1 Introduction

From the continuous increment of fossil fuels cost and its less availability, most of the automotive industries are focusing on alternative energy sources which are ultra-capacitors, batteries, and fuel cells (Fu, et al. 2021). The features of fuel cell power generation systems are less noise, a long lifetime period, high energy density, less CO2 emission, and high-efficiency when compared to the solar and wind power generation systems. In addition, it does not affect the environmental conditions and gives a continuous power supply to the electric vehicle during all spells as long as fuel is offered. From the literature survey (https://www.marketsandmarkets.com/Market-Reports/fuel-cell-market-348.html), it is clearly observed that the fuel cell demand is increasing every year. From the world fuel cell market survey, the fuel cell power generation cost may reach 848 million US dollars by 2025. Based on the kind of electrolyte substance recycled, the fuel cells are characterized as Photonic Ceramic Fuel Cell (PCFC), Direct Methanol Fuel Cell (DMFC), Zinc Air Fuel Cell (ZAFC), Phosphoric Acid-based Fuel Cell (PAFC), Proton Exchange Membrane Fuel Cell (PEMFC), Alkaline Fuel Cell (AFC), and Solid Oxide Fuel Cell (SOFC) (Zakaria, et al. 2021).

Among all of the fuel cells, the PEMFC is the most popular and predominately used for electric vehicle application and distributed energy systems in order to meet the required load demand. In addition, the merits of the PEMFC stack are low corrosion, small in size, easy to construct, less working temperature, fast start-up, and very high power density (Alaswad, et al. 2021). The PEMFC stack gives nonlinear voltage versus current characteristics, and it consists of a unique operating power point. The operating point varies based on the fragmentary pressure of hydrogen. In order to maintain the operating point constant at the peak power point, an MPPT method is applied in article (Mallick and Mukherjee 2020) for enhancing the performance of the fuel cell stack.

At present, most of the research scholars focusing on computational intelligence-based MPPT techniques for solving the nonlinear issues of PEMFC-based power generation system (Salvado, et al. 2021). The merits of these techniques are more flexible, easy to implement, and highly robust when compared to the other conventional MPPT techniques. In this work, an Improved Beta-Fuzzy Logic Controller (IBeta-FLC) is proposed and it is compared with other hybrid fuzzy logic-based MPPT controllers in terms of tracing speed, fuel cell output power, and settling time of converter output voltage. The compared power point tracking methods are Variable Step Size Perturb and Observe (VSS-P&O), Radial Basis Functional Network (RBFN), Fuzzy Logic Controller-based Variable Step Size Incremental Conductance (FLC-VSSIC), and Fuzzy Logic Controller-based Improved Hill Climb (FLC-IHC). The fuel cell output voltage (VFC) and current (IFC) are given to the proposed hybrid MPPT controller in order to find out the required duty cycle of the boost converter.

The PEMFC stack gives a high output current and less output voltage which is not desirable for industrial loads and electric vehicle applications. So, the fuel cell stack cannot be directly connected to the load. The high step-up circuit topology is placed in between the source and load in order to improve the fuel cell output power. For limiting the disadvantages of conventional boost converters, in this work, a single switch, universal input voltage, wide input and output operation-based boost converter is introduced (see in Fig. 1) to improve the power transfer efficiency of a fuel cell stack system.

Fig. 1
figure 1

Block diagram of PEMFC fed single switch transformerless UIBC system

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2 Literature survey

From the literature survey (Naseri, et al. 2018), the most frequently used MPPT method is Perturb & Observe (P&O). In this technique, the trial and error process is recommended to extract the extreme power of the fuel cell stack. At each and every point on V-I characteristics, the sensors are used to determine the PEMFC stack voltage and current. After that, the calculated power is compared with the existed power. If the change of power consists of the + ve sign, then it perturbs in the same direction or, otherwise, the perturbation has been done in the opposite way. The demerits of P&O technique are compensated by applying an Incremental Conductance (IC) power point tracing method.

In IC technique, the PEMFC power is perturbed by using the instantaneous conductance of the fuel cell. Here, the slope of the V-I curve is considered to trace the MPP of fuel cell. At MPP, the slope of the V-I curve is zero and it is + ve when the working point of PEMFC is left side of the V-I curve. Otherwise, it is −ve when the working point is on the right side of the MPP (Harrag and Messalti 2017). The drawback of this method is high design complexity when compared to the P&O.

In article (Shetty and Chakrasali 2020), a Hill Climb (HC) method is applied to transfer the maximum power of the PEMFC stack from source to load. The working principle of this method is similar to the conventional P&O. Here, the fuel cell voltage (VFC) is used as a reference variable for obtaining the required duty value of the dc–dc converter. The drawback of this method is excessive power loss at the time of step change of power. So, an Improved Beta-Fuzzy Logic Controller is proposed for the effective operation of fuel cell stack.

Another drawback of fuel cell is low output voltage. So, different kinds of dc-dc boost converters are used to improve the power transfer capability of PEMFC stack and which are organized as isolated boost converters and non-isolated boost converters. The major drawback of solid oxide-based fuel cell power generation system is high installation cost. A low cost isolated boost converter is used in article (Török, et al. 2019) to reduce the overall fuel cell power generation cost. The drawback of this converter is high design complexity. In article (Zhou, et al. 2019), a quasi-Z source, and isolated boost converter is used in a fuel cell distribution power generation system to increase the power density of the system.

However, the isolated boost converters are having the drawbacks of high implementation cost, and more complexity in design. In addition, it requires an additional high switching frequency transformer to eliminate the DC-link between the source and load. So, the drawbacks of the isolated converters are overcome by using the non-isolated boost converters. The merits of non-isolated boost converters are less cost, compact in size, and high efficiency (Garrigós et al. 2019).

In article (Villarreal-Hernandez, et al. 2020), an Interleaved Double Dual (IDD), non-isolated dc-dc converter, is used in fuel stack-based electric vehicle application. The merits of this converter are high voltage conversion ratio and less switching losses. Here, an interleaved concept is used to solve the issue of low output voltage plus high output current of PEMFC stack. The drawback of this converter is pulsating output current and high voltage stress on power switches. To overcome the drawbacks of IDD boost converter, a cascaded two-phase interleaved and two level boost converters are used in article (Ma, et al. 2019) to increase the voltage conversion ratio of a fuel stack. The drawback of this topology is required high number of power semiconductors.

