Energy optimization of PV systems under partial shading conditions using various technique-based MPPT methods – Nature

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Scientific Reports volume 16, Article number: 5128 (2026)
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This study investigates the problems associated with the nonlinear power–voltage characteristics of photovoltaic (PV) systems, especially under partial shading conditions (PSC), which reduce energy efficiency and tracking accuracy. To overcome these limitations, two improved maximum power point tracking (MPPT) controllers based on Artificial Neural Network (ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) techniques are proposed. The controllers are designed with a suggested architecture that uses the power-voltage derivative ((:frac{dV}{dt})) and the voltage time derivative ((:frac{dP}{dV})) as input features, enabling predictive, non-iterative control. This approach eliminates the steady-state oscillations inherent in conventional perturb-and-observe (P&O) algorithms and achieves superior dynamic response under rapidly changing environmental conditions. Simulation results demonstrate significant improvements compared with the traditional P&O method. The proposed ANN and ANFIS controllers achieved average tracking efficiencies ((:{eta:}_{text{avg}})) of 99.4% and 99.75%, respectively, with a response time reduction of about 55% and steady-state oscillation suppression exceeding 70%. The ANFIS controller exhibited higher stability, reducing the duty-cycle fluctuation index ((:{sigma:}_{text{DCy}})) by approximately 20% compared with the ANN controller, resulting in smoother and more reliable power extraction. A comparative evaluation with recently published metaheuristic and hybrid AI-based MPPT approaches confirmed that the proposed ANFIS model achieves equal or better performance while maintaining very low computational complexity. The average execution time per control step remained below 0.2 ms, confirming the suitability of both controllers for real-time deployment on low-cost digital signal processors (DSPs). These findings demonstrate that the proposed intelligent MPPT framework provides a fast, accurate, and computationally efficient solution for improving the reliability and energy yield of PV systems operating under dynamic and partially shaded conditions.
The use of renewable energy sources has attracted much concern in the last two decades, primarily because of the change to sustainable sources of energy. Solar energy is a unique and accessible power resource to address the energy supply issue of the world1,2. Solar photovoltaic (PV) systems, in which direct sunlight is converted into electricity, are the leading types of modern renewable electricity generation technologies3,4. However, the performance and availability of PV systems are highly sensitive to their integrated nonlinear power-voltage (P–V) characteristics. These characteristics are all the more important under different environmental conditions, such as partial shading, requiring robust control strategies to improve the energy conversion process5,6. Over the past two decades, the integration of smart energy controllers, precision design and computer intelligence into PV systems has remained an exciting area of research and development. Studies conducted show that PV has scaled through the global market and reached and exceeded 630GW of power in 2023, which is estimated to double by 2030. While the irradiation fluctuations, temperature fluctuations and shading concern the operation of the PV systems and are in the developmental stage7,8,9. Internationally, the solar energy market is expected to reach an average annual growth rate of 20.5% and an installed capacity of 2.500 MW by 2030. The integration of high MPPT techniques is essential to ensure that PV systems are optimized for this growth10,11. Recent studies reveal that AI-based-MPPT controllers can enhance the system efficacy by 5% to 15% than other methods, making them crucial in modern PV structures12,13. Furthermore, the application of improved MPPT efficiency can lead to enhanced energy return, besides lowering storage and grid infrastructure costs14. New market research indicates that the implementation of improved MPPT technologies can reduce the Levelized Cost of Energy (LCOE) of solar energy by 10–20%, improving the competitiveness of solar energy compared to traditional energy sources15,16. Advanced optimization methods are, therefore, critical in determining the suitability of PV systems for the growing need for renewable energy compared to other sources. The power delivered by PV systems is adjusted according to a certain characteristic of the system known as the maximum power point (MPP)17,18. Various MPPT algorithms are used to monitor and operate the PV system at this point, so that energy can be extracted as efficiently as possible at maximum output. Conventional MPPT control algorithms include the perturb and observe (P&O) and incremental conductance (IncCond) methods, which are relatively medium-performance and easy to implement but suffer from slow convergence, oscillation around the MPP and poor efficiency when irradiance uncertainty levels change19,20,21. These constraints require the use of other efficient and flexible control techniques. Off-grid and grid-connected PV systems generally require MPPT techniques because of the benefits obtained in terms of improved power conversion efficiency22. Based on previous experimental and simulation cases, MPPT technology can be precisely