Real-Time Implementation of a New MPPT Control Method for a DC-DC Boost Converter Used in a PEM Fuel Cell Power System

Abstract

Polymer electrolyte membrane (PEM) fuel cells demonstrate potential as a comprehensive and general alternative to fossil fuel. They are also considered to be the energy source of the twenty-first century. However, fuel cell systems have non-linear output characteristics because of their input variations, which causes a significant loss in the overall system output. Thus, aiming to optimize their outputs, fuel cells are usually coupled with a controlled electronic actuator (DC-DC boost converter) that offers highly regulated output voltage. High-order sliding mode (HOSM) control has been effectively used for power electronic converters due to its high tracking accuracy, design simplicity, and robustness. Therefore, this paper proposes a novel maximum power point tracking (MPPT) method based on a combination of reference current estimator (RCE) and high-order prescribed convergence law (HO-PCL) for a PEM fuel cell power system. The proposed MPPT method is implemented practically on a hardware 360W FC-42/HLC evaluation kit. The obtained experimental results demonstrate the success of the proposed method in extracting the maximum power from the fuel cell with high tracking performance.

1. Introduction

Fossil fuel is considered to be one of the main causes of environmental problems related to global warming. Therefore, the need for using alternative sources of energy from petroleum substances and their derivatives is necessary. To this end, many scientists and researchers have been conducting studies and research to obtain alternative clean energies.

During the last few years, several clean energy sources such as solar, wind, geothermal etc., have been developed to generate electric energy and replace conventional fuel [1,2,3,4,5,6,7]. However, these alternative sources necessitate sophisticated and high-cost technologies, and they are not suitable for many applications. Moreover, most of these sources are depending on certain climatic and geographical conditions. For example, solar energy needs the sun and it could not be used in overcasted areas. The same for the wind energy which could also be used only when the wind blows. The use of tidal phenomenon and waves movement require to be near the sea and this is also not available everywhere. By virtue of its abundance in the earth, hydrogen has emerged as an available and advantageous fuel. In this sense, PEM fuel cells which use hydrogen as the main fuel have shone the horizon as a comprehensive and general alternative to fossil fuel. They are considered to be the energy source of the twenty-first century due to their high power densities, lightweight, low operating temperature (quick start-up), long cycle life, as well as zero pollution [8,9,10]. Therefore, they have been used in many fields such as transportation, aircraft, distributed generation, and especially in stationary and mobile applications [11,12,13,14,15,16,17,18]. In these applications, the PEMFC is usually coupled with a DC-DC power electronic converter that provides an efficient power conversion to the load, and also offers highly regulated output voltage [19,20,21,22,23]. Therefore, the control loop is needed so as to obtain an applicable output dc voltage. Besides, since the fuel cell is largely influenced by the load and its inputs variations (temperature, oxygen, and hydrogen), the application of the MPPT algorithm is desired so as to keep the PEMFC operating at the optimal power point.