In article (Thounthong, et al. 2021), a high step-up, switched inductor, multiphase, and an interleaved dc-dc converter is explained to obtain the continuous output power of the fuel cell-based hybrid distribution power generation system. A multi-switch, an interleaved dc-dc converter is used in the PEMFC to enhance its dynamic response (Habib et al. 2017). In addition, the authors analyzed the performance of 5 kW fuel cell fed boost converter system at different operating temperature circumstances. From the software and hardware results, the authors says that the multi-switch converter voltage conversion ratio is improved when its corresponding duty cycle is increased.

In article (Youn, et al. 2020), the authors investigated the hybrid, interleaved boost converters at Discontinuous Conduction Mode (DCM) of operation for the application of fuel cell-based induction motor drive system. From the performance results, the authors says that the proposed converter is operating effectively and efficiently at DCM of operation. The drawback of this converter is high conduction losses. Here, a SSUIBC is proposed and it is implemented by interconnecting a circuit (D2C3L2) in middle of the basic dc–dc converter and consumer load (R0). The interfaced network acts as a filter and it is used to suppress the capacitor voltage distortions and inductor current ripples. In addition, it improves voltage profile of the converter and reduces the voltage stress across the power semiconductor devices. From Fig. 1, it is clearly observed that the input supply terminal of the converter is connected to the output negative terminal. As a result, the parasitic capacitance is bypassed to remove the undesirable leakage currents.

3 Modelling of PEM fuel cell

The PEM fuel cell is an electrochemical instrument which translates the chemical energy into electrical energy. The block diagram of PEM fuel cell plus its electrical equivalent circuits are shown in Fig. 2a and b (Kurnia, et al. 2021). It comprises the three main parts which are anode, cathode and electrolyte. The electrolyte is inserted in middle of the anode plus cathode. The electrolyte is designed by using a polymer electrolyte membrane. From Fig. 2a, it is clearly given that the hydrogen (H2) and oxygen (O2) are the inputs to the fuel cell stack. The hydrogen and oxygen are compressed and humidified with the help of air compressor and humidifier.

Fig. 2
figure 2

a Working principle of PEM fuel cell. b Equivalent circuit of PEM fuel cell stack

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The pressurized hydrogen gas flows toward the anode is divided into protons and electrons. The electrons are transferred from anode to the outside circuit for generating the electricity. The protons flow from the anode to cathode via electrolyte membrane layer which reacts through the oxygen atoms to harvest the heat and water. From Fig. 2a, the anode and cathode side chemical reactions are derived as follows (Banham, et al. 2018):

$$ {\text{H}}_{2} \Rightarrow 2{\text{H}}^{ + } + 2{\text{e}}^{ - } $$
(1)
$$ 2{\text{H}}^{ + } + 2{\text{e}}^{ - } + \frac{1}{2}{\text{O}}_{2} \Rightarrow {\text{H}}_{2} {\text{O}} $$
(2)
$$ {\text{H}}_{2} + \frac{1}{2}{\text{O}}_{2} \Rightarrow {\text{H}}_{2} {\text{O}} + {\text{energy}} $$
(3)

The total voltage generation of the fuel cell stack is determined by using Eq. (4).

$$ V_{{{\text{total}}}} = nV_{{{\text{FC}}}} $$
(4)

where ‘n’ indicates the total number fuel cells in the PEMFC stack and ‘VFC’ is each cell output voltage which is derived as (Ijaodola et al. 2019),

$$ V_{{{\text{FC}}}} = E_{{{\text{Octv}}}} - V_{{{\text{Ohmic}}}} - V_{{{\text{Active}}}} - V_{{{\text{Concen}}}} $$
(5)

where ‘EOctv’ is the open circuit thermodynamic voltage which is derived as follows:

$$ E_{{{\text{Octv}}}} = 1.29 - 0.8e^{ - 3} \left( {T_{{{\text{FCop}}}} - 298.12} \right) + \lambda $$
(6)
$$ \lambda = 4.3e^{ - 5} *\log (P_{{{\text{H}}_{2} }} \sqrt {P_{{{\text{O}}_{2} }} } )T_{{{\text{FCop}}}} $$
(7)

where TFCop is the fuel cell operating temperature. The partial pressure of hydrogen \((P_{{{\text{H}}_{2} }} )\) and oxygen \((P_{{{\text{O}}_{2} }} )\) is derived as follows:

$$ P_{{{\text{H}}_{2} }} = \frac{1}{2}RH_{{{\text{Ano}}}} P_{{{\text{H}}_{2} {\text{O}}}}^{{{\text{sat}}}} \left( {\frac{1}{{\frac{{RH_{{{\text{Ano}}}} *P_{{{\text{H}}_{2} {\text{O}}}}^{{{\text{sat}}}} }}{{P_{{{\text{Ano}}}} }}*\exp \left( {\frac{{1.6*(I_{{{\text{cell}}}} /A)}}{{T_{{{\text{FCop}}}} }}} \right)}}} \right) $$
(8)
$$ P_{{{\text{O}}_{2} }} = \frac{1}{2}RH_{{{\text{Cat}}}} P_{{{\text{H}}_{2} {\text{O}}}}^{{{\text{sat}}}} \left( {\frac{1}{{\frac{{RH_{{{\text{Cat}}}} *P_{{H_{2} O}}^{{{\text{sat}}}} }}{{P_{{{\text{Cat}}}} }}*\exp \left( {\frac{{4.1*(I_{{{\text{cell}}}} /A)}}{{1.33*T_{{{\text{FCop}}}} }}} \right)}}} \right) $$
(9)

where RHAno, and RHCat are the relative humidity vapors at anode and cathode. Similarly, PAno and PCat are the inlet pressures of anode and cathode, respectively. Finally, ‘A,’ ‘Icell,’ and \(P_{{{\text{H}}_{2} {\text{O}}}}^{{{\text{sat}}}}\) are the electrode area, fuel cell current, and saturation pressure of water vapor, respectively. The active, ohmic, and concentration polarization losses are derived as follows:

$$ V_{{{\text{Active}}}} = C_{1} + C_{2} T_{{{\text{FCop}}}} + (C_{3} + C_{4} )T_{{{\text{FCop}}}} * \log (C_{{{\text{O}}_{2} }} + I_{{{\text{cell}}}} ) $$
(10)
$$ V_{{{\text{Concen}}}} = - \frac{{RT_{{{\text{FCop}}}} }}{nF}\log \left( {1 - \frac{j}{{j_{\max } }}} \right) $$
(11)
$$ V_{{{\text{Ohmic}}}} = I_{{{\text{cell}}}} * (R_{{{\text{ef}}}} + R_{{{\text{pf}}}} ) $$
(12)

