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A modified fractional short circuit current MPPT and multicellular converter for improving power quality and efficiency in PV chain
A modified fractional improving power quality and efficiency in PV chain
https://orcid.org/0009-0002-5991-8759
Byanpambé Geoffroy Conceptualization Data curation Methodology Software 1 *
Djondiné Philippe Project administration Validation 2 3
Guidkaya Golam Formal analysis Resources 2
F. Elnaggar Mohammed Software Visualization 4 5
Paldou Yaya Alexis Investigation Visualization 1 6
Tchindebé Emmanuel Writing – original draft 1
https://orcid.org/0000-0002-0160-010X
Kitmo Writing – review & editing 7
Djongyang Noel Supervision 7
1 Faculty of Science, Department of Physics, University of Maroua, Maroua, Cameroon
2 Faculty of Science, Department of Physics, University of Ngaoundere, Ngaoundere, Cameroon
3 Department of Physics, Higher Teacher Training College, University of Bertoua, Bertoua, Cameroon
4 Department of Electrical Engineering, College of Engineering, Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi Arabia
5 Faculty of Engineering, Department of Electrical Power and Machines Engineering, Helwan University, Helwan, Egypt
6 Department of Materials Engineering and Natural Resources Valorization, Laboratory of Applied Physics and Engineering, Avanced School of Mines Processing and Energy Resources, University of Bertoua, Bertoua, Cameroon
7 Department of Renewable Energy, National Advanced School of Engineering, University of Maroua, Maroua, Cameroon
Bajaj Mohit Editor
Graphic Era Deemed to be University, INDIA
Competing Interests: The authors have declared that no competing interests exist.

* E-mail: geoffroybyanpambe@gmail.com
3 9 2024
2024
19 9 e030946011 3 2024
13 8 2024
© 2024 Byanpambé et al
2024
Byanpambé et al
https://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

This article presents the contribution of multicellular converters in improving of the quality of power produced in photovoltaic chain, with the aim of exploiting the maximum power produced by the photovoltaic generator with low oscillations around of the maximum power point (MPP) at steady state and to reduce switching losses. After modeling the multicellular parallel boost converter, fractional short circuit current (FSCC) MPPT was modified to get an estimated photocurrent as a reference to control the inductance current for good functioning of the converter in pursuit of the maximum power point. To verify the performance of the proposed solution, the system was submitted to irradiance and temperature variations. The simulations carried out in the Matlab/Simulink environment presented satisfactory results of the proposed solution, in comparison with the high-gain quadratic boost converter we have a response time of 0.04 s, power oscillations at maximum point around 0.05 W and efficiency of 99.08%; in comparison with the interleaved high-gain boost converter the results show a response time of 0.1 s for the transferred power, a very low output voltage ripples of 0.001% and 98.37% as efficiency of the chain. The proposed solution can be connected to a grid with a reduction of level of the inverter and active filter.

http://dx.doi.org/10.13039/100009392 Prince Sattam bin Abdulaziz University PSAU/2024/R/1445 https://orcid.org/0009-0002-5991-8759
Byanpambé Geoffroy This project is supported via funding from Prince Sattam Bin Abdulaziz University, project number (PSAU/2024/R/1445). Data AvailabilityAll relevant data are within the manuscript and its Supporting Information files.
Data Availability

All relevant data are within the manuscript and its Supporting Information files.
==== Body
pmc1. Introduction

Electrical energy is an essential element for development and improvement of living conditions of a society; its shortage disrupts household life and leads to a slowdown in activities in certain areas of country. The promotion of the use of renewable energies is among the initiatives undertaken by several countries to alleviate electrical energy problems while preserving the environment. Several research projects are being carried out to develop the field of renewable energies. Among renewable energy sources, photovoltaic energy presents itself as the most promising starting from its raw material. The design of optimized photovoltaic systems is by nature difficult due to the fact: on the source side, the power produced by a photovoltaic generator strongly depends on environmental conditions (irradiance and temperature) [1–4] but also the overall state (age) of the system; on the load side, which the nature can be continuous or alternative, each has its own behavior which can be random[1,2,5,6]. For optimal operation of the photovoltaic generator (GPV), the introduction of an optimal power point tracker is necessary. The power point tracker built around a static converter acting as a source-load adapter with the aim of forcing the generator to operate at its maximum power point (MPP). For the control of the static converter, several maximum point tracking techniques forcing the photovoltaic generator to follow the optimal point despite the environmental conditions have been developed. [7–12]. However, the maximum power point varies depending on the surface of the photovoltaic generator, the temperature and the irradiance [13–16]; the aim of the control technique is to automatically modify the duty cycle to bring the generator to its maximum operating point whatever the weather conditions or load variations that may occur as illustrated on Fig 1 [17]. Several maximum power point tracking algorithms have been developed [18–44], according classification made by [29] the different technics can be classified in three large groups: Indirect techniques (fraction of VOC and fraction of ISC …), direct techniques (perturb and observe (P&O), incremental conductance…) and techniques by intelligent control (fuzzy logic, sliding mode, etc.). Good dynamic behavior is very useful in the event of rapid variation of the source (irradiance) or the characteristics of the load.