Usually, the MPPT algorithms are used for PV and wind systems. Thus, different techniques have been designed including fractional open-circuit voltage (FOCV) [24,25], hill climbing (HC) [25], perturb and observe (P&O) [24,26,27], incremental conductance (INC) [24,27], golden section search (GSS) [28], newton’s quadratic interpolation (NQI) [28], extremum seeking control (ESC) [29], sliding mode control (SMC) [27], model predictive control (MPC) [30], fuzzy logic control (FLC) [24,26], backstepping algorithm (BSA) [10], genetic algorithms (GAs) [24,31], particle swarm optimization (PSO) [27], cuckoo search (CS) [32], nature-inspired algorithms (NIA) [25], recurrent learning gradient algorithm (RLGA) [33], flower pollination algorithm (FPA) [34], etc. Although the great research occurred on the MPPT methods, only a few of these techniques have been designed for fuel cell systems. For instance, authors of [35] proposed a smart MPPT algorithm based on FLC aiming to track the maximum power of the PEMFC. Comparative results with the well-known P&O have demonstrated the effectiveness of the proposed algorithm. Thus, a ripple reduction of 90% in the steady-state oscillations could be attained using the proposed MPPT algorithm. In [36], a variable step-size FLC was used to track the output power of a 7KW PEMFC power system. Comparative results with fixed step-size FLC, variable step-size INC, and fuzzy scaled INC, have shown that reductions of 82.35% in response time, 100% in overshoot and current ripple could be attained using the proposed MPPT algorithm. An MPPT-based SMC control was proposed by authors of [37] so as to overcome the drawbacks of the PI application in non-linear systems. Robustness and fast converging to the maximum power point (MPP) are achieved through the proposed method. This latter also was proposed by authors of [38] aiming to extract the maximum power from a fuel cell/battery storage system. Satisfactory results in terms of robustness and tracking accuracy have been achieved. A neural network algorithm (NNA) was designed by authors of [39] for 1.26KW PEMFC electric vehicle power-train. Simulations results have shown that the proposed NNA track the MPP faster when compared with FLC. The NNA also was developed by authors of [40]. However, an intelligent algorithm-based chaotic particle swarm optimization (CPSO) is used to optimize the weights of the proposed algorithm. Simulation results have demonstrated the effectiveness of the proposed algorithm to track the MPP with high robustness and low steady-state oscillations. The authors of [41] proposed neural generalized model predictive control (NGMPC) aiming to track the maximum efficiency or the MPP of a grid-connected fuel cell power system. Simulation results have proved the effectiveness of the proposed method to track the desired power point. The authors of [42] used PSO algorithm for a 53KW PEMFC interfaced with a high step-up dc-dc converter aiming to maintain the stack power extremely close to the maximum operating power point. Comparative results have indicated that the proposed PSO algorithm shows better tracking efficiency, slightly shorter rise time, and an overshoot of 2% lower than the FLC. In [43], a novel single sensor algorithm was designed to track the MPP of a 7KW PEMFC. Comparative results with conventional two sensors algorithm have demonstrated the effectiveness of the proposed algorithm to enhance the efficiency and the lifetime of the PEMFC. In [44], an extremum seeking control (ESC) is used for a hybrid fuel cell power system. The maximum efficiency power point is achieved by controlling the hydrogen flow-rate through the boost converter. Satisfactory results such as an increase of 2% in the average efficiency of the system and 12% in the fuel economy have been obtained. A novel PID-based grey wolf optimizer PID-GWM was proposed by authors of [45] to track the maximum power. The authors used the $\frac{dP}{dI}$ feedback control scheme. The presented results have indicated the effectiveness of the proposed MPPT algorithm over the P&O, INC, and PID-based PSO. The PID also was used by authors of [46] aiming to maximize the power of the PEMFC. However, a slap swarm algorithm (SSA) was designed to determine the optimal gain of the PID. The obtained results were compared with FLC, GWM, grey antlion optimization (GAO), incremental resistance algorithm (IRA), and mine-blast algorithm (MBA). It has been demonstrated that the proposed MPPT algorithm shows better results in terms of reliability and efficiency. A robust MPPT-based backstepping algorithm was proposed by [47]. Comparative results with PI, one of the most studied, have indicated the outperformance of the proposed method in terms of robustness, settling time, and control precision. Despite the effectiveness of these methods, they have been validated only by simulation work. Actually, the use of the MPPT algorithm in a real fuel cell could be a hard task for many cells topologies and this is due to the application of the security systems that prevent them to operate in the concentration zone at which the locale of the MPP. In other words, for many cells, the current that corresponds to the MPP could be near to the fuel cell maximum current at which the security system turns off the system so as to prevent the damage of the membrane. To overcome these barriers, an effective operating zone was built in our previous work [48] to keep the fuel cell operating near to its MPP. The operating zone could provide up to more than 90% of the MPP for lower temperatures. However, due to the fixed reference, it only could provide around 72% of the MPP for higher temperatures. Therefore, this paper presents an effective solution to overcome these restrictions. Thus, based on the P-I characteristic curves of the fuel cell, the authors construct an MPPT method that keeps the system operating at the maximum possible power point. The highest power point provided by the fuel cell could be attained using the reference current estimator (RCE) method. The corresponding current of this MPP was taken by the HO-PCL algorithm as a reference current and it generates the adequate command signal so as to drive the power converter device.

This rest of the paper is organized as follows: a brief review of the PEM fuel cell model and its operating principle are given in Section 2. The MPPT-based HO-PCL technique is designed in Section 3. The hardware system is explained in Section 4. Section 5 is devoted to the discussion of the experimental results. Finally, some conclusions are indicated in Section 6.

2. PEM Fuel Cell Stack

2.1. Operating Principle

A fuel cell is composed of two electrodes (known as anode and cathode) and an electrolyte membrane which is the main component in a fuel cell device. It is supplied by pressurized oxygen and hydrogen to produce electricity. The operating principle of the PEMFC is detailed in Figure 1.

