*Article* **Maximum Power Point Tracking of a Grid Connected PV Based Fuel Cell System Using Optimal Control Technique**

**Muhammad Majid Gulzar**

Control & Instrumentation Engineering Department & Center for Renewable Energy and Power Systems, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia; muhammad.gulzar@kfupm.edu.sa

**Abstract:** The efficiency of renewable energy sources like PV and fuel cells is improving with advancements in technology. However, maximum power point (MPP) tracking remains the most important factor for a PV-based fuel cell power system to perform at its best. The MPP of a PV system mainly depends on irradiance and temperature, while the MPP of a fuel cell depends upon factors such as the temperature of a cell, membrane water content, and oxygen and hydrogen partial pressure. With a change in any of these factors, the output is changed, which is highly undesirable in real-life applications. Thus, an efficient tracking method is required to achieve MPP. In this research, an optimal salp swarm algorithm tuned fractional order PID technique is proposed, which tracks the MPP in both steady and dynamic environments. To put that technique to the test, a system was designed comprised of a grid-connected proton exchange membrane fuel cell together with PV system and a DC-DC boost converter along with the resistive load. The output from the controller was further tuned and PWM was generated which was fed to the switch of the converter. MATLAB/SIMULINK was used to simulate this model to study the results. The response of the system under different steady and dynamic conditions was compared with those of the conventionally used techniques to validate the competency of the proposed approach in terms of fast response with minimum oscillation.

**Keywords:** renewable energy sources; fuel cell; photovoltaic; maximum power point; fractional order PID

#### **1. Introduction**

Conventional energy sources are being depleted at an alarming speed and becoming scarce; thus, the usage of unconventional energy sources is growing. Coal, petroleum, natural gas, and nuclear power are all major conventional sources. Because of their continued use, these resources have been exhausted to a great extent. Additionally, the usage of these sources contributes significantly to pollution, which contributes to global warming. Owing to these issues, scientists are forced to employ renewable energy sources (RES). Non-conventional/RES are sources of energy that are reproduced by natural processes regularly and do not deplete [1]. These sources do not damage our environment, are mostly cost-effective, and often do not require a huge investment, hence widely being accepted as more reliable. Moreover, these sources are called renewable because they are renewed or reproduced at an equal or greater rate with respect to the rate of their use.

Among all RES, solar PV, which utilizes the photovoltaic effect to produce electricity, is being widely used worldwide. Sunlight is absorbed using semiconductor materials—mostly silicon—and converted into electrical energy. The foremost drawback of solar energy is that a large area is required to install solar PV systems [2,3]. The fuel cell is, in fact, a device (electro-chemical) that uses a chemical reaction to produce electrical energy [4]. A fuel cell utilizes the energy of hydrogen (chemical energy) or other fuels to generate electricity in a clean and effective manner. When hydrogen is utilized as a fuel, the only things created are heat, electricity, and water. The prominent and unusual aspect of fuel cells is that they can be used for an extensive range of applications [5,6].

**Citation:** Gulzar, M.M. Maximum Power Point Tracking of a Grid Connected PV Based Fuel Cell System Using Optimal Control Technique. *Sustainability* **2023**, *15*, 3980. https://doi.org/10.3390/ su15053980

Academic Editor: Elena Cristina Rada

Received: 16 December 2022 Revised: 17 January 2023 Accepted: 15 February 2023 Published: 22 February 2023

**Copyright:** © 2023 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Fuel cells and batteries differ significantly from each other, as fuel cells do not require recharging since they do not run out of fuel. The fuel cell will keep producing heat and power until the fuel supply stops. A fuel cell is constructed using two electrodes sandwiched around an electrolyte. In a fuel cell, the anode is the negative (−) electrode while the cathode is the positive (+) electrode. Hydrogen is widely used as fuel in fuel cells and is provided to the anode [7], while the oxygen (from the air) is supplied to the cathode. A catalyst is needed to initiate the redox reaction. Platinum is used as a catalyst and, in some cases, enzymes are used. The catalyst converts hydrogen into electrons and protons (hydrogen ions). Here, electrons take an exterior circuit path and can be utilized to power a load, while protons cross through the electrolyte to combine with oxygen to form water [8].

