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Scientific Reports volume 15, Article number: 14540 (2025) Cite this article
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Partial shading conditions (PSC) in photovoltaic (PV) systems degrade energy harvest by generating multi-peak power-voltage (P–V) curves, trapping conventional maximum power point tracking (MPPT) algorithms at local maxima. This paper presents a Multi-Peak to Single-Peak Conversion (MSMPPT) framework that enables conventional algorithms like Perturb & Observe (P&O) and Incremental Conductance (INC) to reliably track the global maximum power point (GMPP) under PSC without structural modifications. The framework operates via two stages: dynamic estimation of optimal voltage boundaries to shrink the GMPP search space to under 10% of the original P–V range, and active voltage regulation to enforce operation within this zone, effectively transforming the multi-peak curve into a single-peak profile. The proposed MSMPP-P&O and MSMPP-INC algorithms achieve 50% faster tracking (64 ms vs. 122 ms for P&O) and near-perfect steady-state efficiency under static shading, reducing power losses below 2%. In dynamic shading scenarios with abrupt irradiance shifts, MSMPPT maintains robustness with less than 1.5 W net loss, outperforming conventional methods that incur over 30 W of power losses. By eliminating oscillations and hotspot risks through voltage regulation, the framework retains algorithmic simplicity while enhancing performance under complex shading scenarios. Validated across benchmark shading profiles, MSMPPT demonstrates fidelity without requiring additional hardware or complex optimizers. This innovation bridges the gap between conventional MPPT simplicity and partial shading resilience, offering a cost-effective, scalable solution to boost PV system reliability in shading environments.
The persistent scarcity of fossil-based energy, along with the present geopolitical tensions affecting the world, has fueled the worldwide transition toward renewable energies (REs). It is becoming increasingly necessary to discover alternatives to conventional energy that do not come within the borders of the described barriers. At a time when the world is mobilized to enhance de-carbonization, the outstanding environmental potentials of REs are emerging as a viable point of interest. Thus, REs represent an outstanding bridge between contemporary energy demands and sustainability requirements. Amid the geopolitical differences and surge in energy demand of the last few years, the expansion of REs has been exorable and expected to be unprecedented in future coming years. As a result, the last years has been marked by increase in the implementations of REs (see Fig. 1a). As illustrated in Fig. 1b, the exponential rise in the capacity of REs during the last decade has been majorly contributed by hydro, wind, photovoltaic and biogas, with a total of 3, 683 GW recorded in 2021. Despite the heightened net contribution by Hydro in comparison with solar and Wind, as revealed in Fig. 1b, several projections are unanimous on the fact that wind and solar are the future of renewable energy and electricity generation as a whole. This is evident from the fast growth rate of these energies. For instant, Hydro recorded an increase in capacity of approximately 270 GW between 2012 and 2021, against an increase of 556 GW, and 750 GW for Wind and Solar PV respectively. Furthermore, it is evident that Wind energy capacity has dominated solar energy up to 2021, wherein the PV capacity reached approximately 855 GW against 823 GW of Wind. This further exemplified that solar energy will play an important role in the nearest future. It is projected to account for 25% of global electricity needs by 2050¹.
Yearly Contribution of REs. (a) Different REs including Hydro, Wind, solar and Bio (b) Total RE capacity. Graphs plotted from raw data in².
According to the international Renewable Energy Agency (IRENA), significant effort needs to be done in order to push the frontiers of solar PV systems to meet the milestone of 2050, notably a steady increase in capacity of PV by almost six fold over the next ten years. In this regards, a wealth of effort is being vested on the enhancement of the energy generated by the PV using efficient material and technologies^3,4. Also, several tendencies are considered on a day-by-day basis on the amplification of the photovoltaic operating performance using maximum power point tracking (MPPT)^5,6,7,8. Operationally, this tendency appears as a pressing one given the nonlinear varying structure of the PV^9,10, which causes the point of greatest energy to fluctuate with environmental conditions such as irradiance and temperature^11,12. In such a scenario, a maximum power point tracker is used to capture the point of highest energy in the PV systems^13,14. A typical maximum power point tracking system integrated into the PV system is illustrated in Fig. 2, consisting of a boost converter, a special type of power electronics converter, regulated by an embedded MPPT algorithm, which targets the adjustment of the converter’s duty-cycle¹⁵. Tracking of the mentioned maximum power point has the ability to enhance the PV system efficiency by up 30%³. When the system is uniformly irradiated, its characteristics presents a single and simple maximum power point (MPP)^16,17,18,19. However, under non-uniform irradiation, the characteristics admits multiple MPPs which becomes more intricate to target the most prolific energy point, called the global maximum power point (GMPP)^20,21,22. In both cases, the efficacy of the system hinges on its potential to operate at its point of maximum energy.
Electrical structure of a typical maximum power point tracking systems.
In recent times, several tracking methods have been conceived in the form of algorithms to harvest the MPP^23,24,25. Conventional algorithms such as perturb and observe (P&O) and incremental conductance algorithms have gained special popularity for their simplicity^26,27,28. Nonetheless, they are only competent within the bounds of uniform irradiance conditions. As a consequence, under partial shading conditions (PSC), they may get trapped at energy points lower than the maximum energy point, called the local maximum power point (LMPP). Nevertheless, it is noteworthy that these algorithms have received tremendous commercial and industrial applications in MPPT charge controllers and inverters. Although very competent within the sphere of uniform irradiance conditions (UIC), several challenges have been identified, which notably impedes their efficiency.
Oscillations around the maximum power point and a trade-off between tracking speed and ripples around the turning point represent the most challenging limitations of these algorithms. In an effort to improve the MPPT accuracy and speed, several modifications and improvement as highlighted in Table 1, ranging from the dynamic adaptation of step-size, enhanced zero oscillation, beta algorithm, optimized beta algorithm, Adjustable step-size, extremum seeking control, confined search space, nonlinear control methods (Lyapunov based model reference adaptive control algorithm, Backstepping), intelligent algorithm (ANN and Fuzzy logic), just to name a few, have been suggested. However, these improvements strengthen the conventional algorithm only within the expertise of uniform irradiance operation, leaving the algorithm incompetent when faced with PSC.
Furthermore, methods that rely on scanning the photovoltaic curve have been suggested as a means to improve tracking of the optimum power point in situations involving partial shading. An example of this can be seen in the duty cycle-based power-voltage scanning algorithm that was proposed in²⁹ to monitor the global power point of distributed PV systems. In order to develop an efficient method for restricting the scanning interval, the methodologies employed analytical procedures on the PV curve. By means of experiments and simulations, they implemented their entire system on a single-ended primary inductance converter. Nevertheless, this method is complicated and expensive, as it necessitates the use of numerous power converters and optimizers.
