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Scientific Reports volume 15, Article number: 21092 (2025)
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When the photovoltaic arrays are subject to partial shading (PS), their output characteristics show a multi-peak phenomenon. Under this circumstance, it will be a challenge to track the maximum power point (MPP), which impacts power generation efficiency. Therefore, achieving efficient maximum power point tracking (MPPT) in a photovoltaic (PV) system under PS is an important element in enhancing PV system efficiency. To optimize PV array output efficiency under PS conditions, this paper investigates a MPPT algorithm for PV arrays in partial shading environments. This algorithm is optimized and improved accordingly based on the Marine Predator Algorithm (MPA). Firstly, the initial position voltage is modified, which provides a more accurate and stable basis for the subsequent calculation. Next, the mechanism of overstepping is optimized to ensure that the particles will not exceed the preset range in the search process. Then, introducing the elite population guidance mechanism and restart algorithm to speed up the tracking of the entire algorithm. Lastly, the Perturbation and Observation algorithm is added to minimize the power fluctuation and improve tracking accuracy. The improved algorithm and the original algorithm, particle swarm algorithm, and incremental conductance method are embedded in the model of the PV system for the simulation of maximum power point tracking, respectively. Experiments show that the tracking time of the improved algorithm is improved by 32.6%, 76.5%, and 50% compared to the original algorithm, particle swarm algorithm, and incremental conductance method, respectively, under uniform illumination. Under dynamic irradiance conditions, the proposed algorithm has a tracking efficiency of up to 99.95%, which is over 15% higher than the comparison algorithm. The outcomes reveal that the improved algorithm is faster and more efficient in tracking compared to the other three algorithms.
In recent years, the carbon peaking and carbon neutrality goals have been introduced, the social demand for sustainable energy has increased significantly, sustainable energy has been listed as one of the most popular and widely used choices. Solar energy is a sustainable and renewable source of energy, gaining immense popularity as a crucial solution to the global energy crisis1. At the same time, the dramatic cut in the cost of photovoltaic technology and its ease of installation have contributed to the rapid growth of the technology2. The photovoltaic system is utilized to convert solar energy into electrical energy, which consists of three main components: photovoltaic arrays, controllers, and inverters. To keep the PV cell’s output at the highest point of the PV curve, an MPPT controller is necessary3. However, photovoltaic cells have very limited photoelectric conversion efficiency. They are susceptible to external environmental (e.g., light intensity, temperature) and load in addition to their internal characteristics, and intermittency during weather changes results in the voltage and frequency fluctuations of the interconnected grid, which provides unreliable power to consumers4. In a photovoltaic power generation system, the output power of photovoltaic cells has a nonlinear correlation with light intensity and ambient temperature. Among them, When the light intensity increases, the photovoltaic module generates more output current and voltage, thereby enhancing the output power. Conversely, a decrease in light intensity causes a decrease in the output power of the module. The MPP is the optimal operating point for a PV array, where it achieves its highest output power.
Partial shading is an important element that influences PV power generation’s efficiency and stability. During daily operation, objects such as trees, buildings, utility poles, etc., can cause PS and block incoming sunlight. This results in weaker light intensity in some areas of the PV arrays, which subsequently leads to a decrease in the power generation capabilities of the entire PV arrays. To maximize the PV systems’ efficiency, it is vital to determine the MPP under normal and transient conditions5.
