hydrogen atoms are reacted with each other and generate power along with the water and heat as the byproducts⁹. The fuel cells give very little pollution and also give more than two times the efficiency of the other renewable energy systems. Based on the operating temperature, the fuel cells are classified as low operating temperature (25–100 °C) fuel cells, medium operating temperature fuel cells (100–500 °C), plus high operating temperature fuel cells (500–1000 °C).

For all the types of fuel stacks, the utilized input fuels are hydrogen, low hydrocarbons, alcohols, hydrazine, metal hydrides, and high hydrocarbons. The supplied input fuel is oxidized at the anode chamber, and the oxidant is reduced at the cathode side. Inside the fuel stack, one species of ions is shifted from anode to cathode via electrolyte to combine these with their counterparts¹⁰. The available electrons flow through the external circuit to generate the electrical current. In¹¹, based on the type of electrolyte, the researchers explained the different categories of fuel stacks which are Solid Oxide Fuel Stack (SOFS), Molten Carbonate Fuel Stack (MCFS), Alkaline Fuel Stack (AFS), and Phosphoric Acid Fuel Stack (PAFS). Certain solid material has the property to conduct electricity at very high temperatures and it works as an electrolyte for the solid oxide-based fuel stack. In¹², the authors selected the SOFS for supplying the power to the auxiliary power storage application. High operating temperature-based solid oxide cells give pollution-free, and clean energy to supply the electrical energy to the local consumers with high operating efficiency¹³. The merits of this solid oxide cell over traditional power supply systems are high reliability, modularity, high input fuel adaptability, and good functioning efficiency. Also, this fuel cell releases very less amount of nitrous oxide and solid dioxide.

Here, due to the high temperature withstand stability of the solid oxide fuel cell, the natural gas is formed inside the fuel stack. As a result, the expensive external reformer is not required in the SOFS. The high-operating pressurized SOFS is used as a combustor in the gas power generation system. The SOFS-based gas turbine electricity supply network’s maximum functioning efficiency is 70%. In¹⁴, the researchers developed the advanced solid oxide cell which is a combination of sealing fewer properties of a tubular cell with integral ribs, and a flatted air electrode. This tubular cell-based SOFS consists of a concise current path. So, the resistance of the solid oxide cell is very low, and more output power over the other fuel cells. The main feature of SOFS is noise-less operation. The drawback of SOFS is high startup time because of its high operating temperature¹⁵. As a result, many chemical and mechanical compatibility issues occur in the solid oxide cell. The applications of solid oxide fuel cells are emergency backup power supply, transportation systems, submarine systems, and rockets. Also, most of the utility vehicles are implemented by utilizing the solid oxide membrane-based fuel stack¹⁶.

From the literature study, the reduction of carbon footprint utilization has been done by using molten carbonate fuel cells¹⁷. Due to this MCFS, the amount of carbon dioxide released from nonrenewable energy sources is reduced. The features of MCFS are highly efficient, and cleaner over to the traditional power supply networks. Also, most of the MCFS are used in stationary applications because of their compact, less noise pollution. In¹⁸, the authors studied the photovoltaic systems along with the MCFS for generating power for all local consumers. Here, the power is equally shared along with the inverters and step-up transformers. This hybrid power network is useful for supplying continuous power to all hospitals as well as shopping malls. In this hybrid power system, the per-unit cost of the solar system is two times of the MCFS power supply. Also, the molten carbonate cell gives slightly higher profits when equated to the solar modules. However, the reduction of operational, and maitainence costs is a challenging task in the MCFS. Also, the natural gas price in the MCFS is very high. To overcome the disadvantages of molten carbonate cells, in¹⁹, the researchers used the PAFS along with the solar, plus wind power system for supplying the power to the microgrid network. Phosphoric acid cells a one of the most popular fuel stacks that are used for food drier systems to protect the food from various chemicals²⁰. In this PAFS, the electrolyte is developed with highly concentrative phosphoric acid along with the silicon carbide. The functioning temperature of this cell is between 150 and 210 °C. The electrodes of the PAFS are developed by utilizing the carbon cloth coating. Finally, the dispersed catalyst is used in the PAFS.

The phosphoric acid fuel cells are used in 100–400 kW stationary applications, backup power supply for industrial as well as commercial applications, residential buildings, and remote accessible areas²¹. The demerits of PAFS are less power density and a very aggressive electrolyte. Also, the PAFS works with very high startup time. As a result, this fuel stack is not useful for emergency power applications. The disadvantages of PAFS are limited by utilizing the AFS. The alkaline cells are anionic exchange membrane fuel cells that are used to replace the liquid electrolyte alkaline cells. Also, different manufacturers developed advanced alkaline catalyst material that has high thermal stability and gives very good performance²². The peak current density and power density of alkaline fuel stacks are 100–300 mA/cm², and 50–300 mW/cm² respectively. The lifetime of this fuel cell is greater than 5000 h, and its degradation rate is 3–20 µV/h²³.

Here, the anode of the alkaline fuel stack is designed by using platinum, and nickel. Similarly, the cathode is implemented by utilizing the Manganese dioxide. At the anode, the platinum catalyst breaks the alkaline liquid into alkaline ions for supplying the electricity to the external load circuit, and the nickel cathode collects the anode ions which are converted into waste chemicals. The features of alkaline fuel stacks are less operating temperature capability, easy handling, and very good operating efficiency²⁴. Also, this AFS is used in the Apollo space mission application. The disadvantages of AFS are high manufacturing cost, and lack of infrastructure to support the hydrogen distribution. However, the above fuel cell drawbacks are overcome by using the PEMFS. The attractive features of PEMFS are fast startup and quick response²⁵.

