**1. Introduction**

Undoubtedly, finding sustainable and renewable energy sources alternative to fossil fuel resources is a necessity. Amongst the various resources, solar energy is considered the most demanding thanks to its reliability, abundance, and effectiveness in alleviating global warming problems [1,2]. One significant advantage of using photovoltaic (PV) systems is that they can produce clean energy and are free of pollution [3]. Furthermore, PV panels are low-cost and require minimal maintenance [4]. Recently, photovoltaic panels are used in numerous applications, including water-pumping systems, battery chargers, and aeronautical applications [5]. Notably, the output energy of the panel is influenced by

**Citation:** Khodair, D.; Motahhir, S.; Mostafa, H.H.; Shaker, A.; Munim, H.A.E.; Abouelatta, M.; Saeed, A. Modeling and Simulation of Modified MPPT Techniques under Varying Operating Climatic Conditions. *Energies* **2023**, *16*, 549. https://doi.org/10.3390/en16010549

Academic Editor: James M. Gardner

Received: 17 October 2022 Revised: 12 December 2022 Accepted: 29 December 2022 Published: 3 January 2023

**Copyright:** © 2023 by the authors. 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/).

both ambient temperature and solar radiation, which consequently results in the nonlinear behavior of the PV panel [1,6]. In addition, the output energy is affected by the internal parameters of the panel, which, in turn, causes the load to impose its characteristics on the output power [7,8]. Hence, acquiring the maximum accessible power from a PV panel, particularly under fluctuating weather conditions, while maintaining high reliability and lower cost is a considerable concern in research. Therefore, much effort has been devoted to obtaining solutions [9–13]. The primary proposed key solution to conquer this issue is to add an MPPT controller to the photovoltaic system to boost the obtained power in any conditions [14,15].

Various techniques have been proposed for MPPT [13,16], including Perturbation and Observation (P&O) [13], Incremental Conductance (INC) [17], Fractional Open Circuit Voltage (FOCV) [18], Fractional Short Circuit Current (FSCC) [19], Fuzzy Logic [20], and Neural Networks [21]. These MPPT algorithms vary in many aspects, including the steady-state-oscillations, the response time of tracking the MPP, cost, effectiveness, implementation complexity, and the accurate tracking of the peak point regardless of unpredictable abrupt changes of solar radiation or temperature under the conditions of partial shading [15,16]. Of the MPPT algorithms, P&O and INC techniques are considered the most common commercialized ones that are utilized in tackling the MPP [22–25], attributed to the algorithms' medium complexity and their simple implementation due to the low hardware requirements. Despite these advantages, P&O techniques suffer shortcomings that are mainly attributed to the oscillations around the MPP because the perturbation size added to the control signal in both directions is continually changing to remain in the MPP position. Furthermore, when the level of incident irradiance changes rapidly, the direction of perturbation may be incorrectly determined by the algorithm, resulting in increased power losses [26,27].

To overcome the drawbacks and shortcomings of the traditional P&O, various developments and implementations regarding the P&O technique have been addressed in the literature, such as the implementation of P&O, by using a variable duty cycle instead of a classical constant one as in [26] and proposing an adaptive P&O control algorithm that has a rapid dynamic response as presented in [27]. Another implementation of the conventional P&O was suggested in [28,29] to enhance the effectiveness of the system by employing an embedded microcontroller-based real-time algorithm with a combination of hardware-in-the-loop (HIL) along with embedded C language. Conversely, by obtaining the slope of the power–voltage curve identified and comparing it against zero at the MPP, the INC technique that has a fixed step size was introduced to minimize the oscillations of the targeted MPP [30]. On the other hand, the INC technique turns out to be much more complex when compared to P&O since it utilizes a set of divisional computations that require a calculation procedure and a stronger microcontroller [25]. Thus, upon utilizing a fixed step size, the algorithm has a low-speed response. Furthermore, in P&O and INC techniques, the tracing of the MPP may fail when solar radiation is abruptly changed or when partial shadowing occurs [15]. Consequently, modifying the INC algorithm was necessary [5,31].

Although some proposed modifications were conducted for both conventional algorithms in the literature, most of them do not achieve a fast and precise response to the first step change in the duty cycle when subjected to abrupt environmental fluctuations [25]. Moreover, to ensure the effectiveness of any of these MPPT algorithms, testing them under various operating circumstances is required. However, it is challenging to achieve the optimal test case since it is hard to control weather variations [32]. Researchers use MATLAB-Simulink [33] and other simulation environments to implement and ensure the accuracy of various MPPT algorithms before their hardware implementation because of the problems associated with the hardware components [34,35].

In the current study, modified variable step-size-based Perturb and Observe and Incremental Conductance (abbreviated as M-VSS-P&O and M-VSS-INC) algorithms are proposed to overcome the limitations of their corresponding traditional algorithms. MATLAB- Simulink software has been applied on two kinds of PV modules, namely, the polycrystalline MSX60 and the thin-film ST40 to investigate the effectiveness of the two modified MPPT algorithms in tracing the MPP under Standard Test Conditions (STC) and three different variation profiles of climatic variations regardless of the PV panel category.

The paper is organized as follows. After the introduction, Section 2 includes the PV system configuration while the model specifications details and the modified algorithms are presented in Sections 3 and 4, respectively. Section 5 is devoted to the results and discussion. Finally, Section 6 represents the conclusions of this simulation study.

## **2. System Configuration and Models**
