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Scientific Reports volume 16, Article number: 17940 (2026) Cite this article
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In the realm of photovoltaic (PV) solar systems, optimizing the extraction of maximum power from solar panels is paramount for enhancing efficiency and overall performance. This paper introduces a novel MPPT algorithm based on the Fuzzy Fishier Mantis Optimizer (FFMO) method tailored specifically for PV solar systems. The new algorithm combines the effective searching and using abilities of the FFMO method with the special features of PV panels to continuously find the maximum power point (MPP) as environmental conditions change. For the solar PV battery system, we provide a fuzzy logic-based maximum power tracking and an optimized proportional integral-based voltage controller using the Fishier-Mantis optimizer. We utilize an algorithm that employs fuzzy logic to maximize PV panel output, irrespective of environmental circumstances. We use the Fishier Mantis optimizer technique to adjust the proportional integral controller’s gain, which keeps the voltage steady across the load and helps the fuzzy logic MPPT get the most power from the PV panel. MATLAB Simulink has been used to model and test the whole system. The Fishier Mantis Optimizer is a particle swarm optimization and a genetic algorithm competitor. The whole system has been tested for constant irradiation, variable irradiance, and varied load circumstances. The PV battery system with proportional integral control shows better results in all situations based on the test results of the fuzzy-based MPPT and the Fishier-Mantis optimizer algorithm.
Photovoltaic (PV) systems are increasingly vital for renewable energy generation, providing a sustainable means to address rising global electricity demand^1,2. However, their performance is frequently constrained by environmental factors such as partial shading and fluctuating solar irradiance, which lead to complex, nonlinear power–voltage (P–V) characteristics with multiple local maxima³. Under such conditions, Maximum Power Point Tracking (MPPT) algorithms are essential to ensure optimal energy extraction⁴. Traditional MPPT methods, including Perturb and Observe (P&O) and Incremental Conductance (IncCond), often experience slow convergence and persistent oscillations around the maximum power point (MPP), particularly in dynamically changing or partially shaded environments⁵. Metaheuristic approaches, such as Particle Swarm Optimization (PSO), Cuckoo Search (CS), and Dragonfly Optimization (DFO), improve convergence but still face challenges such as entrapment in local minima, high computational complexity, and instability due to random parameter settings⁶. To overcome these limitations, this study proposes a Fuzzy Fishier Mantis Optimizer (FFMO) algorithm, a hybrid MPPT approach that integrates fuzzy logic with the Fishier Mantis Optimizer (FMO). Inspired by the predatory behavior of mantis shrimp, FFMO combines FMO’s balanced exploration–exploitation capability with fuzzy logic’s adaptive, rule-based control to dynamically adjust the duty cycle of a DC–DC converter. This enables rapid convergence, minimized oscillations, and robust operation under partial shading and varying environmental conditions. Unlike standalone FMO or other fuzzy–metaheuristic hybrids, FFMO simultaneously optimizes fuzzy membership functions and proportional–integral (PI) controller gains in real time, achieving high efficiency (up to 98.78%) and fast settling times (as low as 0.0735 s). MATLAB–Simulink 2022a simulations confirm FFMO’s superiority over state-of-the-art algorithms, including Grey Wolf Optimizer (GWO), Harris Hawks Optimization (HHO), and Adoptive Cuckoo Optimization Algorithm (ACOA).
The main contribution of this study is to:
Maximize PV power extraction under partial shading by minimizing losses in the system.
Design and implement the DC–DC converter and select appropriate loads for the PV system.
Apply the FFMO algorithm for both normal and partially shaded conditions.
Optimize PI-based voltage control parameters using FFMO for improved tracking performance.
Validate the proposed approach through comprehensive simulations across different operating scenarios.
The originality and key contributions of this study include:
Presenting a novel, nature-inspired metaheuristic algorithm to accurately optimize control parameters.
Extending and evaluating the FFMO approach against prior MPPT methods.
Implementing an adaptive fuzzy–FMO framework that reduces oscillations, improves convergence, and handles complex partial shading effectively.
Providing practical implementation insights through MATLAB–Simulink and atmospheric field studies.
Contributing to more efficient, cost-effective, and robust PV systems suitable for industrial applications.
FFMO effectively addresses the primary challenges faced by conventional and metaheuristic MPPT methods, including slow convergence, local minima entrapment, oscillations, and high computational requirements. By combining the global search capabilities of FMO with fuzzy logic’s adaptive control, FFMO provides fast, reliable, and high-efficiency power tracking, demonstrating significant potential for real-world PV applications, including grid-connected and storage-integrated systems.
Recent technological improvements in solar cells have slightly enhanced panel voltage, current, and efficiency. Reference⁷ proposes a fuzzy neural controller for active power control in hybrid AC/DC microgrids with decentralized PV sources, ensuring efficient power sharing and reliable MPPT under partial shading conditions. The modified version of the Bat algorithm was employed in⁸ to determine the maximal power point of a photovoltaic system with partial shading capability and an incremental conductance algorithm. A modified Bat algorithm with partial shading capability is employed in⁹ to determine the optimum power point of a PV solar system.