The polymer membrane fuel stacks give nonlinear voltage versus current characteristics²⁶. Also, the functioning point of the fuel stack changes from one point to another point on the V-I characteristics of the fuel stack at different water membranes, and operating temperature conditions. So, the peak power extraction from the fuel stack is highly difficult. At this time, the MPPT controller plays an important role in stabilizing the maximum power point of the fuel stack at various water membrane conditions²⁷. As a result, the overall fuel stack system supplies constant power to the electric vehicle load. From the previously published articles, the MPPT technologies are differentiated as traditional, artificial intelligence, metaheuristics, and soft computing methods. The most popular traditional MPPT technologies are Perturb & Observe (P&O)²⁸, fractional current, Incremental Conductance (IC)²⁹, fractional voltage, Incremental Resistance (IRR), and Ripple Correlation Method (RCM). In³⁰, the researchers utilized the P&O concept for a standalone DC–DC converter-fed fuel array system to vary the duty cycle of the interleaved converter thereby enhancing the load voltage profile of the electric vehicle system. Here, the P&O is investigated along with the Proportional and Integral (PI) controller in terms of steady-state oscillations of the fuel cell output voltage, converter voltage gain, and oscillations of MPP under different water membrane conditions of the fuel stack. From the simulation results, the authors concluded that the P&O methodology gives better performance when equated to the PI controller.

Similarly, in³¹, the researchers introduced the drift-free P&O controller for improving the voltage extraction capability of the fuel stack at dynamic water membrane conditions. The P&O controller tracks the MPP by equating the instantaneous slope value of the V–I curve with the previously stored slope value. The comparative slope value consists of a positive indication then the perturbation moves in the front direction. Otherwise, the perturbation of the P&O controller moves in the backward direction. This process continues until the functioning point of the fuel stack comes to the one stable position on the V–I curve of the fuel stack. However, this MPPT method does not give an accurate MPP position and also gives an oscillated MPP position because of the improper decision made by the P&O controller at dynamic operating water membrane conditions of the fuel stack³². So, the drift-free P&O methodology is used in the 100 W standalone fuel stack system to eliminate the disadvantages of a basic P&O controller. The drawbacks of drift-free P&O methodology are less convergence speed and more time for reducing the oscillations of MPP. So, the fractional current power point tracking controller is used in the PV/PEMFS hybrid power generation system for identifying the functioning point of the overall power supply network³³. The merits of this controller are fast-tracking speed, very low cost, easy handling, and very good static response. But it gives a less accurate MPP position. So, the entire system gets affected by the heat and conduction losses.

The fractional voltage-based PI controller is utilized in the hybrid grid-connected fuel stack system to maintain the voltage stability of the grid at diverse water membrane conditions of the fuel stack system³⁴. In this method, a separate switch is required for evaluating the open circuit voltage of the fuel stack. Here, the open circuit fuel stack voltage is measured by the shutdown of the entire system. As a result, the hybrid system gives a very bad dynamic response. So, the IRR MPPT concept is used in the article³⁵ for reducing the oscillations of MPP. In this method, the current density function is utilized for moving the functioning point of the fuel stack near the actual MPP position³⁶. At the starting point of the fuel stack V–I curve, the variation of the current density value is positive then the functioning point of the fuel stack goes in the forward direction. If the operating point of the fuel stack reaches the global MPP position then the current density function value is zero. The merits of an IRR controller are fast static and dynamic response when equated to the traditional MPPT techniques³⁷. The fuel stack-fed multiphase DC-DC converter circuit generates fluctuated output current ripples and voltage ripples which are sent to the RCM block for identifying the suitable operating duty cycle of the DC-DC converter. Due to this controller operation, the entire system’s heat conduction losses are reduced. As a result, the operating and maitainence costs of the fuel stack are reduced extensively³⁸. The drawbacks of this controller are less applicable for quick changes in the operating temperature conditions of the fuel stack and needs high space for installation.

The fractional order variable step value-based IC power point identifier is applied to the PEMFS power supply system for effective tracking of the fuel stack MPP. Here, the main aim of the variable step fractional order IC controller is improving the steady state as well as dynamic response of the PEMFS at quick changes in water membrane conditions³⁹. The merits of this controller are good tracking speed, a smaller number of sensing devices required for sensing the fuel stack parameters, and extracting the maximum power of the fuel stack thereby enhancing the overall system efficiency. As a result, the PEM fuel stack system input fuel utilization is reduced. So, this controller reduces the maintenance and installation cost of the entire power supply network⁴⁰. The Hill Climb Controller (HCC) working is quite similar to the large perturbation size-based P&O method. Here, in this HCC, there are different perturbation step size values are selected which are the high perturbation step, and the low perturbation step. The high perturbation step concept is utilized at the beginning stage of the HCC operation to enhance the convergence speed of the controller⁴¹. After that, the perturbation step value is reduced to eliminate the distortions of converter output voltage. The disadvantages of these traditional controllers are less MPP tacking speed, and may not be applicable for quick changes of water membrane conditions of the fuel stack.

In⁴², the authors focused on the conventional neural network controller for estimating the fuel stack output power thereby generating the suitable duty cycle to the three-phased z-source power converter. Here, the input signals fed to the artificial intelligence controller are oxygen consumption, hydrogen decomposition, utilized temperature, and the Faraday constant of the fuel stack. The features of neural network-based MPPT controllers are fast response, required less formal statistical training, and the capability to handle highly complex nonlinear issues. However, the neural network drawbacks require high training time, plus highly knowledgeable candidates are required to operate the controller⁴³. In this work, there are various types of hybrid MPPT controllers are studied for generating the optimum duty cycle to the conventional boost converter and which are compared in terms of fuel stack output voltage, converter output voltage, fuel stack output current, converter output current, the efficiency of MPPT controller, settling time of the load voltage, number iterations required to track the MPP, and design complexity of the controller⁴⁴. Here, these hybrid controllers overcome the disadvantages of traditional, and soft computing controllers. The detailed differentiation of all types of MPPT methodologies is illustrated in Fig. 1 The utilized fuel module technology is mentioned in Fig. 2.

Fig. 1

Types of power point identifying controllers for PEMFC.

Fig. 2

Detailed utilization of polymer cell under quick variation of temperatures.