In the anode, the hydrogen dissociates into electrons and protons as described by Equation (1). Since the electrolyte membrane allows only the protons to pass, then the electrons flow through the external load to produce electricity and come to the cathode side at which will join the protons. In the cathode, as described by Equation (2), hydrogen dissociations react with the oxygen to produce heat and water (vapor). Therefore, the overall electrochemical reaction of a fuel cell can be given as Equation (3) [48,49,50].

$$H_2⟹2H^{+}+2e^{-}$$

(1)

$$4H^{+}+O_2+4e^{-}⟹2H_{2}O$$

(2)

$$2H_2+O_2⟹2H_{2}O+ElectricalEnergy$$

(3)

2.2. Model and Analysis

Figure 2 shows the performance of an individual cell operating at a standard temperature and pressures. Besides, this graph represents the variations of the real operating voltage in comparison with the ideal voltage value. It is noticed that the voltage decreases in the beginning, then it behaves as linear, and finally, a sudden fall is occurred at a higher current density. This voltage difference is a result of three main polarization losses: activation, ohmic and concentration.

The activation polarization loss $V_{act}$ is characterized by a strong non-linear demeanour. This is due to the reaction kinetics at the electrode of the PEMFC. The activation polarization is important at low current densities (mostly affect in the initial part of the polarization curve) due to the slowness and maintenance of the chemical reaction. The ohmic polarization loss $V_{ohm}$ is affected by the ohmic losses of energy derived from the impedance of the membrane. It is also influenced by the resistances of the construction materials (collecting plates and carbon electrodes). The concentration polarization loss $V_{con}$ (also called mass transportation loss) is the phenomenon that occurs due to the propagation of ions through the electrolyte membrane which leads to the lack of reactants mass transfer at the electrode caused by the rapid consumption of the respective reactant. This loss is important especially at higher current densities. Therefore, according to the empirical equation developed by Amphlett et al. [51] and Kim et al. [52], the cell voltage is given by Equation (4).

$$V_{fc}=E-V_{act}-V_{ohm}-V_{con}$$

(4)

where E is the electrochemical thermodynamic potential; $V_{act}$, $V_{ohm}$, and $V_{con}$, respectively, are activation, ohmic, and concentration loss. Each term of the above equation is defined in Equation (5) [51,52,53].

$$\left\{\begin{array}{c}E=1.229-0.85·{10}^{-3}·(T-298)+4.3·{10}^{-5}T[ln(P_{H2})+\frac{1}{2}ln(P_{O2})]\hfill \\ \hfill & \\ V_{act}={\xi }_1+{\xi }_{2}T+{\xi }_{3}T·ln(C_{O2})+{\xi }_{4}T·ln(I)\hfill \\ \hfill & \\ V_{con}=-B·ln(1-\frac{J}{J_{max}})\hfill \\ \hfill & \\ V_{ohm}=I(R_m+R_c)\hfill \\ \hfill & \end{array}\right.$$

(5)

where T, I, J, $P_{H2}$, $P_{O2}$, and B, respectively, are the cell temperature, the cell operating current, the current density, the hydrogen partial pressure, the oxygen partial pressure, and a constant parameter depends on the cell type. The parameters $R_c$, $R_m$, $C_{O2}$, ${\xi }_k$ $(k=1,2,3,4)$, were developed and calculated in [53] which represent, respectively, the proton resistance and the equivalent resistance of the electron flow, the oxygen concentration, and the parametric coefficients.

3. MPPT Control Design

MPPT is a technique used for maximizing the power extraction from any source of energy. The main feature of this technique is that the produced power could be maximized under any operating conditions. It has been widely used for systems such as wind turbines, PV, and fuel cells. The MPPT method used in this work is built based on a combination of an RCE and an HO-PCL algorithm. The control process including the RCE, the HO-PCL algorithm, the power converter, as well as the fuel cell, is presented in Figure 3. The RCE has the objective of researching the highest power point provided by the fuel cell. The corresponding current of this maximum power point is taken by the HO-PCL algorithm as a reference current and it generates the adequate command signal so as to drive the power converter device.

3.1. DC/DC Boost Converter

Boost converter circuits are devices that step-up an unregulated DC input low voltage and generates a regulated DC output at a higher voltage. As presented in Figure 4, the device is composed of a filtering capacitor C, an inductor L, and two switches (transistor T and diode D) [54,55].

According to [56], the relationship between the input voltage $V_{stack}$ and the output voltage $V_{out}$ is determined by Equation (6), where u is a duty cycle signal generated by the controller.

$$V_{out}=\left(\frac{1}{1-u}\right)·V_{stack}$$

(6)

The boost converter circuit presented in Figure 4 operates in two fundamental different modes: Continuous-Conduction Mode (CCM) and Discontinuous-Conduction Mode (DCM) [54,57,58,59]. However, in this work, the boost converter is assumed to operate in CCM. In this sense, the electronic circuit shifts between two states for each switching cycle T. The first state is called the ON state ($t_{ON}$) at which the transistor switch is close and the diode switch is open. The configuration of the boost converter circuit in the ON state is shown in Figure 5A. Hence, the inductor is connected to the source voltage for energy storage. In this case, the boost converter circuit can be expressed as Equation (7).