From Eq. (10), C1, C2, C3, and C4 are the empirical coefficients of each fuel cell. The concentrated oxygen \((C_{{O_{2} }} )\) is derived as follows:

$$ C_{{{\text{O}}_{2} }} = \frac{{P_{{{\text{O}}_{2} }} }}{{5.08e^{6} *\exp ( - 498/T_{{{\text{FCop}}}} )}} $$
(13)

Similarly, from Eqs. (12), and (13), the current density (j) and electron flow equivalent resistance (Ref) are derived as follows:

$$ j = \frac{{I_{{{\text{cell}}}} }}{A} $$
(14)
$$ R_{{{\text{ef}}}} = \frac{{\gamma_{{{\text{ef}}}} *Q}}{A} $$
(15)

From Eq. (15), the membrane specific resistivity is derived as follows:

$$ \gamma_{{{\text{ef}}}} = \frac{{181.6\left[ {1 + 0.03j + 0.62(T_{{{\text{FCop}}}} /303)^{2} j^{2.5} } \right]}}{{(W - 0.634 - 3j)*\exp \left( {\frac{{4.18(T_{{{\text{FCop}}}} - 303)}}{{T_{{{\text{FCop}}}} }}} \right)}} $$
(16)

The parameters used for the design of PEMFC system are given in Table 1, and its polarization curve is given in Fig. 3.

Table 1 PEM fuel cell stack design parameters
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Fig. 3
figure 3

PEM fuel cell voltage versus current characteristics

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4 Design and analysis of MPPT Techniquies

The working behavior of fuel cell is mainly depending on the parameters: hydrogen, oxygen, applied load variations, and fuel cell operating temperature. Here, the hybrid MPPT techniques are discussed and compared for improving the efficiency of PEM fuel cell stack at different working temperature conditions. The compared MPPT techniques are classified as VSS-P&O (Harrag and Rezk 2021), RBFN (Zhang and Wang 2018), FLC-VSSIC (Aly and Rezk 2020), FLC-IHC (Alajmi, et al. 2010), and IBeta-FLC-based MPPT techniques. The comparative analysis has been done in terms of steady-state oscillations across MPP, maximum power output, sensing parameters, tracking speed, rising time of output power, and power conversion efficiency.

(a). VSS-P&O-based MPPT technique for fuel cell stack.

From the literature survey, the P&O is a most popular and conventional power point tracing technique because of its attractive features are easy to design and high simplicity. The major drawback of this technique is not suitable for diverse temperature conditions of PEMFC stack. In article (Harrag and Rezk 2021), a VSS-P&O is applied to trace the required peak power point of the fuel cell. Here, at starting, a high perturbation step is applied to the PEMFC in order to reach the operating point of fuel cell closer to the true MPP. Finally, less perturbation step size is used to find out the real MPP with high accuracy.

(b). RBFN-based MPPT technique for fuel cell stack.

From the literature survey (Zhang and Wang 2018), Artificial Neural Networks (ANN) are the information processing networks and which are used to design the computational complex systems. The ANN consist of multiple neurons and which are interconnected in the form of layers. At the time of training, the fuel stack information is distributed to all over the neurons in order to start the learning process of the network.

In article (Lin-Kwong-Chon, et al. 2019), a RBFN is used in neural network to trace the MPP of the fuel cell stack. The RBFN involving three layers which are input layer, middle layer, and production layer. The structure of RBFN is shown in Fig. 4. The fuel cell generated voltage (VFC) and output current (IFC) are given to RBFN input layer, and its output is given to the middle layer. The number of hidden layer neurons is chosen based on the realistic process. The training of RBFN has been done in two steps which are supervised learning and unsupervised learning. The unsupervised learning is functional to the input constraints and which are controlled by using radial basic functions. From Fig. 4, the net input and output of an input layer is derived as follows:

$$ {\text{net}}_{p}^{(1)} = x_{p}^{1} (k);\;k = 1,2 $$
(17)
$$ y_{p}^{(1)} (k) = f_{p}^{(1)} ({\text{net}}_{p}^{(1)} (k)) = {\text{net}}_{p}^{1} (k);\;k = 1,2 $$
(18)

where \(x_{p}^{1}\) indicates the input layer and it consist of a fuel cell output voltage \((x_{1}^{1} = V_{{{\text{FC}}}} )\), and output current \((x_{2}^{1} = V_{{{\text{FC}}}} )\). The input layer net and output are indicated as \({\text{net}}_{p}^{1}\) and \(y_{p}^{1}\). Similar to the input layer, the net input and output of hidden layer are derived as follows:

$$ {\text{net}}_{q}^{(2)} (k) = - (X - \mu_{q} )^{T} * \sum\nolimits_{q} {(X - \mu_{q} )} $$
(19)
$$ y_{q}^{(2)} (k) = f_{q}^{(2)} ({\text{net}}_{q}^{(2)} (k));q = 1,2,3,4, \ldots ,k $$
(20)
Fig. 4
figure 4

Radial basic functional network MPPT controller, (Lin-Kwong-Chon, et al. 2019)

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The terms \(\sum {_{q} }\) and \(\mu_{q}\) are the Gaussian function and standard mean, respectively.

$$ \sum\nolimits_{q} = {\text{ diag}}\left[ {\begin{array}{*{20}c} {{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {\sigma_{1q}^{2} }}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${\sigma_{1q}^{2} }$}}} & {{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {\sigma_{2q}^{2} }}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${\sigma_{2q}^{2} }$}}} & {....} & {...} & {{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {\sigma_{kq}^{2} }}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${\sigma_{kq}^{2} }$}}} \\ \end{array} } \right] $$
(21)
$$ \mu_{q} = \left[ {\begin{array}{*{20}c} {\varepsilon_{1q} } & {\varepsilon_{2q} } & {....} & {...} & {\varepsilon_{kq} } \\ \end{array} } \right] $$
(22)

The final layer has a single neuron, and it gives a controlled output signal by using a linear activation function in order to generate the optimum duty cycle of the boost converter. The net and output of the final layer are derived as (Srinivasan, et al. 2021) follows:

$$ {\text{net}}_{r}^{(3)} = \sum\nolimits_{q} {W_{q} y_{q}^{2} (k)} ;\quad k = 1,2, \ldots ,n $$
(23)
$$ y_{r}^{(3)} (k) = f_{r}^{(3)} (({\text{net}}_{r}^{3} (k)) = {\text{net}}_{r}^{3} (k) $$
(24)

The matrix form of the input (x) and output (y) signals is given to the RBFN controller, and their corresponding orders are 700 by 2 and 700 by 1.