The fuel stack gives very high-level output currents. Due to this, the system power conduction losses are increased extensively⁴⁵. So, there are various categories of power DC–DC converters are used to improve the voltage profile rating of the induction motor-fed fuel stack system⁴⁶. The major classification of power converters are non-isolated, and isolated power converters. All the isolated converters needed separate transformers, and rectifiers. In addition, these converters needed more space for installation. Also, the manufacturing cost of the isolated converters is very high. From the literature survey, the generally isolated converters consist of an output load that is separated from the input signal and are classified as bridge-type forward converters and flyback converters⁴⁷. In a forward converter, the load voltage gain mainly depends on the input transformer. The features of a forward converter are galvanic isolation, multiple outputs, and the ability to provide low as well as high output voltage supplies simultaneously. However, the major disadvantage is the high cost of implementation. In the article⁴⁸, the authors referred to the flyback technology for DC–DC power conversion. The flyback converter is capable of accommodating the non-isolated and isolated formations. However, the drawbacks of the isolated converter are less operating efficiency, very high leakage current, and high sensitivity to operating temperature. So, in this work, a conventional non-isolated DC–DC converter is utilized for optimizing the overall cost of the PEMFS-fed non-isolated converter system. The features of this converter are less space required for installation, more efficiency, and high flexibility.

Mathematical implementation of PEM fuel stack

Present non-renewable sources reduction, and environmental considerations, the fuel cell stacks are acting as renewable energy systems for supplying electricity to electric vehicle systems. Most of the fuel stacks’ input source is H₂ which is produced from the various biological sources⁴⁹. The major H₂ production methodologies are steam reforming of CH₄ and Coke. In steam reforming of methane, the CH₄ chemical is reacted with the water at 800 °C⁵⁰. As a result, the hydrogen, plus carbon monoxide chemical compounds are generated. The combined chemical composition of hydrogen and carbon monoxide is sent to the cooling compression chamber to separate the pure hydrogen content. Similarly, in the steam reforming of coke, the coke is combined with the water in the presence of nickel catalyst at 1000 °C to produce the carbon monoxide, and hydrogen⁵¹. The general features of hydrogen are tested less, odorless, colorless, and lightweight gas.

In this work, the PEMFC is used as a source for the electric vehicle load. The input source of PEMFC is hydrogen which is sent to the anode of the fuel stack. The proton-conducting polymer is worked as an electrolyte in the PEMFS. The chemical reactions of the polymer membrane fuel stack are explained in Fig. 3(a), and its resultant circuit is given in Fig. 3(b). The PEMFS is designed by using the polymer membrane electrolyte. The utilized electrolyte consists of different layers which are diffusion layer, catalyst layer, anode, plus cathode chambers. In this fuel stack, the paper-type carbon is covered by both anode and cathode electrodes to protect the PEMFS from the higher operating temperature conditions. The major observation of this fuel stack is polymer membrane is not conducting electrically. Also, the PEMFS works at 100 °C temperature for the effective utilization of the hydrogen.

Fig. 3

Utilized polymer membrane electrolyte fuel stack, (a). Chemical reactions, plus (b). Equalized circuit of the fuel stack.

From Fig. 3(a), the direct combination of O₂, and H₂ generates the heat energy. Here, the hydrogen moves near the anode chamber and it separates into hydrogen ions and electrons. The resultant hydrogen ions move from the anode chamber to the cathode chamber. The available electrons in the PEMFS are collected by using an external circuit. The proposed PEM fuel stack chemical reactions are derived as,

$$\:{\text{H}}_{2}\to\:2{\text{H}}^{+}+2{\text{e}}^{-}$$

(1)

$$\:2{\text{H}}^{+}+2{\text{e}}^{-}+\frac{1}{2}{\text{O}}_{2}\to\:{\text{H}}_{2}\text{O}$$

(2)

$$\:{\text{H}}_{2}+\frac{1}{2}{\text{O}}_{2}\to\:{\text{H}}_{2}\text{O}+\text{E}$$

(3)

From the equivalent circuit of the fuel stack, the single cell output voltage is represented as V_FC which mainly depends on the three types of fuel stack resistors which are concentrative (R_Co), active polarization resistors (R_Ac) plus ohmic resistors (R_Oh). The voltage drops across the three resistors, and the open circuit voltage of the fuel stack is represented as active voltage (V_Ac), ohmic voltage (V_Oh), concentrated voltage (V_Co), and thermodynamic voltage (V_otv). Finally, there is a total N number of fuel cells interconnected to generate the high output voltage which is represented as V_total.

$$\:{\text{V}}_{\text{t}\text{o}\text{t}\text{a}\text{l}}=\text{N}\text{*}{\text{V}}_{\text{F}\text{C}}$$

(4)

$$\:{\text{V}}_{\text{F}\text{C}}={\text{V}}_{0\text{t}\text{v}}-{\text{V}}_{\text{O}\text{h}}-{\text{V}}_{\text{C}\text{o}}-{\text{V}}_{\text{A}\text{c}}$$

(5)

$$\:{\text{V}}_{\text{O}\text{t}\text{v}}=1.29-0.8{\text{e}}^{-3}\left({\text{T}}_{\text{F}\text{o}\text{p}}-298.12\right)+4.3{\text{e}}^{-5}\text{In}({\text{P}}_{{\text{H}}_{2}}\sqrt{{\text{P}}_{{\text{O}}_{2}}}){\text{T}}_{\text{F}\text{o}\text{p}}$$

(6)

$$\:{\text{P}}_{{\text{H}}_{2}}=\frac{1}{2}{\text{H}\text{V}}_{\text{A}}\text{*}{\text{P}}_{{\text{H}}_{2}\text{O}}^{\text{s}\text{a}\text{t}}\left(\frac{1}{\frac{{\text{H}\text{V}}_{\text{A}}{\text{*}\text{P}}_{{\text{H}}_{2}\text{O}}^{\text{s}\text{a}\text{t}}}{{\text{P}}_{\text{A}}}\text{exp}\left(\frac{1.65({\text{I}}_{\text{c}\text{e}\text{l}\text{l}}/\text{A})}{{\text{T}}_{\text{F}\text{o}\text{p}}}\right)}\right)$$

(7)

$$\:{\text{P}}_{{\text{O}}_{2}}=\frac{1}{2}{\text{H}\text{V}}_{\text{C}}\text{*}{\text{P}}_{{\text{H}}_{2}\text{O}}^{\text{s}\text{a}\text{t}}\left(\frac{1}{\frac{{\text{H}\text{V}}_{\text{C}}*{\text{P}}_{{\text{H}}_{2}\text{O}}^{\text{s}\text{a}\text{t}}}{{\text{P}}_{\text{C}}}\text{exp}\left(\frac{4.12\text{*}({\text{I}}_{\text{c}\text{e}\text{l}\text{l}}/\text{A})}{1.22\text{*}{\text{T}}_{\text{F}\text{o}\text{p}}}\right)}\right)$$