Two widely implemented traditional MPPT algorithms in existing PV systems are the Perturbation and Observation (P&O) and Incremental Conductance (INC) methods6,7. However, there are obvious oscillations and defects under the conditions of external environmental changes, which can only track to the local maximum power point (LMPP), resulting in the tracking process quickly falling into local optimization. The PV arrays generate power output loss8. The authors of the literature9 proposed an improved P&O method to enhance PV arrays’ conversion power. Its efficiency can reach 95% under uniform atmospheric conditions. However, it is not possible to track the MPP under changing atmospheric conditions. Differential Evolution or Fuzzy Logic Controller (FLC) have also been proposed to track the MPP of PV power generation, but these methods are not flexible enough. The authors of the literature10 propose a MPPT based on differential evolutionary algorithm, which optimizes the standard differential equations so as to deal with the dynamic objective function problem effectively. Despite the high tracking accuracy, the tracking speed remains comparatively sluggish. In the literature11, a DC-DC converter utilizing PWM switches with a FLC to adjust the duty cycle, tracking of the MPP has been achieved, yet there exists a notable fluctuation in power. Recently, various meta-heuristic algorithms have been proposed, such as Particle Swarm Optimization algorithms (PSO)12,13, Gray Wolf Optimization algorithms (GWO)14,15,16, Ant Colony Optimization algorithms (ACO)17, Artificial Bee Colony algorithms (ABC)18,19, and Cuckoo Search Algorithm (CSA)20,21 etc. These algorithms not only boast ease of implementation but also possess the capability of seeking global optimization. However, they are stochastic in nature. When the initialized particles are not close to the MPP, the optimization time will be greatly increased, and fluctuations occur during late convergence. Therefore, a hybrid meta-heuristic optimization algorithm is introduced to achieve the optimal operational performance of MPPT technology22. Literature23 proposes a hybrid ELPSO-P&O MPPT technique that utilizes the ELPSO algorithm to globally explore in the initial phase to determine the optimal leader, and then switches to the P&O algorithm for fine-grained tracking once the global solution space is detected. Literature24 proposes an intelligent adaptive PSO hybrid linear active disturbance rejection control algorithm, which improves the maximum power point tracking speed and overall dynamic performance. In literature25, researchers proposed to combine the Whale Optimization Algorithm (WOA) with Simulated Annealing (SA). WOA simulates the hunting behavior of a whale population and optimizes the search process through the steps of encircling, hunting, and attacking the prey.SA, on the other hand, avoids falling into a local optimum by probabilistically accepting inferior solutions. Literature26 combines salp swarm algorithm (SSA) and hill climbing (HC), SSA works when atmospheric conditions fluctuate rapidly while HC works when atmospheric conditions fluctuate slowly. Literature27 applied the MPA to photovoltaic arrays and simulated the tracking performance of the algorithm when four external environments are static. The results demonstrate that the algorithm’s tracking efficiency reaches over 98%. Although its tracking efficiency is high, there is no guarantee that it can be maintained in all dynamic and complex environments. In summary, most of the hybrid MPPT techniques are intelligent algorithms combined with traditional MPPT techniques, so in this paper, the P&O algorithm is combined to the improved algorithm and complemented with the global optimization algorithm in this paper.
To address the issue present in the aforementioned algorithm, this paper proposes an Improved Marine Predator Algorithm (IMPA) based on the highly efficient MPA, which boasts the following advantages over other algorithms:
The balance between global and local fine-grained search.
Simple parameterization.
Dynamic Adaptation. The Marine Predator Algorithm can dynamically adjust its search strategy in response to changes in the external environment to better adapt to such changes.
The robustness is high. The Marine Predator Algorithm is insensitive to changes in initial conditions and parameter settings.
The contribution of this paper is that the proposed IMPA has efficient energy yield and fast convergence speed, in addition, the proposed algorithm is characterized by low computational complexity and strong global optimization capability compared to other hybrid MPPT algorithms. This research achievement provides a new solution to the MPPT problem in partially shaded environments.
Here is an overview of the paper’s organizational structure: Chap. 2 describes the output characteristics of PV arrays under PS, as well as analyzing the causes of multi-peak curves. Chapter 3 discusses the MPA and its enhancements. Chapter 4 presents the outcomes of the simulation experiments, underscoring the precision of the analysis and the validity of the improved algorithm. Chapter 5 concludes the paper with a summary of the research.
To generate more electrical energy from photovoltaic cells, multiple cells are interconnected in series and parallel configurations, forming a photovoltaic array that boosts the output voltage, current, and overall capacity of the solar array28. In the case where the PV arrays are shaded, its output P-V curve changes. It turns out that when the PV arrays are subjected to uniform light, theirs output curve have only one peak point, and when they are subjected to inhomogeneous light, there are multiple peak points. At this time, traditional MPPT algorithms frequently encounter difficulties in pinpointing the global maximum power point (GMPP), making the achievement of swift, accurate, and reliable GMPP tracking a crucial area of research in photovoltaic power generation systems29. In this way, studying the power curve of shaded PV arrays holds significant importance.
