Power equalization and optimization of photovoltaic module based on forward‑flyback converter

This paper focuses on enhancing the energy extraction efficiency of photovoltaic (PV) modules through the use of a straightforward power converter and control algo-rithm. This research delves into the electrical characteristics of PV modules, explaining the concepts of global maximum power point


Introduction
The evolution of human civilization has escalated the necessity for energy, notably electricity, on a day-to-day basis.The utilization of fossil fuels has triggered energy deficiencies, while the emission of greenhouse gases has negatively impacted the global ecosystem (Ibraheem et al. 2020;Mao et al. 2020;Nordin et al. 2021).As a consequence, there has been a surge in interest in renewable energy resources, with a particular focus on photovoltaic (PV) power due to its abundant availability, eco-friendliness, and user friendliness.Enhancing the efficiency of power generation is imperative for the advancement of PV power applications and has become a prominent subject of study (Ahmed et al. 2020;Al-Shahri et al. 2021).Diverse technologies have been implemented in the fabrication of essential components in PV modules to enhance the efficiency of PV gen-When establishing PV generation systems, typically identical PV modules are employed to ensure that the output characteristics of the entire system display a singlepeak attribute, thus facilitating the use of traditional maximum power point tracking (MPPT) control techniques.Systems with fewer PV modules and low power requirements can comprehensively consider the influence of environmental factors during design, often employing constant voltage tracking (CVT) methods (Xu et al. 2014), offline techniques such as the short-circuit current method (Husain et al. 2017), and the open-circuit voltage method (Montecucco and Knox 2015) to attain favourable outcomes.While these approaches can be readily implemented through analogue circuits without intricate computations, their efficacy diminishes when irradiance or environmental temperature fluctuates, impacting the efficiency of PV generation systems.With the rapid progress of computer and electronic technology, the utilization of microprocessors to compute and compare the power, voltage, and current of PV modules and their variations in real-time to ascertain the direction and extent of adjustments in the duty cycle of DC/DC converters, thereby achieving MPPT, is known as an online algorithm.These methods include the Hill climbing (HC) method (Xiao and Dunford 2004), incremental conductance (INC) algorithms (Houssamo et al. 2013), perturb and observe (P&O) algorithms (Motahhir et al. 2020), and their enhanced versions.Nevertheless, these algorithms struggle to track the global maximum power point of PV generation systems under intricate conditions such as non-uniform irradiance, partial shading, or module performance deterioration.With the evolution of intelligent control technology, artificial intelligence (AI) algorithms such as fuzzy logic controller (FLC) (Napole et al. 2021), particle swarm optimization (PSO) (Pragallapati et al. 2017), artificial neural network (ANN) (Villegas-Mier et al. 2021), and genetic algorithm (GA) (Saadaoui et al. 2021), have been continuously refined to effectively trace the global maximum power point (GMPP) of PV generation systems in medium and large-scale applications.Nevertheless, these algorithms necessitate the gathering of extensive data from the system, substantial computations, high-performance microprocessors, and numerous sensor components, rendering the system architecture intricate and costly.
The shading of modules in a PV generation system can lead to energy loss due to the activation of bypass diodes connected in parallel with the shaded modules.In an effort to combat power loss resulting from shading on PV modules, Shimizu et al. (2001) introduced a general control circuit (GCC) concept, similar to voltage equalization technology, aimed at maximizing the power output of each PV module to alleviate shading effects.Although promising, the GCC technology faced limitations in widespread adoption due to constraints in the processing speed and data capabilities of microprocessors at that time.Shenoy et al. (2012) presented buck-boost and flyback converters to optimize the power of PV systems through differential power processing (DPP) technology, addressing power differentials between PV modules.The study of the DPP concept expanded beyond PV systems, encompassing three variations: cell string-to-cell string (CS-CS), cell string-to-PV module (CS-PV), and cell string-to-isolated port (CS-IP) (Zhang and Jiang 2020).While CS-CSs ensure a power equalisation between adjacent cell strings, they incur significant power loss and efficiency reduction for distant cell strings due to multiple power conversion processes (Niazi et al. 2021).CS-PVs facilitate direct energy transfer between cell strings and PV modules, achieving rapid equalization and high efficiency (Chu et al. 2020).CS-IP enhances system safety by introducing electrical isolation between cell strings and isolated DC buses (Ko et al. 2021).Both DPP structures utilize bidirectional isolated DC converters, commonly the flyback converter, necessitating separate converters for each solar cell string, thereby increasing costs (Chu et al. 2017;Zhu et al. 2022).Du et al. (2013) proposed a power compensator with a multi-winding flyback converter to address power mismatch in PV submodules, albeit with limited effectiveness under varying load conditions.Another approach involves employing low-loss boost converters in conjunction with distributed maximum power point tracking (DMPPT) using the P&O algorithm (Başoğlu 2020) on PV modules or submodules.Multiple DPPs may be necessary for high-power PV modules, potentially increasing system costs.
This paper introduces a novel scheme that integrates DPP technology with the P&O algorithm to enhance PV module efficiency.The proposed scheme employs a singleswitch multi-winding forward-flyback converter to equalize the power discrepancies among PV submodules caused by varying irradiance levels, subsequently optimizing the PV module output performance.By applying the traditional P&O algorithm, the proposed scheme enhances the overall PV system efficiency, achieving power equalization and optimization with a single converter, thereby simplifying the structure and control system.
After the introduction, the paper explores the performance characteristics of PV modules, discussing the concepts of global maximum power point and local maximum power points under nonuniform irradiation conditions.This paper thoroughly examines the operational principles of power equalization and optimization of PV modules via forward-flyback converters.The following section outlines the methodology for modelling and simulating the proposed scheme using PLECS.The fourth section critically analyses the simulation results and the collected data.Finally, the fifth section offers a brief summary of the paper.