$$\left\{\begin{array}{c}\frac{{di}_L}{dt}=\frac{1}{L}(V_{stack})\hfill \\ \hfill & \\ \frac{{dV}_{out}}{dt}=\frac{1}{C}(-i_{out})\hfill \end{array}\right.$$

(7)

The state-space representation of the ON state circuit can be written as Equation (8).

$$\left\{\begin{array}{c}\dot{x}=A_1·x+B_1·v\hfill \\ \hfill & \\ y=C_1·x+E_1·v\hfill \end{array}\right.$$

(8)

where $x=\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]=\left[\begin{array}{c}{I}_L\\ V_{out}\end{array}\right]$, $A_1=\left[\begin{array}{cc}0& 0\\ 0& -\frac{1}{RC}\end{array}\right]$, $B_1=\left[\begin{array}{c}\frac{1}{L}\\ 0\end{array}\right]$, $C_1=\left[\begin{array}{cc}0& 1\end{array}\right]$, $E_1=0$, and $v=V_{stack}$. The waveforms of the inductor voltage $V_L$, inductor current $I_L$, transistor current $I_T$, and diode current $I_D$ during the ON state, are presented in Figure 6.

On the other side, the configuration of the boost converter circuit in the OFF state is shown in Figure 5B. Thus, the inductor will be connected to the output filtering capacitor C and to the resistance R. In this case, the boost converter circuit can be expressed as Equation (9).

$$\left\{\begin{array}{c}\frac{{di}_L}{dt}=\frac{1}{L}(V_{stack}-V_{out})\hfill \\ \hfill & \\ \frac{{dV}_{out}}{dt}=\frac{1}{C}(i_L-i_{out})\hfill \end{array}\right.$$

(9)

The state-space representation of the OFF state circuit can be written as Equation (10).

$$\left\{\begin{array}{c}\dot{x}=A_2·x+B_2·v\hfill \\ \hfill & \\ y=C_2·x+E_2·v\hfill \end{array}\right.$$

(10)

where $A_2=\left[\begin{array}{cc}0& -\frac{1}{L}\\ \frac{1}{C}& -\frac{1}{RC}\end{array}\right]$, $B_2=\left[\begin{array}{c}\frac{1}{L}\\ 0\end{array}\right]$, $C_2=\left[\begin{array}{cc}0& 1\end{array}\right]$, and $E_2=0$. The waveforms of $V_L$, $I_L$, $I_T$, and $I_D$ during the OFF state, are presented in Figure 6.

Consequently, the state-space representation of the boost converter for both ON and OFF states can be expressed as Equation (11).

$$\left\{\begin{array}{c}\dot{x}=A·x+B·v\hfill \\ \hfill & \\ y=C·x+E·v\hfill \end{array}\right.$$

(11)

where A, B, C, and E are defined in Equation (12).

$$\left\{\begin{array}{c}A=u·A_1+(1-u)A_2\hfill \\ \hfill & \\ B=u·B_1+(1-u)B_2\hfill \\ \hfill & \\ C=u·C_1+(1-u)C_2\hfill \\ \hfill & \\ E=u·E_1+(1-u)E_2\hfill \end{array}\right.$$

(12)

The state-space representation of the boost converter given in Equation (11) also can be written and detailed as Equation (13)

$$\left\{\begin{array}{c}\dot{x}=\left[\begin{array}{cc}0& \frac{u-1}{L}\\ \frac{1-u}{C}& -\frac{1}{RC}\end{array}\right]x+\left[\begin{array}{c}\frac{1}{L}\\ 0\end{array}\right]V_{stack},\hfill \\ \hfill & \\ y=\left[\begin{array}{cc}0& 1\end{array}\right]x,\hfill \end{array}\right.$$

(13)

3.2. Reference Current Estimator $I_{mpp}$

To determine $I_{mpp}$ which will recently be used as a reference current ($I_{ref}$), the performance of the fuel cell at different operating conditions must be studied. In any fuel cell, variation in temperature, oxygen, or hydrogen has an influence in its performance. However, the fuel cell used in this work is FC-42 Evaluation Kit 360W, and is equipped with an internal control system which provides the required quantities of hydrogen and air (oxygen) for each operating condition. In other words, variations in the ambient temperature will automatically result in variation in supplied hydrogen and air. Therefore, to study the performance of the fuel cell at different operating conditions, experiment tests were executed at several temperature values as presented in Figure 7. The MPP bold red curve depicted in this figure is constructed using Matlab Curve Fitting Toolbox^TM (CFT) which provides functions and applications for fitting curves and surfaces to data. The CFT bolsters non-parametric modeling techniques such as smoothing, splines, and interpolation. It also provides optimized solver parameters so as to improve the quality of the fit. In order to construct the MPP curve, the following steps should be performed:

• Gather the data of $P_{max}$ and $I_{max}$ for each P-I polarization curve in two vectors and load this data at the MATLAB command line. The experimental data obtained from the FC-42 Evaluation Kit is enlisted in

  Table 1. Experimental P_max and I_max values obtained from the FC-42 Evaluation Kit.