$$ [x] = \left[ {\begin{array}{*{20}c} {x_{1} } & {x_{2} } & {x_{3} } & {, \ldots ,x_{n}^{{}} } \\ \end{array} } \right] $$
(25)
$$ [y] = \left[ {\begin{array}{*{20}c} {y_{1} } & {y_{2} } & {y_{3} } & {, \ldots ,y_{n}^{{}} } \\ \end{array} } \right] $$
(26)

The input layer process the entire inputs, and it gives a output which is derived as follows:

$$ z = \left( {x - x_{\min } } \right)\left( {\frac{{y_{\max } - y_{\min } }}{{x_{\max } - x_{\min } }}} \right) + y_{\min } $$
(27)

The bias (b) and weights (W) are determined by using a supervised learning. The output of the hidden and output layers are calculated as follows:

$$ h = (zw + b)*\log ({\text{sigmoid}}) $$
(28)
$$ z = \left( {h - y_{\min } } \right)\left( {\frac{{y_{\max } - y_{\min } }}{{x_{\max } - x_{\min } }}} \right) + x_{\min } $$
(29)

The error signal of the output layer is derived as follows:

$$ {\text{error}} = \sum {\frac{1}{2}\left( {V_{{\text{dc - ref}}} - V_{{{\text{MPP}}}} } \right)} $$
(30)

where Vdc-ref is the required reference voltage and VMPP is the peak voltage of fuel cell.

(c). FLC-VSSIC-based MPPT technique for fuel cell stack.

As discussed previously, the conventional fixed step size IC MPPT technique is having a drawback of high steady-state oscillations, less convergence speed, high settling time of MPP, less efficiency, and high implementation complexity (Harrag and Messalti 2018). In addition to that, it is not useful for dynamic temperature condition of fuel cell. In article (Aly and Rezk 2020), a fuzzy logic controller is used in order to decide and vary the step size of the IC MPPT technique. As a result, the tracking speed of the MPP is increased. The block diagram of FLC-based VSSIC MPPT controller is shown in Fig. 5.

Fig. 5
figure 5

FLC-based VSSIC MPPT controller for PEMFC stack system

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From Fig. 5, the term dPFC is defined as the variation of fuel cell output power which is calculated by multiplying the variation of fuel cell output voltage (dVFC) and the current (dIFC). The slope (SP) of V-I curve and old step value (ST-old) are the inputs to the fuzzy controller, and its output is the new step value (ST-new) which is given to the IC technique in order to obtain the optimum duty cycle of the boost converter. The FLC consist of three fuzzy sub-sets (small, medium, and large), and nine rules which are shown in Figs. 6 and 7. The fuzzy rules are formed to minimize the slope of the V-I curve.

Fig. 6
figure 6

Membership functions of FLC, a Input slope (SP), b Input old step (ST-old), and c. Output new step (ST-new)

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Fig. 7
figure 7

FLC rules for VSSIC MPPT technique

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Here, the Mamdani’s max–min combination is used to decide the step size of IC technique. If the operating point of the PEMFC stack is at the left side of MPP, then the duty cycle of the SSUIBC is updated by using Eq. (31). Otherwise, Eq. (33) is used to adjust the duty value of the boost converter.

$$ D(k) = D(k - 1) + S_{{\text{T - new}}} *{\text{sig}}\left( {\frac{\Delta I}{{\Delta V}} + \frac{I}{V}} \right) $$
(31)

where

$$ S_{T - new} = N*\frac{\Delta P}{{\Delta V}}; \quad S_{P} = \frac{\Delta P}{{\Delta V}} = \frac{P(k) - P(k - 1)}{{V(k) - V(k - 1)}}$$
(32)
$$ D(k) = D(k - 1) - S_{{\text{T - new}}} *{\text{sig}}\left( {\frac{\Delta I}{{\Delta V}} + \frac{I}{V}} \right) $$
(33)

where D (k) and D (k-1) are the present and existed duty cycles of the universal input voltage boost converter. The term ‘N’ indicates the scaling factor. At starting, the selected scaling factor value is high in order to reduce the tracing time of MPP and finally small step value is considered to suppress the steady-state oscillations across the MPP.

(d). FLC- IHC MPPT technique for fuel cell stack.

The drawbacks of HC MPPT technique are overcome by using an FLC-IHC technique. Here, the fuzzy logic controller is used to improve the searching mechanism of HC MPPT technique. The advantages of the hybrid MPPT technique are high convergence speed, less settling time, and high accuracy when compare to the conventional HC method (Alajmi, et al. 2010). The block diagram of FLC-IHC technique is shown in Fig. 8. The PEMFC stack power (PFC) and currents (IFC) are the inputs to the FLC, and its output is controlled duty cycle.

$$ \Delta P = P(i) - P(i - 1) $$
(34)
$$ \Delta I = I(i) - I(i - 1) $$
(35)
$$ \Delta D = D(i) - D(i - 1) $$
(36)

where \(\Delta P\), \(\Delta I\), and \(\Delta D\) are the change of fuel output power, current and converter duty cycle. Here, the operating point of PEMFC is not coincide with the true MPP at diverse temperature conditions. So,\(\Delta P\) is flows through the gain controller to reverse its direction. The FLC inputs and output are transferred into four fuzzy subsets which are Positive Big (PB), Negative Big (NB), Positive Small (PS), and Negative Small (NS). Based on four fuzzy sets, the FLC consist of sixteen fuzzy rules and which are formed based on the controlling of HC technique. The Mamdani’s Max–min technique is used for the operation of fuzzy combination. The fuzzification of IHC rules is given in Fig. 8, and the membership functions of fuel cell output power, current, and duty cycle are shown in Fig. 9a, b and c.

Fig. 8
figure 8

Fuzzification rules of improved HC MPPT controller

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Fig. 9
figure 9

Membership functions of, a Fuel cell current, b Voltage, and c Duty cycle

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(e). Proposed IBeta-FLC MPPT technique for fuel cell stack.

The major drawback of fuzzy logic controller is required high knowledge person for training its complicated rules. In order to overcome the drawback of this basic fuzzy technique, a hybrid (IBeta-based FLC) MPPT technique is proposed to improve the dynamic response of the fuel cell stack. Here, beta (β) is varied instead of varying fuel cell output voltage and power. The variable β is given to the FLC in order to operate the PEMFC fed boost converter system at dynamic temperature conditions. In addition to that, the β is used to optimize the number of fuzzy rules.