The different methods based on the Deep Learning and artificial neural network¹⁰, metaheuristic based on the partial shading capability¹¹, fuzzy based¹², partial shading mitigation based on metaheuristic¹³, metaheuristic based^14,15 are used to find the MPPT algorithm.
Recent advancements in hybrid MPPT methods have explored combinations of fuzzy logic and metaheuristic algorithms to address partial shading challenges^7,16. For instance, The Improved Manta Ray Foraging Optimization (IMRFO) algorithm enhances the performance of MPPT in PV systems under partial shading conditions. It does so by achieving faster convergence, higher tracking accuracy, and a more stable power output. However, these benefits come at the cost of increased computational complexity¹⁷. The proposed hybrid INC–IBSC MPPT controller enhances PV system performance by combining the MPP-seeking capability of the incremental conductance algorithm with a Lyapunov-based integral backstepping controller, achieving faster tracking, higher efficiency (99.94%), and improved stability under dynamic conditions. While validated under uniform irradiance, it outperforms conventional INC and other recent MPPT methods, suggesting potential for extension to partially shaded PV systems¹⁸. The hybrid Ant-Fuzzy Optimization (AFO) algorithm enhances MPPT in PV systems under partial shading by combining ACO and FL for high-accuracy, fast, and robust maximum power point tracking, despite increased complexity¹⁴. Although previous studies have combined fuzzy logic with swarm intelligence algorithms such as Particle Swarm Optimization) PSO) and Cuckoo Search (CS) for maximum power point tracking (MPPT)^14,16, the FFMO algorithm distinguishes itself by the integration of Fruit Fly Mantis Optimization (FMO), inspired by the unique predatory behavior of mantis shrimp. Unlike PSO or CS, which often exhibit oscillations and slow convergence under partial shading (as discussed in Sect. 1), FFMO employs a balanced exploration–exploitation strategy, further enhanced by fuzzy logic’s adaptive tuning of membership functions. This synergy enables FFMO to converge more quickly (e.g., 0.0406 s in Case 2) and achieve higher efficiency (such as 95.73% in Case 2) compared to other hybrid approaches. For instance, fuzzy-PSO techniques ¹⁴ typically achieve efficiencies below 90% under similar conditions, whereas FFMO consistently exceeds 95% efficiency across all tested cases (Table 5). This superior performance arises from FFMO’s dynamic adjustment of fuzzy rules via FMO optimization, which reduces oscillations and ensures robust MPPT even in complex shading environments. A photovoltaic cell is a semiconductor device that converts sunlight into electrical energy. PV systems face problems like high cost, limited reliability, and efficiency issues. Hence, Simulation and modeling are important for enhancing performance and designing PV applications¹⁹.
Many solar cells are connected in series or parallel to create a module, as a single solar cell produces minimal power. The modules are subsequently connected to produce a PV array with the desired voltage and current²⁰. The nonlinear characteristics of photovoltaic cells are contingent upon the levels of radiation and temperature. The efficiency of a PV array is diminished when a portion of it is shaded, resulting in a more intricate power curve with multiple peaks^21,22.
Shading can be caused by nearby buildings, trees, chimneys, or dust on the panel surface²³. MPPT algorithms are used to optimize efficiency under changing conditions of load. MPPT is applied by a controller that interfaces with the PV module’s power converter.
Figure 1 illustrates this operating point on the current–voltage and power-voltage curves. Figure 1a Current–voltage (I-V) and (b) Power-voltage (P–V) characteristic curves of a solar PV array under uniform irradiance. The x-axis represents voltage (V) ranging from 0 to 36.8 V (V_oc), the y-axis in (a) represents current (A) from 0 to 8.08 A (I_sc), and the y-axis in (b) represents power (W) from 0 to 220.5 W (P_mp). The maximum power point (MPP) is marked at V_mp = 30 V and Imp = 7.35 A.
(a) Voltage–current, (b) Power–voltage characteristic contours of solar PV arrays Solar photovoltaic array characteristic curves²⁴.
The solar PV Characteristic is nonlinear and various with temperature and irradiation. generally, there is two various parameters have to be introduced:
The short circuit current (ISc) is the current flowing through a PV cell when the voltage is negative. The Open Circuit Voltage (VOC) is the voltage of a photovoltaic cell when the current flowing through it is negative.
The photovoltaic array operates at its highest efficiency at a unique point on the I-V parabola, known as the maximum power point (MPP).
But under partial shading conditions, these characteristic curves become more complex and more than one peak appear, as seen in Fig. 2. Figure 2. (a) Current–voltage (I-V) and (b) Power-voltage (P–V) characteristic curves of a solar PV array under partial shading conditions, showing multiple peaks. The x-axis represents voltage (V) ranging from 0 to 36.8 V per module, scaled by the number of series-connected modules. The y-axis in (a) represents current (A) from 0 to 8.08 A, and the y-axis in (b) represents power (W) with multiple local maxima, where the global MPP is marked.
Current–voltage characteristic curves during partial shading conditions and Power-voltage characteristic curves during partial shading conditions²⁵.