Methods based on optimizations algorithm, belong to a class called optimizer, have emerged as the most qualified approaches for tracking the GMPP of the PV systems under PSC^30,31,32. They are especially successful because of their ability to distinguish between the LMPPs and the GMPP. Thus, unlike conventional MPPT algorithms they can escape the trap of LMPPs. Lately, with the surge of research in metaheuristic algorithms, several of these optimizers including particle swarm optimizer³³, grey wolf³⁴, ant colony optimizer³⁵, bat optimizer³⁶, and Cuckoo search optimizer³⁷ just to name a few, have been applied to track the GMPP. Moreover, hybrid methodologies have been developed, including the MPPT optimizer, which combines the voltage search and cuckoo search optimizers³⁸. In principle MPPT optimizer have a common scheme of operation, maintaining search agents within a defined search space to explore the global maximum power point. Although specialized in PSC operations, optimizers face the inherent large search space of the PV system as highlighted in Fig. 3, as well as significant oscillations around the GMPP. When deployed, searching agents require a significant search time to navigate within the search space. As a consequence, the tracking time of optimizer is inherently comprised. Furthermore, the search time of the optimizer can affect the stability of the PV system, where in a special case the operating point oscillates around the GMPP leading to loss of power. Finally, and most importantly, the optimizer –based MPPTs are very complex and intricate to integrate within practical system. This characteristic makes them very unfeasible.
P–V curve under PSC highlighting the competence and limitations of optimizers.
A way out of the problems of GMPPT in PV system would be to habilitate the conventional MPPT algorithm with PSC operation competence. Such a scheme can potentially yield to a guaranteed practical reliability and dependability of the system, principally because of the simplicity and explicit nature of the resulting algorithms. This habilitation scheme can be achieved in two ways. In the first habilitation, the conventional algorithms can be modified with suitable adaptation in order to assist them with PSC operation competence. In the second habilitation scheme, the multiple MPP P–V curve of the system under PSC operation can be adjusted to an equivalent one-MPP characteristic, thereby granting direct competence to the conventional algorithm which are specialized in such environment.
In the first habilitation, modifying the conventional algorithms can introduce intricacy at different level, which is ideally not desired, as it would complicate the implementation design as well as hamper the accuracy and efficiency of the PV system. A review of the literature reveals that only the first habilitation scheme has been explored to give competence to the conventional schemes in order to tackle the GMPP in a PSC setting. Nevertheless, it is noteworthy, that contemporary works have given relatively little attention to this habilitation, as the focus of research has been MPPT optimizers. In the realm of the first habilitation, an improved MPPT algorithm was propose to tackle the GMPP under PSC⁶³. This method combines an extremum seeking control to handle the robustness of the PV system and a modified P&O algorithm to track the GMPPT. The P&O is modified using a gradient detection framework on the P–V curve together with an adaptive step-size which guides the system to the effective maximum power point. The resultant algorithm has noticeable improved performance in terms of PSC. However, the fundamental problems of oscillations around the MPP and slow tracking performance are not handled by the algorithm. The large search space of the PV system contributes to the aforementioned shortcomings. Furthermore, although the algorithm has the competence to track the GMPP, the simplicity of the system is compromised. Notably by its reliance on an extra control algorithm, extremum seeking control, which significantly complicates the algorithm. In an effort to enhance the simplicity of the MPPT algorithm, an improved version of the previously algorithm was proposed, that seeks to track the GMPPT in the realm of the first habilitation⁴⁶. Although the extremum seeking does not feature in this algorithm, it implements two adaptive P&O algorithm in series in order to handle the GMPP. Although, the resulting algorithm can track the GMPP, its procedure is intricate and may fail for some PSC conditions. Similarly, the algorithm also suffers from oscillations around the MPP and slow tracking performance. Other recent contribution to MPPT include the INC MPPT Algorithm with Integral Regulator by Using Boost Converter in Grid-Connected PV Array proposed in⁶⁴. The study enhanced the INC algorithm with an integral regulator to minimize steady-state oscillations, achieving 98.5% efficiency in grid-tied PV systems under uniform irradiance. In terms of limitation, it fails under partial shading due to reliance on single-peak assumptions, leading to convergence at local maxima. Another study proposed a Model Predictive Control (MPC) strategy that forecasts the optimal power point by leveraging reference current adjustments, enabling precise tracking under rapidly changing irradiance and temperature. However, it requires high computational resources for real-time optimization, limiting practicality for low-cost PV systems⁶⁵. This demonstrates the value of dynamic adaptation but underscores the need for simpler, computationally lightweight solutions like MSMPPT, which avoids complex predictive models. Also, a comprehensive review categorizing MPPT methods into conventional, metaheuristic, and hybrid algorithms, emphasizing the rise of AI-based techniques for partial shading mitigation, was proposed⁶⁶. The study identified unresolved trade-offs between algorithm complexity, tracking speed, and hardware costs, particularly for conventional methods under PSC. This validates the research gap in empowering conventional algorithms for PSC, positioning MSMPPT’s second habilitation approach as a novel solution bridging simplicity and robustness.
It is evident that the first habilitation can endow competence to the conventional algorithm, however they come with heightened complexity which may endanger their performance and reliability. Therefore, at this level, it is a crucial requirement to seek simplified methods that can smoothly track the GMPP of the PV system under PSC. To address these requisites, the second habilitation emerges as a potential candidate. Throughout the literature of GMPPT, this direction has not been explored. Potentially, it can be the ultimate straightforward solution to PV systems under PSC.
In our recently published study, we paved an opening to the conversion of the multiple MPP P–V curve under PSC to a single MPP curve, which will establish the foundation of the second MPPT habilitation in this current paper⁶⁷. In the previous work, we demonstrated that it is accurately possible to rely on measurements of current and voltage only to predict optimum boundary regions of the GMPP. Thus, in this current study, a similar notion is employed to innovatively suggest a Multiple-to-Single MPP (MSMPP) conversion structure. This structure is envisioned to provide an ideal GMPPT platform for conventional algorithms, without bringing any form of modification to their original structure. As a result, the great simplicity of the conventional algorithm is consolidated, with high assurance of effectiveness and reliability under PSC. Furthermore, in order to surmount the problems of oscillations and slow tracking performance within the single MPP operation of the conventional algorithm, the MSMPP structure initially reduces the search space of the system to less than 10% of the actual P–V curve area. As opposed to existing works the problem of search space is carefully treated by the proposed structure leading to a significantly improved operating performance. The proposed MPPT is implemented on a standalone PV system, composed of three PV modules in series for PSC demonstration, with a boost converter and substantiated though several simulations conducted in MATLAB/Simulink. The newly acquired results revealed the powerful potency of the MSMPP framework to efficiently enhance the tracking performance of conventional algorithms under PSC conditions, leading to an efficient and dependable system with heightened mitigation of power losses due to PSC. The main innovations of this study are appended as follows:
A Novel Multiple-to-Single MPP (MSMPP) structure for PV system is proposed.
The novel MSMPP is integrated into the PV systems, providing an ideal tracking environment for conventional MPPT algorithm under PSC.
A novel PSC-competent variant of the P&O algorithm is proposed called MSMPP-P&O algorithm.
A novel PSC-competent variant of the INC algorithm is proposed called MSMPP-INC algorithm.
A comprehensive comparison between the MSMPP based algorithms and the conventional P&O and INC is conducted, revealing the suitability of the new MPPT structure, notably fast tracking of the GMPPT under all configurations of PSC.
As opposed to existing algorithms, the novel structure stand-out for its high simplicity and feasibility.
The remainder of this paper is configured as follows: The general structure of the proposed system is overviewed in Section “General overview of the proposed system”, followed by the analysis and discussion of the operation of PV systems under PSC in Section “Analysis of the PV system under PSC”. In Section “Maximum power point tracking”, the limitations of the conventional algorithms are discussed, followed by the development of the new MSMPP structure. The results and discussion of this study are provided in Section “Results and discussion”, followed by conclusion and recommendations in Section “Conclusion”.