controlled to achieve efficiency increases of 5–25% in solar energy, depending on technical and environmental conditions23,24. In addition, the selection of an MPPT algorithm is essential to reduce system losses, improve reliability, manage the size of energy storage components and, ultimately, reduce costs of nonrenewable sources in the power grid when achieving high amounts of energy from solar panels. With growing international interest in low-carbon and renewable energy societies, improving MPPT techniques remains a central concern for the industrial process and commercial communities25,26. Recent advances have led to the development of artificial intelligence (AI) based control techniques that could easily overcome all the shortcomings of the traditional MPPT algorithms. Artificial neural networks (ANN) and adaptive neuro-fuzzy inference systems (ANFIS) are among the promising control techniques due to their ability to be easily implemented and developed to achieve high efficiency and accuracy in solar energy tracking with reduced computation time, and used in both simulation and experimental-style cases with a given set of operating conditions27,28,29. ANNs use past and real-time data to estimate MPP; on the other hand, ANFIS hybridizes the learning performance of ANNs with the compatibility of fuzzy inference systems. Intelligent-based MPPT controllers have made considerable progress over conventional controllers in terms of tracking performance and operating stability in PV systems. ANNs, trained on large data sets, are able to achieve MPP tracking efficiencies in excess of 99%, even in sub-optimal scenarios such as partial shading30,31. Similarly, ANFIS controllers have demonstrated greater flexibility, reduced oscillations and allowed the system to converge more quickly to MPP. Taken together, these capabilities enable intelligence-based solutions to better manage PV systems, with the promise of scale and reliability for large, real-world PV systems32,33. In addition, ANN and ANFIS methods perform better than more fixed AI rule-based methods implemented using machine learning (ML) when the environment changes rapidly with uncertain operation conditions, such as shading or temperature increases32,34. As a result, this approach avoids substantial power loss, which is a unique strength of the proposed approach compared to MPPT techniques that do not use prediction and forecasting. Therefore, as systems become larger, more complex and more distributed, AI-driven controllers like ANN and ANFIS become the key to maximizing energy efficiency and ensuring the stability and reliability of PV systems35,36. The main problem with PV systems is that the P-V characteristics of normal PV modules are non-linear and further exacerbated by complicating factors such as partial shading conditions (PSC). PSC is an effect that results from exposing one or more sections of a PV array to different levels of irradiation and, therefore, to several local MPPs, thereby reducing the global maximum-power point (GMPP). This not only reduces the efficiency of energy conversion but also compromises the possibility of achieving MPPT37,38. In addition, temperature changes affect the overall open circuit voltages and short circuit currents of the PV panels, which also necessitate the use of dynamic MPPT techniques. The effects of PSC on PV output have been well analyzed, revealing efficiency reductions of up to 15% in PSC-managed systems. Managing these losses requires MPPT controllers able to identify between GMPP and local MPP, which is a major challenge for most algorithmic approaches. In addition, PV temperature fluctuations lead to a voltage variation of 0.45 mV/k per cell, which requires continuous correction at the cell level. All these challenges present a scope for implementing AI controllers. The benefits of this implementation will result in shorter convergence time, higher accuracy and better performance when the system is confronted with complex operating conditions39,40. By using real-time data analysis and integrating the intelligent control techniques in MPPT systems, performance can be optimized by detecting device misalignments and predicting energy consumption patterns in several daily conditions, which will improve energy economic dispatch and minimize the energy cost of the PV power system, leading to a higher profit for consumers41,42. To address these challenges, recent research has focused on developing novel frameworks and methodologies. For instance, the Environmental Sensor-Less Hybrid Analytical-Machine Learning (ESHAML) framework combines an analytical PV model with a machine learning-based neural network for ultra-fast and sensor-less solar irradiance estimation, achieving high accuracy with a Mean Absolute Percentage Error (MAPE) between 2.67% and 4.94%85. Similarly, an intelligent environmental-sensorless model based on an IVR-Neural Network (IVRNN) has been proposed for MPP voltage estimation, demonstrating high accuracy (MAPE 2.89%–3.27%) and robustness against system aging86. Furthermore, to bridge the gap between simulation and real-world deployment, the Real-Climatic Microcontroller-in-the-Loop (RCMIL) framework has been introduced as a cost-effective and realistic verification platform for MPPT controllers87. For addressing the critical issue of partial shading, the Multi-Peak to Single-Peak Conversion (MSMPPT) framework has been developed to empower conventional MPPT algorithms like P&O and INC to reliably track the GMPP under PSC, achieving 50% faster tracking and near-perfect steady-state