When a photovoltaic cell is shaded, it can create a hotspot effect, which turns the shaded module into a “load” that fails to generate electricity and instead consumes power. This can lead to overheating and, ultimately, destruction of the module. To prevent this, a bypass diode is installed in each photovoltaic cell. When the photovoltaic arrays are shaded, the bypass diode conducts to short-circuit it, preventing the component from being burned out and enhancing the system’s safety and stability.
A 4 × 3 simulation model of the PV array is developed to investigate the output characteristics of photovoltaic arrays under local shading scenarios, ensuring uniformity in the parameters and models of each photovoltaic cell, as shown in Fig. 1. This paper sets up three control groups: horizontal shade, vertical shade, and uniform light. The light intensity set is shown in Table 1. The temperature is uniformly set at 25 °C.
The simulation model of photovoltaic array.
Photovoltaic array output curve: (a) I-V output curve of photovoltaic array; (b) P-V output curve of photovoltaic array.
According to the parameters setting in the table, the PV array is simulated. The I-V curve is shown in Fig. 2a, and the P-V curve is shown in Fig. 2b.
It is observable that when the PV array is exposed to uniform light, the maximum power point of its external output is equivalent to the maximum power provided by a single high-power PV array. Therefore, there is only one MPP. The PV array is subjected to vertical shade can still be equivalent to a high-power photovoltaic cell externally after being connected in parallel. Thus, the output curve possesses a singular maximum power point, albeit with a diminished maximum output power. However, under conditions of horizontal shade on the photovoltaic module, the P-V curve exhibits four distinct peaks.
To simplify the analysis, the 4 × 1 photovoltaic array is built in Simulink, and its shading conditions are shown in Fig. 3. The darker color in the figure, the more shading severe situation. The temperature is uniformly set at 25 °C, and the illumination intensity parameters in Table 1 are simulated.
Photovoltaic array shading working condition diagram: (a) Uniform light condition; (b) Local shade condition 1; (c) Lo-cal shade condition 2; (d) Local shade condition 3.
Output characteristic curves of the photovoltaic array under the local shadow.
As illustrated in Fig. 4., the PV array only outputs one maximum power value under uniform lighting, and two or more peaks appear under the other three shade conditions. It can be seen that the number of peaks is related to the light intensity. When a series-connected PV array is subjected to multiple different light intensities, its output power will exhibit multiple peaks corresponding to these light intensities. There is only one GMPP, and the rest are LMPP; using the traditional tracking method will fall into the LMPP and cannot continue the optimization search.
In local shading condition 3, it can be seen that PV2, PV3, and PV4 are all partially shaded, and PV1 is subjected to the greatest light intensity, so PV1 has the largest output current at this time. As PV2, PV3, and PV4 are shaded, the output current is small, and the bypass diode conducts, at this time, the output current equation of the four PV modules in Fig. 3d can be expressed as:
where Isc_s1, Isc_s2, Isc_s3, and Isc_s4 indicate the short-circuit current when the light intensity is S1, S2, S3, S4.
The MPA is a nature-inspired meta-inspired optimization algorithm30 that has been used for various optimization problems. Some applications of it include estimating solar photovoltaic cell parameters and COVID-19 image classification, to name a few. Drawing inspiration from the foraging tactics commonly utilized by predators in marine environments, the MPA has been developed; that is, there is an optimal predation rate strategy between predators and prey. To survive in the natural environment, predators must choose an excellent strategy to elevate the confrontation rate with their prey. The tracking process is shown below:
Set the algorithm parameters, initialize the population and form the prey matrix.
Determine the fitness value for each individual in the prey matrix, and then make n duplicates of the individual exhibiting the highest fitness to constitute the elite matrix.
Predators and prey choose the corresponding update method according to different iteration stages.
The high-speed ratio stage, at this point (Iter < 1/3Max_Iter). The optimal approach for the predator lies in remaining stationary, whereas the prey’s movement adheres to Brownian motion.