As was previously highlighted, this study introduces a MSMPP framework for efficient deployment of conventional maximum power point tracking under partial shading conditions. The envisioned system is synoptically presented in Fig. 4. The shaded PV system generates a complex characteristic, noticeable from the presence of multiple MPPs in its P–V curve. To handle this complexity and enhance the tracking potential of conventional algorithms, a MSMPP framework is constructed. This structure surfaces to convert the multiple MPP P–V curve of the shaded PV system to an approximated curve that contains only a single MPP as highlighted by the yellow graph in Fig. 4. Thus, once deployed, the conventional algorithms such as P&O and INC consistently see the image of a single MPP P–V curve, which represent an ideal environment for their simple and efficient operation.
A Synoptic structure of the proposed PV system.
Partial shading is an operating scenario that occurs there is unequal distribution of solar irradiance across connected PV modules, with some modules turning to be more irradiated than others. Such a scenario can occur as a result of standing objects, dust and clouds accumulation on PV modules. A typical unequal distribution of solar irradiance for three series connected PV modules is presented in Fig. 5(b). The modules in series receive the irradiance of (:400 , W/{m}^{2}:), (:900,W/{m}^{2}) and (:600,W/{m}^{2}) respectively. When PV system is partially shaded, the voltage across the shaded PV modules is negative as they operate in a reverse bias mode, behaving as a load⁶⁸. This results to the shaded module calling more power from the unshaded module. As a consequence, the concentration of power on the shaded module increases significantly, leading to internal heating, widely known as Hotspots.
Interconnected PV connected modules. (a) unshaded (uniform) and (b) shaded setting.
The generation of Hotspots in PV has been categorized as a dangerous fault with the potential to cause permanent damage to cells or modules⁶⁹. To avoid such a fault, series modules are connected with bypass diode (BPD), which provide an alternative path for current. Although the BPD, is protection against Hotspots, it leads to the modification of the standard P–V curve of the system as seen in Fig. 6. Also, for a safe operation, a blocking diode (BLD) is used to prevent back flow of current into the PV array.
Characteristic curves of the PV system under uniform irradiance and shaded conditions.
The typical operation regime of PV system is presented in Fig. 5, for both uniform and shaded irradiation conditions. In the uniform regime, all the PV modules are exposed to an irradiance level of (:1000,W/{m}^{2}). Additionally, all modules are connected to BPD, and the entire array is connected with a series BLD.
For the unshaded and shaded PV modules described by Fig. 5(b), the corresponding I-V and P–V curve is plotted in Fig. 6, revealing the presence of a single MPP in a uniform irradiance regime. Conversely, for the partially shaded modules, there exist three MPPs, with two LMPP and a single GMPP. In general, the magnitude of LMPPs and the GMPP depends on the PV modules and the irradiance magnitude. The multitude of maximum power point constitute the complexity related to the operation of the PV system under partial shading. Therefore, continually capturing the unique GMPP in such a setting is an absolute necessity to ensure and efficient PV system. A prime challenge lies in the fact that the GMPP is not steady, thus varies with environmental conditions, especially irradiance. Therefore, the global maximum power point tracker should be dynamic enough to capture new GMPPs induced by changing PSC patterns. It is very expensive and difficult to precisely tell the position of the GMPP at any point in time. Nevertheless, every GMPP has an optimum region, which can serve as a pivotal direction to tracing the GMPP. Thus, regardless of the pattern of partial shading, the GMPP can take three positions⁶⁷. These positions named: GMPP-L, GMPP-M, and GMPP-R are demonstrated in Fig. 7. In GMPP-L, the GMPP occurs at the extreme left of the P–V curve, in GMPP-R, it occurs at the extreme right of the P–V curve, while in GMPP-M, it occurs between two neighboring LMPPs.
Optimum position of the GMPP under PSC (i) GMPP-R (ii) GMPP-M (iii) GMPP-L.
Irrespective of the position, the GMPP on the P–V curve occur in pair of (:{(V}_{GMPP},:{P}_{GMPP})), while the local MPP occurs in (:{(V}_{LMPPn},:{P}_{LMPn})), where n represents the position specification of the LMPP. Also the open circuit voltage of the PV array system is denoted by (:{V}_{oc}). Therefore, exploring these optimum regions can enable a quick identification of the GMPP.
The P&O and INC have been established as the most popular algorithm in PV systems^{39,70,71,72,73}. They both follow a common working principle of injecting linear perturbation at the terminal of the PV and making decision according to the resulting voltage/current or power of the PV. While the P&O compares the present and previous power of the in relation to the voltage, to determine the maximum power point, the INC uses the incremental and instantaneous conductance of the PV. The direction of perturbation in the duty cycle for the P&O is given by⁷⁴:
Where (:{P}_{pv}), (:{V}_{pv}), and (:{I}_{pv}) stand for a change in power, voltage and current respectively. These change is approximately obtained from the discrepancy between the current and measurement previous instant. Also, (:dleft(k+1right)) represent the updating perturbation, while (:dleft(kright)) stands for the perturbation at the previous instant, finally (:varDelta:d) stands for the perturbation step size. Similarly, in the INC operation, the direction of subsequent perturbation is obtained by⁷⁴:
In both INC and P&O, increasing the duty cycle results to a decrease in the PV voltage for the Boost type converter⁷⁵. The operation of the conventional INC and P&O can be summarized in Fig, 8. By supposing that initially the operating point is a at 0 V, and after a perturbation the PV is shifted to the point with voltage (:{V}_{1}). At this point, since both change in power and voltage are positive, the (P&O/INC) increases the voltage by decreasing the duty according to Eq. (1) or (2) so that a perturbation continues in the positive direction. A further supposition that at a some instant the algorithm (P&O/INC) is at the point on the P–V curve with voltage (:{V}_{3}), such that a subsequent perturbation drives the PV voltage to (:{V}_{4}), with the power at (:{V}_{4}), (:{P}_{4}) being lower than (:{P}_{3}), then according to Eq. (1) or (2), the operating point of the PV will move backwards as demonstrated by the red dotted arrow in Fig. 8. Such a backward movement represent a convergence at the LMPP. Subsequent perturbation will only stir the operating point around this point. Therefore, it is evident that conventional algorithms, lack competence to arrive at the GMPP.
Operating principle of MPPT algorithms under PSC.
In order to smoothly track the GMPP, we propose a novel structure that is aimed at emulating a new P–V characteristic in the PV system. Notably this characteristic contains only a single MPP, the GMPP. The proposed structure is termed multiple-to-single MPP conversion (MSMPP) structure. From previous description and analysis, it is evident that conventional algorithm can effectively track the maximum power point provided the PV curve has only a single MPP. In fact, rather than targeting the GMPP between the large search space bounded by (:left[0:{V}_{oc}right]), the proposed algorithm targets a reduced search space (:left[{V}_{a}:{V}_{b}right]). In our previous studies we showed across over 700 shading patterns that the search space (:{V}_{a}) and (:{V}_{b}) can contribute to less than 10% of the original search space⁶⁷. Such a reduce search space would amount to an enhance and very fast tracking of the GMPP.