efficiency88. In this paper, two improved MPPT controllers using ANN and ANFIS control techniques are presented to address these issues. The learning process for these controllers is based on the P&O method, but is further improved upon to take advantage of the predictive and learning capabilities of AI techniques. The input variables developed from the voltage and power derivatives provide an accurate prediction of the duty cycle (DCy) required for optimum operation. This work has shown that these controllers outperform the conventional controller for convergence time, oscillation rate and tracking performance under standard and PSC conditions, based on the obtained findings from simulations using MATLAB/Simulink. In particular, the contribution of this work is based on the ANN and ANFIS controllers. It provides an overview of the use of these controllers to handle nonlinear P-V characteristics and PSC situations. The ANN controller was found to be effective in terms of tracking performance, with 99.5% efficiency during dynamic performance. Furthermore, the ANFIS controller produced a higher efficiency of 99.75%, low voltage ripple and much higher stability than the other methods in comparison with the traditional P&O technique. In addition, the proposed controllers also address practical issues such as computational time and scale, as well as improving tracking efficiency. This ensures that these controllers can be deployed in both small, simple domestic systems and large, complex PV systems. In addition, they can be interfaced with other hardware and software structures, making them highly flexible and cost-effective. These findings confirm the potential of intelligent control techniques to optimize PV power management by improving current MPPT techniques. This article is organized by section: A review of previous research and related work is presented in Sect. 2, along with their advantages and limitations. The modeling of the PV system and boost converter (BC) is discussed in Sect. 3. Section 4 presents the MPPT techniques using ANN and ANFIS, the design and learning technique of each algorithm and their approaches. In Sect. 5, simulation results based on different irradiance and temperature profiles are discussed, and the performance of the proposed controllers that evaluate the effects of PSC on the MPPT process is described. Finally, conclusions and recommendations for further studies are presented in Sect. 6.
Over the last decade, a number of researchers have studied new and improved MPPT algorithms for PV systems with standard and PSC. Partial shading was largely addressed by metaheuristic algorithms, hybrid methods and bio-inspired techniques in these studies. Both approaches have shown certain advantages but have also highlighted the need for certain improvements. A new metaheuristic optimization algorithm was proposed in43 to solve the nonlinear characteristics of PV systems under PSC. This technique demonstrated greater accuracy and better resistance to various conditions than the previous method. However, it has the weakness of high computational complexity and is not suitable for real-time systems where time is an important factor. An improved MPPT technique based on the falcon optimization algorithm (FOA) was introduced in44, where greatly improved convergence speed and reliability in reaching the GMPP were demonstrated. However, this method proved problematic in achieving consistent performance when the dynamics of the environment changed rapidly. In45, a new MPPT algorithm was developed based on the P&O method and optimized to control multiple peaks due to shading effects. This method achieved faster convergence rates, although the training of the learning algorithm required careful tuning to improve its ability to perform optimally under different conditions. Similarly46, examined and compared swarm optimization algorithms, for example, particle swarm optimization (PSO) and ant colony optimization (ACO) for MPPT operation. Although these algorithms allowed the system to handle different and complicated shading patterns, they had problems with parameter tuning and computational overhead. Other mixed strategies were investigated in47, where MPPT was handled by integrating the simulated annealing (SA) algorithm and P&O. These strategies improved features such as accuracy and dynamic response, but also led to considerable computational complications. In48, the effectiveness of genetic algorithms (GA) and bat-inspired optimization (BIO) algorithms for MPPT under different shading was tested. These methods improved tracking efficiency and were considered better because they optimized the power for efficiency. Still, they increased computation time, and therefore, when real-time tracking is required, these methods are not very useful. The cuckoo search algorithm (CSA) is implemented for MPPT operation in49, which shows high accuracy and adaptability to fluctuations. However, it was found that it needs time to respond to sudden changes in irradiance, so it is outperformed by other protocols. An arithmetic optimization algorithm (AOA) was proposed in50, which is applicable to the PV system with energy storage and guarantees reliable operation under all conditions. Still, its scalability has not been confirmed, and the number of tests required for large-scale validation is large. Further studies on swarm intelligence-based designs were conducted in51, where a two-level control strategy combining PSO with other methods was investigated, and the effect on energy production was evaluated under different shading