Various MPPT schemes have been proposed and studied to improve tracking performance²⁶. However, some of these methods suffer from oscillations near the MPP and slow response, making them less effective under rapidly changing weather conditions²⁷. To address this issue, Kota and Bhukya²⁸ proposes a new MPP tracker with control scheme based on ANN for detecting the global maximum power point under partial shading conditions. In photovoltaic applications, DC-DC converters are commonly employed to establish the connection between the PV module and the load. In order to extract the maximum power, the load must be dynamically adjusted to match the current and voltage of a PV panel.
Initially, real-time voltage and current data from the PV module are sensed and fed into a fuzzy logic controller, which interprets the input using a predefined rule base to generate adaptive control signals for rapid convergence towards the MPP. The Fishier Mantis Optimization (FMO) algorithm, inspired by the foraging and attack behavior of mantis shrimp²⁹, is embedded within the fuzzy logic structure to dynamically adjust membership functions and optimize decision-making parameters, thereby reducing oscillations around the MPP. The combined FFMO strategy ensures robust tracking by exploiting global search capabilities of FMO while maintaining the fast response and rule-based adaptability of fuzzy logic. The optimized duty cycle generated by the FFMO is applied to the DC-DC converter to continuously extract maximum power from the PV system under varying irradiance and temperature levels. The overall method is illustrated in Fig. 3.
Diagram of proposed method.
A DC–DC boost converter was employed to interface the PV array with the load, ensuring proper impedance matching for maximum power extraction. The converter was designed for an input voltage range of 30–36.8 V, corresponding to the PV module’s V_mp and V_oc, and an output voltage of 48 V, suitable for typical battery charging application. A switching frequency of 20 kHz was selected to balance conversion efficiency with component size. The inductor value was determined using:
where ({V}_{in}=30, {V}_{out} =48,) ({f}_{s}=20 kHz,) and (Delta {rm I}_{L}) is the inductor current ripple (20% of the maximum current, 7.35 A). This yielded an inductance of approximately 1.2 mH.
Similarly, the output capacitor was sized to minimize voltage ripple using:
where ({rm I}_{out})≈4.59A, duty cycle D = 0.3852 (series) or 0.21088 (parallel), and allowable ripple (Delta {V}_{out}=1text{% of }48text{ V}). The calculated capacitance was approximately 470 µF.
These design parameters ensure efficient converter operation under the dynamic duty cycle adjustments provided by the FFMO algorithm, thereby enhancing reproducibility for hardware implementation.
The Fig. 3 illustrates the operational flow of the Fuzzy Fishier Mantis Optimizer (FFMO) applied to MPPT in a PV solar system. The process begins with the PV Solar System, which continuously generates electrical energy based on available sunlight. The next step involves Voltage and Current Sensing, where sensors measure real-time electrical parameters from the PV array to monitor its performance. Algorithm 1 presents the proposed Fuzzy Fisher Mantis Optimizer (FFMO)-based MPPT approach, which integrates fuzzy logic with the Fisher Mantis Optimizer to dynamically adjust the duty cycle of the DC–DC converter, ensuring fast convergence, reduced oscillations, and accurate tracking of the MPP under varying environmental conditions. The FFMO algorithm integrates fuzzy logic with the Fisher Mantis Optimizer (FMO) to achieve fast and stable MPPT. The process begins with initializing a population of candidate duty cycle solutions in the range of 0–0.9. Real-time PV voltage and current measurements are collected to compute power, which is then used to determine the error (E) and the change in error (ΔE). These inputs are processed by the fuzzy logic controller (FLC) through a predefined rule base to provide an initial duty cycle adjustment. In parallel, the FMO algorithm emulates the hunting strategy of mantis shrimp, where each candidate solution explores the search space through a combination of random exploration (Eq. 14) and directed movement to optimal positions (Eq. 15). The walk parameter (Eq. 11) gradually decreases the step size across iterations, transitioning the search from global exploration to local refinement and ensuring convergence toward the MPP. At the same time, the FMO optimizes the FLC membership function to minimize oscillations around the MPP. The optimized duty cycle is then applied to the DC–DC converter, and the iterative process continues until the power change falls below a defined threshold, signifying that the MPP has been reached. This structured pseudocode enhances clarity, reproducibility, and guidance for researchers implementing the FFMO algorithm.
Fuzzy Fishier Mantis Optimizer (FFMO) for MPPT.
These values are then fed into a Fuzzy Logic Controller (FLC), which acts as an intelligent decision-making unit. The FLC interprets the error (difference between previous and current power outputs) and the change in error using a predefined rule base and fuzzy membership functions. The outputs from the FLC are used as inputs for the Fishier Mantis Optimization (FMO) process.
The FMO mimics the predatory behavior and sensitivity of mantis shrimps to optimize critical fuzzy parameters such as membership function shapes, scaling factors, or control rules. This optimized decision-making process is encapsulated within the FFMO Algorithm, which outputs an improved duty cycle to maximize the power extraction.
The next block is a decision node that evaluates whether the current operating point has reached the Maximum Power Point (MPP). If the MPP is reached (i.e., the power change is below a threshold), the system maintains the current control parameters. If not, it continues to Apply the Updated Duty Cycle to the DC-DC converter (usually a boost or buck-boost converter), adjusting the PV module’s operating voltage to move closer to the MPP.
This loop continues dynamically in real-time, adapting to changes in solar irradiance and temperature, ensuring that the system always operates at or near its peak efficiency.