Therefore, with the notion that the GMPP can occupy three optimal position, the MSMPP seeks to estimate (:left[{V}_{a}:{V}_{b}right])
to define the new single MPP P–V curve as demonstrated in Fig. 8. Specially, two routines are implemented within the MSMPP framework.
The estimation of (:left[{V}_{a}:{V}_{b}right]) as presented in Appendix-A of the Supplementary section and supported by our previous study⁶⁷. A flowchart of the overall process is presented in Figure A1, in the same appendix.
Regulation of the PV voltage to impose the region (:left[{V}_{a}:{V}_{b}right])
When the aforementioned routines are implemented and integrated within the PV system, the conventional algorithms will consistently see a new P–V curve emulated by the MSMPP framework. Thus, given that the emulated curve (right of Fig. 9) admits only a single MPP, the competence of the conventional algorithms would be guaranteed.
Operation principle of the MSMPP structure.
At this stage, we are in position to describe the implementation and integration of the MSMPP structure into the PV system in order to have a smooth tracking of the GMPPT. The integration of the proposed structure into the PV system can either yield a MSMPP-P&O algorithm or the MSMPP-INC algorithm, depending on which conventional algorithm is considered. Nevertheless, the proposed framework can be used in synergy with several other advanced algorithms. In this paper, the conventional algorithms (P&O, and INC) are specially considered for their high simplicity and practical dependability.
The integration of the MSMPP into the MPPT system is based on two straightforward stages:
The flowchart of the MSMPP based GMPPT algorithm is presented in Fig. 10. The sequence begins though the sensing of the PV voltage and current (:{V}_{pv},:{I}_{pv}), followed by the determination of (:{V}_{a}), and (:{V}_{b}) respectively. In the regulation stage, the MSMPP seeks to force the PV operating point within the region (:left[{V}_{a}:{V}_{b}right]). This is achieved by the following Eq. 
Flowchart of the proposed MSMPP based GMPPT algorithm.
Where (:{V}_{a}) is the lower bound of the optimum power region and (:{V}_{b}) representing the upper bound. The term (:lambda:d) is a the regulation parameter that controls the speed of the regulation stage. Therefore, if the voltage is lower than the lower bound of the optimum power voltage, then it is understood that the operating point is still at a risk of getting trapped in an LMPP, as such the operating voltage is increased by reducing the perturbation size using Eq. (3). On the hand, if the PV voltage is greater than the upper bound, in order to escape LMPP, the MSMPP reduces the PV voltage by increasing the duty cycle. It is worth emphasizing that in either case, (:lambda:d) should be chosen so that regulation is done and achieved in the swiftest possible step. Ones the algorithm senses that the voltage of the PV is bounded by (:{V}_{a}) and (:{V}_{b}), then the MSMPP interprets that the new P–V curve has been emulated. Thus it calls a conventional MPPT algorithm to terminate the search for the GMPPT in a very reduced effort.
This stage is executed if the PV voltage fulfils the following inequality:
The satisfaction of these condition confirms that the emulated P–V curve is free from any possible LMPPs. Thus the conventional MPPT algorithm is deployed. It should be noted that because the space (:left[{V}_{a}:{V}_{b}right]) is too small, the conventional step-size (:varDelta:d) should be small enough to mitigate the oscillations around the GMPP. The operation of the proposed algorithm can further be described using Fig. 8. The principal notion is that with the proposed algorithm the operating point is assured to rapidly bypass the LMPP as long as the condition in Eq. (4) is not fulfilled. For instance, at (:{V}_{3}) where the conventional algorithm converged and entered the oscillation loop, the proposed MSMPP would increase the PV voltage from (:{V}_{4}) to (:{V}_{5}:)by reducing the duty cycle, since (:{V}_{4}<{V}_{a}), till the operating point enters the optimum power region, say (:{V}_{9}.:)
In order to verify the effectiveness of the developed MSMPP based algorithm, a series of simulations are performed in MATLAB with consistent step size of (:1times:{10}^{-06}s). Furthermore, the MSMPP structure, is applied to the INC and P&O, yielding to the MSMPP-P&O and MSMPP- INC. All the algorithms are implemented on a neutral platform. In order to position the contribution of the MSMPP, a comprehensive comparison is carried between the P&O and MSMPP-P&O, and the INC and MSMPP-INC. In the implementation stage, a boost converter is used for all the algorithm with the parameters: (:{L}_{boost}=10mH,:{C}_{boost}=200uF,:{C}_{pv}=100uF), and a pulse width modulation (PWM) frequency of 30 kHz. The full parameters of the system can be found in Table B of Appendix. B of the Supplementary section. A 60 W PV module is employed in accordance with⁶⁷.
Additionally, all the algorithms are incorporated with a perturbation delay (:{T}_{p}=5ms). This delays as highlighted in the flowchart of Fig. 10 allows the algorithm to accurately determine when the PV system is at steady-state. Finally the other parameters related to the algorithms are as follows:(::varDelta:d) for the (P&O/INC) is designed with optimal value of 0.02. The (:varDelta:d) for the proposed algorithm is designed to be 0.008 for MSMPP- P&O, and 0.001 for MSMPP- INC. While the regulation parameter is designed to be (:lambda:d=0.05) for both MSMPP- P&O and MSMPP- INC. The MATLAB Simulink diagram of different blocks and the overall system are presented in Appendix C of the supplementary section, Figs. C1, C2 and C3
Five benchmarking PSC patterns are used to validate the different experiment. As seen in Fig. 11, in Pattern-A, all the PV modules operate in a uniform irradiance condition, with (:G=1000,W/{m}^{2}). The unequal distribution of irradiance in the Pattern-B, Pattern-C, Pattern-D, and Pattern-E is presented in Fig. 11. It is noteworthy that all the PV modules are identical and have power rating of approximately 60 W. The full characteristic of this PV module is found in⁶⁷.
Partial shading pattern used in this study.
The response of the maximum power point tracking algorithms to irradiance conditions in Pattern-A is presented in Figs. 12 and 13, while the duty cycle is presented in Fig. 15. The optimum voltage region (:{V}_{a}) and (:{V}_{b}) estimated by the MSMPP is presented in Fig. 14. It can be seen that the MSMPP based algorithms track the GMPP of 181.3 W in approximately 64ms for the MSMPP-P&O and 68ms for the MSMPP-INC. In contrast, the P&O and INC converge at 122 ms and 114 ms respectively. However, it can be seen that the INC effectively tracks the GMPP while the P&O does not. The numerical results of this outcome is summarized in Table 2, revealing that the conventional algorithms record efficiency of 94.62% and 99.28% for P&O and INC in the set shading pattern. The proposed MSMPP increases the tracking speed of the algorithms to approximately two times. This is expected as the MSMPP reduces the search space, determined by the voltage region (:{V}_{a}) and (:{V}_{b}) as seen in Fig. 14. The estimated values of these voltages are found to be 50.11 V and 54.37 V respectively. Interestingly, it can be seen that (:{V}_{a}) and (:{V}_{b}) were estimated in just 1ms. By focusing the region of convergence in Fig. 14, the time taken to estimate these optimum points was recorded as (:{T}_{ab}=1ms). This very small estimation time explains the rapid convergence of the overall GMPP algorithm. As a consequence, optimum power harvesting is guaranteed. It must be noted that the voltage estimation stage is an integral part of the proposed MSMPPT scheme, thus it directly determines the performance of the algorithm.