  Pmax	363	$362.6$	$367.2$	361	336	$357.8$	346
  Imax	$16.89$	$16.88$	$16.92$	$16.86$	$16.77$	$16.83$	$16.80$

  .
• Execute CFT by entering the function “sftool” or “cftool” in the Command Window.
• Select $I_{max}$ as X data, and $P_{max}$ as Y data so as to import the database. The CFT will create a default interpolation to fit the loaded data.
• Using the fit category drop-down list (Interpolant, Polynomial, Fourier, Gaussian, Weibull…), select various types and try to find the best curve by comparing the graphical and numerical fit results including fitted coefficients and the goodness of fit (GOF). Regarding to the latter mentioned, it includes the sum of squared due to error (SSE), the R-square, the adjusted R-square and the root mean squared error (RMSE); these metrics are tools that contribute to find the best curve that fits the data, for instance, a small SSE indicates a good fitting.
• Export the best fit to the Matlab workspace.

In this work, assorted tests were performed in order to achieve excellent statistics of the GOF. Hence, the MPP fitting curve constructed using the CFT is presented in Equation (14).

$$f(x)=P_1\ast x^9+P_2\ast x^8+P_3\ast x^7+P_4\ast x^6+P_5\ast x^5+P_6\ast x^4+P_7\ast x^3+P_8\ast x^2+P_9\ast x+P_{10}$$

(14)

were the coefficients $P_i$ (i = 1…10) and the goodness of the function are given in

Table 2. Goodness and coefficient parameters of the fitting function.

Goodness of the fit
SSE: $6873\times {10}^{-2}$	R-square: $9998\times {10}^{-4}$	Adjusted R-square: $9996\times {10}^{-4}$		RMSE: $3708\times {10}^{-3}$
Coefficients with 95% confidence bounds
$P_1=-1514\times {10}^{-9}$	$P_2=1034\times {10}^{-7}$	$P_3=-2898\times {10}^{-6}$	$P_4=433\times {10}^{-4}$	$P_5=-3741\times {10}^{-4}$
$P_6=1887\times {10}^{-3}$	$P_7=-5321\times {10}^{-3}$	$P_8=7463\times {10}^{-3}$	$P_9=-3863\times {10}^{-3}$	$P_{10}=2661\times {10}^{-5}$

.

Figure 8 explains the operation of the RCE. Thus, by occurring several projections on MPPT curve (red curve), the PEMFC will be brought from the operating power point to the desired point at which the stack will deliver its maximum power. In other words, assuming that the stack is operating at $P_{01}$ with an operating current $I_{01}$. The tracking control will force $P_{01}$ to be projected onto the MPPT curve which results in changing its operating current from $I_{01}$ to $I_{02}$ and as a consequence, the operating power point will be $P_{02}$. The same process is occurred with $P_{02}$ and $P_{03}$ and many other power operating points until the stack achieves the point at which the MPPT curve crossed the P vs. I curve.

This intersection point is called the MPP and its current “$I_{mpp}$” is used as a reference current for the control algorithm.

3.3. Current Regulation

The sliding surface of the PCL algorithm could be written as Equation (15):

$$s=e+c_1\int e·dt$$

(15)

where $c_1>0$ and $e=x_1-x_{1mpp}$.

Based on the state-space model given in Equation (13), an uncertain second-order system could be written as Equation (16):

$$\left\{\begin{array}{c}{\dot{z}}_1=y_2\hfill \\ {\dot{z}}_2=\chi (x,t)+\varphi (x,t)·\sigma \hfill \end{array}\right.$$

(16)

where $z_1=s$, $z_2=\dot{s}$, $\sigma$ is the derivative of the control u. In order to calculate the two smooth functions $\chi (x,t)$ and $\varphi (x,t)$, first, the calculation of the second derivative (with respect to time) can be done as in Equation (15).