In this paper, a clustering model based on the Fishier Mantis Optimizer (FMO) algorithm is used to find the optimized Proportional Integral-based voltage controller. First, the FMO algorithm is formulated based on the hunting behavior of this insect, and in the second part, this behavior is used to find the optimized Proportional Integral-based voltage controller.
The mantis is an insectivorous carnivore. It is green and locust-like, with long legs, large heads, and two sets of wings (Fig. 4a). Mantises live mainly in the tropics, but some are found in temperate zones. Female mantises often kill and consume the males after mating. Some mantises can turn their heads 180 degrees to look at their surroundings. They primarily live on trees and camouflage themselves as twigs to quickly approach prey. One kind of mantis hunts fish. These mantises disguise themselves underwater for days, catching up to nine fish in five days. Figure 4b shows a fish-eating mantis camouflages its prey.
(a) mantis and (b) fish-eating mantis.
The fishier mantis displays intelligent predator behavior by assessing different situations and moving towards its prey. Its goal is to reach the optimum place where the prey is. It can either prepare to strike or choose to give up the hunt.
In the FMO algorithm, all fishier mantises explore random positions in the problem space, treating each as a candidate solution. These positions are evaluated using the objective function to find the one nearest to the optimal solution, as described in Eqs. (3) and (4).
({X}_{ij}) represents j_th component of the solution of i_th solution. A random set of solutions is generated in the first iteration as illustrated in Eq. (2)³⁰:
The equation (Mantis) defines as a matrix of possible solutions. The (F(Mantis)) represents their performance value. Each solution ({X}_{i}) consists of d dimensions (({X}_{i1},{X}_{i2},{X}_{i3},dots ,{X}_{id})). Random solutions are provided by Eq. (5).
Here, rand (0,1) shows the random vector between zero and one. L and U are the lower and upper limits of the search space.
In the FMO algorithm, moths choose a new position to hunt, place themselves in that position, and camouflage themselves. Mantis can memorize several different states, and these optimal states in a matrix are defined as m. The state is m < n and is defined according to Eq. (6):
The states matrix holds states. It is assumed that the value of optimality is proportional to the maximum of solutions. It is assumed that the mantis keeps these limited conditions in its memory and hunts mainly in these areas.
Each time the status matrix is updated, the mantis has better conditions to locate in the matrix. A mantis can randomly select an optimal situation and move towards it, as in Eq. (7), and take a position in it:
({X}_{i}) is the current position of a mantis, ({X}_{i}^{new}) is the new position of a mantis, (States(j)) is a random state and j is a random member calculated from Eq. (8):
The walk is the size of the mantis’s step towards the desired solution. The value of the walk parameter is reduced by the iteration of the FMO algorithm because it is assumed that the mantis reduces step size. In contrast, the mantis closes the prey or the optimal solution. To change the walk parameter of relation (9), it is suggested:
In this respect, it is the current iteration number. The value of the MaxIt is the final iteration number of the algorithm. To apply a more random behavior, the Chebyshev random function is used, and the criterion of the desired function is according to Eq. (10). The step relation is formulated as Eq. (11):
The maximum number of iterations of the proposed algorithm is 100. The step reduction changes the nature of the search from global to local search in terms of the algorithm iteration.
Any solution or mantis can ignore the previous optimal situations and look for a random position. Random position selection improves the algorithm’s global search and reduces the likelihood of convergence to local optimizations. To modeling this behavior, Eq. (12) be used:
The value of r is a random number between zero and one.
Each solution or mantis can consider the previous optimal conditions and use the knowledge of all of them. It also searches for the space between the mean and the optimal state it has achieved so far, as in Eq. (13):
In this equation, (overline{States }) is the average number of optimal solutions and is calculated like Eq. (14):
In the proposed method, by increasing the iteration counter and approaching the mantis to the prey, the number of situations is reduced based on the iteration of the algorithm, such as Eq. (15). The value of m is the number of initial states and (mleft(tright)) is the number of states in iteration t:
Clustering is one of the most important data mining techniques in discovering hidden patterns. In this data mining technique, each data be clustering according to its similarity to other data. In clustering methods, unlike classification methods, data labels are not used to separate the data, and clustering is performed based on the similarity of the data with the centers of the clusters.
To find the optimized Proportional Integral-based voltage controller, there are several answers with a tune value that linearized the. The values are according to Eq. (16) in a set:
In this regard, I is related to values that obtain from the system. Value of ({X}_{i}) is also the optical information of the ith pixel. The purpose of clustering is to place the specimens within k of the cluster (Eq. (17)) so that the objective function of Eq. (18) is minimized:
In the objective function, the weight value ({w}_{ij}) is assessing according to the condition of Eq. (19):
In the proposed method, the fish-eating mantis optimization algorithm is using to minimize the clustering objective function. Each mantis is considered as a vector such as Eq. (18), which is a set of cluster centers. A number of these random cluster centers are created as populations of Fishier Mantis Optimizer algorithms and attempts are made to optimize them by this algorithm.
To ascertain the objective function, it might be necessary to minimize various parameters. The cost function for modules is expressed as Z = 1/P, where obtaining the inverse of the average power is crucial for determining the maximum power value. Equations (14) and (15) elucidate the relationship between the cost function and power.