This phase is denoted as:
Unity velocity ratio stage, at this point (1/3Max_Iter<Iter<2/3Max_Iter). The prey takes charge of exploitation and performs Lévy flight movements, whereas the predator oversees exploration and executes Brownian movements. For predators indicated as:
For prey indicated as:
Low-velocity ratio, at this point. The best strategy for predators is the Lévy flight campaign. This phase is denoted as:
Determine the fitness value and then proceed to update the optimal position accordingly.
Solve Eddy formation or fish aggregating devices (FADs) effects. The purpose of this step is to help the algorithm escape from local optimal options during the iterative process and look for the global optimal solution.
The initialized population of the meta-heuristic algorithm is random in nature. To enhance the tracking speed of the MPA, positioning the initial population within a specified range, which can lead to a more concentrated distribution of individuals, thereby accelerating the process of tracking the maximum power point.
The MPA has a robust global search ability, so it is equipped with the P&O method to carry out accurate local search after implementing the MPA, reducing the waveform’s late oscillation. It is experimentally verified that adding the P&O method and deleting the FADs of the original algorithm makes the algorithm more accurate.
This paper also adds a restart mechanism; when the light intensity changes, the algorithm restarts. In this paper, when the changed power exceeds 30 W, and the light intensity is judged to have changed, the algorithm restarts and starts from scratch to find the MPP.
Throughout the algorithm’s operation, the particles are compared with the boundary point in the iterative process. If they exceed the range, they are replaced with the historical optimal value, which is also called the elite guidance algorithm.
In summary, the steps of the improved marine predator algorithm are as follows:
Initialize the prey matrix. The collector collects the output voltage of the photovoltaic array in real time, which corresponds to the “prey” individuals in the marine predator algorithm. The power corresponding to the collected voltage is used as the fitness value, and the individual with the highest fitness value is copied into n copies to form the elite matrix.
Based on the current number of iterations it is judged to enter the optimization phase and select the best strategy for predator and prey.
The iterative process to determine whether the particles are beyond the boundary, or whether the external illumination intensity has changed, and if there is a change, the corresponding method is used in a timely manner to deal with it.
At the end of the iteration, the variable step size perturbation observation method is entered for final tracking, and the corresponding step size is adjusted according to the number of iterations of the variable step size perturbation observation method to obtain the optimal output voltage.
In response to the difficulties in defining voltage boundary values (Umax and Umin) and the problem of population distribution dispersion caused by a wide initialization range during the initialization phase of traditional MPA algorithms, this paper innovatively introduces Constant Voltage Control to optimize the initialization mechanism. By limiting the initialization voltage range to 0.4–0.9 times the open circuit voltage (i.e. 0.4Uoc ~ 0.9Uoc), the population distribution boundary is effectively constrained. This improvement strategy significantly increases the optimal individual locking probability while maintaining population diversity, making the subsequent constructed correlation matrix elements closer to the maximum power point, thereby accelerating the convergence efficiency of the algorithm. Specifically, the simulation model uses·12 photovoltaic cells (four in series and·three groups in parallel), its initialization voltage range is accurately quantified as 4*0.4*Uoc to 4*0.9*Uoc, where Uoc represents the open circuit voltage of a single photovoltaic cell. Through this quantitative constraint, the feasibility of the initial solution of the population is ensured, and an efficient foundation is laid for subsequent global optimization.
There is no elite guidance mechanism in the original MPA algorithm, which may lead to problems such as easy loss of high-quality solutions and increased risk of premature convergence. Therefore, this article incorporates an elite guidance mechanism. Instead of directly passing from the “elite” of the previous generation to the next generation, it retains the “elite” generated by each iteration. It is passed on to populations beyond the boundary so that all the populations move towards the optimal place. The advantage is that makes use of past search results, avoids the futile work of particle swarm, and thus expediting the convergence rate of the algorithm. Meanwhile, the algorithm has a better chance of finding a better solution due to the retention of exemplary individuals.
In order to further improve the convergence and stability of the original MPA algorithm, this paper proposes an innovative method that combines the variable step size P&O method with MPA. If the number of iterations exceeds a predefined maximum limit, the algorithm automatically jumps to the variable step size P&O method to track the MPP according to the following equations, where M is a variable whose step size is adjusted according to the number of loops, i.e., the more loops there are, the smaller M becomes.