Power tracking curves for Pattern-A. Left: Standard P–V curve. Right: Power curves of the P&O and the MSMPP-P&O, along with the target GMPP.
Power tracking curves for Pattern-A. Left: Standard P–V curve. Right: Power curves of the INC and the MSMPP-INC, along with the target GMPP.
Optimum Voltage areas estimated by the MSMPP structure in Pattern-A. Zoom region shows the time of estimation of V_a and V_b, denoted as (:{T}_{ab})
Initially, when the PV voltage is out of this bound, the MSMPP fast reduces the duty cycle to increase the PV voltage till is bounded by the said range. This can be confirmed in Fig. 15 as the duty cycle evolves faster in the MSMPP based algorithms. Furthermore, an evidence that there is fine-regulation achieved by the MSNPP can be seen from the steady-state. Firstly, the steady state duty cycle in the MSNPP algorithms shows smoother regulation as compared to the INC and P&O. This is because within the optimum region, the MSNPP uses a very small step-size compared to INC and P&O. The consequence, is a significant mitigation of power oscillation achieved by the MSNPP as seen in Fig. 14. For instants, between 0.2 and 0.25s while the MSNPP aligns consistently with the expected GMPP, the INC oscillates between 181.3 W and 177.5.
Evolution of the duty cycle in the algorithms for Pattern-A. Above: P&O and MSMPP-P&O. Below: INC and MSNPP-INC.
The response of the maximum power point tracking algorithms to irradiance conditions in Pattern-B is presented in Figs. 16 and 17, while the duty cycle is presented in Fig. 18. The optimum voltage region (:{V}_{a}) and (:{V}_{b}) estimated by the MSMPP is presented in Fig. 19. In this PSC scenario, the GMPP has the value of 79.46 W, while the first LMPP has the value of approximately 54.19 W. For all the power tracking sequences, it is clearly seen that the MSMPP structure integrated in the MSMPP-INC and MSMPP-P&O achieves a tracking speed which is approximately twice the speed of the conventional (P&O/INC). It can be seen that the P&O gets stuck at the around the LMPP, with a converging power of 51.84 W with important oscillations at stead-state. Similarly, the INC converges with a better power level than the P&O, recorded to be 53.92 W. It thus achieves efficiency of 67.86% as compared to 65.24% for the P&O (refer to Table 2). Conversely, the proposed MSMPP effectively tracks the GMPP, smoothly converging at 79.46 W as expected, with zero oscillations in the steady-state, This represent approximately 100% efficiency in tracking the GMPP. Explicitly, the (P&O/INC) detects the first LMPP at approximately 0.07s. At this point, the duty-cycle get stuck and begins to stir around the value of 0.66. On the other hand, the MSMPP based algorithm perceived the LMPP at the time of 0.034s, with the duty cycle constantly decreasing to bypass the detected LMPP till it enters the (:left[{V}_{a}:{V}_{b}right]) region. It is evident that the at steady-state, the MSMPP mitigates ripple through a fine-adjustment of the duty-cycle. The estimated values of the optimum voltages were found to be 50.11 V and 54.37 V respectively. Similar to the previous pattern, it can be seen that (:{V}_{a}) and (:{V}_{b}) were estimated in just 1ms. By focusing the region of convergence in Fig. 19, the time taken to estimate these optimum points was recorded as (:{T}_{ab}=1ms). This very small estimation time explains the rapid convergence of the overall GMPP algorithm.
Power tracking curves for Pattern-B. Left: Standard P–V curve. Right: Power curves of the P&O and the MSMPP-P&O, along with the target GMPP.
Power tracking curves for Pattern-B. Left: Standard P–V curve. Right: Power curves of the INC and the MSMPP-INC, along with the target GMPP.
Evolution of the duty cycle in the algorithms for Pattern-B. Above: P&O and MSMPP-P&O. Below: INC and MSNPP-INC.
Optimum Voltage areas estimated by the MSMPP structure in Pattern-B. Zoom region shows the time of estimation of V_a and V_b, denoted as (:{T}_{ab})
In the third case, the modules are exposed to PSC of Pattern-C, with the resulting response of the maximum power point tracking algorithms presented in Figs. 20 and 21, while the duty cycle is presented in Fig. 22. The optimum voltage region (:{V}_{a}) and (:{V}_{b}) estimated by the MSMPP is presented in Fig. 23. In this PSC scenario, the GMPP has the value of 61.83 W, while the first LMPP has the value of approximately 34.88 W. It can be seen that the P&O/INC do not track the GMPP. They both converge around the first LMPP, with the INC recording a higher power of 35.46 W in comparison with the P&O with record of 33.08 W. Thus it is evident that the INC records a greater GMPP efficiency than the P&O (refer to Table 2). Both algorithms demonstrate significant ripples in steady-state as noticeable from Figs. 21 and 22. It is clearly evident that the proposed MSMPP based P&O and INC respectively swiftly converge to the target GMPP of 61.83 W, with no oscillation in steady-state. This represents a 100% GMPP efficiency as illustrated in Table 2. In addition, it is worth mentioning that the MSMPP maintain a constant estimation time, in estimation of the optimum voltages., It can be seen in Fig. 23, that only 1 ms is required to to accurately estimate the optimum voltages.
Power tracking curves for Pattern-C. Left: Standard P–V curve. Right: Power curves of the P&O and the MSMPP-P&O, along with the target GMPP.
Power tracking curves for Pattern-C. Left: Standard P–V curve. Right: Power curves of the INC and the MSMPP-INC, along with the target GMPP.
Evolution of the duty cycle in the algorithms for Pattern-C. Above: P&O and MSMPP-P&O. Below: INC and MSNPP-INC.
Optimum Voltage areas estimated by the MSMPP structure in Pattern-C. Zoom region shows the time of estimation of V_a and V_b, denoted as (:{T}_{ab})
Furthermore, in the fourth PSC scenario, the modules are subject to Pattern-D. The resultant response of the maximum power point tracking algorithms to irradiance levels in this pattern is presented in Figs. 24 and 25, while the duty cycle is presented in Fig. 26. The optimum voltage region (:{V}_{a}) and (:{V}_{b}) estimated by the MSMPP is presented in Fig. 27. In this PSC scenario, the GMPP has the value of 77.42 W, while the first LMPP has the value of approximately 41.61 W. It can be seen that the P&O/INC do not track the GMPP. They both converge around the first LMPP, with the INC recording a higher power of 41.42 W in comparison with the P&O which record 39.48 W. The GMPP efficiency of the algorithms is indicated in Table 2. Both algorithms demonstrate significant ripples in steady-state as noticeable from Figs. 24 and 25. Noticeably, the P&O oscillates between 39.48 W and 38.26, while the INC between the values 40.26 W and 41.42 W. Furthermore, the duty cycle evolution of the algorithm endorses the fact the proposed MSMPP completely treats the problem of steady-state ripple in conventional algorithm. It is seen that the proposed MSMPP based algorithms smoothly converge to the expected GMPP of 77.42 W with no steady state ripple, which represent approximately 100% GMPP efficiency (refer to Table 2).