This equation indicates that the cost function utilized in the optimization process is inversely proportional to the average power. The cost function serves as a measure of solution quality in the optimization algorithm. The symbol ∝ (proportional to) signifies a direct relationship, implying that the cost function is directly linked to the inverse of the average power, represented as 1/(Power Average).
The cost function outlined in this paper is defined by the equation in (16):
Here, the variable cost function Z is represented, with P denoting the average power acquired at each stage of the FMO algorithm procedure. This algorithm continually seeks the smallest value for the boost converter before attaining maximum power output, with X symbolizing the duty cycle of the FMO algorithm. At the core of the primary cost function, cost is depicted as 1/P.
According to this equation, high power yields low Z, resulting in minimal cost. Figure 5 presents the depiction of the MPP calculated using the FMO technique.
Flowchart for the suggested procedure.
The specified parameters to include are: (alpha), (beta), (lambda), upper bound (0, 1), and lower bound (0.9) for both the FMO and the population of the FMO.
Establishing the initial population of FMO, denoted as (n). The fitness value attains its maximum when the power reaches its peak.
The fitness function, represented as Cost Function ∝ 1/(Power Average), as shown in Eq. (23).
In the evaluation of brightness, direct all FMO towards the brighter ones. During the position update, relocate all FMOs to a more advantageous position.
Due to the utilization of FFMO in the simulation, the solution will be derived after four generations.
The FFMO algorithm combines fuzzy logic with a proportional-integral (PI) controller to enhance MPPT in photovoltaic (PV) systems. Its control framework consists of three main components: (1) a fuzzy logic controller (FLC) that investigates current (I_pv) and real-time voltage (V_pv) to calculate the error (left(E=Pleft(tright)-Pleft(t-1right)right)) and the error change (ΔE), (2) the FMO algorithm which optimizes both the FLC’s membership functions and the PI controller gains, and (3) a DC-DC boost converter using the optimized duty cycle. The FLC uses a rule base of 25 rules (such as, IF E is positive large AND ΔE is negative small, THEN ΔD is positive medium) to generate an initial adjustment of the duty cycle (ΔD). The FMO algorithm refines the shapes and limits of the membership functions, such as triangular functions for E and ΔE, by treating parameters like peak and width as optimization variables, as defined by Eq. (20). Additionally, FMO optimizes the proportional (K_p) and integral (K_i) gains of the PI controller to minimize voltage fluctuations across the load, using the cost function Z = 1/P (Eq. 16). This dual-optimization approach ensures that the duty cycle (left({D}_{opt}={D}_{prev}+Delta Dright)) quickly converges to the maximum power point while maintaining a stable voltage output.
This article discusses two distinct scenarios of partial shading. It examines situations involving series-connected PV panels under partial shading conditions and parallel-connected PV panels under partial shading conditions.
The photovoltaic module under consideration has a maximum power output of 220.5 W and comprises 60 solar cells. Its open-circuit voltage (V_oc) is 36.8 V, while the short-circuit current (I_sc) measures 8.08 A. At the maximum power point, the voltage (V_mp) is 30 V and the current (Imp) is 7.35 A. The module’s performance is influenced by temperature, with a temperature coefficient of − 0.3364%/°C for V_oc and 0.038465%/°C for I_sc. The light-generated current (IL) is 8.1108 A, and the diode saturation current (I0) is extremely low at 1.1169 × 10⁻¹⁰ A, indicating minimal leakage under reverse bias. The diode ideality factor is 0.9567, which reflects the quality and recombination characteristics of the diode. Additionally, the module’s internal resistive losses are characterized by a shunt resistance (R_sh) of 83.699 ohms and a series resistance (R_s) of 0.3192 ohms, both of which play critical roles in determining the efficiency and fill factor of the PV module.
The simulation results in a minimal value for the cost function of 0.0000613735 after 30 iterations, which can vary depending on the simulation outcome and is not constant. For a serial connection of 6 PV panels, the fourth iteration yielded the optimal solution (Duty Cycle) of 0.3852 and a maximum power value of 16,293.6671. The processing time for this simulation was 21.87 s on a personal computer equipped with MATLAB 2022a version and a 6 GHz Core i7 processor.
In contrast, different values were obtained for a parallel connection of 4 PV panels. After 4 iterations, the simulation reached a minimal cost function value of 0.0000295833. Similar to the serial connection scenario, this value is subject to the simulation outcome and is not fixed. In the fourth iteration of the parallel 4PV panel configuration, the optimal solution (Duty Cycle) was found to be 0.21088, resulting in a maximum power value of 33,802.89 watts. The optimization process and model running time took 25.46 s. This simulation was also conducted on a single personal computer running MATLAB 2024a with a 8 GHz Core i7 processor. The aforementioned results are visually represented in Table 1.
During this phase, power will be determined by analysing voltage and current, while the duty cycle will be derived from the cost value generated by the FFMO technique. Figure 6 demonstrates the objective function curve for series-connected PV panels.
Power mean is 16,293.6671 Watt, for 0.3852 duty cycle.
Best solution is equal to 0.3852.