10.1371/journal.pone.0309460.g001 Fig 1 Research and recovery of the Maximum Power Point [17].

(a)Variation of irradiance. (b) Load variation.

The static converter playing the role of interface between the source and the load most used in photovoltaic applications is the boost converter, the basic boost converters although they raise up the voltage at their output, are more suitable for low power applications [45–49]. For high power applications, several converters structures have been used: fly-back converters, buck-boost converters, multi-cell converters, high-gain quadratic boost converters.

Fly-back converters [49–52] first perform a DC-AC conversion to obtain a high amplitude alternative voltage, then an AC-DC conversion; buck-boost converters [53,54] presented high dynamic losses and low efficiency. Multicellular converters appeared in the 1990s, offering the possibility of reducing voltage or current stresses in power switches. Parallelizing the base converters allows the use of low current levels per block to promote long component life and increase the reliability of the base converters [48,55]. Still contributing in high power applications, a single switch quadratic power converter based on a switched capacitor to achieve high voltage gains and low voltage constraints on power components and reduce the complexity of controller designs has presented by [43,49] proposes a high-gain quadratic boost converter (HG-QBC) to overcome the limitations of conventional boost converter and [44] presents a solar-powered interleaved high-gain boost converter (IHGBC) that increases the voltage gain with less ripples in the output voltage compared to existing DC-DC converters.

The massive use of non-linear loads designed using power electronics converters degrades the quality of electrical energy by generating harmonic currents; these power converters can also exhibit chaotic effects or behavior at certain switching frequencies [56,57]. According to [58], increasing the number of switching cells connected in parallel would lead to a reduction in output current ripples (Fig 2). Non-perfect coupling between the photovoltaic generator and the load, oscillations around the maximum point in steady state and occasional loss of tracking the maximum point during rapid change in climatic conditions, and chaotic behavior in static converters are all among the problems which degrade the energy efficiency of a photovoltaic chain.

10.1371/journal.pone.0309460.g002 Fig 2 Output current ripples function of the cells number.

In this article, the objective is to contribute for improving of energy efficiency and power quality of photovoltaic system by optimizing the power produced based on the operating of GPV on principle of current controlled voltage source (CCVS) and the use of multicellular converters; firstly to improve the indirect short-circuit current fraction (FSCC) method by estimating a photo-current (reference current) to control the inductance current in order to follow the maximum power point (MPP), secondly use the parallel multicellular converter integrating synchronous rectification to reduce switching losses in the switches (by reducing the switching frequency), operating in interleaving mode for the reduction of power oscillations in steady state.

This paper is structured as follow: section 1 presents the introduction where the state of art is presented, section 2 reserved for models, control techniques and calculation of efficiency, in section 3 is presented the simulation results and discussions, finally conclusion in section 4.

qq2. Method

2.1 Photovoltaic generator model

In its constitution, photovoltaic generator (GPV) contains a set of elementary photovoltaic cells; to obtain the desired electrical characteristics (short-circuit current ISC, open circuit voltage VOC), the elementary cells are connected in series and/or parallel. A photovoltaic cell can be illustrated by its equivalent following diagram [59,60]:

By applying KCL (Kirchhoff’s current law) on node N in Fig 3: I=Iph−ID−IR (1)

with: ID=I0(exp[q(V+RsInKT)]−1) (2)

IR=V+RSIRP (3)

10.1371/journal.pone.0309460.g003 Fig 3 Equivalent circuit of the photovoltaic cell.

By replacing ID et IR by their expressions in Eq (1) we obtain: I=Iph−I0(exp[q(V+RsInKT)]−1)−V+RsIRP (4)

Where I is the cell current (A), Iph is the photocurrent (A), V is the cell voltage (V), RS is series resistance of the cell (Ω), RP is parallel resistance of the cell (Ω), T is the cell temperature (K), q is electron charge (q = 1,6.10−19C), IO the saturation current (A), K is Boltzmann constant (k = 1,3854.10−23J/K), n is the diode quality factor.