Here, the Mamdani’s, Max–min, and center of gravity techniques are used for fuzzy interference, fuzzy combination, and defuzzification, respectively. The block diagram of hybrid MPPT controller is shown in Fig. 10.

$$ \beta (i) = \log \left( {\frac{{I_{{{\text{FC}}}} }}{{V_{{{\text{FC}}}} }}} \right) - n * V_{{{\text{FC}}}} $$
(37)

where VFC and IFC are fuel cell voltage and current. The term ‘n’ indicates the total number of cells in the PEMFC stack. Based on different operating conditions of PEMFC stack, the parameter \(\beta\) is divided into three parts (\(\beta_{\min } ,\beta_{\max }\), and \(\beta_{\bmod e}\)) which are varied continuously until obtaining the optimum value of beta parameter. If the determined beta value is within the range, then the operating point of fuel cell is nearer to the MPP. After that, the FLC is used to suppress the oscillations of MPP. The fuzzy controller membership functions are shown in Fig. 11. From Fig. 11, the formation fuzzy rules are given in Table 2.

Fig. 10
figure 10

Block diagram of proposed MPPT controller

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Fig. 11
figure 11

Membership functions of, a Fuel cell voltage, b Power, c beta parameter, and d Duty cycle of boost converter

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Table 2 Fuzzy rules of the proposed MPPT technique
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From Table 2, the output is PB at minimum beta value and it is NB at maximum beta value. The maximum possible fuzzy sets at moderate beta value are PS, NS, and ZE.

5 Design and analysis of SSUIBC

The universal input voltage, high step-up, and transformerless boost converter consist of four semiconductor devices which are classified as three diodes (Dx, Dy, and Dz), and one Metal Oxide Field Effect Transistor (MOSFET) switch (Q). In addition, it consists of four capacitors (Cx, Cy, Cz, and Ca), three inductors (Lx, Ly, and Lz), and one resistor (R0). The elements Cx, Lx, Q, and Dx act as a conventional boost switching converter and the components Dy, Dz, Lx, Ly, Cy, and Ca, and Cz are formed as a filter network (see in Fig. 1) and it is interfaced in between the conventional converter and output capacitor (C0).

The interfacing network is useful for improving the output voltage profile of the fuel stack. In addition, it reduces the voltage stress across the diodes and switch. Based on the switching behavior of MOSFET, the proposed converter works in three modes of operations (see in Table 3).

Table 3 Switching behavior of UIVBC
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6 Switching state: I

The first switching state of the converter is shown in Fig. 12a. From Fig. 12a, the output voltage and currents of fuel cell are defined as VFC, and IFC. The instantaneous voltages across the capacitors (Cx, Cy, Cz, C0, and Ca) and inductors (Lx, Ly, and Lz) are VCx, VCy, VCz, VC0, VCa, VLx, VLy, and VLz, respectively. Similarly, the current flowing through the capacitors and inductors are ICx, ICy, ICz, IC0, ICa, ILx, ILy, and ILz, respectively. The charging and discharging currents of the capacitors are ICx-chg, ICy-chg, ICz-chg, IC0-chg, ICa-chg, ICx-disg, ICy-disg, ICz-disg, IC0-disg and ICa-disg, respectively. Here, there are three assumptions have been considered to analyze the CCM, and DCM of operation of the boost converter. The first assumption is, all the semiconductor switches are in ideal condition, and second one is, the equivalent series resistance of the inductors plus capacitors are zero. Finally, the third assumption is the selection of capacitors and inductors are high in order to run the converter at CCM of operation.

Fig. 12
figure 12

a Block diagram of SSUIBC at first switching state. b Block diagram of SSUIBC at second switching state. c Block diagram of SSUIBC at third switching state

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In the first switching state, the voltage across the gate to source terminals of the MOSFET is extreme then the power converter starts working in CCM and DCM of actions. When the switch (Q) is in conduction state, then the diodes (Dx, Dy, and Dz) are in OFF state and capacitors, Cy and Ca, starts charging, and Cx, Cz, and C0 starts discharging as shown in Fig. 12a. The current flowing through the five capacitors (refer Eq. 38) and voltage across the three inductors (refer Eq. 39) are derived by using Kirchhoff’s Current Law and Kirchhoff’s Voltage Law.

$$ \left\{ \begin{gathered} I_{{\text{Cy - chg}}} = I_{{\text{Cx - disg}}} = I_{Ly} + I_{Lz} \hfill \\ I_{{\text{Cz - disg}}} = I_{{\text{Ca - chg}}} = I_{Lz} \hfill \\ I_{{\text{C0 - disg}}} = I_{0} \hfill \\ \end{gathered} \right. $$
(38)
$$ \left\{ \begin{gathered} V_{Lx} = V_{FC} \hfill \\ V_{Ly} = V_{Cx} - V_{Cy} \hfill \\ V_{Lz} = V_{Cx} + V_{Cz} - V_{Ca} - V_{Cy} \hfill \\ \end{gathered} \right. $$
(39)

6.1 Switching state: II

In this switching state, the voltage (Vgs) across the gate to source is very low. As result, the switch (Q) is in blocking state and the diodes (Dx, Dy, and Dz) are in conduction state. The converter works in both the modes of operation as given in Fig. 12b. From Fig. 12b, the capacitors Cy and Ca starts discharging and the capacitors Cx, Cz and C0 starts charging.

The Kirchhoff’s Current and the Kirchhoff’s Voltage Laws are applied to the converter in order to derive the current flowing through the inductors and voltage across the capacitors.

$$ \left\{ \begin{array}{l} I_{{\text{Cy - disg}}} = I_{{\text{Ca - disg}}} + I_{Lz} + I_{{\text{Lz - chg}}} - I_{Ly} \hfill \\ I_{{\text{Cx - chg}}} = - I_{{\text{Cy - disg}}} + I_{Lx} - I_{Ly} + I_{{\text{Cz - chg}}} \hfill \\ I_{{\text{C0 - chg}}} = I_{{\text{Ca - disg}}} + I_{Lz} - I_{0} \hfill \\ \end{array} \right. $$
(40)
$$ \left\{ \begin{array}{l}V_{Lx} = V_{FC} \hfill \\ V_{Ly} = - V_{Cy} = - V_{Cz} \hfill \\ V_{Lz} = V_{Cx} + V_{Cz} - V_{Ca} - V_{Cy} \hfill \\ \end{array} \right. $$
(41)

6.2 Switching state: III

In this switching state, the converter works in DCM of operation. Here, the voltage across the gate to source terminal is very low. As a result, all the semiconductors devices are in reverse biased state as illustrated in Fig. 12c.

From Fig. 12c, the constant current flowing through the inductors (Lx, Ly, and Lz) are ILx-min, ILy-min, and ILz-min and its summation is zero. In addition, the voltage across each inductor is zero which is given in Eq. (43).

$$ I_{Lx - \min } + I_{Ly - \min } + I_{Lz - \min } = 0 $$
(42)
$$ V_{Lx} = V_{Ly} = V_{Lz} = 0 $$
(43)

(a). Steady-state behavior of boost converter under CCM of operation.