(8)

$$\:{\text{V}}_{\text{A}\text{c}}={\text{g}}_{1}+{\text{g}}_{2}{\text{T}}_{\text{F}\text{o}\text{p}}+({\text{g}}_{3}+{\text{g}}_{4}){\text{T}}_{\text{F}\text{o}\text{p}}\text{log}({\text{C}}_{{\text{O}}_{2}}+{\text{I}}_{\text{F}\text{C}})$$

(9)

$$\:{\text{V}}_{\text{C}\text{o}}=-\frac{\text{R}\text{*}{\text{T}}_{\text{F}\text{o}\text{p}}}{\text{N}\text{F}}\text{In}(1-\frac{\text{X}}{{\text{X}}_{\text{m}\text{a}\text{x}}})$$

(10)

$$\:{\text{V}}_{\text{O}\text{h}}={\text{I}}_{\text{c}\text{e}\text{l}\text{l}}\text{*}({\text{R}}_{\text{e}\text{f}}+{\text{R}}_{\text{p}\text{f}})$$

(11)

$$\:{\text{C}}_{{\text{O}}_{2}}=\frac{{\text{P}}_{{\text{O}}_{2}}}{5.08{\text{e}}^{6}*\text{exp}(-498/{\text{T}}_{\text{F}\text{o}\text{p}})}$$

(12)

$$\:\text{X}=\frac{{\text{I}}_{\text{c}\text{e}\text{l}\text{l}}}{\text{A}}$$

(13)

$$\:{\text{R}}_{\text{e}\text{f}}=\frac{{{\upgamma\:}}_{\text{e}\text{f}}\text{Q}}{\text{A}}$$

(14)

$$\:{{\upgamma\:}}_{\text{e}\text{f}}=\frac{181.6\:\left[1+0.01\text{X}+0.52\text{*}({\text{T}}_{\text{F}\text{o}\text{p}}/303{)}^{2}{\text{*}\text{X}}^{2.5}\right]}{(\text{W}-0.634-3\text{X})\text{exp}(\frac{4.02({\text{T}}_{\text{F}\text{o}\text{p}}-304)}{{\text{T}}_{\text{F}\text{o}\text{p}}})}$$

(15)

Where T_Fop, P_H2, and P_O2 are indicated as operating fuel stack temperature, hydrogen partial pressure, plus oxygen partial pressure. The terms HV_A, HV_c, P_A, P_C, plus P_H2O are represented as anode humidity vapor, relative humidity vapor at the cathode, anode partial pressure, cathode partial pressure, plus water pressure of the fuel stack. Here, the empirical coefficients are indicated as g₁, g₂, g₃ plus g₄. Finally, the parameters I_FC, F, X, and A are each cell current, faraday constant, overall stack current, and fuel stack chamber area. In the diffusion layer, the oxygen concentration is determined by using Eq. (12). From Eq. (15), the effective resistance of the single cell, and the overall resistance of the fuel stack are represented as r_ef, plus R_ef. The PEMFS design parameters are given in Table 1, and also the proposed fuel stack power versus current nonlinear characteristics are shown in Fig. 4.

Fig. 4

(a) Fuel stack generated V–I curve. (b). Fuel stack generated P–I curve.

Table 1 Detailed design parameters of the proton exchange membrane fuel stack.

Design, and investigation of controllers

Due to the nonlinear characteristics of the fuel stack, the maximum power extraction from the source is very difficult. So, the MPPT technology plays an important role in tracking the fuel stack MPP position at different water membranes, and operating temperature conditions⁵². Also, from section “Introduction”, it is identified that the general power point tracing methodologies are not suitable for rapid changes in operating temperature conditions of the fuel stack. The conventional MPPT controllers’ disadvantages are high output voltage fluctuations, more time for extracting the maximum output voltage, high convergence time, plus needed a greater number of sensing devices. The limitations of conventional controllers are overcome by using the advanced MPPT controllers which are ASV with P&O⁵³, ASS with IC⁵⁴, RBFN⁵⁵, IS with FLC⁵⁶, CSV with PSO⁵⁷, and ASV with CSA.

Adjusted step value-based P&O MPPT technique

As we know the general P&O method is useful only for constant operating temperature conditions of the fuel stack, and it is applied where the accuracy of MPPT is not necessary. This controller’s disadvantages are high oscillations across MPP, high power conduction losses, less life span of the system, plus less efficiency. Also, this controller depends on the initial working conditions of the PEMFS⁵⁸. In article⁵⁹, the authors focused on the ASV-P&O method which is implemented by using the different steps which are system modeling, power loop control, step constant variation, performance evaluation, and stability. In the system modeling step, the PEMFC characteristics are studied. In the second step, the power loop control continuously adjusts the overall system impedance to track the fuel stack MPP. Here, the PEMFS voltage is perturbated to enhance the power rating of the fuel stack. The advantages of the adjusted step value-based P&O MPPT technique are moderate oscillations across MPP, fast system response, plus high efficiency when equated to the conventional P&O controller⁶⁰. Based on Eq. (16), when the functioning point of the fuel stack is lying on the last corner of the P–I curve then the duty value of the DC-DC converter is improved to move the operating point of the fuel stack near to the actual MPP position. Otherwise, the duty cycle of the converter is reduced which is given in Eq. (17).

$$\:{\updelta\:}\left(\text{t}\right)=\:{\updelta\:}(\text{t}-1)+{\upalpha\:}\left(\frac{\text{p}\left(\text{t}\right)-\text{p}(\text{t}-1)}{\text{v}\left(\text{t}\right)-\text{v}(\text{t}-1)}\right)$$

(16)

$$\:{\updelta\:}\left(\text{t}\right)=\:{\updelta\:}\left(\text{t}-1\right)-{\upalpha\:}\left(\frac{\text{p}\left(\text{t}\right)-\text{p}(\text{t}-1)}{\text{v}\left(\text{t}\right)-\text{v}(\text{t}-1)}\right)$$

(17)

Where the parameters $\:{\updelta\:}\left(\text{t}\right)\:,\:\text{a}\text{n}\text{d}\:{\updelta\:}\left(\text{t}-1\right)$ are the instant duty cycle, plus the previous duty cycle. Here ^‘α^’ is an adjustable constant parameter that is used to adjust the duty value. Similarly, the parameters v(t), p(t), v(t–1) & p(t–1) are the present and previous voltages and powers of the fuel stack.