conditions. This method was the most effective in terms of adaptation and measurement accuracy, but was sensitive to initial parameters. Similarly, in52, a saltpeter swarm optimization (SSO) algorithm enabled dynamic adjustment to change conditions, but its computational complexity perturbed hardware realization. These shading effects influencing the MPPT were studied in detail in53, and a new technique for dealing with these effects was also discussed in the same context. This work highlighted the fact that more complex algorithms are needed to solve complex and realistic shading cases, but did not provide as much effective experience as the previous study. The study in20 describes the recent development of MPPT techniques. It shows that the complexity of the algorithm and the efficiency of the system are inversely proportional to the different techniques. Researchers proposed different MPPT techniques in54 with an emphasis on the use of P&O and AI techniques for maximum power extraction. Although this method showed better efficiency, the problem was the heavy reliance on additional hardware components. Improved PSO algorithms were presented in55; experiments showed their effectiveness, but their inability to scale to different PV configurations. In56, cat swarm optimization (CSO) was developed for global MPPT with very accurate tracking but a poor convergence rate under sudden environmental changes. Following a study of single and multiple MPPT structures in57, the authors highlighted that direct DCy controllers offer advantages for MPPT designs, but there are still scaling issues. In58, the author studied MPPT algorithms based on neural networks (NN) compared to traditional approaches and showed greater efficiency and better adaptability, but data-intensive training. In59, a simple algorithm based on a parabolic hypothesis (PHY) was able to obtain a global MPPT with a lower computational load, but it had to be validated under a highly dynamic scenario. Different MPPT controllers in60 improved the transient response of PV systems, but they were computationally intensive and, therefore, not scalable. In61, deterministic and metaheuristic methods were compared, with the metaheuristic performing better under non-uniform shading conditions but with higher computational costs. To overcome these drawbacks, the control method presented in this article uses ANN and ANFIS to optimize the MPPT algorithm. These techniques use the P&O method in their learning process while varying the DCy proportionally to the voltage and power derivatives. Thus, the control systems involved in the proposed approaches justify enhanced performance under dynamic environmental conditions. It is found that the proposed ANN and ANFIS controllers offer better performance than conventional MPPT algorithms in terms of convergence rate, tracking accuracy and system stability under normal and partial shading scenarios. Both AI-based methods help minimize voltage and current variations, increase overall efficiency and respond to irradiance or temperature fluctuations. They can be adapted to a variety of PV applications ranging from residential use to utility-scale grid-integrated real systems.
The structure of the studied PV system is shown in Fig. 1. This system consists of an array of PV panels; the parameters of each panel are shown in Table 1. This panel array is connected to a BC and supplies an ohmic load. The BC is controlled via an MPPT system, the inputs of which are the PV–V&I, and the output is the D signal, which is passed through a plus-width modulation stage to generate pulses applied to the transistor switch in the BC.
The structure of the studied PV system.
PV cells are used in PV systems to convert PV energy directly into electrical power. To maximize the power of the PV panels, the system is composed of panels coupled to a BC. The primary component of a PV panel is its PV cells, which are made of semiconductor materials. The electrical circuit model of a PV cell is frequently depicted in Fig. 2.
PV cell model.
The PV cell model is provided as62,63,64:
Kirchhoff’s law aplied to the above circuit gives Eq. (1)
The current flowing throught the diode is shown in Eq. (2)
The expression for the photocurrent is given by the following equation (Eq. (3))
Equation (4) describes the saturation current expression
Where,
q: is the charge of the electron, 1.6 × 10–19 C.
A: is the diode ideality factor.
N: is a number of series connected cells in the module.
K: is Boltzmann’s constant.
TC: is the cell’s operating temperature.
ISC: is the short-circuit current.
Ki: is the T coefficient of the short circuit (A/K).
Tref: is the cell reference T in Kelvin, 298 K.
Gr: represents the reference G, 1kW/m2.
Is.ref: is the cell reverse saturation current in standard conditions.
Eg., is the band-gap energy of the semiconductor.
The technical completeness of this study is ensured by the explicit use of the Single-Diode Model (SDM) for the PV array simulation. The output current ((:I)) of the PV cell is given by the fundamental I-V characteristic equation:
The thermal dependence of the model is captured by the following equations:
During the research, the performance of the MPPT systems was selected for two scenarios. The first scenario includes the application of homogeneous levels of irradiance (G), with a change in its value or a change in the values of the temperature (T). Table 2 illustrates the nominal values obtained from the characteristics of the studied PV system, where they used parallel strings of 10 and 7 module series-connected per string.