Here, the switching state-I and switching state-II are used to analyze the CCM of operation of the boost converter. From Fig. 12a and Eqs (39) and (41), the voltage gain of proposed boost converter is derived as follows:

$$ V_{Cy} = V_{Ca} = V_{Cz} = \frac{D}{(1 - D)}V_{FC} $$
(44)
$$ V_{Cx} = \frac{1}{(1 - D)}V_{FC} $$
(45)
$$ V_{0} = \frac{1 + 2D}{{1 - D}}V_{FC} $$
(46)
$$ Gain_{CCM} = \frac{{V_{0} }}{{V_{FC} }} = \frac{1 + 2D}{{1 - D}} $$
(47)

From Fig. 12a, the voltage stress across the power semiconductors is equal to VCx. Eqs (38)-(41) are used to derive the voltage stress across the diodes (VD) switch (VQ).

$$ \left\{ \begin{array}{l} V_{D} = V_{Q} = V_{FC} *\frac{1}{1 - D}V_{Cx} \hfill \\ V_{Dx} = V_{Dy} = V_{Dz} = V_{D} \hfill \\ \end{array} \right. $$
(48)

Eqs (46), and (47) are used to derive the voltage stress across the switch in terms voltage gain.

$$ V_{D} = V_{Q} = \frac{{2 + {\text{Gain}}_{{{\text{CCM}}}} }}{{3*{\text{Gain}}_{{{\text{CCM}}}} }}*V_{0} $$
(49)

The current stress across each inductor is obtained by considering the generated converter power (P0 = V0*I0) is equal to the fuel cell power (PFC = VFC*IFC).

$$ I_{Ly} = I_{Lz} = I_{0} $$
(50)
$$ I_{Lx} = \frac{1 + 2D}{{1 - D}}I_{0} = {\text{Gain}}_{{{\text{CCM}}}} I_{0} $$
(51)

The charge-second balance principle is applied to each capacitor in order to derive their charging and discharging currents.

$$ \left\{ \begin{array}{l} I_{{\text{Cy - chg}}} = 2I_{0} \hfill \\ I_{{\text{Cy - disg}}} = 2I_{0} \frac{D}{1 - D} = \frac{{{\text{Gain}}_{{{\text{CCM}}}} - 1}}{3}2I_{0} \hfill \\ \end{array} \right. $$
(52)
$$ \left\{ \begin{gathered} I_{{\text{Ca - chg}}} = I_{0} \hfill \\ I_{{\text{Ca - disg}}} = I_{0} \frac{D}{1 - D} = \frac{{{\text{Gain}}_{{{\text{CCM}}}} - 1}}{3}I_{0} \hfill \\ \end{gathered} \right. $$
(53)
$$ \left\{ \begin{array}{l} I_{{\text{Cz - chg}}} = 2I_{0} \frac{D}{1 - D} = 2I_{0} \frac{{{\text{Gain}}_{{{\text{CCM}}}} - 1}}{3} \hfill \\ I_{{{\text{Cz\_disg}}}} = 2I_{0} \hfill \\ \end{array} \right. $$
(54)
$$ \left\{ \begin{array}{l} I_{{\text{Cx - chg}}} = I_{0} \frac{D}{1 - D} = \frac{{{\text{Gain}}_{{{\text{CCM}}}} - 1}}{3}I_{0} \hfill \\ I_{{\text{Cx - disg}}} = I_{0} \hfill \\ \end{array} \right. $$
(55)
$$ \left\{ \begin{array}{l} I_{{\text{C0 - chg}}} = I_{0} \frac{D}{1 - D} = \frac{{{\text{Gain}}_{{{\text{CCM}}}} - 1}}{3}I_{0} \hfill \\ I_{{\text{C0 - disg}}} = I_{0} \hfill \\ \end{array} \right. $$
(56)

From Fig. 12b and c, the currents passing over the power diodes plus the switch are calculated as follows:

$$ I_{Q} = I_{Lx} + I_{Ly} + I_{Lz} = I_{0} \frac{3}{1 - D} $$
(57)
$$ I_{Dx} = I_{Lx} - I_{{{\text{Cy\_disg}}}} = I_{0} \frac{1}{1 - D} $$
(58)
$$ I_{Dy} = I_{Ly} + I_{{\text{Cy - chg}}} - I_{{\text{Ca - disg}}} = I_{0} \frac{1}{1 - D} $$
(59)
$$ I_{Dz} = I_{{\text{Ca - disg}}} = I_{0} \left( {1 - \frac{3}{1 - D}} \right) $$
(60)

By using Eqs (51), and (57)–(60), the current stress across the switch is obtained as follows:

$$ I_{Q} = ({\text{Gain}}_{{{\text{CCM}}}} + 2)I_{0} $$
(61)
$$ I_{Dx} = I_{Dy} = I_{Dz} = \left( {\frac{{{\text{Gain}}_{{{\text{CCM}}}} + 2}}{3}} \right)I_{0} $$
(62)

The RMS currents flowing through the semiconductor devices and capacitors are derived as follows:

$$ I_{{Q_{{{\text{RMS}}}} }} = \sqrt {({\text{Gain}}_{{{\text{CCM}}}} + 2)*({\text{Gain}}_{{{\text{CCM}}}} - 1)} *I_{0} $$
(63)
$$ I_{{{\text{Dx - }}_{{{\text{RMS}}}} }} = I_{{{\text{Dy - }}_{{{\text{RMS}}}} }} = I_{{{\text{Dz - }}_{{{\text{RMS}}}} }} = \sqrt {\frac{{{\text{Gain}}_{{{\text{CCM}}}} + 2}}{3}} *I_{0} $$
(64)
$$ I_{{{\text{Cy - }}_{{{\text{RMS}}}} }} = I_{{{\text{Cx - }}_{{{\text{RMS}}}} }} = \sqrt[2]{{\frac{{{\text{Gain}}_{{{\text{CCM}}}} - 1}}{3}}}*I_{0} $$
(65)
$$ I_{{{\text{Cz - }}_{{{\text{RMS}}}} }} = I_{{{\text{Ca - }}_{{{\text{RMS}}}} }} = I_{{{\text{C0 - }}_{{{\text{RMS}}}} }} = \sqrt[{}]{{\frac{{{\text{Gain}}_{{{\text{CCM}}}} - 1}}{3}}}*I_{0} $$
(66)

(i). Internal resistance effect on voltage gain.