Adaptive step size with incremental conductance

One of the most commonly used conventional MPPT controllers is IC which is applied in traffic signal control systems. The IC concept implementation has been done by utilizing the nonlinear V-I characteristics of the fuel stack. Here, the system conductance is varied continuously until the functioning point of the fuel stack reaches the actual MPP position⁶¹. In article⁶², the adjusted step value-based IC controller is used in the electric vehicle-fed fuel stack system for running slip ring induction machines under continuous changes of water membrane content of the fuel stack. Here, the water electrolysis concept is used for supplying H₂ to the fuel cell banks, and the fuel stack electrodes are designed using copper materials. In this ASS-IC controller, the equivalent impedance of the fuel stack is used for identifying the optimum duty value of the interleaved DC–DC converter. The adjustment of the converter duty cycle by using this MPPT controller is given in Eq. (18), and Eq. (19)⁶³.

$$\:\Psi\left(\text{t}\right)=\Psi\left(\text{t}-1\right)+\text{k}\text{*}\left(\frac{\text{P}\left(\text{t}\right)-\text{P}(\text{t}-1)}{\text{V}\left(\text{t}\right)-\text{V}(\text{t}-1)}\right)$$

(18)

$$\:\Psi\left(\text{t}\right)=\Psi\left(\text{t}-1\right)-\text{k}\text{*}\left(\frac{\text{P}\left(\text{t}\right)-\text{P}(\text{t}-1)}{\text{V}\left(\text{t}\right)-\text{V}(\text{t}-1)}\right)$$

(19)

Where the terms $\:\Psi\left(\text{t}\right)\:\&\:\Psi(\text{t}-1)$ is the present duty value, and past duty cycle parameters and their related power changes are represented as p(t), and p(t-1). Finally, the evaluated fuel stack past and instant voltages are v(t−1), and v(t).

Radial basis functional network-based MPPT controller

Mostly, the ANN is used in nonlinear decision-making problems applications⁶⁴. These networks are implemented from the inspiration of biological neurons, and the ANN is designed from the combination of activation functions, mathematical operations, and optimization methodologies. In the article⁶⁵, the RBFN model neural controller is interfaced in the automotive fuel stack system to improve the dynamic behavior of EVs⁶⁶. The RBF networks have the capability of approximation of complex functions, good modeling of nonlinear relationships, plus capturing the complex patterns from the available data to determine the accurate MPP position of the fuel stack. The RBF-related power point identifying the network working nature is illustrated in Fig. 5. Based on Fig. 5, the radial function is used as an activation function for obtaining the desirable duty to the DC–DC converter circuit. The RBF demonstrates the smooth transition from the center point to the surroundings of the neurons to adapt to the source space very efficiently. Based on available data sets, the RBF interpolates the input-output relations, and it generalizes the input-output relations for non-available data. The major advantage of RBF is its high computational efficiency.

Fig. 5

RBFN work process for PEMFC-based power supply system.

$$\:\text{n}\text{e}{\text{t}}_{\text{T}}^{\left(1\right)}={\text{S}}_{\text{T}}^{1}\left(\text{x}\right);\text{x}=\text{1,2},\text{3,4},...,\text{n}$$

(20)

$$\:{\text{H}}_{\text{L}}^{\left(1\right)}\left(\text{x}\right)={\text{f}}_{\text{T}}^{\left(1\right)}\left(\text{n}\text{e}{\text{t}}_{\text{T}}^{\left(1\right)}\left(\text{x}\right)\right)=\text{n}\text{e}{\text{t}}_{\text{T}}^{1}\left(\text{x}\right);\:\text{T}=\text{1,2},3$$

(21)

$$\:\text{n}\text{e}{\text{t}}_{\text{Y}}^{\left(2\right)}\left(\text{x}\right)=-(\text{S}-{{\upmu\:}}_{\text{Y}}{)}^{\text{T}}\text{*}{\sum\:}_{\text{Y}}(\text{S}-{{\upmu\:}}_{\text{Y}})$$

(22)

$$\:{\text{H}}_{\text{Y}}^{\left(2\right)}\left(\text{x}\right)={\text{f}}_{\text{Y}}^{\left(2\right)}\left(\text{n}\text{e}{\text{t}}_{\text{Y}}^{\left(2\right)}\right(\text{x}\left)\right);\text{Y}=\text{1,2},\text{3,4},....,9$$

(23)

$$\:{{\upmu\:}}_{\text{Y}}=\left[\begin{array}{ccccc}{{\upmu\:}}_{1\text{Y}}&\:{{\upmu\:}}_{2\text{Y}}&\:{{\upmu\:}}_{3\text{Y}}&\:.\dots\:\dots\:&\:{{\upmu\:}}_{\text{T}\text{Y}}\end{array}\right]$$

(24)

$$\:{\sum\:}_{\text{Y}}=\text{d}\text{i}\text{a}\text{g}\left[\begin{array}{ccccc}\raisebox{1ex}{$1$}\!\left/\:\!\raisebox{-1ex}{${\text{ɳ}}_{1\text{Y}}^{2}$}\right.&\:\raisebox{1ex}{$1$}\!\left/\:\!\raisebox{-1ex}{${\text{ɳ}}_{2\text{Y}}^{2}$}\right.&\:\raisebox{1ex}{$1$}\!\left/\:\!\raisebox{-1ex}{${\text{ɳ}}_{3\text{Y}}^{2}$}\right.&\:.\dots\:\dots\:&\:\raisebox{1ex}{$1$}\!\left/\:\!\raisebox{-1ex}{${{\upsigma\:}}_{\text{L}\text{M}}^{2}$}\right.\end{array}\right]$$

(25)

$$\:\text{n}\text{e}{\text{t}}_{\text{U}}^{\left(3\right)}={\sum\:}_{\text{U}}{\text{W}}_{\text{Y}}{\text{H}}_{\text{Y}}^{2}\left(\text{x}\right);\text{x}=\text{1,2},\text{3,4},5,.....,\text{n}$$