Power tracking curves for Pattern-D. Left: Standard P–V curve. Right: Power curves of the P&O and the MSMPP-P&O, along with the target GMPP.
Power tracking curves for Pattern-D. Left: Standard P–V curve. Right: Power curves of the INC and the MSMPP-INC, along with the target GMPP.
Evolution of the duty cycle in the algorithms for Pattern-D. Above: P&O and MSMPP-P&O. Below: INC and MSMPP-INC.
Optimum Voltage areas estimated by the MSMPP structure in Pattern-D. Zoom region shows the time of estimation of V_a and V_b.
Finally, the modules are subject to Pattern-E. The resulting response of the maximum power point tracking algorithms to irradiance levels in this pattern is presented in Figs. 28 and 29, while the duty cycle is presented in Fig. 30. The optimum voltage region (:{V}_{a}) and (:{V}_{b}) estimated by the MSMPP is presented in Fig. 31. In this PSC scenario, the GMPP has the value of 99.63 W, while the first LMPP has the value of approximately 60.41 W. It can be seen that the P&O/INC do not track the GMPP. They both converge around the first LMPP, with the INC recording a higher power of 60.00 W in comparison with the P&O which record 57.80 W. Thus the INC records a GMPP efficiency of 60.22% and the P&O records 58.10% (refer to Table 2).
Power tracking curves for Pattern-E. Left: Standard P–V curve. Right: Power curves of the P&O and the MSMPP-P&O, along with the target GMPP.
Power tracking curves for Pattern-E. Left: Standard P–V curve. Right: Power curves of the INC and the MSMPP-INC, along with the target GMPP.
Evolution of the duty cycle in the algorithms for Pattern-E. Above: P&O and MSMPP-P&O. Below: INC and MSMPP-INC.
Optimum Voltage areas estimated by the MSMPP structure in Pattern-E. Zoom region shows the time of estimation of V_a and V_b.
By observing the response of the MSMPP-P&O, it is noticed that there is relatively significant level of oscillations as compared to the negligible oscillations level in the MSMPP-INC. This attributed by the fact that, the perturbation parameter (:varDelta:d) in the MSMPP-P&O is very high, about 8 times bigger than the value in MSMPP-INC. This larger perturbation size causes the response of the MSMPP-P&O to oscillate around the GMPP. Therefore, fine-tuning this parameter is a necessity to completely remove the oscillations around the GMPP. Nonetheless, the MSMPP-P&O still stays within a very good average of the GMPP. Due to this impaction around he GMPP, the MSMPP records an average GMPP efficiency of 97.22% (refer to Table 2). The MSMPP-INC with negligible oscillations records an efficiency of 99.78%. In summary, it is evident that the MSMPP structure can provided an MSMPP efficiency greater than 99.7%, with convergence time of at most 108ms. This thus reveals the prowess of this new structure.
An extended steady-state analysis of the different MPPT algorithms is conducted, wherein the power tracked by the different MPPT systems and their shading loss is recorded. The shading loss in this study is computed at the steady state as follows:
Where (:{P}_{pv(steady-state)}) is the power tracked by the MPPT algorithm at stead-state, while (:{P}_{GMPP}) is the expected GMPP. A bar plot of the power tracked by the different MPPT algorithms is presented in Fig. 32, revealing that the MSMPP-P&O and MSMPP-INC are in exact agreement with the (:{P}_{GMPP}), with the exception of Pattern-E, where the MSMPP-P&O oscillates at steady-state and introduces a shading loss of approximately 2.13 W. The shading loss of the different MPPT for the five different PSC patterns is showcase in Fig. 33, while the numerical results are presented in Table 3. It is evident that with the exception of the 2.13 W loss in Pattern-E, the proposed algorithm features no loss of power at steady-state due to PSC. On the contrary the P&O and INC record a shading loss of up to 30 W in different shading patterns. For instance, in Pattern-E, the P&O records a loss of 41.83 W, while the INC records a loss of 39.63 W (refer to Table 3). Based on the above experiments, the records presented in Table 4 can be deduced.
Power Tracked by the different MPPT algorithms.
Plot of Shading loss as a function of different PSC patterns.
In real time operation, the shading level on PV modules could be subject to a change due to intermittent variations in environmental conditions. As a result, the GMPP will be prone to fluctuations. Therefore, the MPPT controller should be able to detect such changes and effectively track the GMPP despite its varying position. To assess this feature on the different algorithms, PV modules are exposed to varying shading conditions. In the first experiment, the modules are exposed to Pattern A-B-C, wherein the systems operate initially in Pattern-A. After a defined time period, the pattern is abruptly changed to B and subsequently changed to C. In the second experiment, the change of patterns follows the order: Pattern-C-D-E and finally in the third experiment the variation follows the order D-B-C. The expected optimum voltage levels, that is (:{V}_{a}) and (:{V}_{b}), along with the target GMPP for a specific pattern is shown in Table 4. In order to quantitatively compare the algorithms, the Net Shading power loss is recorded as the sum of power loss in all the three shading sequences.
The power responsiveness of the different MPPT algorithms in the presence of the three changing PSC patterns is presented in Figs. 34, 35 and 36. The dynamic behavior of the optimum voltage region (:{V}_{a}) and (:{V}_{b}) are plotted in Figs. 37, 38 and 39. From a power response point of view, it can be seen that the power captured through the MSMPP based algorithms consistently leads that captured by the INC/P&O. A close observation of the power levels along with Table 4, shows that although the INC/P&O algorithms noticeably respond to a changes in shading patterns, they consistently get trap at the LMPP of respective shading pattern. The local convergence of these algorithms to the LMPPs introduces an important discrepancy between the targeted GMPP and the actual tracked power, which is recorded as net shading loss. On the other hand, the proposed MPPT structure consistently converges at/around the target GMPP with negligible discrepancy. The dynamic response of the optimum voltage regions reveals an exact alignment with the record of Table 4. Therefore, the proposed MPPT algorithms operates smoothly with fast tracking of the desired GMPPT in all the shading patterns. Consequently, the net maximum shading loss in the MSMPP-based tracker is very small and lower than 1.5 W as seen in Fig. 40. Conversely, the INC/P&O records relatively significant power losses. The maximum net power loss recorded for the P&O is 107.75 W which occurs in Pattern-C-D-E, while a maximum loss of 95.19 W in Pattern-D-B-C is recorded for the INC. Based on this evidence the MSMPP framework is a powerful approach to mitigating power losses in PV systems under shading conditions.
Power tracking curves for Pattern-A-B-C. Above: P&O and MSMPP-P&O. Below: INC and MSMPP-INC.
Power tracking curves for Pattern-C-D-E. Above: P&O and MSMPP-P&O. Below: INC and MSMPP-INC.
Power tracking curves for Pattern-D-B-C. Above: P&O and MSMPP-P&O. Below: INC and MSMPP-INC.
Optimum Voltage areas estimated by the MSMPP structure in Pattern-A-B-C.
Optimum Voltage areas estimated by the MSMPP structure in Pattern- C-D-E.
Optimum Voltage areas estimated by the MSMPP structure in Pattern- D-B-C.
Plot of Net Shading loss as a function of different changing PSC patterns.