The active and passive components of the proposed converter consist of internal resistances which are affect the boost converter voltage profile. The non-ideal model proposed universal input voltage, high step-up boost converter is given in Fig. 13. From Fig. 13, the internal resistances of the all inductors are same (rLx = rLy = rLz = rL) and all capacitors internal resistances are same (rCx = rCy = rCz = rC0 = rC). Similarly, the forward voltage drop across the three diodes are same (VFx = VFy = VFz = VF) and their corresponding internal resistances are same (rFx = rFy = rFz = rF). The MOSFET conduction resistance is indicated as rQ.

Fig. 13
figure 13

Internal resistances effect on voltage gain

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By considering the internal resistances of active and passive elements, the modified voltage gain of the proposed converter is given in Eq. (67).

(b). Analysis of proposed converter under DCM of operation.

Here, the switching state-I, II and III are used to analyze the DCM of operation. From Eqs (44)–(47), the voltage gain of dc-dc converter is evaluated as follows:

$$ {\text{Gain}}_{{{\text{CCM}}}} = \frac{{R_{0} (1 - D)*(V_{FC} - 3V_{F} + 3DV_{F} + 2DV_{FC} )}}{{V_{FC} (R_{0} + 3r_{F} + 3r_{L} + D(6r_{C} - 2R_{0} - 3r_{D} + 3r_{Q} + D(R_{0} - 6r_{C} + 6r_{L} - 12r_{Q} )))}} $$
(67)
$$ V_{Cy} = V_{Ca} = V_{Cz} = \frac{{V_{0} - V_{{{\text{in}}}} }}{3} $$
(68)
$$ V_{Cx} = V_{{{\text{FC}}}} + V_{Ca} = \frac{{V_{0} + 2V_{{{\text{FC}}}} }}{3} $$
(69)
$$ V_{0} = V_{Cx} + 2V_{Ca} $$
(70)

By considering Eqs (38), (40), (42), the voltage-second working principle is applied on Lx in order to determine the boost converter voltage gain at discontinuous mode.

$$ \frac{1}{T}\left( {\int_{0}^{dt} {V_{FC} *{\text{d}}t - } \int_{0}^{{d_{x} t}} {\frac{{(V_{0} - V_{FC} )}}{3}*{\text{d}}t} } \right) = 0 $$
(71)

From Eq. (51), the variable dx is required in order to derive the voltage gain of SSUIBC. From Eqs. (57)–(60), the current passing through the switch is equal to the summation of inductor currents and the current passing through the diode is equal to the one third of the inductor currents. The peak currents of the inductors and diodes are derived as follows:

$$ \left\{ {\begin{array}{*{20}c} {\Delta I_{Lx} = \frac{{DV_{{{\text{FC}}}} }}{{f_{s} L_{x} }}} \\ {\Delta I_{Ly} = \frac{{DV_{{{\text{FC}}}} }}{{f_{s} L_{y} }}} \\ {\Delta I_{Lz} = \frac{{DV_{{{\text{FC}}}} }}{{f_{s} L_{z} }}} \\ \end{array} } \right. $$
(72)
$$ I_{{{\text{Dpeak}}}} = \frac{1}{3}\left( {\Delta I_{Lx} + \Delta I_{Ly} + \Delta I_{Lz} } \right) $$
(73)

From Eqs. (71) and (72), the peak diode current is rewritten as follows:

$$ I_{{{\text{Dpeak}}}} = \frac{{D*V_{{{\text{FC}}}} }}{{3f_{s} L_{{{\text{eq}}}} }} $$
(74)

The average current flowing through each diode is equal to I0.

$$ \frac{1}{2}D_{x} I_{{{\text{Dpeak}}}} = \frac{{V_{0} }}{R} $$
(75)

By substituting Eq. (75) in Eq. (74), the term Dx is derived as follows:

$$ D_{x} = \frac{{6V_{0} }}{{D*V_{{{\text{FC}}}} }}\tau $$
(76)

where \(\tau\) is the time constant of the inductor. By substituting Eq. (75) in Eq. (70), then the voltage gain of the converter under DCM is derived as follows:

$$ {\text{Gain}}_{{{\text{DCM}}}} = \frac{1}{2}\left( {1 + \sqrt {1 + \frac{{2D^{2} }}{\tau }} } \right) $$
(77)

(c). Boundary conditions of the proposed converter.

Here, the voltage gain of proposed converter is equal under CCM and DCM of operations. From Eqs. (46) and (76), the time constant of the inductor is derived as follows:

$$ \tau_{{{\text{boun}}}} = \frac{D*(1 - D)}{{12D + 6}} $$
(78)

If the time constant \(\tau > \tau_{{{\text{boun}}}}\), then the proposed converter works in CCM of operation.

(d). Comparative analysis of non-isolated boost converters.

Here, the universal input voltage boost converter is analyzed along with the other dc-dc converters in terms of number of semiconductor devices that are utilized to implement the converter and voltage stress across the diodes and switch. The detailed comparison of transformer less boost converters is given in Table 4.

Table 4 Comparative analysis of non-isolated high step-up DC-DC boost converters
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7 Discussion of simulation results

Here, the major contribution of the work is design of the SSUIBC and it is used to step-up the fuel cell output voltage. As discussed previously, the SSUIBC converter is designed by interfacing a network in between the basic boost converter and load. The selected basic boost converter parameters are input inductor (Lx = 1.21 mH), output capacitor (C0 = 300 µF), and load resistor (R0 = 40 Ω). The added network capacitors (Cy = Cz = Ca = Cx) and inductors (Ly = Lz) values are 90 µF and 0.813 mH, respectively. From the block diagram (Fig. 1), the inductor Lx is used to suppress the low order distortions of PEMFC output voltage and C0 is used to supply a constant voltage to the load. The fuel cell gives nonlinear voltage versus current characteristics. As a result, the maximum power extraction from the fuel cell is very difficult. In addition, the V-I curve consists of unique MPP and it varies based on the operating temperature conditions of PEMFC. Here, an IBeta-FLC is used to trace the peak power point of PEMFC and it is compared with other MPPT techniques at static temperature conditions.

(a). Static operating temperature condition of PEMFC (320 K).