In the second scenario, the case of applying heterogeneous levels (PSC) was studied. Figure 3 shows the characteristics of the current under PSC, where its value was 49.7845 A at 151.124v.
I-V characteristic of PV panels for PSC.
Figure 4 indicates the nominal characteristics of the power under PSC, where the GMPP is fixed at 7523.62 w.
P-V characteristic of PV panels for PSC.
The BC model is depicted in Fig. 5; its dynamic mathematical model is presented as follows:
BC modelling.
The primary difficulties with PV systems are their intrinsic poor conversion efficiency and nonlinearity, which are greatly impacted by external variables since the T and irradiance differences cause MPPT to fluctuate dynamically. To function effectively, PV systems need to use MPPT systems. To optimize the quantity of energy received from sunlight, these systems continuously adjust the PV operating point to maintain it running at or near its MPP65,66. With its low cost and ease of application in PV systems, the P&O method is a preferred option for MPPT. Through constant operating point adjustment to be near the MPP, the P&O approach seeks to maximize the power collected from the PV panels. Nonetheless, its shortcomings are well-known, including long response times, particularly in the face of abrupt weather changes, oscillations at the MPP, and low efficiency in comparison to more advanced control systems. This algorithm’s flow chart can be seen in Fig. 6.
Flow chart of the P&O Algorithm.
ANN has experienced significant advancements recently in both theory and real-world applications. The inputs to the ANN-based-MPPT systems can be PV array parameters or recorded signals like voltages and currents, and conservation data like T and radiation, or a combination of these variables or any available data. Typically, the outputs consist of one or more reference signals, like a DCy, which are utilized to operate the electronic converter at or close to the MPP. The results of model-based simulations and module experimental observations provide the input and output data67,68. In this research, an ANN was designed, shown in Fig. 7, and trained according to the data shown in Table 2. This data depends on the general principle of the P&O algorithm shown in Fig. 6. When the voltage and power of the PV panels increase together or decrease together, this means reducing the value of the DCy, and otherwise, this value must be increased. Figure 8 shows the proposed ANN training regression, and Fig. 9 shows the ANN training performance. Figure 10 shows the Simulink model of the proposed ANN method, which is based on measuring the current and voltage of the PV and generating the DCy according to Table 3. Where dx = x(k)-x(k-1) for x = p, v or D.
The proposed ANN architecture.
The proposed ANN training regression.
The proposed ANN training performance.
Simulink model for ANN method.
In order to produce accurate and effective results, an ANFIS combines the capabilities of fuzzy logic control systems (FLCs) and ANNs. FLCs use fuzzy logic to make decisions based on experience-based rules; however, choosing the right rules by hand is a problem. However, because they don’t offer a clear explanation of the decision-making process, ANNs are regarded as “black boxes” even if they are capable of learning complicated patterns in nonlinear systems. By fusing the interpretative accuracy of FLC with the adaptive learning of ANN, ANFIS seeks to overcome the drawbacks of both systems and is applicable to a variety of domains, including complex systems control, prediction, and optimization69,70. In this research, an ANFIS MPPT controller is designed based on the rules shown in Table 2 and in a manner similar to what was done in Sect. 4.2. However, as mentioned previously, the ANFIS controller provides greater accuracy and better dynamic performance, as the results will be shown later. Figure 11 shows the structure of the proposed ANFIS MPPT controller, and Fig. 12 shows the surface graph of the proposed ANFIS controller. Figure 13 shows the Simulink model of the proposed ANFIS method, which is based on measuring the current voltage of PV and generating D.
The proposed ANFIS architecture.
Surface graph of the proposed ANFIS controller.
Simulink model for the ANFIS method.