The current in the cell is maximum during the short circuit (V = 0,I = ISC), Eq (4) becomes: ISC=Iph1+RsRP (5)

In the ideal case (RS≈0,RP≈∞) the short-circuit current becomes: ISC=Iph (6)

2.2 Modeling of boost converter

The converter is modeled after analysis of the different operating sequences of the switches, the durations of which are fixed by the command [61].

2.2.1 Single cell boost converter

Fig 4 represents the structure of the single-cell Boost converter where T is a switch controlled by the signal SC.

10.1371/journal.pone.0309460.g004 Fig 4 One-cell boost converter.

The differential equations system given by Eq (7), represents the state equation of the converter.

{dILdt=VPVL−(1−Sc)VSLdVSdt=ILC2(1−Sc)−VSRC2 (7)

The state equation of the boost converter being non-linear, its affine form can be written: X˙=fX+g1U1+g2U2 (8)

with:

X = [ILVS]T The state vector;

U1,U2: Discontinues command; Thestatematrixf=[0−1L1C2−1RC2]

g1=[VSL−ILC2],g2=[VPVL0]

According to [62], the system is controllable if det[g1g2]≠0 det[g1g2]=det[VSLVPVL−ILC20]=ILVPVLC2 (9)

2.2.2 Multicellular boost converter

In reality, static converters can only provide a chopped voltage (or current), due to the qualification of the power electronics as forced or natural switching electronics [57]. To reduce the undesirable effects of the output voltage chopping, and thus move a little more towards the "ideal converter", solutions such as increasing the number of levels available at the output of static converter, increasing the switching frequency of the output voltage so as to push the switching harmonics further and optimization of the control strategy so as to ensure the best possible tracking of the reference signal had been adopted. However, putting several switching cells in parallel presents itself as a better solution for reducing the undesirable effects of the output current chopping (Fig 2), this through to the magnetic coupler which acts as a filter by only allows pass the current that harmonics content is multiple of the cells number connected in parallel (S3 Fig) [63,64], Fig 5 shows the cases where 3 and 5 cells are connected in parallel.

10.1371/journal.pone.0309460.g005 Fig 5 Magnetics coupler behavior for various harmonic order.

(a) 3 cells and (b) 5 cells connected in parallel.

The state equation of the converter made up of P cells put in parallel described in Fig 6 is given by the differential equation system described by Eq (10). For operation in multi-phase or interleaving mode, the control signals must be shifted from each other by Delay=periodP, the current in each branch must be value Ibranch=1P∑n=1PILn.

{dIL1dt=VPVL−(1−Sc1)VSLdIL2dt=VPVL−(1−Sc2)VSL...dILPdt=VPVL−(1−Scp)VSLdVSdt=1C2(∑n=1PanILn−VSR) (10)

with an = 1−Scn,

Its affine form is: X˙=fX+g1U1+g2U2+⋯+gPUP+gP+1UP+1 (11)

with:

f: state matrix;

X = [IL1IL2…ILPVS]T The state vector;

U1,U2,…,UP,UP+1: discontinues command.

10.1371/journal.pone.0309460.g006 Fig 6 Parallel multicellular converter with P switching cells.

(a) P switching cells. (b)Internal structure of each cell.

For 5 cells connected in parallel, the state equation is given by Eq (12): {dIL1dt=VPVL−(1−Sc1)VSLdIL2dt=VPVL−(1−Sc2)VSLdIL3dt=VPVL−(1−Sc3)VSLdIL4dt=VPVL−(1−Sc4)VSLdIL5dt=VPVL−(1−Sc5)VSLdVSdt=IL1C2(1−Sc1)+IL2C2(1−Sc2)+IL3C2(1−Sc3)+IL4C2(1−Sc4)+IL5C2(1−Sc5)−VSRC2 (12)

X˙=fX+g1U1+g2U2+g3U3+g4U4+g5U5+g6U6 (13)

X = [IL1IL2IL3IL4IL5VS]T the state vector;

U1,U2,U3,U4,U5,U6: Discontinues command; f=[00000−1L00000−1L00000−1L00000−1L00000−1L1C21C21C21C21C2−1RC2]

g1=[VSL0000−IL1C2],g2=[0VSL000−IL2C2],g3=[00VSL00−IL3C2],g4=[000VSL0−IL4C2],g5=[0000VSL−IL5C2],g6=[VPVLVPVLVPVLVPVLVPVL0]

Controllability: det[g1g2g3g4g5g6]=VPVVSL5C2(IL1+IL2+IL3+IL4+IL5) (14)

det[g1g2g3g4g5g6]≠0, then the system is controllable.