(26)

$$\:{\text{O}}_{\text{U}}^{\left(3\right)}\left(\text{x}\right)={\text{f}}_{\text{U}}^{\left(3\right)}\left(\right(\text{n}\text{e}{\text{t}}_{\text{U}}^{3}\left(\text{x}\right))=\text{n}\text{e}{\text{t}}_{\text{U}}^{3}(\text{x})$$

(27)

Where the terms T, U, and Y are the first layer, output layer, plus middle layers. The variables $\:{\text{S}}_{\text{T}}^{1}\left(\text{x}\right),$$\:\text{n}\text{e}{\text{t}}_{\text{T}}^{\left(1\right)}\left(\text{x}\right)$ represents the net value of the source layer, and its corresponding output signal. The total selected data samples are identified as ‘x’. The $\:{\text{H}}_{\text{L}}^{\left(1\right)}\left(\text{x}\right)$, $\:{\text{H}}_{\text{Y}}^{\left(2\right)}\left(\text{x}\right)$ gives the center layer the first, and second node overall input signal. The hidden layer output net value is determined as $\:\text{n}\text{e}{\text{t}}_{\text{Y}}^{\left(2\right)}\left(\text{x}\right)$. The variables ‘S’, $\:{\upmu\:}$, $\:\text{ɳ},$$\:\text{W},$ and $\:\text{O}$ are indicated as input vectors, the mean value of the signal, controller coefficient, neuron weight, and required RBF output signal.

Incremental step-fuzzy logic controller

The radial functions have certain drawbacks which are high training complexity. Especially, the training of large data sets and multidimensional input parameters is very difficult. The overfitting problem occurs in RBF networks due to the number of radial basis functions. Selection of suitable radial basis functions is a challenging task for the greater number of radial functions. In the article⁶⁷, the fuzzy controller is integrated into the Z-circuit converter-fed fuel stack system to enable the peak power supply of PEMFC at diverse water membranes, and operating temperature conditions⁶⁸. The fuzzy is formed from the mathematical framework which especially deals the impression and uncertainty. Also, the fuzzy handles the linguistic variables and terms to allow the experts to represent their expertise naturally. The fuzzy systems are easily adapted for various multidimensional problems. The features of fuzzy are high flexibility, best suitable for dynamic environmental conditions, and high robustness for handling noisy, and incomplete data⁶⁹. Also, this system works inherently for uncertainty issues, and it consists of more transparency, plus provides high interpretability.

In a fuzzy MPPT block, there are different blocks integrated which are fuzzification of input parameters, execution of various rules of the controller, plus defuzzification of output variables to crisp value for finding the error parameter of the system⁷⁰. The fuzzy controller for the MPPT application is given in Fig. 6, and its rules and membership functions are stated in Fig. 6. The error variables of fuzzy are given in Eq. (28). From Fig. 6, the fuzzy adapts the continuous variation of EV fed fuel stack temperature, and it traces the functioning point of PEMFC on P-I curve with high convergence speed. Here, the fuzzy membership functions are chosen based on the application of optimization techniques. The fuzzy does not involve any mathematical formulas⁷¹. So, the entire controller implementing cost, and size are reduced. The efficiency of fuzzy MPPT is high when equalized with the neural network because of the multiple-step value selection on the V–I curve. The fuzzy enhances the duty of the converter because the working point of PEMFC is the right-side corner of the actual MPP or else, the duty is varied in a descending fashion to reduce the fluctuations of load power.

$$\:\text{e}\left(\text{n}\right)=\frac{\text{P}\left(\text{n}\right)-\text{P}\left(\text{n}-1\right)}{\text{V}\left(\text{n}\right)-\text{V}\left(\text{n}-1\right)}\:;\:{\Delta\:}\text{e}\left(\text{n}\right)=\text{e}\left(\text{n}\right)-\text{e}\left(\text{n}-1\right)$$

(28)

Fig. 6

Improved fuzzy MPPT for fuel stack application.

Continuous step variation-based PSO MPPT controller

Sometimes, fuzzy systems are more complex because they need more rules and membership functions. So, the entire controller design, plus maintenance cost is increased⁷². In a hybrid fuel stack/PV power supply, the PSO controller is applied for the continuous improvement of the efficiency of the converter. PSO is one of the metaheuristic swarm controllers that can be used for solving any nonlinear issue of the fuel stack⁷³. Also, all the fuel stacks are highly complex, plus nonlinear systems. The fuel cells involve many conflicting requirements which are minimum fuel usage, maximizing the available power, plus optimizing the environmental emissions. The PSO handles the multiple objectives of PEMFS at continuous changes in the working temperature of the fuel stack. In the initial stage of PSO, all the swarm agents’ weights are given by applying the random probability technique. Here, all the agents work cooperatively, and a single agent is represented as one particle⁷⁴.

At the first iteration of PSO, all the agents move away from the required object in various directions with different velocities. After completing certain iterations, the agents try to come near the required target position. In the search process, all the agents exchange their information to extract the peak voltage of the fuel stack⁷⁵. The agent’s successive velocity (V), and its associated position (y) are varied based on Eq. (29), plus (30). The MPPT tracking process using PSO is given in Fig. 7.

$$\:{\text{V}}^{\text{s}+1}=\text{W}\text{*}{\text{V}}_{\text{k}}^{s}+{\text{L}}_{1}{\text{g}}_{1}\left({\text{P}}_{\text{b}\_\text{k}}-{\text{Y}}_{\text{k}}^{\text{s}}\right)+{\text{L}}_{2}{\text{g}}_{2}\left({\text{G}}_{\text{b}\_\text{k}}-{\text{Y}}_{\text{k}}^{\text{s}}\right)$$

(29)

$$\:{\text{Y}}^{\text{s}+1}={\text{Y}}_{\text{k}}^{\text{s}}+{\text{V}}_{\text{k}}^{\text{s}+1}$$

(30)

Fig. 7

Continuous step value adjustment of PSO controller for PEMFC system.

Where, the variables V^s+1, and Y^s+1 are adjusted velocities, plus the position of agents. The terms ^‘s^’, ^‘k^’, P_{b_k,} and G_{b_k} have selected iterations, particle number, each iteration’s best global position, and the global position of MPP after completing all the iterations⁷⁶. The constraints L₁, and L₂ are acceleration factors. Similarly, the variables g₁, and g₂ are particle random values.