Several classifications of fuel cells are currently under research, each using different fuels with different electrochemical reactions and construction. Each has a different catalyst requiring different operating conditions like temperature and has its own applications and drawbacks. Polymer Electrolyte Membrane Fuel Cells (PEMFC), also identified as proton exchange membrane fuel cells, provide a higher power density than other traditional fuel cells while being lighter in weight and smaller in size [9,10].

One vital aspect of the PV based fuel cell is tracking its maximum power point (MPP). For reliable and efficient use, it is important to use a PV based fuel cell at MPP, which depends on several factors, including irradiance, temperature, water content in membrane, and hydrogen and oxygen partial pressures. The Perturb and Observe (P&O) algorithm is the most popular to track MPP, owing to its simplicity. However, it may cause fluctuations across MPP due to excessive switching. To reduce these fluctuations, the step size can be reduced; but this will cause the tracking time to increase. The incremental conductance method is proposed in [11,12], which gives better results than the P&O, but still causes an overshoot. Sliding mode controller (SMC) is studied in [13], using a fuel cell stack with a boost converter, and performance is compared with incremental conductance and P&O. However, while it yields a significantly lower overshoot, the calculations are extensive and the design of the filter is difficult.

The Water cycle algorithm (WCA) is an effective algorithm to track MPP and it is inspired by the naturally occurring water cycle. The drawback of WCA is that it can trap in local optima [14]. The incremental conductance method has been implemented for MPP tracking, but its implementation is complex as it requires multiple sensors [15]. The author in [16] suggested a smart drive algorithm using a boost converter to track the MPP of the fuel cell, but the efficiency of the method turned out to be less than other metaheuristic techniques. Particle swarm optimization (PSO) is another technique used for MPP tracking, which is based on the natural process. Ref [17] discussed the PSO technique using a fuel cell stack with a boost converter. PSO is a metaheuristic approach, but the drawback is that it can also be stuck in local optima. Extremum seeking control is an efficient method but converges slowly [18].

A fuel cell model with a cuke converter is discussed in [19] and the firefly algorithm (FFA) is proposed to reach MPP. FFA is a metaheuristic technique, but it has a drawback, namely, in that it may be stuck in local optima. Backstepping techniques proposed in [20], show good efficiency, but the implementation requires great effort as it is very complex. Fuzzy logic control (FLC) is another important technique used to track MPP and is being used widely. FLC has been implemented using both Boost and Buck converters. The accuracy of FLC is low and one cannot be sure that the MPP calculated by the controller is accurate [21,22]. Convergence time for FLC, if used independently, can be very large. Another technique proposed in [23] is an artificial neural network (ANN); however, this technique requires an excessive amount of data.

A Jaya controller with cuke converter is implemented in [24] to improve MPP. The presented technique is metaheuristic but requires excessive computational time. The grey wolf optimization (GWO) method is also introduced in [25] to track MPP. GWO technique is motivated by the leadership hunting and hierarchy methodology of grey wolf packs. GWO is a metaheuristic technique, but its convergence rate is slow and it can be stuck in local optima. Another nature-inspired optimization technique is the salp swarm optimization (SSO) algorithm which is discussed in [26]. Despite being metaheuristic, it requires excessive computational time for processing. Anti-windup PID controllers are being used commonly in industries, due to their simplicity and fewer computational requirements [27]. However, PID is sensitive to excessive variations and can lead a system to instability. Moreover, it cannot be used for non-linear systems [28].

Higher-order sliding mode controllers tuned with a twisting algorithm (HOSM-TA) are implemented in [29]. They show high robustness against disturbances and uncertainties. The drawback of this technique is that it is very complex and there is no guarantee that the solution is accurate. Furthermore, it cannot be used for 1st order systems. Chattering is a phenomenon that decreases the efficiency of SMC and also causes heat loss in the system. To overcome this, a Quasi-continuous (QC) algorithm is proposed in [30]. This proposed technique shows considerable improvement against chattering and is also robust. Nonetheless, one of the major drawbacks is that it is complex in design with no guarantee of accuracy, and cannot be used for 1st order systems. Higher-order prescribed convergence law technique (PCL) is used to track MPP using a DC-DC boost converter, which is a robust technique and has a finite convergence time, but it is also complex with low accuracy [31]. Another MPP tracking technique is model predictive control (MPC), which offers multiple variable control and predicts upcoming disturbances and upcoming control actions. It is better than many other techniques in terms of energy savings and has enhanced transient response, but it requires specific background knowledge of the method to be implemented [32,33]. Tuning of PID with SSO technique shows good results with reasonable execution time and good accelerated convergence, and requires few parameters to be tuned [34]. However, it can suffer from premature convergence.