.
Flowchart of the improved algorithm.
The flowchart of the improved algorithm is shown in Fig. 5. As shown in the figure, the black box represents the original portion of the algorithm, but an optimization has been made in the initialization of particles. The blue box highlights the innovative aspects of the elite population guidance mechanism and the mechanism of overstepping. And the green box diagram labels the optimized P & O method.
To ascertain the superiority of MPPT for IMPA in PSC, IMPA, MPA, PSO, and INC methods are simulated and compared. Figure 6 depicts the schematic diagram of the MPPT control circuit. To ensure stable power output and smooth operation, photovoltaic storage hybrid systems combine energy storage batteries with photovoltaic modules. The algorithm is written in the S-Function module. PV Array is a 4 × 3 photovoltaic array, as shown in Fig. 1.
The output voltage U1 and output current I1 of the PV array are used as input for the MPPT Controller, and the improved algorithm is written in this module. After the algorithm is executed, the output voltage Vpv and U1 are input into the PID controller at the same time, which eliminates the error between them. Subsequently, the output signal wave is sent to the PWM circuit, which is modulated to output the duty cycle to the Boost circuit to realize the matching of the PV array and the load, thus outputting the maximum power of the PV array. Since the PV array is composed of multiple PV cells connected in series and parallel, the model specifications of the PV cells used in this paper will be presented: Pmpp = 199.872 W, Uoc = 35.4 V, Isc = 7.44 A, Umpp=28.8 V, Impp = 6.94 A. In addition to that, this paper only sets a simulation time of 0.6s based on the experimental observation that the light changes are concentrated in this time period. If longer illumination fluctuations are to be simulated, the simulation time can be extended linearly, and the algorithm will continue to track the MPP until the new steady state.
MPPT control circuit structure diagram.
In uniform light, all photovoltaic cells receive a light intensity of 1000 W/m2, the temperature is set to 25 °C, and the theoretical MPP is 2384 W, as shown in Fig. 7. The four algorithms mentioned above are applied to the model to evaluate their respective performance, and their output is shown in Fig. 8.
Figure 8 represents the comparative results of the INC algorithm, PSO algorithm, MPA, and IMPA when they are under the condition of uniform light. All the algorithms have similar stabilized power levels, which are stabilized at 2387.3 W, 2382.6 W, 2379.5 W, and 2383.6 W. Notably, the power fluctuation range of all algorithms is strictly controlled within ± 0.05%, which verifies the stable operation capability of the system. In terms of dynamic response characteristics, the tracking speed differences between algorithms are significant: the INC algorithm takes 0.062s, the PSO algorithm needs 0.132s, the MPA algorithm is shortened to 0.046s, and the IMPA algorithm becomes the fastest convergence scheme with a response speed of 0.031s. Comparative analysis shows that the improved IMPA algorithm not only maintains a comparable steady-state accuracy with the traditional algorithm in the uniform illumination scenario, but also achieves a significant improvement in tracking efficiency, and its comprehensive performance is significantly better than that of the other three compared algorithms.
P-V curve of uniform light output characteristic of photovoltaic array.
Simulation results of uniform illumination.
PV arrays are subject to local shading in daily operation, so this experiment simulates the P-V curves of PV arrays for three different operating environments. The set PV arrays operating environments are shown in Table 2. Since the illumination intensity and temperature of the three groups of PV arrays connected in parallel are the same, Table 2 only lists the working environment of one of the groups. Figure 9. visually displays the resulting P-V characteristic curve of the photovoltaic array operating under the conditions listed in Table 2, with the light intensity changing every 0.2 s.
As can be seen from Fig. 9 that when the PV arrays are in PSC1 condition, its GMPP is 2077 W, and the first LMPP is 1770 W. When the PV array is in PSC2 condition, its GMPP is 1603 W, and the first LMPP is 1156 W. When the PV array is in PSC3 condition, its GMPP is 1171 W, and the first LMPP is 541.6 W.