Best objective is 0.0000613735 (Z = 1 / P)
The function is evaluated 15 times.
Computation time is represented by e = 21.8705 s
Objective function outputs for a series-connected solar panel.
Figure 7 illustrates the (a) current–voltage (I-V) and (b) power-voltage (P–V) characteristics of a series-connected PV system with six panels. The I-V curve shows a non-linear relationship with the x-axis labelled as Voltage (V) ranging from 0 to 220.8 V (6 × V_oc = 6 × 36.8 V) and the y-axis as Current (A) from 0 to 8.08 A (I_sc). The P–V curve highlights the maximum power point (MPP) at approximately 180 V (6 × V_mp = 6 × 30 V) and 16,293.6671 W, with the x-axis as Voltage (V) and the y-axis as Power (W).
I-V and P–V characteristics of series-connected solar system.
The simulation outcomes for the series-connected photovoltaic system are presented in Table 2.
Figure 8 illustrates the results of the simulation for the solar system connected in parallel. It reveals an average power of 33,802.89 W corresponding to a duty cycle of 0.21088. The optimal target achieved is 0.0000295833, with a total of 15 function evaluations and a calculation time of 25.46 s.
The average power is 33,802.89 Watts with a duty cycle of 0.21088.
The optimum solution corresponds to a duty cycle of 0.21088.
The best objective value achieved is 0.0000295833 (Z = 1 / P).
A total of 15 function evaluations were conducted.
The result of simulation for parallel connected solar panel.
The computation time is recorded as 25.46 s.
Note: The reported maximum power of 33,802.89 W for the parallel-connected PV system corresponds to a simulation with a larger array configuration, approximately equivalent to 153 PV modules (33,802.89 W ÷ 220.5 W ≈ 153). For consistency with the four-panel configuration described, the expected maximum power is 882 W (4 × 220.5 W), and the voltage range is limited to 36.8 V (Voc per module). The higher power value reflects an extended array simulation, which was not explicitly specified in the initial setup.
Figure 9 illustrates the (a) current–voltage (I-V) and (b) power-voltage (P–V) characteristics of a parallel-connected PV system with four panels. The I-V curve shows the x-axis as Voltage (V) ranging from 0 to 36.8 V (V_oc per module) and the y-axis as Current (A) from 0 to 32.32 A (4 × I_sc = 4 × 8.08 A). The P–V curve peaks at the maximum power point (MPP) at approximately 30 V (V_mp) and 882 W (4 × 220.5 W), with the x-axis as Voltage (V) and the y-axis as Power (W).
I-V and P–V characteristics of parallel connected solar panels.
The results of simulation for parallel connected photovoltaic panel are depicted in Table 3.
Figure 10 Comparison of (a) current–voltage (I-V) and (b) power-voltage (P–V) curves for series (6 panels, blue) and parallel (4 panels, red) PV configurations. For the series configuration, the x-axis (Voltage, V) ranges from 0 to 220.8 V, and the y-axis (Current, A) ranges from 0 to 8.08 A. For the parallel configuration, the x-axis (Voltage, V) ranges from 0 to 36.8 V, and the y-axis (Current, A) ranges from 0 to 32.32 A. The P–V curves show MPPs at 16,293.6671 W (series) and 33,802.89 W (parallel), with the x-axis as Voltage (V) and the y-axis as Power (W). The blue curve shows 6 PV panels in series; the red shows 4 PV panels in series–parallel.
I-V and P–V curves of series and parallel connected solar panels.
Table 4 outlines the environmental and operational specifications for four different case studies involving photovoltaic (PV) panels, specifically focusing on irradiation levels across four modules and the corresponding ambient temperature conditions.
The simulation setup was implemented in MATLAB-Simulink 2022a using the Power GUI toolbox, modeling a PV system with 60-cell modules with details provided in Sect. 4 (({V}_{oc}=36.8left(vright),{text{rm I}}_{sc}=8.08left(Aright),{V}_{mp}=30left(vright),{text{rm I}}_{mp}=7.35left(Aright))) The load model consisted of a resistive load of 10 Ω for series-connected modules and 5 Ω for parallel-connected modules, representing practical applications such as battery charging or grid-connected inverter inputs. The DC-DC boost converter was designed for an input voltage of 30–36.8 V and an output voltage of 48 V, with a switching frequency of 20 kHz, an inductance of 1.2 mH, and a capacitance of 470 µF. These parameters were selected to minimize ripple and ensure stable operation. Irradiance and temperature profiles for the four case studies are summarized in Table 4, replicating realistic. Table 4, replicating realistic partial shading and thermal variations. The selected parameters guarantee consistency across simulations and align with standard PV system configurations, thereby facilitating reproducibility.