To address the limitations of conventional MPPT algorithms, particularly their slow response and steady-state oscillation under dynamic conditions, the proposed ANN and ANFIS controllers incorporate a novel input/output mapping strategy that significantly differentiates them from existing AI-based MPPT literature. The core of this improvement lies in the utilization of an enhanced input vector that captures the dynamic state of the Photovoltaic (PV) system, specifically the power-voltage derivative (dP/dV) and the voltage time derivative (dV/dt). The inclusion of dP/dV allows the AI to accurately determine the direction of the Maximum Power Point (MPP). At the same time, the dV/dt term is crucial for predictive tracking, as it quantifies the rate of change in environmental conditions (irradiance or temperature), enabling the controller to anticipate and adjust to shifts in the MPP location. Furthermore, the output of both AI models is the optimal Duty Cycle (DCy) value required by the Boost Converter (BC), establishing a direct mapping from the dynamic state to the control variable. This design replaces the iterative, step-by-step adjustment process of the P&O algorithm with a single-step, non-iterative calculation, resulting in faster convergence and the elimination of steady-state oscillation. While the training data is generated under a wide range of operating conditions using a modified P&O approach to ensure comprehensive coverage, the AI’s function is to learn the optimal predictive control surface, not the P&O algorithm itself. This distinction—using P&O as a data generation tool for a superior, predictive AI controller—is the key methodological contribution that ensures robust performance under Partial Shading Conditions (PSC). Mathematically, the control mapping can be expressed as:
The reproducibility of our results is ensured by a detailed, transparent description of the training and validation process for both the ANN and ANFIS models. The training data were collected from a high-fidelity MATLAB/Simulink model of the PV system operating under a wide range of conditions (irradiance from 200 W/m2 to 1000 W/m2 and temperature from 25 °C to 50 °C). The P&O algorithm was used only to ensure the system reached the true MPP for each condition, thereby generating the target optimal (:text{D}text{C}text{y}) value corresponding to the calculated input vector (:left[frac{dP}{dV},frac{dV}{dt}right]). The training process utilizes a small, highly efficient, and carefully curated dataset to ensure rapid convergence and high accuracy. The dataset consists of approximately 500 continuous, numerical data points. The specific architectural and training parameters are summarized in Table 4.
To validate the efficacy of the proposed ANN and ANFIS control strategies, MATLAB/Simulink-based simulations were conducted under different scenarios. The simulation model involves a photovoltaic system with 10 strings connected in series, of which 7 PV modules are connected in series. The specifications for each module are an open-circuit voltage of 37.92 V, a short-circuit current of 8.62 A, an MPPT voltage of 30.96 V and a current of 8.07 A. The MPPT system uses the BC, which has been developed with a switching frequency of 20 kHz, and the DCy has been modified interactively based on the tested ANN, ANFIS and P&O control techniques.
In the first scenario, solar irradiation levels were used for all modules of G = 0.5, 0.7 and 1 kW/ m², with temperature values of T = 15 °C, 45 °C and 25 °C. The simulation input parameters were chosen to mimic realistic conditions frequently occurring in operational photovoltaic systems. The irradiance and temperature profiles for the tests described in this study are shown in Figs. 14 and 15, respectively. The parameters for the standard test conditions for the PV array are: rated power, voltage = 454.94 V, current = 38.62 A, G = 1 kW/m2, T = 25 °C. These input data provide a reference point against which the performance of the control systems can be evaluated in the context of different environmental conditions.
The profile of irradiance values.
The profile of temperature.
Figures 16 and 17, and 18 show the PV panel’s power, voltage, and current, respectively.
The power of PV panels.
The voltage of the PV panels.
The current of PV panels.
It is clear from Fig. 16 that the power extracted from the PV panels is at higher values when using the ANFIS MPPT controller, followed by the ANN MPPT controller and, finally, the P&O MPPT controller. This indicates the effectiveness of the ANFIS control system and its high dynamic performance, as it contributes to achieving greater efficiency and fewer vibrations in the extracted power. For example, the extracted power at moment 0.6 s when using the ANFIS controller is 16,030 W. At the same time, it is 15960w watts for the ANN controller, and it is 15900w when using a P&O controller, knowing that the optimal value, according to the Figure, is 16076w. The extracted power at the moment of 0.7 s when using the ANFIS controller is 16,030 W. At the same time, it is 15960w watts for the ANN controller, and it is 15900w when using a P&O controller, knowing that the optimal value according to Table 1 is 16076w, where T = 45° and G = 1000w/m2. The extracted power at the moment 1.7 s when using the ANFIS controller is 12288w, while it is 12,280 watts for the ANN controller, and it is 12150w when using a P&O controller, knowing that the optimal value according to Table 1 is 12313w, where T = 25° and G = 700w/m2. Therefore, it can be said that the efficiency of the controllers ANFIS, ANN and P&O are 99.75%, 99.5% and 98.79%, respectively. The effectiveness of the ANFIS controller is also shown in reducing voltage ripples, as shown in Fig. 17, and obtaining a larger current with fewer vibrations, as shown in Fig. 18. For example, at moment 0.8 s, the difference between the highest and lowest voltage value (peak to peak of voltage) using the ANFIS controller is 9 V, while it is 10 V when using the ANN controller. It is 12 V when using the P&O controller, so the peak-to-peak current using the ANFIS controller is 4 A, while it is 5 A when using the ANN controller, and it is 6 A when using the P&O controller. The reason for the superiority of the ANFIS controller is its great ability to analyze signals coming from voltage and current sensors and its ability to make the best decision at a faster speed compared to other control systems. It generates the best DCy with the least possible ripples, as shown in Fig. 19.