The instantaneous PEMFC current and voltage are taken as inputs to the proposed MPPT controller, and its output is duty cycle. At static operating temperature condition, the PEMFC current and voltage by applying different MPPT techniques are given in Fig. 14a and b. Similarly, the converter operating duty cycle, output current, output voltage, output power by applying diverse power point tracing techniques are shown in Fig. 14c, d, e, and f. From Fig. 14a and b, the extracted PEMFC output current and voltage of VSS-P&O and RBFN-based MPPT techniques are 112.5A, 39.37 V, 113.2A, and 40.60 V, respectively. Similarly, the fuel cell current and voltage of FLC-IHC and FLC-VSSIC-based MPPT techniques are 112.8A, 42.60 V, 113.7A, and 42.02 V, respectively. The rising and settling of time of PEMFC output voltage by applying RBFN and an IBeta-FLC are 0.015 s, 0.041 s, 0.010 s, and 0.18 s, respectively.

Fig. 14
figure 14

a PEMFC current, b PEMFC voltage, c Duty cycle, d Converter O/P current, e Converter O/P voltage, f Converter O/P power at static temperature condition

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The VSS-P&O, FLC-IHC, and FLC-VSSIC power point tracking controller gives the required duty cycle (0.79, 0.808, and 0.798) to the SSUIBC in order to improve the voltage profile of the fuel cell stack. From Fig. 14c, the fuel cell fed SSUIBC duty cycle by using IBeta-FLC is 0.793 which is less than the FLC-IHC. From Fig. 14d, e, and f, the converter output current, output voltage, and output power of RBFN and FLC-VSSIC-based power point tracking controller are 8.460A, 528.50 V, 4471.2 W, 8.751A, 531.522 V, and 4650.82 W, respectively. Similarly, the converter output voltage and output power of VSS-P&O, FLC-IHC, and IBeta-FLC-based controllers are 526.40 V, 4269.16 W, 533.61 V, 4716.49 W, 538.88 V, and 4750.77 W, respectively. From Fig. 14f, it is clearly observed that the efficiency of IBeta-FLC is 98.78% which is greater than the RBFN and VSS-P&O. In addition, the IBeta-FLC MPPT controller gives less steady-state oscillations across MPP, high tracking speed, and less design complexity when compared to the other MPPT controllers.

(b). Dynamic operating temperature condition of PEMFC (320 K, 300 K, and 340 K).

At the dynamic operating temperature condition of PEMFC, the IBeta-FLC is compared with other power point tracking controller in terms of settling time, tracking speed, fuel cell output power, and efficiency. From Fig. 15a, the fuel cell temperature starts increasing from 0 to 320 K (0 to 0.3 s). At 0.3 s, the temperature is suddenly stepped down to 300 K up to the period of 0.6 s. Finally, at 0.6 s, the fuel cell temperature is stepped up to 340 K. The performance of PEMFC fed SSUIBC system is analyzed at step varying temperature condition by using different hybrid and conventional MPPT techniques.

Fig. 15
figure 15

a Variation of temperature. b PEMFC current. c PEMFC voltage. d PEMFC power. e Duty cycle. f Converter O/P current. g Converter O/P voltage. h Converter O/P power at dynamic temperature condition

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From Fig. 15b, c, and d, at 300 K, the extracted fuel output current, voltage, and power by applying FLC-VSSIC, FLC-IHC, and IBeta-FLC-based MPPT techniques are 107.1A, 40.2 V, 4290.4 W, 106.5A, 40.33 V, 4297.2 W, 104.4A, 41.05 V, and 4288.2 W, respectively. At 340 K, the operating duty cycles of SSUIBC by applying VSS-P&O, RBFN, and FLC-VSSIC MPPT techniques are 0.781, 0.774, and 0.8, respectively. The IBeta-FLC is used to obtain the optimum duty cycle (see in Fig. 15e) which is given to the high step-up boost converter in order to improve the voltage profile of the PEMFC stack.

The converter output current, output voltage, and output powers of RBFN-based controller are 8.9462A (see in Fig. 15f), 557.5 V, and 4987.55 W, respectively. The converter output power rising and settling time of IBeta-FLC-based power point tracking controller are 0.01 s, and 0.155 s, respectively. Hence, from the above observation, it is determined that the IBeta-FLC-based MPPT technique is giving good dynamic response and high tracking speed when compared to the other power point tracking controllers. The detailed analysis of proposed fuel cell fed SSUIBC by applying diverse MPP tracking controller is given in Table 5.

Table 5 Performance parameters of PEMFC fed SSUIBC by applying different MPPT techniques
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8 Experimental design and analysis of SSUIBC

Here, M62020P8058 programmed direct power supply is used to investigate and analyze the proposed single switch boost converter for fuel cell-based electric vehicle application as shown in Fig. 16. The high switching frequency-based Metal Oxide Field Effect Transistor switch is used in the proposed boost converter in order to reduce the overall system heat and conduction losses. In addition, its consumption and dissipation power losses are very less when compare to the BJT and IGBT. The experimental design parameters of SSUIBC are given in Table 6.

Fig. 16
figure 16

Experimental setup for the non-isolated DC-DC converter

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Table 6 Experimental design parameters of SSUIBC
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The analog discovery (Digilent 520-445) acts as a pulse width modulator in order to supply the switching pulses to the SSUIBC. The TLP-250 isolated MOSFET gate driver circuit is used to protect the power semiconductor devices from the sudden change of input voltages. The gate driver circuit consists of light-emitting diode (GaAlAs) which receives the signal from the source and it gives the signal to the PWM generator by using an integrated photo detector. The maximum operated voltage rating of the driver circuit is 4.66 V. The 4N28 optocoupler is connected between the control circuit and load to control the converter output voltage. The MOSFET operated frequency is 20 kHz, and the selected duty for analyzing the performance of SSUIBC is 20.93% (see in Fig. 17).

Fig. 17
figure 17

MOSFET Switching pulses and its output voltage

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The optimum duty cycle is given to the single switch high step-up converter in order to boost the voltage from 68.166 to 121.54 V as shown in Fig. 18. From Fig. 18, it is observed that the current is stepped down and the voltage is stepped up. As a result, the converter reduces the overall system conduction losses and improves the efficiency.

Fig. 18
figure 18

SSUIBC output voltage, output current, input voltage and inductor voltage

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9 Conclusion

The proposed IBeta-FLC-based MPPT technique performance is evaluated successfully in terms of converter output power, operating efficiency, settling time, design complexity, dependency on PV array, and oscillations across MPP. The proposed MPPT technique is compared with other hybrid MPPT techniques. From the comparative simulation results, it is concluded that the proposed improved Beta-based fuzzy logic MPPT controller gives high MPP tracking speed and less oscillations. In addition, it gives optimum duty cycle to the fuel cell fed single switch boost converter. As a result, the overall system switching and conduction losses are reduced. Also, the proposed DC-DC converter is giving constant and continuous output voltage with less distortions. The features of SSUIBC are high voltage conversion ratio, wide input operation and less voltage stress on power semiconductor devices.