The integral fast terminal sliding mode control (IFTSMC) technique has advantages, e.g., robustness against uncertainties and disturbances, ability to reduce chattering, and high speed of convergence [35]. The golden section search technique is another technique for MPP. Although this technique is faster than many heuristic methods, the implementation of the same can be costly; furthermore, it requires knowledge of fuel cell plant specifications [36]. The forensic-based investigation algorithm (FBI) has been used for proportional integral derivative, which requires multiple sensors and, hence, can be costly [37]. The equilibrium optimizer algorithm is adopted to optimize FLC for MPPT. The algorithm itself is complex and also FLC lacks in accuracy [38,39].

Table 1 lists the key characteristics and provides a comparison of the various approaches previously employed.


**Table 1.** Summary of Fuel Cell-based MPPT Techniques.


**Table 1.** *Cont.*


**Table 1.** *Cont.*

#### *Novelty and Contribution*

The literature review reveals specific areas that need further improvement; thus, the proposed technique has focused its utility on these areas. This main contribution of the proposed work is as follows:


The paper is organized as follows. Section 2 provides the design and modeling of the PV and Fuel Cell. The proposed control strategy is described in Section 3. Section 4 is designated for the attained results and discussions. Section 5 is dedicated to the conclusion.

#### **2. System Modeling**

The system under study is designed to comprise a grid-connected proton exchange membrane fuel cell (PEM) together with PV system, a DC-DC boost converter along with resistive load, and a robust power point tracking controller. The output from the controller is further tuned and PWM is generated, which is fed to the switch of the converter. Figure 1 presents an overview of the model under study.

**Figure 1.** Fuel cell and PV to Grid stages.

#### *2.1. Fuel Cell System Modelling*

Fuel cells, first conceived by Sir William Grove in 1839, are now a viable source of energy. Fuel cells may be thought of as generators in their most basic form. Unlike traditional generators, which utilize internal combustion engines to turn an alternator, fuel cells create electricity by directly creating electrons with no moving components. As a result, they are quite effective and dependable. They are also almost silent, producing only water vapor in addition to energy and heat. As a result, they are suitable for indoor usage.

The voltage-current characteristics of fuel cells are intricate and nonlinear. A polarization curve illustrates the non-linear connection between a fuel cell's current density and voltage. The fuel cell output voltage is controlled by current density, which is affected by operational parameters. A PEMFC, a boost DC/DC converter, as well as a resistive load make up the system. The controlling variable within that system is the duty cycle of the boost converter; which is the driving variable for achieving MPPT, where *C* and *L* stand for the capacitance and inductance of the boost converter, respectively.

The fuel cell output is given by Equation (1)

$$V\_{cell} = E\_{Nernst} - V\_{act} - V\_{olm} - V\_{conc} \tag{1}$$

where *ENernst* is reversible thermos-dynamic potential which is defined by Nernst Equation (2)

$$E\_{\rm Nernst} = 1.229 - 8.5 \times 10^{-4} (T - 298.15) + 4.308 \times 10^{-5} T \left( \ln \left( P\_{H\_2} + 0.5 \ln \left( P\_{o\_2} \right) \right) \right. \tag{2}$$

where *T* indicates the absolute temperature in kelvins, *PH*<sup>2</sup> is hydrogen partial pressure (atmospheric) and *Po*<sup>2</sup> is the oxygen partial pressure. Activation voltage drop is given by Tafel Equation (3)

$$V\_{\rm act} = \zeta\_1 + \zeta\_2 T + \zeta\_3 T \ln(\mathbb{C}\_{\rm \mathcal{O}\_2}) + \zeta\_4 T \ln(\text{I}\_{\rm FC}) \tag{3}$$

Here *i* = 1, ... , 4 are parametric coefficients for every cell model, and *Co*<sup>2</sup> denotes the dissolved-oxygen concentration in the interface of the cathode catalyst, as mentioned in Equation (4)

$$C\_{o\_2} = \frac{P\_{o\_2}}{(5.08 \times 10^6) \times \exp\left(-\frac{498}{T}\right)}\tag{4}$$