The DCy generated by the MPPT controllers.
In the second scenario, PSCs were applied at the output of the PV array to model a non-uniform distribution of irradiance across the array. The shading configuration was modeled with three distinct irradiance levels: G = 1 kW/m2, 0.7 kW/m2 and 0.5 kW/m. The voltage and current characteristics of the array under PSC were taken to evaluate the performance of the proposed controllers of the array output to detect and track the GMPP, whose value was set at 7523 W. This scenario provided a realistic representation of phenomena such as shading by clouds, nearby buildings or trees that are often experienced in practical photovoltaic installations. In the presence of PSC, the PV extracted power value will certainly be less than the extracted value in the presence of homogeneous irradiance values. In addition, more than one peak appears on the power-voltage curve, as shown in Fig. 4. Here lies the importance of using advanced and improved MPPT systems to track the GMPP. The PV extracted power is shown in Fig. 20. The ANFIS and ANN controllers are able to track GMPP. In contrast, the P&O controller fails to do so, as the value of the power extracted from the PV energy using the ANFIS controller reaches the value of 7472w and the value of 7436w using the ANN controller, while it is at the value of 5457w when using the P&O controller, knowing that the optimal value is 7523 w. Figure 21 presents the PV panel voltage for PSC.
The power of the PV panels for PSC.
The voltage of the PV panels for PSC.
According to Fig. 3, the voltage of the panels for PSC should equal 151 V, and the current should equal 49 A. The proposed AI controllers achieve this, while the P&O controller fails to achieve this, as shown in Figs. 21 and 22. This is because Intelligent controllers keep the operating point very close to the optimal operating point, while using a P&O controller is far from it, as shown in Fig. 23.
The current of the PV panels for PSC.
The DCy generated by the MPPT controllers for PSC.
To ensure a rigorous and quantitative evaluation, the following metrics are used:
Average Tracking Efficiency ((:{eta:}_{text{avg}})): The mean efficiency calculated over the entire test duration ((:{T}_{text{test}})) and for all test profiles ((:{N}_{text{profiles}})).
Tracking Error Percentage ((:text{TEP})): Quantifies the difference between the theoretical Global Maximum Power Point ((:{P}_{text{GMPP,:opt}})) and the average power tracked ((:{overline{P}}_{text{tracked}})) under PSC.
Standard Deviation of Efficiency ((:{sigma:}_{eta:})): Measures the consistency of the tracking efficiency across different test profiles.
Average MPPT Tracking Time ((:{T}_{text{MPPT}})): The average time taken for the controller to converge to within a (:pm:1text{%}) band of the MPP/GMPP.
Duty Cycle Fluctuation Index ((:{sigma:}_{text{DCy}})): The Standard Deviation of the Duty Cycle signal during steady-state operation, quantifying stability.
The performance results, evaluated using the defined metrics, are presented in Table 5.
The training of the ANN model took approximately 1 min, and the ANFIS model required 8 min on a standard desktop environment. The real-time execution complexity is minimal. The execution time per step for both controllers was measured to be less than 50 µs in the simulation environment, confirming their suitability for low-cost Digital Signal Processors (DSPs).
To demonstrate robustness against real-world imperfections, band-limited white noise (simulating sensor error) was introduced to the voltage and current inputs. The noise level was set to (:pm:1text{%}) of the nominal signal value. The ANFIS controller maintained a tracking efficiency of 99.5% even with the added noise, confirming the superior robustness of the AI controllers.
To benchmark the results, a Comparative Literature Table (Table 6) is presented, which confirms that the 99.75% efficiency achieved by the ANFIS controller is competitive with, or exceeds, the performance of current State-of-the-Art metaheuristic and hybrid methods.