Both Δd and λd are essential for the efficient functioning of the MSMPP structure. By dividing the PV system’s response into steady-state and transient components, the impact of these variables can be accurately assessed. The results of the MSMPP for different values of Δd, with a fixed value of λd = 0.05 (5%), are illustrated in Fig. 41. G=[1000, 1000, 1000] represents the initial instance of uniform irradiation conditions; see Fig. 41a and b. Observed that the value of λd is optimally designed. The observation that augmenting the value of Δd does not affect the initial response of the photovoltaic system indicates that the transient portion of the response remains unaltered (refer to the magnified view of the transient states). Conversely, the parameter Δd exerts a discernible impact on the steady state. As illustrated in Fig. 41a, the steady state response remains unchanged even after the initial value of Δd is decreased by a factor of five, from Δd = 0.001 to Δd = 0.0002. Under the partial shading condition, where the initial value is decreased by 50 to become Δd = 0.00002, a comparable response is maintained. This indicates that minimizing the value of this parameter may represent the optimal configuration for the MSMPP-designed structure. This is logically consistent with the assertion that the space is exceedingly limited, which is confirmed by the MSMPP methodology. Nevertheless, it is conceivable that despite the MSMPP reducing the area, it may be relatively larger for large PV systems (on the order of kilowatts). In such cases, extreme caution should be exercised to avoid over minimizing this parameter, as the system may necessitate a comparatively greater number of substantial steps to achieve steady-state GMPP (this can be determined offline through trial and observation prior to implementing the system under investigation). Furthermore, it is observed that the primary focus in the determination of Δd pertains to its maximal value, given that augmenting Δd has the capability to induce oscillations at stable state. An illustration of this premise is provided when Δd is increased by a factor of 50 to Δd = 0.05. It is apparent that the system experiences discernible oscillations at steady state under both G=[1000, 1000, 1000] and G=[400, 900, 600] conditions of operation, resulting in power losses. Consequently, despite the absence of a precise formula for determining the optimal value of this parameter, the aforementioned inquiries and observations offer valuable insights into the impact of Δd. Therefore, the approach of designing through trial and observation continues to be feasible.
Observation of the effect of (:varDelta:d) on the performance of MSMPP. (a) Uniform irradiation G=[1000, 1000, 1000. (b) Partial Shading condition irradiation G=[400, 900, 600].
Furthermore, by maintaining Δd at its empirically determined optimal value (Δd = 0.001), one can examine the MSMPP’s performance under different values of λd. Figure 42 illustrates the results of this experiment based on observations, encompassing both partial shading and uniform irradiation. For a given optimal value of Δd, it is evident that decreasing the value of λd has the capability to impede the photovoltaic system’s response time. When the value of λd is set to 0.005, the system may converge at exceedingly slow rates and may fail to reach the GMPP entirely, as illustrated in Figures 42a and b. Conversely, augmenting this parameter results in a surge in the speed of the photovoltaic system, though at the cost of power losses and steady-state oscillations, which is the case when λd = 0.5, as illustrated in Fig. 42 (b). Additionally, it is observed that the identical value of λd produces the most rapid response for G=[400, 900, 600], but prevents the system from attaining the GMPP, as illustrated in Figure 42a. This demonstrates that adaptation schemes can be utilized to further optimize the MSMPP structure’s performance.
Observation of the effect of (:lambda:d) on the performance of MSMPP. (a) Partial Shading condition G=[400, 900, 600]. (b) Uniform irradiation condition G=[400, 900, 600].
In the end, the MSMPP structure was evaluated in conjunction with conventional algorithms under complex partial shading patterns, which encompass all the potential obstacles encountered by shaded PV systems. Recent research in³ has established the reference complex shading patterns. As shown in Table 5, this is accomplished by modulating the shading profile (SP) with four distinct shading patterns; a characteristic curve is depicted in Fig. 43. The PV modules in profile 1, SP-1, function according to the profile regulated by the irradiance G= [300,800,1000]. This pattern persists for a duration of 0.2 s, denoted as 0 ≤ t < 0.2s. This profile illustrates the PV system experiencing partial shading, as indicated by three peaks labeled P11, P12, and P13, which have respective power ratings of 60.44 W, 101.9 W, and 60.88 W, as well as voltage ratings of 17.14 V, 34.97 V, and 55.31. The shading pattern abruptly transitions to SP2-2 at precisely 0.2s, with the governing irradiance pattern G= [400,500,800]. The new peak values, designated P21, P22, and P23, are 47.94 W, 63.99 W, and 77.92 W, respectively, and have voltages of 17.01 V, 35.22 V, and 53.17. The remaining profiles correspond to those listed in Table 3. The presence of the GMPP in the various patterns is clearly observed at positions P12*, P23*, P32*, and P41* (with * denoting the GMPP, see Fig. 43).
Complex partial shading PV curve. Benchmark pattern supported by³.
A graphical representation of the PV system’s response to the intricate shading patterns can be observed in Fig. 44. As illustrated in Fig. 44a and d, the conventional P&O and INC converge at the local maximum power point (LMPP), precisely point P11, within the time interval 0 ≤ t < 0.2, when the system is operating under SP-1. At this juncture, the steady state power attains an approximate value of 60.30 W. When compared to the data in Table 5, this indicates an approximate power loss of 41.6 W. Conversely, the MSMPP algorithms demonstrate efficacy in monitoring the target GMPP, as evidenced by their convergence at an estimated 101.9 W. Upon the system transitioning to SP-2 at precisely 0.2s, it becomes evident that both INC and P&O become entangled in the LMPP, P21, which has an approximate power value of 47.75 W. When compared to the data in Table 5, this indicates an approximate power loss of 30.17 W. In contrast, the proposed MSMPP exhibits its effectiveness through its ability to track the new GMPP, which is approximately 77.92 W. As illustrated in Fig. 44a and d, the theoretical GMPP and the power monitored by the MSMPP-based algorithms are in net consistent alignment. It is apparent that upon abruptly transitioning to SP-3, all algorithms in the photovoltaic system directs it toward a prompt reaction to the altered operating conditions. At P32*, the new theoretical GMPP occurs. All the algorithms, including the traditional INC and P&O, tracks this GMPP effectively. In order to determine the GMPP (P32*), conventional algorithms can circumvent the LMPP at P31 due to the proximity of the voltage at their previous conditions (P21, V = 17.01) to the voltage at which the subsequent LMPP in the new PV curve transpires (P31, V = 17.07). Thus, the algorithms are capable of bypassing this local point due to the step size. They reach the subsequent turning point, the GMPP (P32*) of the system, in doing so. On the other hand, oscillations around the GMPP are produced by conventional algorithms (see magnification view of Fig. 44b). In contrast, the MSMPP exhibits a diminished degree of oscillation within the same figure. Ultimately, when the system transitions to pattern SP-4 at 0.4s, it is evident that all algorithms reach the GMPP at P41* without difficulty, given that it is in close proximity to the previous GMPP (P32*). Additionally, Fig. 44c and f illustrates the search space produced by the MSMPP structure, indicating that a satisfactory response is observed in response to variations in coloration patterns. The MSMPP’s ability to produce dependable outcomes can be attributed to the newly reduced search space it produces. Ultimately, Fig. 44g verifies the accuracy of the designed values of Δd and λd, revealing that MSMPP-INC and MSMPP-P&O both possess a value of λd = 0.05. Since the parameter is linked to the transitory section in question, this can be deduced. It is evident from the magnification view in Fig. 44g that the disparity between the two perturbation sizes is 0.05, or 0.75 − 0.7. An analogous deduction and verification can be made regarding the alternative parameter, Δd; this is verified in the steady-state segment of the diagrams. It is evident from the magnification view in Fig. 44g that the disparity between the two perturbation sizes of the MSMPP-P&O is 0.008, or 0.502–0.51, whereas it is 0.001, or 0.509 − 0.508.