2.3 Method based on control of the inductance current

2.3.1 Principle of the method

The diagram of the method is illustrated in Fig 7.

10.1371/journal.pone.0309460.g007 Fig 7 Basic diagram of the method by controlling the inductance current.

According to Eqs (9) and (14), the system can be control from the current flowing through the inductance. Fig 7 gives according to KCL, the relationship linking the PV generator current (Ipv), inductance current (IL) and the capacitor current (IC): Ipv=IL+IC1 (15)

OùIC1=C1dVC1dt=C1dVpvdt≈C1ΔVpvΔT (16)

In steady state or for small variations Vpv Voltage, Eq (15) becomes: Ipv≈IL (17)

From Eqs (17) and (6), we will choose the reference current by estimating the photocurrent due to the high influence of irradiance on the output current from GPV. The relationship linking the photocurrent to the irradiance and temperature is given by [61,65]: Iph=[ISC+α(TC−Tr)](GGr) (18)

Where α is the short circuit current temperature coefficient (A/K), TC is the temperature of the cell (K), Tr is the reference temperature (25°C or 298K), G is the irradiance (W/m2) and Gr the reference irradiance (1000/m2).

α=dISCdTC (19)

When TC = Tr, Iph=ISC(GGr)

According to [66] for a polycrystalline silicon material, α = 0,0021A/K; according to [67] for a silicon material, α = 0,00238A/K for polycrystalline structure and 0,00175A/K for the single crystal structure. Given these values, Eq (18) can be expressed: Iph=ISC(GGr) (20)

In control technics based on the proportionality relation of the linear relation in first approach between IOPT and ISC described by [68,69], IOPT=KIISC (21)

ISC=IOPTKI (22)

Eq (22) in Eq (20) give the following relation: Iph=IOPTKI(GGr) (23)

KI being a current factor generally between 0,78 et 0,92; let’s put 1KI≈1, then Eq (23) can be written: Iph,ref≈IOPT(GGr)

The reference current can be formula in the form Iref=Iph,ref=KGIOPT (24)

2.3.2 Controller

To ensure control of current through the inductance, the controller whose goal is to oblige the inductance current to follow the reference current by automatically updating the corresponding duty cycle is built around PI regulator whose the transfer function is given by Eq (25): C(s)=KP+KIs (25)

From Fig 7, ε(s)=Iref(s)−IL(s) (26)

S′(s)=ε(s)C(s) (27)

The parameters KP and KI must be chosen so as to make if possible ε(s)≈0°; for this the particle swarm optimization (PSO) algorithm which the objective function shown on Fig 8 and describe by Eq (28) was used for choose the values of KP and KI.

{Vi+1=μ1Vi+μ2(xip−xi)+μ3(xg−xi)xi+1=xi+Vi+1 (28)

10.1371/journal.pone.0309460.g008 Fig 8 PSO characteristics.

(a)PSO flowchart. (b)Objective function.

Where,

Vi+1,xi+1 are respectively the updated speed and position of each particle i;

Vi,xi are respectively the actual speed and position of particle i;

μ1,μ2,μ3 ∈ [0,1]; xip,xg are respectively the best position visited by the particle i and the best position visited by the swarm.

With parameter values: Number of iterations = 100; Number of particle s = 100; Speed_max = 2.5; Speed_min = -2.5; p_best_init = 100000000; g_best_init = 100000000; Kp_min = 0; Kp_max = 2000;

Ki_min = 0; Ki_max = 2000;

2.4 Method of control by sliding mode

The diagram of control by sliding mode illustrated in Fig 9, shows that the reference current generated previously can be used as reference current in sliding mode control. The Lyapunov criterion is used to define switching functions because of the simplicity of its implementation. The quadratic Lyapunov function is define around energies stored in capacitors and inductances as follow: V=12ΔXT.H.ΔX (29)

10.1371/journal.pone.0309460.g009 Fig 9 Diagram of control by sliding mode.