$$\begin{array}{ccc}\hfill \ddot{s}& =& {\dot{y}}_2\hfill \\ & =& \frac{1}{L}\left({\dot{V}}_{stack}-{\dot{x}}_2\right)+\lambda \dot{e}+\frac{1}{L}\left({\dot{x}}_2·u+x_2·\dot{u}\right)\hfill \\ & =& \frac{1}{L}\left({\dot{V}}_{stack}-{\dot{x}}_2\right)+\lambda \left(\frac{1}{L}\left(V_{stack}-x_2\right)+\frac{1}{L}{x}_2·u\right)+\frac{1}{L}\left({\dot{x}}_2·u+x_2·\dot{u}\right)\hfill \\ & =& \frac{1}{L}\left[(u-1){\dot{x}}_2+{\dot{V}}_{stack}+\lambda (u-1)x_2+\lambda ·V_{stack}\right]+\frac{1}{L}{x}_2·\dot{u}\hfill \\ & =& \frac{1}{L}\left[(u-1){\dot{x}}_2+{\dot{V}}_{stack}+\lambda (u-1)x_2+\lambda ·V_{stack}\right]+\frac{1}{L}{x}_2·\sigma \hfill \end{array}$$

(17)

Therefore, using Equations (16) and (17), $\chi (x,t)$ and $\varphi (x,t)$ can be determined as Equations (18) and (19).

$$\chi =\frac{1}{L}\left[(u-1){\dot{x}}_2+{\dot{V}}_{stack}+c_1(u-1)x_2+c_1·V_{stack}\right]$$

(18)

$$\varphi =\frac{1}{L}{x}_2$$

(19)

Assuming that $\chi$ and $\varphi$ are bounded as:

$$|\chi |\le {\chi }_d,0<{\varphi }_{min}\le \varphi \le {\varphi }_{max}.$$

(20)

where ${\chi }_d$, ${\varphi }_{min}$ and ${\varphi }_{max}$ are positive scalars.

The general formulation of the HO-PCL control scheme is given by Equation (21) [60]:

$$\sigma =-\alpha ·sign(z_2-g_c(z_1))$$

(21)

where $g_c(z_1)$ is a continuous smooth function defined as:

$$g_c(z_1)=-\beta ·{|z_1|}^{1/2}·sign(z_1)$$

(22)

$\alpha$ and $\beta$ are two positive designed parameters. They should be determined according to the sufficient condition given in Equation (23) so as to guarantee the convergence in finite time to the sliding surface [60]:

$$\alpha ·{\varphi }_{min}-{\chi }_d>\frac{{\beta }^2}{2}$$

(23)

The implementation of the HO-PCL command law in MATLAB/Simulink is shown in Figure 9. Whereas the convergence trajectory of the continuous function $g_c(z_1)$ is presented in Figure 10.

4. Description of the Experimental System

The experimental system presented in Figure 11 consist of: FC-42 Evaluation Kit 360W, FC-42 Control unit, DC/DC converter, slide adjustable power resistor, programmable DC power supplies (BK Precision 1788), MicroLabBox dSPACE DS1202 and a host computer.

The FC-42 Evaluation Kit is a system that operates fuel cell stacks. It provides reliable and easy operation for FC-42/HLC stack series module, which is manufactured by Schunk Bahn industry. The technical data of this system are shown in

Table 3. Technical data of the FC-42 Evaluation Kit.

General Properties		Electrical Properties
Type	FC-42/HLC (42 cells)	Operating voltage	20–45 V
Cooling	Liquid (drinking water)	Open-circuit voltage	36–42 V
Fuel	Hydrogen $H_2$	Nominal stack voltage	24 V
Service life	>1500 h	Booster voltage	12 V (11–14 V)
W× D× H (mm)	168 × 230 × 115	Operating current	0–30 A
Total weight	17.1 kg	Nominal stack current	15 A
Starting time	2 min	Nominal stack power	360 W
Noise	Max 65 dB	Power consumption	70 W
Thermal Properties		Fuel Properties
Max. temperature of the surface	60 ${}^{\circ }\mathrm{C}$	$H_2$ inlet pressure $P_1$	1–11 bar
Exhaust air temperature	10–60 ${}^{\circ }\mathrm{C}$	$H_2$ operating pressure $P_2$	50–360 mbar
Ambient temperature	10–30 ${}^{\circ }\mathrm{C}$	Purity of $H_2$	99.99%
Coolant temperature	10–57 ${}^{\circ }\mathrm{C}$	$H_2$ Consumption	0–4 L/min
Cooling capacity	400 W @ 25 ${}^{\circ }\mathrm{C}$	Air volume flow rate	65 L/min
Coolant volume flow rate	240 L/h	Air pressure	400 mbar
Coolant pressure	320 mbar	Excess air	1.50–4.00

.