PV performance under complex partial shading patterns. (a, d) Complex PV curve indicating LMPP and GMPP of all shading patterns. (b) Performance of PV system for both P&O and MSMPP-P&O. (c ,f) New search space set by the MSMPP structure (e) Performance of PV system for both INC and MSMPP-INC. (g) Perturbation profile of the all MPPT algorithms, specially indicating the adopted step size of the MSMPP structures in this paper, (:lambda:d) and (:varDelta:d)
The optimal operational performance of PV systems heavily hinges on maximum power point tracking facility. In order to enhance the simplicity of PV systems, these facilities should be inherently simple. Partial shading conditions is a complex scenario, that impedes the simplicity of PV system. Under PSC, the P–V curve admits several local maximum power points and a single global maximum power point. This paper developed a new framework for simplified and rapid tracking of the global maximum power point. The novel structure termed the MSMPP, is able to bring-in an online adjustment of the operational characteristic of the PV. This emulated adjustment is obtained by conditioning the PV to exhibit a single MPP. In order to achieve this operation, the MSMPP uses two operating routines. Firstly, it estimates an optimum region for which the global maximum power point is prone to occur, and subsequently it regulates the actual operating point of the PV according to the estimated optimum region. When the two aforementioned routines are performed, the PV system is said to behave as an equivalent single MPP system. Therefore, conventional MPPT algorithms such as perturb & observe and incremental conductance, which are specialized in MPP operation can be deployed in such a facilitated environment. Additionally, the structure that was proposed greatly improved the implementation of basic conventional MPPT algorithms in the context of PSC. The effectiveness of the MSMPP has been demonstrated by introducing two improved MPPT algorithms: the MSMPP-P&O and MSMPP-INC. Through the MSMPP framework, these two algorithms are PSC-habilitated variants of the conventional INC and P&O. By employing various benchmarking shading patterns, a thorough comparison was conducted between the P&O/INC and its habilitated MSMPP-based counterparts. Initially, it was noted that the implementation of the MSMPP significantly accelerated tracking speed, and ultimately, it endowed these traditional algorithms with a solid foundation for PSC operations. Several numerical results demonstrate that the proposed MSMPP structure can monitor the global maximum power point of a shaded PV system with a maximum convergence time of 108ms and an efficiency of up to 100%. A number of numerical investigations provided additional confirmation of the MSMPP’s ability to discern the global maximum power point amidst dynamic, complex shading patterns. Thus, it is confirmed that conventional MPPT algorithms would be adequate for PV systems operating within the limits of simplicity via this new framework. This paper thus closes established research voids by presenting an explicit and novel scheme for optimizing the performance of photovoltaic (PV) systems through the utilization of the most elementary algorithms. In contrast to previous research, the MSMPP is distinguished by its exceptional adaptability, which strikes a marvelous equilibrium between improved PV system functionality and simplified design. To advance research and development the following key recommendations should be prioritized in future works.
The proposed MSMPP structure revealed an interesting feature of mitigating power losses in PV power systems under PSC. Therefore, an extensive and specialized study of this feature can further unveil new insights on the performance of the MSMPP.
The newly introduced regulation parameter (:lambda:d), should be extensively studied under diverse conditions, for possibility of optimization in view of further performance enhancement.
The MSMPP structure, specifically its future of search space regulation should be investigated synergically with several existing optimization algorithms. The MSMPP has the potency to enhance the deployment of optimization algorithm.
Lastly, leveraging the proposed MSMPP to appraise and assess large-scale grid-connected solar energy systems presents another research opportunity that can be pursued as an extension of this current study.
Data/files can be obtained from the corresponding author [A. Harrison] upon request.
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This work is supported by the Deanship of Scientific Research, King Khalid University, under Grant (RGP2/472/45)
Department of Electrical and Electronics Engineering, College of Technology, University of Bamenda, P.O. Box 39, Bambili, Cameroon
Njimboh Henry Alombah
Department of Electrical and Electronics Engineering, College of Technology (COT), University of Buea, P.O. Box 63, Buea, Cameroon
Ambe Harrison
Technology and Applied Sciences Laboratory, U.I.T. of DoualaUniversity of Douala, P.O. Box 8689, Douala, Cameroon
Wulfran Fendzi Mbasso
Laboratory of Engineering Sciences for Energy National School of Applied Sciences, University of Chouaib Doukkali, El Jadida, Morocco
Hamid Belghiti
Unit of Condensed Matter Research, Electronics and Signal Processing, Faculty of Science, Department of Physics, LAMACET, University of Dschang, P.O. Box 67, Dschang, Cameroon
Hilaire Bertrand Fotsin
Department of Biosciences, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai, 602 105, India
Ambe Harrison
Innovation Center for Artificial Intelligence Applications, Yuan Ze University, Taoyuan, 320315, Taiwan
Pradeep Jangir
Electrical Engineering Department, Faculty of Engineering, King Khalid University, Abha, Saudi Arabia
Saad F. Al-Gahtani
Department of Electrical Engineering, College of Engineering, King Khalid University, P.O. Box 394, Abha, 61421, KSA, Saudi Arabia
Z. M. S. Elbarbary
Center for Engineering and Technology Innovations, King Khalid University, 61421, Abha, Saudi Arabia
Z. M. S. Elbarbary
Applied Science Research Center, Applied Science Private University, Amman, 11937, Jordan
Wulfran Fendzi Mbasso
Centre for Research Impact & Outcome, Chitkara University Institute of Engineering and Technology, Chitkara University, Rajpura, 140401, Punjab, India
Pradeep Jangir
Department of Electrical and Electronics Engineering, J.J. College of Engineering and Technology, Tiruchirappalli, Tamilnadu, India
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N. H. Alombah: Investigation, Writing & Review, Methodology, Validation, resources, supervision A. Harrison: Conception, Simulation/Experimentation, Writing of original draft, Review & Editing, Investigation, Methodology, ValidationW.F. Mbasso: Writing & Review, Methodology, ValidationH. Belghiti: Validation, Review & EditingH. Fotsin: Review & Editing, resources, supervision P.Jangir: Review & Editing, Validation, resources, S.F. Al-Gahtani: Resources, Review & Editing, Funding AcquisitionZ.M.S. Elbarbary: Resources, Review & Editing, Funding Acquisition.
Correspondence to Njimboh Henry Alombah or Ambe Harrison.
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Alombah, N.H., Harrison, A., Mbasso, W.F. et al. Multiple-to-single maximum power point tracking for empowering conventional MPPT algorithms under partial shading conditions. Sci Rep 15, 14540 (2025). https://doi.org/10.1038/s41598-025-98619-3
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DOI: https://doi.org/10.1038/s41598-025-98619-3
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