Characteristics of the PV module
PV generation directly converts solar energy into electrical energy via the photovoltaic effect (Stornelli et al. 2019).In practical applications, PV modules are typically Fig. 1 Photograph of the solar cell, PV module and PV array composed of multiple solar cells interconnected in series, as depicted in Fig. 1, while PV arrays are created by connecting multiple PV modules in series-parallel to meet specific output requirements (Häberlin 2012).
A solar cell serves as the fundamental unit in a PV module with a single diode model, as illustrated in Fig. 2, which is commonly employed in both theoretical and engineering contexts.
The I-V characteristics of an ideal solar cell are mathematically described by Eq. (1) according to semiconductor theory (Ding et al. 2014).The output characteristics of the PV module are considered to be a superposition of multiple solar cell characteristics, as in Eq. ( 2), with distinct parameters influencing the overall output.
where the variables represent the following: I pv, cell : current generated by incident light; I d : Shockley diode equivalent current; I 0, cell : reverse saturation or leakage current of the diode; q: electron charge (1.60217646 × 10 −19 C); k: Boltzmann constant (1.3806503 × 10 −23 J/K); T: temperature of the p-n junction (in Kelvin); α: Diode ideality constant; R s : PV module equivalent series resistance; R p : PV module equivalent parallel resistance; N p : number of cells connected in parallel; N s : number of cells connected in series.
The P-V and I-V characteristic curves of the PV module under varying levels of uniform light conditions are depicted in Fig. 3.Each curve features a maximum power point, denoted by the maximum operating voltage V m and maximum operating current I m .The open circuit voltage V oc signifies the module's voltage when open-circuited, while the short circuit current I sc represents the current when short-circuited (Elbaset and Hassan 2017). (1) (2) Table 1 presents the electrical parameters of the PV module under different irradiance conditions as illustrated in Fig. 3.
Analysis of the curves in Fig. 3 and the data in Table 1 reveals that with increasing irradiance, I sc and I m of the PV module demonstrate nearly proportional growth, whereas the increase in V oc and V m is marginal.The maximum power P m exhibits a similar trend to that of I m , increasing almost proportionally with irradiance.
When a PV module is exposed to varying light conditions, the presence of bypass diodes causes a loss of power in short-circuited solar cell strings or PV submodules, resulting in the appearance of multiple peaks in the P-V characteristic curve of the PV module.Figure 4 shows the output characteristic curves of the PV module with four submodules under the different lighting scenarios.It is evident that the occurrence of a GMPP is only possible when PV submod 3 and submod 4 are bypassed, while the other peak points on the power curve represent LMPPs.Operating the PV module at the GMPP enables the maximum power output, as highlighted in the literature (Mahmood et al. 2020;Zhang et al. 2014); however, the electrical energy generated by PV submod 3 and submod 4 is forfeited.
The analysis above indicates that to enhance the efficiency of the PV generation system, each submodule within the PV module must operate at the maximum power  point (MPP).Initial efforts and studies concentrated on maximizing the output power of PV modules under consistent irradiance conditions.Nevertheless, factors such as partial shading, uneven irradiance, degradation-induced changes in submodule performance parameters, and others (Eltamaly and Abdelaziz 2020) necessitate the adoption of DPP to equalize the output power of PV submodules (Ayan and Toylan 2021).Moreover, the implementation of the MPPT algorithm is essential for enhancing the efficiency of the PV generation system.