The FC-42/HLC stack is composed of 42 cells supplied by hydrogen and cooled with water. It delivers 360 W as a rated power with a current of 15 A and voltage 24 V. The FC-42 360 W Evaluation Kit is equipped with complex hydrogen and air supply system, cooling system, as well as protection and regulation system. The main role of the protection system allows for low range variations in quantities of temperature and supplied air. One of the most important factors which influence the stack effectiveness is moistening the membrane. This latter is required for assuring the conductivity of protons in the membrane and prevent the dryness. On the other hand, high humidity results in water condensation in the membrane surface which leads to limit the bonding between oxygen and hydrogen. However, proper moistening could be done by supplying an adequate amount of air via the cathode side. Since the supplied air is dependent on the stack temperature, then, a proper setting of temperature leads to proper moistening which will result in an increase in the overall stack efficiency. A cooling tank can be used to achieve a proper humidity of supplied air (RH ≈ $95\%$). Hydrogen inlet pressure $P_1$ is supplied at the anode side with a constant level ($P_1$≈ 28 kPa). The outlet of the anode is kept closed using a valve. This latter opens periodically in pulses so as to perform the purging of the anode. Regulation and protection systems also have the role of avoiding the destruction of the stack by preventing the exceeding values of temperature, current, and voltage. Thus, an automatic disconnection is done when the cooling water temperature is above 55 ${}^{\circ }\mathrm{C}$, voltage below 20 V and current above 35 A.

The FC-42 360 W Evaluation Kit is also equipped with measuring and control system as shown in Figure 12. It is used to determine the following quantities:

• Stack current (with an accuracy of 0.8 A)
• Stack voltage (with an accuracy of 0.1 A)
• Stack power (calculated)
• Cooling temperature $T_1$ (with an accuracy of $0.7$ ${}^{\circ }\mathrm{C}$)
• Exhaust air temperature $T_2$ (with an accuracy of $0.7$ ${}^{\circ }\mathrm{C}$)
• hydrogen inlet pressure $P_1$
• hydrogen operating pressure $P_2$
• Excess air (calculated)

It should be noted that the authors also have used external devices for current and voltage measurements so as to avoid the low accuracy of the measuring system.

The DC/DC converter was designed and constructed by the TEP-192-Research Group of Huelva university. It is equipped with a PWM switching input (20 kHz) which allows the user to perform the control process. Technical data and some detailed specifications concerning the used converter are listed in

Table 4. Technical data of the DC/DC converter.

Parameter	Description
Switching frequency	20 KHz
Schottky diode	2MURF1560 GT, 0.4 V, 10 A, 600 V, 15 A/150 ${}^{\circ }\mathrm{C}$
Capacitances	2TK Series, $C_1$ = 1500 $\mathsf{\mu }$$\mathrm{F}$ and $C_2$ = 3000 $\mathsf{\mu }$$\mathrm{F}$
Inductance	6PCV2-564-08 94 $\mathsf{\mu }$H, 7 A, 42 m$\mathsf{\Omega }$
IGBT	1HGT40N60B3, 600 V, 40 A, 1.5 V, 150 ${}^{\circ }\mathrm{C}$
Maximum input values	$V_{in}max$ = 60 V, $I_{in}max$ = 30 A
Maximum output values	$V_{out}max$ = 250 V, $I_{out}max$ = 30 A

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The host computer has an important role in the experimental systemsince it organizes and exchanges the data between the software (Simulink, Controldesk, etc.)and the hardware (dSPACE, FC-42 Control unit, etc.). The characteristics of the host computer used in the experiments are as follows; operating system: windows 10; processor: Intel${}^{(\mathrm{R})}$ Core^TM i7 CPU; RAM:16 GB; Hard disk space: 500 GB; ports: 6 free USB ports; graphical user interface with resolution of 1920 × 1200 pixels; and I/O boards interface for physical interactions with the DS1202.

The dSpace used in this experiment is MicroLabBox dSPACE-DS1202, which is a compact system that offers excellent performance and versatility. It helps the user to turn the theoretical concepts into reality, as well as it enables the user to setup the experiments quickly and easily. MicroLabBox has more than 100 channels with different I/O types which make it a versatile development system that could be used in many fields such as development areas and mechatronic applications. Besides, it has a dual-core processor with 2 GHz and a programmable FPGA which allow the user to test even exceedingly fast control loops. It is supported by Real-Time Interface (RTI) and ControlDesk software packages so as to enable the linkage with Simulink${}^{(\mathrm{R})}$. The integration of the MicroLabBos with the host computer and the power converter is shown in Figure 13.