As mentioned above, to compare the MPPT performance of the improved algorithm, the INC method, PSO algorithm, MPA, and IMPA proposed in this paper are respectively applied to the simulation model shown in Fig. 6. The simulation results are shown in Fig. 10, and the tracking performance is shown in Table 3. As depicted in Fig. 10. and Table 3, in the case of dynamic shading, only MPA and IMPA can track the vicinity of the MPP in all three cases.
In the case of the first illumination intensity, the INC method stops when it tracks the first local maximum power point. As long as the extreme point can meet the stopping condition of the INC method, therefor it stops after finding the first MPP. Similarly, when the illumination intensity changes, it also stops at the first LMPP. When the illumination intensity changes again, the fluctuation power is immense because its step size is fixed and does not change with the change of the external environment, so high fluctuation occurs.
The PSO algorithm is simple compared to the MPA, so its tracking speed is faster, but the accuracy is not high, which occurs in the third light condition. Moreover, the verification algorithm in this paper does not add a restart mechanism, the PSO algorithm is incapable to recognize rapid changes in light intensity, so sometimes it is unable to track the MPP. When the initial light intensity rapidly changes to the second light intensity, it is due to the lack of a restart mechanism that the algorithm cannot recognize the changes in light intensity, and therefore can’t track the MPP.
The overall accuracy and tracking speed of the MPA are also not bad, and the MPP can be tracked within about 0.04–0.05 s after the change in light conditions. The accuracy can reach more than 97%, which belongs to one of the better meta-heuristic algorithms, but it is still not as good as IMPA.
The IMPA in this paper can quickly adjust and track the vicinity of the MPP in the short time of 0.03–0.04 s when facing the change of light intensity. The fluctuation range in the tracking process is strictly controlled within 0.3 W to ensure stable performance. In terms of accuracy, the tracking result of the IMPA is more than 99.95% accurate, demonstrating its high efficiency and precision.
In the comparison of dynamic response characteristics, the IMPA algorithm exhibits significant advantages, with an average convergence time of only 0.036 s, which is about 21.7% shorter than other algorithms. Although the PSO algorithm can respond quickly during the second and third irradiation mutations, there is a risk of getting stuck in local optima, resulting in the output power not stabilizing at the theoretical maximum value; The INC algorithm has a fast tracking speed, but the steady-state fluctuation amplitude is large, which can cause significant energy loss; The MPA algorithm has a faster convergence speed, but its tracking efficiency is not as good as IMPA. The simulation outcomes the IMPA demonstrates superior tracking performance in comparison to the other three algorithms combined with tracking speed and tracking accuracy under dynamic shading, proving the improved algorithm’s effectiveness.
Photovoltaic array local shading outputcharacteristics P-V curve.
Local shading simulation results.
Photovoltaic arrays may experience extreme shading conditions during daily operation, so this experiment simulates the tracking ability of four algorithms under three extreme shading conditions. The operating environment of the set photovoltaic array is shown in Table 4. Due to the same light intensity and temperature of the three parallel photovoltaic arrays, Table 4 only lists the working environment of one of them. Figure 11 visually displays the P-V characteristic curve of the photovoltaic array operating under the conditions listed in Table 4, with the light intensity changing every 0.2 s.
From Fig. 11, it can be seen that when the photovoltaic array is in PSC1 state, its GMPP is 1538.3 W; When the photovoltaic array is in PSC2 state, its GMPP is 1185.3 W; When the photovoltaic array is in PSC3 state, its GMPP is 1511.6 W. The tracking performance of the four algorithms is shown in Fig. 11.
Photovoltaic array extreme shading conditions output characteristics P-V curve.
Extreme shading conditions simulation results.
As shown in Fig. 12, in the PSC1 condition, both IMPA and MPA successfully track to the vicinity of the maximum power point, but IMPA exhibits a higher tracking accuracy of 99.95%, while the accuracy of MPA is about 97%. In contrast, the PSO algorithm exhibits significant power fluctuations ranging up to ± 900 W. This instability stems from the mismatch between the global search mechanism of the particle swarm algorithm and the dynamic response of the PV system, as well as oscillations caused by improperly set algorithm parameters. The INC algorithm, on the other hand, due to the intrinsic defects of traditional algorithms, stops tracking after reaching the LMPP, and fails to continue to search for the GMPP. In terms of time efficiency, IMPA quickly tracks to the maximum power point in only 0.033 s, demonstrating a very high tracking speed.