Where H is a diagonal constant matrix containing inductive and capacitive elements; H=[L10…000L2…00⋮⋮⋱⋮⋮000LP00000C2]

According to Eqs (9) and (14), we pose the error ΔX = Xref−X as follow: ΔX=[Iref−IL1Iref−IL2⋮Iref−ILpVref−Vpv]

The system will be stable in a closed loop if the derivative of the Lyapunov function is negative, V˙=ΔXT.H.ΔX˙ (30)

ΔX˙=X˙=fX+g1U1+g2U2+⋯+gPUP+gP+1UP+1 (31)

Switching functions are defined through the following relationship: Si=−ΔXT.H.gi,i=1,2,…p,p+1 (32)

For P = 5, H=[L1000000L2000000L3000000L4000000L5000000C2]

ΔX=[Iref−IL1Iref−IL2Iref−IL3Iref−IL4Iref−IL5Vref−Vpv]

ΔX˙=X˙=fX+g1U1+g2U2+g3U3+g4U4+g5U5+g6U6

Si=−ΔXT.H.gi,i=1,2,3,4,5,6

S1=(Vref−Vpv)IL1−(Iref−IL1)VS

S2=(Vref−Vpv)IL2−(Iref−IL2)VS

S3=(Vref−Vpv)IL3−(Iref−IL3)VS

S4=(Vref−Vpv)IL4−(Iref−IL4)VS

S5=(Vref−Vpv)IL5−(Iref−IL5)VS

S6=−Vpv[5Iref−(IL1+IL2+IL3+IL4+IL5)]

Error ΔX is stable if Si = 0°; for S6 = 0, we obtain: Iref=IL1+IL2+IL3+IL4+IL55

Thus giving the current to pass through each branch for multicellular use.

2.5 Calculation of efficiency

According to [17], the calculation of the efficiency in a photovoltaic chain is product of the MPPT efficiency (ηMPPT) and the conversion efficiency (ηCONV) of the static converter. The MPPT efficiency determines the effectiveness of control technics in terms for tracking the maximum power point; it is given by the following relation: ƞMPPT=PpvPMPP (33)

Where Ppv is the power delivered by the photovoltaic generator, PMPP the maximum power of the photovoltaic generator at the maximum power point.

The efficiency of a static converter can be defined as its ability to transfer at its output the maximum of available power at its input [49]: ƞCONV=PoutPpv=PoutPout+Ploss=11+PlossPout (34)

Ppv is the power delivered by the photovoltaic generator which becomes the input power of converter, Pout is the power transferred to the converter output.

The total efficiency of the chain is given by: ƞCHAIN=ƞMPPT×ƞCONV (35)

3. Simulation results and discussion

In this part, we present the different simulations carried out in Matlab/Simulink environment and their results. We compared the suggested solutions based on the control of the inductance current and multicellular firstly to some traditional MPPT technics control, and to some solutions proposed by others works in term of improvement of power quality. Simulations were carried out in various cases: under constant irradiance, variable irradiance and variable temperature. The photovoltaic module used is type Kyocera Solar KC200GT which some characteristics depending on the irradiance under a constant temperature of 25°C are given in S1 Table and S1 Fig; Table 1 give the designed parameters for simulation.

10.1371/journal.pone.0309460.t001 Table 1 Designed parameters for simulation.

Components	Values	
C1 = C2	200μF	
L	100μH	
R	58Ω	
Switching frequency (Fsw)	5KHz	
K P	12.73	
K i	10000	

3.1 functioning of conventional boost converter with the suggested MPPT for various duty cycle

The proposed MPPT was simulated on the conventional boost to check if it responds to operating criteria of this converter.

Some duty cycles were used: 0.25 (Fig 10), 0.5 (Fig 11) and 0.75 (Fig 12). for 0.5 duty cycle value, the output voltage of the boost converter must be equal to twice the value of its input voltage, this is verified by Fig 11.

10.1371/journal.pone.0309460.g010 Fig 10 Conventional boost with suggested MPPT for duty cycle = 0.25.

(a)Currents. (b)Voltages.

10.1371/journal.pone.0309460.g011 Fig 11 Conventional boost with suggested MPPT for duty cycle = 0.5.

(a)Currents. (b)Voltages.

10.1371/journal.pone.0309460.g012 Fig 12 Conventional boost with suggested MPPT for duty cycle = 0.75.

(a)Currents. (b)Voltages.