Adaptive step value-cuckoo search algorithm

One of the known metaheuristics’ optimization methods is cuckoo search controllers which are implemented from the breeding nature of cuckoos⁷⁷. This algorithm solves all types of optimization issues, especially in global optimization where the search space is very high. In this technique, there are three conditions involved which are in the initial iteration each cuckoo should give one egg after that in the second condition, all available eggs have more quality then the controller moves to the next condition or else it goes into the previous condition⁷⁸. The algorithm starts initializing the all-cuckoos weights randomly in the overall search space. Each egg gives a solution for the particular optimization issue. Here, each cuckoo egg is identified by applying the fitness function. The main objective of the fitness function is identifying good quality cuckoo eggs. Another major parameter of CS MPPT is levy flight which is incorporated for initializing the random walk of cuckoos⁷⁹. Also, the levy is useful for the deciding step value of the cuckoos in the multidimensional search region. After applying levy flights, there are a few cuckoos laying their eggs in the host nest⁸⁰.

The CS controller selects the best solution from the available solution. A good solution for cuckoos is to have the chance to go to the next iteration⁸¹. To eliminate the overcrowding of nests, the diversity of the population is continued, and some of the worst solutions are removed from the search space for achieving potentially good solutions. The application of adaptive CS MPPT for the fuel stack system is illustrated in Fig. 8. From Fig. 8, the voltage supplying of the fuel stack, and power of the converter circuit are determined at the initial stage of the adaptive CS MPPT controller. Later, the cuckoos start searching for the required object of the system with the speed (V)⁸². The continuous updating of solutions has been done by applying multiple iterations, and various levy flights. The levy limits of the CS technique are derived in Eq. (31). The parameters$\:\:\text{\S\:}$, s, q, X, plus Y are represented as operating constant, number iterations, cuckoo length, and distribution curves. Also, parameters a, and b are the levy flight sizes⁸³.

$$\:\text{L}\text{e}\text{v}\text{y}\:\left(\text{\S\:}\right)={\text{L}\text{e}\text{n}\text{g}\text{t}\text{h}}^{-\text{\S\:}}\:;\:1.5<\text{\S\:}<3.5$$

(31)

$$\:{\text{q}}_{\text{j}}^{\text{s}+1}={\text{q}}_{\text{j}}^{\text{s}}+{\upalpha\:}\oplus\:\text{l}\text{e}\text{v}\text{y}\left(\text{\S\:}\right)\:$$

(32)

$$\:\text{l}={{\upalpha\:}}_{0}\left({\text{q}}_{\text{b}\text{e}\text{s}\text{t}}-{\text{q}}_{\text{j}}\right)\oplus\:\text{l}\text{e}\text{v}\text{y}\left(\text{\S\:}\right)\approx\:\text{c}\left(\frac{\text{u}}{{\text{v}}^{\raisebox{1ex}{$1$}\!\left/\:\!\raisebox{-1ex}{$\text{\S\:}$}\right.}}\right)\text{*}\left({\text{q}}_{\text{b}\text{e}\text{s}\text{t}}-{\text{q}}_{\text{j}}\right)$$

(33)

$$\:\text{X}=\text{a}\left(0,\:{{\uprho\:}}_{\text{u}}^{2}\right),\:\:\:\text{Y}=\text{b}\left(0,\:{{\uprho\:}}_{\text{v}}^{2}\right)$$

(34)

Fig. 8

Improved adaptive CS controller for rapid change of fuel stack temperature.

Design of conventional boost DC–DC converter

All the fuel stacks supply very low voltages. So, the output of PEMFC is enhanced by interfacing the DC–DC converter. From the previously existing articles, the isolated converter circuits needed high design costs⁸⁴. Also, these converters need more additional components which are transformers, and rectifier circuits. Due to the additional requirement of the converter, the entire fuel cell power system size is increased. This is undesirable for electric vehicle-fed fuel stacks. So, the conventional non-isolated converter circuit is integrated with the fuel cell to enhance the working efficiency of PEMFC⁸⁵. The general boost converter circuit is frequently used in many applications because of its advantages are easy to design, more flexibility, fewer components required for implementation, optimal size, plus easy understanding and operation. The working stages of this converter circuit are given in Fig. 9(a), (b), and (c)⁸⁶. The step-up of fuel cell voltage is obtained by the application of the MPPT controller which is mentioned in Eq. (35). From Fig. 9, the consumer load current is given in Eq. (36). Based on Eqs. (35), and (36), the current plus voltage conversion ratios are determined which are given in Eq. (37).

$$\:{\text{D}\text{T}}_{\text{p}}\text{*}{\text{V}}_{\text{F}\text{C}}+\left(1-\text{D}\right){\text{T}}_{\text{p}}\text{*}\left({\text{V}}_{\text{F}\text{C}}-{\text{V}}_{0}\right)=0$$

(35)

Fig. 9

DC–DC Converter circuit, (a). block diagram, (b). switch working, plus (c). switch blocking stage.

$$\:-{\text{I}}_{0}\text{D}\text{*}{\text{T}}_{\text{P}}+(\left({\text{I}}_{\text{F}\text{C}}-{\text{I}}_{0}\right)\text{*}\left(1-\text{D}\right){\text{T}}_{\text{p}}=0$$

(36)

$$\:{\text{V}}_{0}=\raisebox{1ex}{${\text{V}}_{\text{F}\text{C}}$}\!\left/\:\!\raisebox{-1ex}{$(1-\text{D})$}\right.\:\&,\:{\text{I}}_{0}={\text{I}}_{\text{F}\text{C}}\left(1-\text{D}\right)\:\:\:$$

(37)

Where T_p, and D are the switching period and converter duty value. Similarly, the terms I₀, plus V₀ are the load currents and voltages.

Analysis of summation results

The resistive load boost converter circuit is integrated with the PEMFC to improve the power supply capacity of the load with less power conduction losses. The entire system investigation has been done by the use of the MATLAB Simulink tool. Here, the polymer-type fuel stack is selected for the power supply of peak load demand. This fuel stack takes hydrogen, and water for the production of electrons. The selected rated power of the stack is 1.26*10³ W, and its supply voltage is 24.23 V. The current flow through the circuit is 52 A which can be optimized by using the DC–DC converter. The fuel stack output capacitor value C_v is 38 µF that is maintained constant supply voltage under rapid changes in fuel stack temperatures. Also, this capacitor optimizes the ripples of fuel stack power thereby enhancing the performance of the entire power supply system. The load capacitor C_w value is 23 µF, and it is helpful for the consumer to maintain the uninterruptable load voltage.