In the PSC2 condition, IMPA and MPA are still able to track near the maximum power point, but the tracking accuracy of IMPA slightly decreases to 99.35%, while the accuracy of MPA decreases to about 92%. It is due to the extreme change of the external environment from the first to the second stage that the tracking accuracy slightly decreases. But overall, the IMPA tracking effect is still very good. the INC algorithm again falls into the local optimum, while the power fluctuation of the PSO algorithm is still large. In terms of time efficiency, the tracking time of IMPA slightly increases to 0.037 s. Although the INC algorithm tracks faster, it can still only find the local optimal solution due to its algorithmic flaws.
In the PSC3 condition, IMPA, MPA and INC all successfully tracked near the maximum power point. However, the INC algorithm exhibits some power fluctuations in the range of ± 30 W, which may lead to power loss. Tracking accuracies of IMPA and MPA both reach 99.95%, but the tracking speed of MPA is slightly slower than that of IMPA, with IMPA taking only 0.042 s to complete the tracking, while MPA takes about 0.056 s. The PSO algorithm in the PSC3 scenario still exhibits large power fluctuations. To summarize, even in the more extreme environments, the improved algorithm is still able to track the GMPP quickly and accurately, which fully proves its superiority and stability.
This paper introduces the IMPA as a solution to the MPPT challenge faced by PV arrays under conditions of local shading in the context of analyzing their multi-peak output characteristic curves. Simulation experiments of uniform illumination and local shading are carried out, and tracking speed and accuracy are evaluated with that of representative algorithms. The experiments prove the superiority of the IMPA in this paper, which can be subsequently considered to be integrated with the real situation into the actual photovoltaic arrays.
The results show that:
PV arrays subjected to horizontal shade will output multiple power extremes, but only one maximum power point exists. The number of peak points in its output is related to the illumination intensity that the series-connected PV cells receive.
For uniform light conditions, the IMPA presented in this paper improves the algorithm’s tracking speed by limiting the position of its initial population, so that the values in the subsequently established correlation matrix are optimized. Experimental results indicate that the accuracy of the IMPA algorithm can reach more than 99.98%, and the tracking time is reduced to 0.031 s in the case of uniform illumination. The experimental results reveal a 50%, 25% and 33.3% reduction in the tracking time of the enhanced algorithm compared to the existing three algorithms.
For dynamic lighting conditions, this paper introduced a restart mechanism in MPA, which is able to restart the algorithm when the light changes rapidly. At the same time, an elite guidance mechanism is introduced to screen and utilize excellent individuals quickly, which speeds up the convergence of the algorithm. In the experiments under different light conditions, IMPA can quickly identify the new MPP within 0.2 s, achieving an efficiency exceeding 99.95%.
The data presented in this study are available on request from the corresponding author. The data have not been made public yet, as the data in this article still needs to be used for further research.
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This work was supported in part by the National Natural Science Foundation of China under Grant 52277139 and 52367014, and in part by the Guangxi Science Fund for Distinguished Young Scholars under Grant 2024GXNSFFA999017.
Guangxi Key Laboratory of Power System Optimization and Energy Technology, Guangxi University, Nanning, 530004, China
Hanbo Zheng, Qi Du, Shuqin Mo & Tuanfa Qin
China Water Northeastern Investigation Design & Research CO., LTD., Changchun, 130021, China
Shusheng Wang & Zhe Li
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H.Z.: Conceptualization, Writing – Review & Editing. Q.D.: Data Curation, Writing – Review & Editing, Formal analysis. S.M.: Formal analysis, Investigation, Methodology, Writing – Original Draft. T.Q.: Resources. S.W.: Supervision. Z.L.: Validation.
Correspondence to Qi Du.
The authors declare no competing interests.
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Zheng, H., Du, Q., Mo, S. et al. Improved marine predator MPPT algorithm for photovoltaic systems in partial shading conditions. Sci Rep 15, 21092 (2025). https://doi.org/10.1038/s41598-025-06408-9
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DOI: https://doi.org/10.1038/s41598-025-06408-9
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