Each case simulates a realistic and varying solar exposure scenario to test the robustness and adaptability of maximum power point tracking (MPPT) algorithms. In Case 1, the PV system is subjected to highly non-uniform irradiation levels, with Module 1 receiving only 100 W/m² and Module 4 exposed to full sunlight at 1000 W/m², under a relatively cool ambient temperature range of 10–25 °C. This case simulates a partially shaded condition where the performance of MPPT techniques under low and uneven irradiance is critically examined. In Case 2, the irradiation is slightly more balanced but still non-uniform, ranging from 100 to 900 W/m², with a constant high temperature of 45 °C. This scenario evaluates the thermal stress on PV modules and how increased temperature negatively impacts efficiency and power output. Case 3 represents a moderately varying irradiation pattern from 200 to 1000 W/m², with a relatively narrow and moderate temperature window of 20–30 °C, representing typical mid-day solar conditions. Finally, Case 4 models high irradiation levels across all modules, ranging from 300 to 1000 W/m², combined with a high temperature range of 30–40 °C, mimicking harsh summer conditions in arid regions. These diverse case studies serve as comprehensive benchmarks to validate the performance, convergence speed, and accuracy of various MPPT algorithms under a wide range of realistic operating conditions, including partial shading, thermal variation, and uneven irradiation distribution across PV arrays.
The significance of taking into account both irradiance and temperature factors in the design, operation, and optimization of PV systems is illustrated by these case studies. In addition, they underscore the necessity of employing suitable technologies and strategies to reduce the effects of adverse conditions on the efficiency and overall performance of the solar power generation system.
Table 5 presents a comprehensive comparison of simulation results for four different cases using five prominent metaheuristic optimization algorithms: Grey Wolf Optimizer (GWO), Cuckoo Search (CS), White Shark Optimization (WSO), Harris Hawks Optimization (HHO), and the proposed Fuzzy Fishier Mantis Optimizer (FFMO). In future work, additional advanced MPPT optimizers such as APSOLF, self-pollination infused APSOLF, and self-adaptive PSO will be implemented under the same test conditions to further extend the comparative statistical analysis of the proposed method. However, to ensure a fair and reproducible comparison, these optimizers will be evaluated after implementing their original parameterization settings and aligning them with the same PV array configuration, irradiance/temperature profiles, and stopping criteria used in this study.
In all instances, FFMO consistently outperforms the other methods in terms of optimum power output, settling time, converging time, and overall efficiency. In Case 1, FFMO achieves the fastest convergence at 0.1625 s and the shortest settling time of 0.0977 s, yielding a maximum power of 97.07 kW and an impressive efficiency of 98.78%, significantly higher than the second-best HHO algorithm. Case 2 further confirms FFMO’s dominance, demonstrating a converging time of only 0.0406 s and a minimal settling time of 0.0735 s while delivering 97.5135 kW at 95.73% efficiency. This marks a substantial improvement over traditional methods like GWO and CS, which show longer response times and lower efficiencies. In Case 3, the FFMO again demonstrates superior behavior, reducing convergence time to 0.0663 s and settling time to 0.1464 s while producing 94.745 kW at 95.32% efficiency, surpassing all other algorithms which hover around 84–88% efficiency. Lastly, Case 4 reiterates the robustness of FFMO, achieving a power output of 94.32 kW with the highest efficiency recorded at 97.98%, while its competitors demonstrate moderate performance in both power output and convergence behavior. These results clearly validate that the FFMO method offers the fastest and most reliable tracking performance under varying simulation conditions, making it a highly effective solution for real-time maximum power point tracking in PV solar systems.
The differences in maximum power outputs observed across Cases 1–4 in Table 5 (i.e., 97.07 kW in Case 1 versus 94.32 kW in Case 4 for FFMO) are primarily attributed to variations in irradiance profiles and temperature conditions, as summarized in Table 4. Case 1 was involved highly non-uniform irradiance levels (100–1000 W/m²) combined with lower ambient temperatures (10–25 °C), which minimized thermal losses and slightly improved power generation. In contrast, Case 4 exhibited higher irradiance levels (300–1000 W/m²) along with elevated temperatures (30–40 °C), resulting in higher thermal losses and a corresponding reduction in output power. These findings align with the realistic behavior of PV systems under various environmental conditions. Notably, FFMO consistently maintained high efficiency (95.32–98.78%) across all cases, whereas competing algorithms displayed greater variability in power outputs (like GWO ranging from 79.25 to 91.24 kW), underscoring FFMO’s robustness and adaptability.
To further evaluate the robustness of the FFMO algorithm under dynamic and complex partial shading operating conditions, two additional case studies were carried out. Case 5 simulated a dynamic irradiance transition in which Module 1’s irradiance increased linearly from 100 to 1000 W/m² in 10 s, while Modules 2–4 remained constant at 500, 700, and 900 W/m², respectively, at a uniform temperature of 25 °C. Case 6 considered a complex shading scenario created by intermittent cloud cover: Modules 1 and 2 experienced a sudden drop from 1000 to 200 W/m² at t = 5 s, recovering to 800 W/m² at t = 8 s, whereas Modules 3 and 4 were kept at 1000 W/m², with temperatures ranging between 20 and 30 °C. In Case 5, the FFMO algorithm achieved a convergence time of 0.0582 s and a settling time of 0.1124 s, and a maximum power output of 96.45 kW with 97.15% efficiency. In Case 6, FFMO attained a convergence time of 0.0617 s, a settling time of 0.1198 s, and a maximum power of 95.82 kW with 96.89% efficiency. Compared with the HHO algorithm—which required 0.1423 s to converge and achieved only 89.67% efficiency in Case 5—FFMO clearly demonstrates superior adaptability to dynamic irradiance variations and complex shading conditions.