Once the Simulink model is compiled, the RTI sends the generated C code to the MicroLabBox. This latter will convert this code to PWM pulses and they will be sent to the power converter so as to track the desired operating power point. The power converter signals are supplied to the MicroLabBox via its analog-to-digital converter (ADC), and they will be linked with the Simulink model using the RTI library. The evolution of all the obtained signals are recorded and visualized online using the Controldesk monitoring software. This latter has the ability to measure and adjust all the model parameters at run time. Besides, it provides different graphical tools which help the user to obtain clear results. Therefore, the observation and evaluation of the parameters changes can be easily done at run time.

The fuel cell system is linked with a programmable electronic load (PEL) called “BK Precision”. It is constructed by Fotronic Corporation Company (USA) with the following characteristics: DC Power Supply, $V_{in}$ = 115 V, $V_{out}$ = [0 V–32 V], $I_{out}$ = [0 A–6 A], $Frequency$ = 47 Hz, $Resistance$ = [ $0.1$ $\mathsf{\Omega }$− 1000 $\mathsf{\Omega }$]. The PEL could be programmed via the “PV-1785B-1788” software.

5. Results and Discussion

The experimental power and potential Vs current characteristic curves of the FC-42 Evaluation Kit are shown in Figure 14. According to this figure, it is clear that the potential characteristic curves validate the theoretical results which already presented in Figure 2. Besides, it is notable that the performance of the FC-42 is enhanced by boosting the operating temperature from 42 ${}^{\circ }\mathrm{C}$ to 45 ${}^{\circ }\mathrm{C}$, while they are dropped for temperatures above than 53 ${}^{\circ }\mathrm{C}$. The increase in the performance could be explained by the rise in membrane conductivity and the exchange current density which leads as a consequence to reduce the activation losses. However, for higher temperatures, the conductivity of the membrane reduces because of the diminishing of the relative humidity in the cell membrane. It is also observed from the characteristic curves that the appearance of the activation and the concentration zones is inconspicuous and this is due to the measurement sensitivity at low and high currents.

The performance of the FC-42 under the use of the proposed MPPT control method is presented in Figure 15 which shows, respectively, the waveforms of stack current, stack voltage and stack power. It should be noticed that the noise occurred in the obtained signals is due to the impact of the control signal time-delay. The noise also could be a result of the parasite signals that come from the hardware system components. Therefore, according to these results, it is clearly demonstrated that the proposed control method succeeded to extract the maximum power from the fuel cell. Thus, by running the fuel cell for up to more than 200 s, the MPP can be extracted for temperature variation in a range of [42–55 ${}^{\circ }\mathrm{C}$]. Before starting the control process and aiming to achieve the influence of the temperature on the MPPT control method, the fuel cell was heated manually until 54 ${}^{\circ }\mathrm{C}$ using the FC-40 control unit which shown in Figure 11. Then, by applying the controller, the FC-42 power could reach about 375 W as shown in Figure 15C. However, with temperature variations, this amount decreases until 355 W or less. This validates that the proposed control method tracks the MPP curve which was presented in Figure 7.

On the other hand, aiming to find out the behavior of the HO-PCL against the unexpected disturbances, a variation of 20 $\mathsf{\Omega }$ in the load resistance was applied each 25s. These variations, as shown in Figure 16A, were done using the programmable electronic load (PEL) that commutes between 30 $\mathsf{\Omega }$ and 50 $\mathsf{\Omega }$. Despite these sharp variations, it is clearly shown in Figure 15, Figure 16B,C and Figure 17, that the proposed HO-PCL shows robustness against external unexpected disturbances. Thus, soft signals with high accuracy and without any overshoots are obtained. Besides, a smooth and fast rise to the desired value also can be seen in Figure 17A,B. Consequently, high tracking performance with proper dynamic behavior and global system stability are obtained.

6. Conclusions

In this paper, a novel MPPT method based on a combination of RCE and HO-PCL has been proposed for an FC-42 Evaluation Kit 360W to extract the maximum power under load and system parameter variations. The experimental system including the FC-42, the converter, the programmable electronic load and the host computer, have been installed with the MicroLabBox dSPACE DS1202. The performance of the FC-42 Evaluation Kit under different operating temperatures was studied. The power and potential Vs current characteristic curves have demonstrated that the performance of the FC-42 is enhanced by boosting the operating temperature. The proposed MPPT method has been designed and built on MATLAB/Simulink and linked with the MicroLabBox using the DS1202 linkage blocks. The performance of the MPPT method has been evaluated and discussed. The obtained experimental results have proven the success of the proposed method in extracting the maximum power from the FC-42 with high tracking performance. Thus, robustness, high tracking accuracy, proper dynamic behavior, and global system stability are obtained even under large load variation. Finally, since the MPPT methods are significantly important for clean energy sources such as Heliocentris FC-42 Evaluation Kit, this work will pave the way for more progressing and sophisticated research on this topic.