Power equalization and optimization of the PV module
The proposed schematic illustrating the power equalization and optimization of the PV module via a single-switch multi-winding forward-flyback converter is depicted in Fig. 5.This configuration combines features from both forward and flyback converters (Lee et al. 2011), in which the primary winding W 1 , excitation inductance Lm, capacitor C 5 , and power switch S are shared components.The forward converter encompasses secondary windings W 3 -W 6 , diodes D 1 -D 8 , energy storage capacitors C 1 -C 4 , and other components aimed at equalizing power among the PV submodules.The capacitors C 1 -C 4 , characterized by their high capacity, serve to stabilize the output voltage of the PV submodules by functioning as an automatic equalization voltage reference while also storing energy from the PV submodules.In this setup, diodes D 1 -D 4 are implemented to prevent reverse current flow, whereas D 5 -D 8 are designated as automatic equalization switches.When the voltage on the equalization winding surpasses the voltage across the parallel-connected capacitor, power equalization is automatically engaged.This process ceases when voltage equilibrium is achieved on both sides.On the other hand, the flyback converter comprises secondary winding W 2 , diode D 10 , and capacitor C 6 , which are primarily employed for battery charging while optimizing the power output of the PV module by applying P&O-based MPPT algorithms.The converter consists of two distinct modes within one operating cycle: a forward conversion mode for power equalization among the PV submodules and a flyback conversion mode for optimizing the output power of the PV module.

Power equalization of PV submodules
The power equalization mechanism in the PV submodules, illustrated in Fig. 5, relies on the turn ratio of the transformer windings: Under conditions of uniform irradiance, the output characteristics (voltage, current, and power) of individual submodules within the PV module are identical.Consequently, the voltage levels across energy storage capacitors C 1 -C 4 and their corresponding windings W 3 -W 6 are equivalent: This situation renders the power equalization circuit inoperative, causing the converter to function solely in flyback conversion mode.
In scenarios where the irradiance is nonuniform, as depicted in Fig. 5, submod 3 of the PV module receives an irradiance of 400 W/m 2 , while the remaining submodules receive an irradiance of 1000 W/m 2 .Consequently, the output current of submod 3 experiences a notable reduction, inducing a voltage drop Δv across capacitor C 3 , which is parallel to this submodule.During power switch S conduction, the voltages across windings W 3 -W 6 are as follows: (6) As a result, diode D 7 in the equalization branch compensates for the electrical energy of the other submodules within the PV module to capacitor C 3 , while the diodes in the remaining equalization branches remain nonconducting.The power equalization process ceases when the voltage across capacitor C 3 equals the voltage across winding W 5 .
Upon the conclusion of the power equalization process, assuming that the voltage across capacitors C 1 -C 4 is V-λΔv, the increased energy ΔE inc of capacitor C 3 and the decreased energy ΔE dec of capacitors C 1 , C 2 , and C 4 can be expressed as: where C represents the capacitance of capacitors C 1 -C 4 .
The power equalization process adheres to the principles of energy conservation.The value of λ can be determined as: The aforementioned analysis solely focuses on power equalization within a single submodule of a PV module under conditions of low irradiance.The operational concept involving multiple submodules within a PV module under uneven irradiance (9 Fig. 6 Power flow during equalization mirrors the scenario detailed above.The power distribution during equalization is graphically depicted in Fig. 6.As depicted in Fig. 6, when nonuniform irradiance is present and there exists a power output discrepancy among the submodules within the PV module, the system compensates for the submodule with lower power output.This compensation aligns the output currents of each submodule within the PV module to promote consistency, thereby optimizing the overall output current of the PV module.Moreover, this process facilitates the operation of each submodule at its maximum power point, thereby maximizing the overall power output of the PV module.