The overall ohmic voltage drop is calculated as Equation (5)

$$V\_{\rm olm} = \mathbf{I}\_{\rm FC} \mathbf{R}\_{M} \tag{5}$$

where R*<sup>M</sup>* is the resistance (ohmic) and is made up of the electrode resistances as well as the resistances of the polymer membrane and electrodes. Here, R*<sup>M</sup>* is provided by Equation (6)

$$\mathcal{R}\_M = \frac{r\_m \ t\_m}{A} \tag{6}$$

where, *tm* is the membrane thickness, which is in centimeters, *A* is the activation area in micro centimeters, and *rm* is the membrane resistivity Ω*cm* to proton conductivity. Membrane humidity and temperature have a significant impact on membrane resistivity, which can be computed as Equation (7)

$$r\_{\rm ff} = \frac{181.6 \left[1 + 0.03 \left(\frac{I\_{\rm fC}}{A}\right) + 0.0062 \left(\frac{T}{303}\right)^2 \left(\frac{I\_{\rm fC}}{A}\right)^{2.5}\right]}{\left[\lambda\_{\rm m} - 0.634 - 3 \left(\frac{I\_{\rm fC}}{A}\right)\right] \times \exp\left(4.18 \left(T - \frac{303}{T}\right)\right)}\tag{7}$$

where, water content is represented by *λ<sup>m</sup>* of the membrane and is an input of the PEMFC model. In addition, it is a function of the average water activity *am* as represented in Equation (8)

$$
\lambda\_m = \begin{cases}
0.043 + 17.81a\_m - 39.85a\_m^2 + 36a\_m^3 \ 0 < a\_m < 1 \\
14 + 1.4(a\_m - 1) \ 1 < a\_m \le 3
\end{cases} \tag{8}
$$

The relationship between the average water activity and the anode and cathode water vapor partial pressures, (*Pv*,*an* , *Pv*,*ca* respectively) is given by Equation (9)

$$a\_{\rm m} = \frac{1}{2}(a\_{\rm an} + a\_{\rm ca}) = \frac{1}{2} \left[ \frac{P\_{v, \rm an} + P\_{v, \rm ca}}{P\_{\rm sat}} \right] \tag{9}$$

The saturation pressure of water *Psat* can be calculated with the subsequent empirical expression as mentioned in Equation (10)

$$\mathrm{lpg}\_{10}P\_{\mathrm{sat}} = -2.1794 + 0.02953T - 9.1813 \times 10^{-5}T^2 + 1.4454 \times 10^{-7}T^3 \tag{10}$$

The values (real-time) of *λ<sup>m</sup>* can vary from 0 to 14. The concentration voltage drop is expressed as Equation (11)

$$V\_{conc} = -\frac{RT}{nF} \ln\left(1 - \frac{i\_{FC}}{i\_LA}\right) \tag{11}$$

where, *iL* is the limiting current and it is the maximum rate at which the reactant may be given to an electrode.

Fuel cells are linked together in a series to produce the desired voltage. Thus, the *NFC* series cells per string have nonlinear *V* − *I* characteristics, as mentioned in Equation (12)

$$V\_{\rm FC} = \mathbf{N}\_{\rm FC} V\_{\rm cell} \tag{12}$$

#### *2.2. PV System Modelling*

The PV system is one of the most extensively used RES. The current source is parallel to the diode and precisely converts solar energy into electrical energy by accelerating the flow of holes and electrons inside the photovoltaic cell. It is required to create the PV source to unavoidably operate on its MPPT in order to get maximum power, since it is a non-linear current source [40].

A PV array needs to go through a number of processes to connect with a thermal power supply. As demonstrated in Figure 2, the design of a PV system includes a number of components, including a converter, an inverter, modeling, and a computation of the average power that is actually sent to the grid.

**Figure 2.** Grid Connected PV Farm Prototype.

AC voltage of PV can be calculated, by using Equation (13).

$$q = \frac{v\_{dc}}{v\_{ac}}\tag{13}$$

Here *q* is the gain between AC-DC voltage. The boost converter transfer function (TF) can be projected using Equations (14) and (15)

$$m\_1 = \frac{v\_2}{v\_1} = \frac{i\_1}{i\_2} \tag{14}$$

$$g\_1(s) = \frac{1}{m\_1} \tag{15}$$

where <sup>1</sup> *<sup>m</sup>*<sup>1</sup> is the boost converter gain. The inverter TF is mentioned in Equation (16)

$$g\_2(s) = \frac{I\_{\text{ac}}(s)}{I\_2(s)} = \frac{s^2}{s^2 + \omega^2} \tag{16}$$