From Table 6, it can be seen that the proposed ANFIS-based MPPT controller achieves a highest average tracking efficiency of 99.75%, outperforming or equalling the most recent state-of-the-art methods. Compared to hybrid metaheuristic approaches such as PSO-ANN, FWA, SSO, and AOA, which exhibit efficiencies ranging between 99.55% and 99.68%, the ANFIS method provides comparable or superior performance while maintaining reduced oscillations, faster response, and lower computational demand. It also clearly exceeds the performance of classical and modified P&O or Incremental Conductance (IncCond) algorithms, whose efficiencies vary between 94% and 98.6%. Furthermore, the proposed controller rivals the drift-free P&O approach (99.8%) but with greater robustness and lower sensitivity to environmental variations. This superior balance between accuracy, dynamic adaptability, and hardware simplicity confirms that the ANFIS controller offers an optimal trade-off between efficiency and implementation complexity, making it highly suitable for real-time PV energy optimization under partial shading conditions.
This paper presented a comparative analysis of ANN- and ANFIS-based MPPT controllers for photovoltaic systems operating under dynamic environmental conditions. The results demonstrate that, while the ANN controller achieves faster convergence, the ANFIS controller offers superior tracking accuracy and robustness, particularly in the presence of irradiance and temperature variations. Computational analysis further confirms that both controllers possess low algorithmic complexity and short execution times, making them well suited for real-time implementation on low-cost digital signal processors. Notably, the ANFIS controller attained a maximum tracking efficiency of 99.75%, highlighting its strong noise immunity and operational stability. Overall, the proposed ANN and ANFIS frameworks constitute intelligent, efficient, and practical MPPT solutions capable of significantly improving photovoltaic energy conversion efficiency. Although the findings are validated through high-fidelity simulations, future work will extend this study to experimental testing and Hardware-in-the-Loop (HIL) implementation to further assess real-time performance and adaptability in practical PV applications.
The datasets generated and/or analyzed during the current study are not publicly available but are available from the corresponding author upon reasonable request.
Ant Colony Optimization
Boost converter
Artificial Intelligence
Adaptive Neuro-Fuzzy Inference System
Artificial Neural Network
Arithmetic Optimization Algorithm
Bat-Inspired Optimization
Cuckoo Search Algorithm
Cat Swarm Optimization
Duty Cycle
Fuzzy Logic Control Systems
Falcon Optimization Algorithm
Genetic Algorithms
Global Maximum Power Point
Incremental Conductance
Levelized Cost of Energy
Machine Learning
Maximum Power Point
Maximum Power Point Tracking
Neural Networks
Perturbation And Observation
Parabolic Hypothesis
Partial Shading Conditions
Particle Swarm Optimization
Photovoltaic
Simulated Annealing
Variable Step Size Incremental Conductance
Saltpeter Swarm Optimization
Improved Increment of Conductance
Fireworks Algorithm
Salp Swarm Optimization
Type-2 Fuzzy Logic
Type-1 Fuzzy Logic
Shuffled Frog Leaping Algorithm-Based Sliding Mode Controller
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Department of Electrical Engineering, L2GEGI Laboratory, University of Tiaret, Tiaret, Algeria
Naima Benabdallah, Belkacem Belabbas & Ahmed Tahri
Department of Electrical Engineering, Institute of Technology, University Centre of Naama, Naama, 45000, Algeria
Riyadh Bouddou
Department of Electrical/Electronic and Computer Engineering, Afe Babalola University, Ado-Ekiti, Nigeria
Ayodeji Olalekan Salau
Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai, Tamil Nadu, India
Ayodeji Olalekan Salau
Department of Mechanical Energy and Management Engineering (DIMEG), University of Calabria, Rende (CS), Arcavacata, Italy
Anna Pinnarelli & Alireza Soleimani
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Naima Benabdallah: Conceptualization, Methodology, Software, Writing- Original draft preparation. Belkacem Belabbas: Data curation, Visualization, and Investigation. Ahmed Tahri: Methodology, Visualization, Investigation. Riyadh Bouddou: Writing- Reviewing, Editing and Validation. Ayodeji Olalekan Salau: Data curation, Methodology, Writing- Reviewing, Editing and Validation.Anna Pinnarelli: Data curation, Visualization, and Investigation. Alireza Soleimani: Methodology, Visualization, Investigation.
Correspondence to Riyadh Bouddou, Ayodeji Olalekan Salau, Anna Pinnarelli or Alireza Soleimani.
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Benabdallah, N., Belabbas, B., Tahri, A. et al. Energy optimization of PV systems under partial shading conditions using various technique-based MPPT methods. Sci Rep 16, 5128 (2026). https://doi.org/10.1038/s41598-026-36117-w
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