PV module power optimization
During the operation of the converter in flyback conversion mode, which occurs when power switch S is in the 'off ' period, the stored energy in W 1 and W 3 -W 6 is released through the secondary winding W 2 and diode D 10 .To achieve MPP operation of the PV module, where the input voltage V C5 of the converter equals the maximum operating voltage V m of the PV module and the output voltage matches the battery voltage V Bat , the following relationship is established: Typically, V Bat remains constant, and the turn ratio of windings N W1 and N W2 is predetermined.By adjusting the duty cycle D, the PV module can operate at its MPP.The MPPT controller detects the output current and voltage of the PV module, calculates the output power of the PV module, compares it with the previous value, and determines the necessary adjustment to the PWM duty cycle D of power switch S based on the comparison results.

Perturb and Observe algorithm
The P&O algorithm is a commonly utilized method for MPPT control in the PV generation system.Its popularity stems from its cost-effectiveness, simplicity, and easy implementation.This algorithm involves perturbing the operating voltage and monitoring power changes to ascertain the adjustment needed in the duty cycle D of the power switch S within the DC/DC converter (Bendib et al. 2015).The flowchart of the P&O algorithm is depicted in Fig. 7. Perturbing the operating voltage of the PV module in a specific direction leads to an increase in the output power of the PV module, signalling proximity to the MPP and necessitating sustained voltage perturbation in that direction.Conversely, a change in the perturbation direction is required when the power output decreases.During each operational cycle, perturbing the operating voltage of the PV module results in oscillation near the MPP once it is reached, causing some power loss that can be mitigated by appropriately adjusting the perturbation of the duty cycle ΔD.Additionally, determining a suitable perturbation size is vital for optimizing the dynamic and steady-state response of the PV generation system. (13)

Modelling
The modelling of the scheme is conducted using the power electronic system simulation software PLECS (Akpolat et al. 2019;Allmeling and Hammer 2023).The simulation model of the proposed scheme, depicted in Fig. 8, encompasses PV submodules, environmental parameter settings, a power equalizer, a maximum power converter and an MPPT controller, and a signal acquisition and display block.

PV submodule
The PV module designated STP-340-72-Vfh is composed of 144 solar cells interconnected in a series-parallel configuration.This module is divided into four submodules and characterized based on the single diode model of solar cells depicted in Fig. 2. The modelling procedure, illustrated in Fig. 9, encompasses creating a schematic circuit model, programming a C-Script module for the photovoltaic current source, applying a mask to the submodule, and editing parameter settings, among other steps.Figure 10 displays the parameter setting interface of the masked PV submodule.This modelling approach is versatile and can be employed to simulate various PV modules by inputting the specific parameters of the respective PV module into the parameter setting interface.

Environmental parameter settings
The environmental temperature is set at a constant value of 25 °C, while various levels of irradiance are configured through the 'From File' block.This block facilitates the adjustment of the real generated power P REAL , global maximum power P GM , and nonbypass diode output power P WOBD of the PV module under different irradiance conditions.The irradiance setting interface is depicted in Fig. 11.

Power equalizer, maximum power converter, and MPPT controller
The power equalizer comprises components such as a power switch S, a primary winding W 1 , secondary windings W 3 -W 6 , an excitation inductance Lm, diodes D 5 -D 9 , capacitors C 1 -C 5 , and other components within the forward converter.Additionally, the maximum power converter involves elements such as winding W 2 , diode D 10 , filter capacitor C 6 , inductance L, current limiting resistor R, and battery Bat.The MPPT controller employs 'Probe 3 ' to detect the output voltage and current of the PV module, facilitating power switch S regulation through the P&O algorithm.The configuration interface for detecting voltage across capacitor C 5 and current through diode D 9 using the 'Probe 3 ' block is exhibited in Fig. 12.