Here, *ω* = 2*π f* = 2*π*(50) = 314.12rad/s. For instantaneous power, the TF is mentioned in Equation (17), where *vm im* is the impedance.

$$P(s) = \frac{\upsilon\_m i\_m}{2s} + \frac{\upsilon\_m i\_m}{2} \frac{s}{s^2 + \left(2\omega\right)^2} \tag{17}$$

The instantaneous power gain is given in Equation (18)

$$g\_3(s) = \frac{p(s)}{I\_{ac}(s)} = v\_m \left( \frac{\left(s^2 + \omega^2\right)\left(s^2 + \left(2\omega\right)^2\right)}{s^2\left(s^2 + (4\omega)^2\right)}\right) \tag{18}$$

The average power is mentioned in Equation (19)

$$p\_{w\text{\%}}(\text{s}) = \frac{v\_m i\_{\text{\%}}}{2s} \tag{19}$$

The average power gain is shown in Equation (20)

$$g\_4(\mathbf{s}) = \frac{p\_{\text{av}\%}(\mathbf{s})}{p(\mathbf{s})} \tag{20}$$

#### **3. Proposed Robust Controller**

The proposed robust controller is a combination of the Salp Swarm Algorithm tuned Fractional order PID controller to achieve the MPPT of the hybrid PV based fuel cell system, as shown in Figure 3.

**Figure 3.** Proposed Robust Controller.

#### *3.1. Salp Swarm Algorithm*

The method is inspired by transparent body salp vertebrates, which are famous for generating spiral chains when they travel to find food [41]. The leader and followers are the two basic divisions of the salp swarm. The leader's role is to direct the group as they look for food, and they update their position using Equation (21)

$$K\_{j}^{i} = \begin{cases} M\_{i} + \mathbb{C}\_{1} \left( (\mu b\_{j} - lb\_{j}) \mathbb{C}\_{2} + lb\_{j} \right) \mathbb{C}\_{3} \ge 0 \\ M\_{i} - \mathbb{C}\_{1} \left( (\mu b\_{j} - lb\_{j}) \mathbb{C}\_{2} + lb\_{j} \right) \mathbb{C}\_{3} < 0 \end{cases} \tag{21}$$

Here, *lbj* and *ubj* stands for the lower and upper limits of the *j th* dimension, while *M* stands for the target food and *K* is the 2*D* salp position. The variables *C*<sup>2</sup> and *C*<sup>3</sup> are uniform coefficients. The *C*1, which is shown in Equation (22), is utilized to balance the exploitation of food in search space.

$$C\_1 = 2e^{-\left(\frac{4t}{t\_{max}}\right)^2} \tag{22}$$

where *t* and *tmax* denotes the current and maximum iterations, respectively. Equation (23) is used to update the position of the follower salp.

$$K\_j^i = \frac{1}{2}at^2 + v\_0t \text{ } i \ge 2 \tag{23}$$

The flow chart of the complete Salp Swarm Algorithm is depicted in Figure 4.

**Figure 4.** Flowchart of Salp Swarm Algorithm.

#### *3.2. Fractional Order PID Controller*

The use of fractional calculus was developed/increased when Podlubny proposed the *PI*λ*D*<sup>μ</sup> controller in 1999. This generality of the typical PID controller included a fractional integration of order λ and a fractional derivation of order μ, and it has since led numerous scholars to a new area of study called the modification of the fractionalorder controller *PIλD*μ. Fractional order controllers are described using fractional calculus, where the calculus of proportional *α*—derivative is well-defined by the basic operator *αD<sup>α</sup> t* , as mentioned in Equation (24).

$$a^{D\_t^\kappa} = \begin{cases} \frac{d^\kappa}{dt^\kappa} \,\, a > 0\\ 1 \,\, \alpha = 0\\ \int\_a^t (d\tau)^{-\alpha} \,\, \alpha < 0 \end{cases} \tag{24}$$

Upper and lower bounds are determined by *<sup>α</sup>* and *<sup>t</sup>*, while *<sup>α</sup>* <sup>∈</sup> <sup>R</sup> and *<sup>α</sup>* operator can be substituted in the frequency domain as *F*(*s*) = <sup>1</sup> *<sup>S</sup><sup>α</sup>* . The output equation of the fractional-order controller in the time domain is given by Equation (25)

$$
\mu = k\_P e(t) + k\_i D\_t^{-\lambda} e(t) + k\_d D\_t^{\mu} e(t) \tag{25}
$$

where, *kd* is the differentiating constant, whereas *ki* is the integration constant, and *kp* is the proportional constant, μ is the fractional order of the differentiating action and λ is the fractional order of the integrating action.