Analysis of MPPT controllers at static 270 K temperature

Here, under the forward stage of a switch, the diode goes into the blocking stage, and the entire supply energy is stored in the inductor L_V. In the second stage, the switch (S) goes off-stage then the diode conducts with supply voltage. Here, the MOSFET is selected for analysis of the DC–DC converter circuit. The features of this device are high input resistance, the switch works very fast manner, less power absorption, plus less output resistance. Also, this device works in both depletion and enrichment mode operations. The ASV with P&O and ASS with IC controllers fed fuel stack system give the maximum power, plus currents are 362.84 W, 24.5 A, 451.98 W, plus 27 A respectively. The obtained current, plus the voltage of the PEMFC system are explained in Fig. 10(a), and (b). The evaluated fuel stack power by interfacing the RBFN, IS with FLC, plus CSV with PSO is 494.13 W, 531.88 W, plus 555.80 W as given in Fig. 10(c). From Fig. 10(c), the resistive load connected to ASV with the CSA controller extracts more power from the PEMFC which is equal to 567.82 W. The supply voltage of PEMFC is increased by the application of CSV with PSO, and ASV with CSA controller. The DC-DC converter circuit is fed to the load and its related voltage, plus powers by the application of ASV with P&O, ASS with IC, RBFN, IS with FLC, CSV with PSO, plus ASV with CSA techniques are 108.5 V, 294.25 W, 118.07 V, 349.48 W, 123.05 V, 375.42 W, 127.21 V, 400.717 W, 128.004 V, 409.86 W, 128.93 V, plus 416.18 W. The application of MPPT controllers for the converter current and voltage improvement is given in Fig. 10(d), and (e). From Fig. 10(f), the generated converter power by utilizing ASV with CS is very high when equated to the ASV with P&O, RBFN, and IS with FLC techniques. The converter voltage and PEMFC system MPP oscillations are more for the application of ASV with a P&O controller. The evaluated parameters of various MPPT controllers for the DC–DC converter circuit fed fuel stack system are given in Table 2.

Fig. 10

PEMFC, (a). Current, (b). Voltage, (c). Power, (d). DC–DC current, (e). DC–DC voltage, and (f). DC–DC power under the static functioning temperature of the fuel stack.

Table 2 Simulative results analysis of different power point identifying methods under quick variation of fuel stack temperatures.

Analysis of MPPT controllers at dynamic temperatures (270 K, 300 K, and 330 K)

The PEMFC system is studied at fast changes in temperature values by the integration of different MPPT blocks. The fuel stack MPP tracking speed by the use of ASV with P&O, ASS with IC, RBFN, IS with FLC, CSV with PSO, plus ASV with CSA controllers at 270 K are 0.081 s, 0.102 s, 0.11 s, 0.127 s, 0.1281 s, plus 0.1288 s. The conventional ASS with IC, plus ASV with P&O controllers’ implementation, and design complexity is quite less than the other power point identifying controllers. At 300 K, the fuel stack, and DC-DC converter circuit available currents, and voltages by applying the CSV with PSO, and ASV with CSA are 37.29 A, 22.8 V, 4.02 A, 152.79 V, 38.09 A, 22.98 V, 4.089 A, plus 153.98 V respectively. At dynamic temperature states of the fuel stack, the supply current, plus voltage waveforms of the PEMFC system are illustrated in Fig. 11(a), and (b). There are multiple types of power point determine controllers utilized for the improvement of the output power of PEMFC under dynamic functioning temperatures as given in Fig. 11(c).

Fig. 11

PEMFC, (a). Current, (b). Voltage, (c). Power, (d). DC–DC current, (e). DC–DC voltage, and (f). DC–DC power under the dynamic functioning temperature of the fuel stack.

Based on Fig. 11(c), the settling time of fuel power is high for the application of ASV with the P&O technique. Also, this ASV with P&O methodology is not useful for supplying the constant current to the load as mentioned in Fig. 11(d). The converter generated voltage and its related powers are mentioned in Fig. 11(e), and (f). From the converter circuit, current waveforms at 330 K by utilizing the ASV with CSA, and CSV with PSO consist of fewer distortions. Also, their tracking speeds under static as well as fast variations of fuel stack functioning temperatures are high which are evaluated as 0.1273 s, and 0.1277 s respectively. Here, the swarm optimization methodologies’ design complexity is moderate. However, these techniques are needed for optimizing the oscillations of fuel stack voltages thereby minimizing the working power and heating losses are decreased extensively. The conventional may not give a good dynamic response because of their accuracy in MPP finding and required high maitainence cost.

Conclusion

The proposed PEMFS-fed ASV with a CSA-based MPPT controller is designed by using the MATLAB/Simulink tool. Here, in the first objective, the PEMFS is selected for the comprehensive analysis of different nature-inspired optimization controllers. The features of PEMFS are high-temperature withstand ability, high operating efficiency, less weight, high scalability, plus more life span. However, the drawback of PEMFS is the high output current. In the second objective, the DC–DC converter circuit is used to optimize the fuel stack output current and increase the fuel stack output voltage. However, the converter needed a suitable duty signal which is generated by using the MPPT controller. Finally, in the third objective, there are different types of MPPT controllers are analyzed in terms of maximum power extraction, settling time of the converter output voltage, oscillations across MPP, convergence speed of the MPPT controller, and implementation complexity. From the comprehensive summary, the ASV with CSA-based MPPT controller is giving high tracking speed of MPP, and high efficiency when compared to the other MPPT controllers.

Future scope of the work

The present studied MPPT controllers have the limitations of moderate MPP tracking accuracy, and less convergence speed when the total number of iterations are required very high at continuous changes of operating temperature conditions of the polymer exchange membrane fuel stack. In the future, the nature-inspired PSO, and ASV with CSA-based MPPT controllers’ hybridization has been done along with the conventional controller to increase the MPP tracking accuracy and find the optimum duty cycle of the DC–DC converter.