Signal acquisition and display
Signal acquisition incorporates the use of 'Probe 1 ' to sense the equalized current of PV submod 1 and output current of C 5 , combining it with the output current detected by 'Probe 2 ' , filtering it through the 'Moving Average' block, and multiplying it by the voltage v C1 to obtain the instantaneous equalized power.The 'Scope' block is employed to showcase various power waveforms, with 'Scope 1 ' illustrating the output power and equalized power waveforms of the PV submod 1 .The MPP trajectory of PV submod 1 is visualized using the 'XY Plot' block.The signal acquisition and display methodologies for the PV module and other PV submodules are identical to those described above.

Simulation parameter settings
Thirty distinct levels of irradiance were established, as detailed in Table 2. Using the information presented in Table 1, the real generated power P REAL of the PV module at varying irradiance levels and the output power P WOBD of the PV module without bypass diodes were calculated.Additionally, the global maximum power P GM of the PV module with bypass diodes achieved through simulation was determined.
The parameters specific to the PV submodule were configured in accordance with the specifications outlined in Fig. 10.Correspondingly, the parameters of other elements within the simulation model were defined as per the details provided in Table 3.The simulation span was established at 30 s.

Simulation results
During the simulation period, the irradiance variation curve is depicted in Fig. 13a, while Fig. 13b presents a range of output power waveforms of the PV module.The instantaneous maximum power p PO achieved by the proposed scheme was lower than the real generated power p REAL of the PV module.However, p PO surpassed both the global maximum power p GM under ideal conditions and the output power p WOBD of the PV module without bypass diodes.
In Fig. 14, the waveforms of the instantaneous real generated power and equalized power of the PV submodules are shown.The comparison shows that the equalized power of PV submod 1 and submod 2 is inferior to their real generated power, while the equalized power of PV submod 3 and submod 4 exceeds their real generated power.This discrepancy indicates that the power equalizer effectively redistributes power from PV submodules with higher power to those with lower power within the PV module.
Figure 15 shows the real power p Mod produced by the PV module during power equalization, the equalized power p Sum , and the equalization power p Equ .The waveforms generated through simulation serve to validate the proposed methodology.
Figure 16 presents the output voltage waveforms of the PV module and its submodules, revealing differences in the output voltages of individual PV submodules due to varying irradiance levels.Nonetheless, the output voltage of the PV module itself remains relatively constant.This exemplifies the unique function of the proposed power   The MPP trajectory of the PV module and its submodules is illustrated in Fig. 17, indicating substantial fluctuations in the MPP trajectory of the PV submodules in response to changing irradiance levels.In contrast, the MPP trajectory of the PV module exhibits stability over time, with the maximum operating voltage remaining consistent after system stabilization.

Data processing
The output power of the proposed solution is determined under various irradiance conditions through simulation.Efficiency calculations for the proposed solution, the solution without a bypass diode configuration, and the ideal GMPPT solution are derived from the power data presented in Table 2 and listed in Table 4.The results in Table 4 indicate that across all scenarios, the efficiency η PO of the proposed solution surpasses both the efficiency η GM of the ideal GMPPT solution and the efficiency η WOBD of the solution lacking the bypass diode configuration.Specifically, the average efficiency of the proposed solution is 94.61%, whereas the average efficiency of the GMPPT algorithm is 80.67%, and the average efficiency of the solution without bypass diodes is only 67.25%.
In Table 5, the means of the real power P Mod from the PV module and its submodules are detailed across various levels of irradiance, alongside the corresponding means of the equalized power P Sum and equalization power P Equ of the PV module.
Analysis of the data in Table 5 reveals that uniform irradiance results in parity among the output powers of individual PV submodules, leading to zeroized equalization power.Conversely, nonuniform irradiance conditions lead to notable disparities in submodule output powers.Upon system stabilization, these power differentials are markedly mitigated, with the total output equalized power P Sum approximating the sum of the real power P Mod from the PV module and the equalization power P Equ .