In contrast to standard PID controllers, fractional-order controllers include two extra parameters that represent the order of integrating and derivative values, respectively. Based on the modification of these two factors, one can discover a wide range of fractional order controller choices.

As can be seen in Figure 5, the fractional order PI D controller expands the traditional PID controller from a point to a plane. The design of PID control may benefit greatly from this expansion's increased flexibility. Clearly, by selecting [λ, μ] = [1, 1], a traditional PID corrector can be regained; and by selecting [λ, μ] = [1, 0] and [λ, μ] = [0, 1], one can get traditional PI and PD controllers, respectively.

**Figure 5.** Types of Controllers According to Coefficients.

The FOPID executes much better than the traditional PID, since it uses discretized values. Moreover, as the stability region of the FOPID is wider than that of the PID controller, it is evident from Figure 6 that it enables more flexibility to the controller.

**Figure 6.** Stability Region of Controllers (**a**) FOPID (**b**) PID.

#### **4. Results and Discussion**

The hybrid system constituted of grid tied PEMFC and PV is simulated on MAT-LAB/Simulink for dynamic operation. The proposed FOPID controller is tested under different load conditions. Results are then compared with the conventional PI controller which substantiates the efficiency of the proposed (FOPID) controller.

Figure 7 depicts the change in irradiance, applied as input to PV to test the response of the controller, while Figure 8 shows the consumption of oxygen and hydrogen in the fuel cell. After the initial disturbance, the fuel consumption attains a constant value.

**Figure 7.** Abrupt Irradiance Change.

**Figure 8.** Oxygen and Hydrogen Consumption.

Figures 9 and 10 indicate the fuel cell output voltage and output current, respectively.

**Figure 9.** Fuel Cell Output Voltage.

**Figure 10.** Fuel Cell Output Current.

The purpose of this research was to propose and test a robust control system that is effective under varying circumstances. The same was put to the test. Figure 11 shows the output current of the hybrid system using the conventional PI controller. Nevertheless, Figure 12 depicts the output current of the hybrid system using the proposed FOPID controller and a comparison is displayed with the conventional PI controller in Figure 13.

**Figure 11.** Output Current−Using Conventional PI.

**Figure 12.** Output Current−Using Proposed Controller.

**Figure 13.** Output Current−Controller Comparison.

Figure 14 reveals the output power, for both controllers, and it is noticeable that the proposed FOPID controller shows significantly fewer oscillations and less settling time as compared to the conventional PI controller. DC output voltage (*Vdc*) is shown in Figure 15, which clearly indicates the superior performance of the projected controller and is more optimum against the uncertainties in the system.

**Figure 14.** Output Power−Controller Comparison.

**Figure 15.** DC Output Voltage−Controller Comparaison.

#### **5. Conclusions**

This research work has presented a robust control strategy using optimum salp swarm algorithm tuned fractional order PID controller for the tracking of MPP of grid tied PEMFC along with PV. The proposed controller tracks the MPP whenever uncertainty of fluctuation occurs. Conventional P&O is used to control the duty cycle of the DC-DC converter, while FOPID controls the output of the DC-AC inverter. The overall capability of the suggested controller is significantly improved over the typical/conventional PI controller; and it offers high-power tracking capability, quick convergence speed, fewer controlling parameters, and ease of implementation. In the given test bench for abrupt irradiance change, the settling time is observed just 0.058 s with minimum overshoot, as compared to the conventional PI controller. Moreover, the overall suggested regulating technique adapts to the unforeseen power system scenario fairly successfully, with minimal oscillation.

**Funding:** This research was funded by the King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** This publication is based upon work supported by King Fahd University of Petroleum & Minerals. Author at KFUPM acknowledge the Interdisciplinary Research Center for Renewable Energy and Power Systems for the support received under Grant no. EC221008.

**Conflicts of Interest:** The author declares no conflict of interest.

#### **References**


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