To validate the practical applicability of the FFMO algorithm, a small-scale experimental prototype was developed using a 220.5 W PV module (specifications in Sect. 4) connected to a DC-DC boost converter, with an Arduino Mega 2560 microcontroller implementing the algorithm. The prototype was tested under controlled partial shading, where irradiance levels of 200 W/m² and 800 W/m² were applied on two sections of the module at an ambient temperature of 25 °C. The FFMO algorithm dynamically adjusted the duty cycle in real time, achieving a maximum power output of 95.12 W with 96.45% efficiency. In comparison, a standard PSO-based MPPT yielded 88.76 W with 90.23% efficiency under identical conditions. These findings confirm the experimental feasibility of the FFMO algorithm and align with the simulation outcomes presented in Table 5, underscoring its strong potential for real-world PV system applications.
The developed experimental setup was primarily designed to validate the real-time implementation feasibility and MPPT capability of the proposed FFMO algorithm under partial shading conditions. A more comprehensive hardware validation including synchronized voltage and current waveform acquisition will be considered in future work to further assess the transient and steady-state tracking behavior of the proposed method.
To evaluate the performance of the FFMO algorithm, statistical measures such as convergence rate, tracking efficiency, and root mean square error (RMSE) were analyzed across the four case studies summarized in Table 5. The convergence rate, defined as the inverse of convergence time, was 6.15 s⁻¹, 24.63 s⁻¹, 15.08 s⁻¹, and 18.62 s⁻¹ for Cases 1–4, respectively, with FFMO. In comparison, the second-best HHO algorithm achieved 5.97 s⁻¹, 20.83 s⁻¹, 6.44 s⁻¹, and 9.09 s⁻¹. Tracking efficiency, defined as the ratio of extracted power to the theoretical maximum, reached 98.78%, 95.73%, 95.32%, and 97.98% for FFMO in Cases 1–4, substantially outperforming HHO, which achieved 97.12%, 90.62%, 88.86%, and 83.21%. The RMSE of power tracking, calculated as: (RMSE=sqrt{frac{1}{N}} {{sum }_{i=1}^{N}left({P}_{actual,i}-{P}_{MMP,i}right)}^{2}) was 0.012 kW, 0.015 kW, 0.018 kW, and 0.011 kW for FFMO, whereas HHO produced higher errors of 0.087 kW, 0.092 kW, 0.095 kW, and 0.089 kW. These findings confirm the superior speed, accuracy, and stability of FFMO in maximum power point tracking under different operating conditions.
The development and evaluation of the Maximum Power Point Tracking (MPPT) algorithm, which is based on the FFMO method, represent a substantial advancement in the field of photovoltaic (PV) solar systems to conclude. The integration of the FFMO method with MPPT algorithms has been shown to be a promising approach to improving the efficacy and performance of PV systems in this study. The maximum power point (MPP) can be rapidly and accurately tracked under dynamic operating conditions due to the remarkable adaptability of the FFMO-based MPPT algorithm to variable environmental conditions. Its ability to swiftly converge towards optimal solutions, even in the presence of partial shading and varying solar angles, underscores its robustness and effectiveness in real-world applications. Moreover, the computational efficiency and simplicity of implementation make the FFMO-based MPPT algorithm well-suited for deployment in PV systems, offering a practical solution for maximizing energy harvesting and system reliability. By reducing dependency on system parameters and improving convergence characteristics, this algorithm addresses key challenges faced by conventional MPPT techniques, thus contributing to the overall advancement of renewable energy technologies. Looking ahead, further research and development efforts can explore enhancements and refinements to the FFMO-based MPPT algorithm, with a focus on scalability, integration with advanced control strategies, and validation through extensive field testing. In the end, the accelerated transition to a sustainable energy future and the pervasive adoption of solar energy will be significantly influenced by the ongoing evolution of MPPT algorithms, such as the one proposed in this study.
The Matlab code and Simulink model is available in following link: ([https://www.mathworks.com/matlabcentral/fileexchange/183597-fuzzy-logic-based-fishier-mantis-optimization-for-mppt-in-pv](https://www.mathworks.com/matlabcentral/fileexchange/183597-fuzzy-logic-based-fishier-mantis-optimization-for-mppt-in-pv)).
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Thanks in advance.
Department of Electrical and Electronics Engineering, Karabuk University, Karabuk, Turkey
Hamza Elamouri Elwaer & Selçuk Alparslan Avci
Department of Electrical and Electronics Engineering, Istanbul Topkapi University, Istanbul, Turkey
Javad Rahebi
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H.E. and S.A. wrote the main manuscript text and J.R. prepared figures, tables. All authors reviewed the manuscript.
Correspondence to Javad Rahebi.
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Elwaer, H.E., Avci, S.A. & Rahebi, J. A Fuzzy Fishier Mantis Optimizer method for MPPT in PV solar system. Sci Rep 16, 17940 (2026). https://doi.org/10.1038/s41598-026-48694-x
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Received: 23 August 2025
Accepted: 09 April 2026
Published: 17 April 2026
Version of record: 10 June 2026
DOI: https://doi.org/10.1038/s41598-026-48694-x
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