Discussion
The assessment and computational findings outlined above demonstrate that the implementation of bypass diodes in safeguarding shaded PV modules within a PV generation system result in a discernible power reduction, albeit this decrease can be mitigated through the application of GMPPT technology.Omitting the utilization of bypass diodes significantly exacerbates power losses.Hence, a majority of enterprises opt for bypass diodes when configuring PV generation systems to enhance overall efficiency.Nevertheless, the utilization of bypass diodes is rare for PV modules generating less than 100 W. Solar cells represent the fundamental component of PV generation systems, and refining protection mechanisms and power optimization at the cellular or submodule level can substantially enhance the operational efficiency and output performance of PV modules.
The power waveforms derived from simulations and the efficiency data calculated based on these results indicate that the proposed power equalization and optimization scheme for PV modules utilizing the forward-flyback converter exhibits superior efficiency compared with the ideal GMPPT scheme and the conventional diode-free scheme.This proposed scheme requires fewer components, features straightforward control mechanisms, and incurs lower costs.Notably, by achieving power equalization among submodules within the PV modules, the multipeak characteristics of the output resulting from factors such as uneven irradiation, partial shading, or performance deterioration over extended usage periods are converted into single-peak features.This transformation enables the utilization of conventional MPPT algorithms to enhance the power output of the PV generation system.Consequently, depending on the specific application context, the proposed equalization scheme can be implemented on the PV modules most severely impacted within the system to enhance the overall efficiency of the PV generation system and reduce expenses.
The voltage waveforms and MPP trajectories derived from simulations underscore the efficacy of employing PV submodule power equalization technology not only for effectively protecting shaded solar cells but also for regulating each submodule within the PV module at its MPP.This approach serves to stabilize the maximum operational voltage of the PV module and curtail the detrimental impacts of disparate irradiance levels.

Conclusion
This paper introduces the output characteristics of PV modules and elucidates the concepts of the LMPP, and GMPP of PV modules.A concise overview of the progress and implementation of MPPT and DPP technology is presented.Through an examination of MPPT technology utilizing P&O algorithms, a single-switch multi-winding forward-flyback converter is proposed for enhancing the power of a PV module, and its operational principles are deduced in detail.A model was formulated and simulated using PLECS simulation software.The simulation waveforms and data indicate that the proposed power equalization and optimization scheme for the PV module is, on average, 13.95% more effective than the GMPP scheme and 27.36% more efficient than the traditional scheme devoid of bypass diodes.
The novelty of the proposed power equalization and optimization scheme for a PV module, which is based on a forward-flyback converter, is its ability to achieve power equalization of the PV submodule and optimize the output power of the PV module utilizing a single converter.By adeptly configuring the turns ratio of the transformer windings, power equalization is achieved automatically without necessitating voltage and current detection of the PV submodule.This results in a straightforward circuit structure that is uncomplicated to implement and cost-efficient.Additionally, this scheme offers the flexibility to operate in series or parallel as per actual application requirements, thereby simplifying the design of various PV generation systems.
Subsequent research will focus on assessing the adaptability of the proposed scheme to intricate environmental conditions (such as uneven irradiation and diverse environmental temperatures), different types of PV module connections, and optimising the MPPT algorithms.

Fig. 2
Fig.2 Single-diode model of solar cell

Fig. 3
Fig. 3 Characteristic curves of the PV module under various irradiances

Fig. 4 Fig. 5
Fig. 4 Characteristic curves of PV modules under nonuniform irradiance conditions.a PV submodules under nonuniform irradiance conditions b Characteristic curves of the PV module

Fig. 9
Fig. 9 Flowchart of modelling the PV submodules

Fig. 10
Fig. 10 Parameter setting interface of the PV submodule

Fig. 11
Fig. 11 Interface of irradiance parameter setting

Fig. 12
Fig. 12 Setting interface for applying the 'Probe 3 ' block to detect voltage and current

Fig. 13
Fig. 13 Simulated power waveforms of different schemes under various irradiance levels.a Curves of irradiance varying b Waveforms of power obtained by different schemes

Table 1
Characteristic parameters of the STP-340-72-Vfh PV module under different irradiance conditions

Table 2
Setting of the irradiance and associated power data of the PV module

Table 3
Parameters of the simulation components

Table 4
Efficiency of the different schemes

Table 5
Power data of equalization