3.2 Comparison with some MPPT technics under constant irradiance G = 1000W/m2 and variable irradiance for temperature T = 25°C

The proposed solutions are compared to some MPPT technics such as: perturb and observe (P&O) in Fig 13, fraction short circuit (FSCC) in Fig 14, fuzzy logic (Fig 15) and hybrid sliding mode assisted by P&O in Fig 16. The operations were simulated under the conditions of constant irradiance, variable irradiance according to the profile of Fig 17, both under a constant temperature of 25°C.

10.1371/journal.pone.0309460.g013 Fig 13 Powers curves with conventional boost based on P&O MPPT.

(a)Constant irradiance. (b)Variable irradiance.

10.1371/journal.pone.0309460.g014 Fig 14 Powers curves with conventional boost based on FSCC MPPT.

(a)Constant irradiance. (b)Variable irradiance.

10.1371/journal.pone.0309460.g015 Fig 15 Powers curves with conventional boost based on fuzzy MPPT.

(a)Constant irradiance. (b)Variable irradiance.

10.1371/journal.pone.0309460.g016 Fig 16 Powers curves with conventional boost based on sliding mode MPPT.

(a)Constant irradiance. (b)Variable irradiance.

10.1371/journal.pone.0309460.g017 Fig 17 Irradiance profile under variation conditions.

To make the comparison between the different maximum point search techniques in terms of speed, stability, precision, an analysis was carried out and grouped in Table 2, and in Table 3 for the comparison in terms of transferred power and efficiency. From the simulation results we notice that the fuzzy MPPT technique (Fig 15A) presents very good stability under constant irradiance compared to the others, but when faced with variations it tends to lose tracking. the sliding control (Fig 16) used here according to Fig 9 is a hybrid control combining the sliding mode assisted by the P&O control. In Fig 18 the proposed MPPT was used to control the conventional boost. The proposed solution which consists to use the proposed MPPT and multicellular converter (Fig 19), despite the use of low values of the filtering elements (C1, C2 and L), presents better results in terms of tracking, stability, precision and power transfer.

10.1371/journal.pone.0309460.g018 Fig 18 Powers curves with conventional boost based on proposed MPPT.

(a)Constant irradiance. (b)Variable irradiance.

10.1371/journal.pone.0309460.g019 Fig 19 Powers curves with parallel boost converter based on proposed MPPT.

(a)Constant irradiance. (b)Variable irradiance.

10.1371/journal.pone.0309460.t002 Table 2 Comparison among some solutions in terms of powers, response times and oscillations.

Type of MPPT	Type of converter	P MPP	P pv	T r_pv	Ppv oscillations	
P&O	Conventional boost	200.14 W	194.5 W	163.1 ms	0.58 W	
FSC	Conventional boost	200.14 W	194.4 W	152.5 ms	0.58 W	
Fuzzy	Conventional boost	200.14 W	196 W	250 ms	19.1 μW	
Sliding	Conventional boost	200.14 W	200.1 W	10.2 ms	0.07 W	
Proposed	Conventional boost	200.14 W	200.1 W	11.1 ms	0.24 W	
Proposed	Multicellular	200.14 W	2001. W	10 ms	0.05 W	
Where PMPP is maximum power of GPV at MPP, Ppv is power delivered at out of GPV, Tr_PV is response time.

10.1371/journal.pone.0309460.t003 Table 3 Comparison among some solutions in terms of transferred powers and efficiencies.

Type of MPPT	Type of converter	P pv	P out	ηMPPT	ηCONV	ηCHAIN	
P&O	Conventional	194.5 W	187 W	97.18%	96.14%	93.43%	
FSC	Conventional	194.4 W	187.5 W	97.13%	96.45%	93.68%	
Fuzzy	Conventional	196 W	188 W	97.93%	95.91%	93.93%	
Sliding	Conventional	200.1W	190.4 W	99.98%	95.15%	95.13%	
Proposed	Conventional	200.1 W	188.78 W	99.98%	94.34%	94.32%	
Proposed	Multicellular	200.1 W	198.5 W	99.98%	99.20%	99.18%	
Where Pout is output power of the converter, ηMPPT is MPPT efficiency, ηCONV is conversion efficiency, ηCHAIN is the total efficiency of the chain.

3.3 Simulation of the proposed solution under temperature variations at constant irradiance G = 1000W/m2

The proposed solution was subjected to a temperature variation that the profile is illustrated on Fig 20, we notice in Fig 21A a very weak influence of the temperature on the current, according to Fig 22B we observe the tracking of the maximum point of the power of the GPV with a response time of 0.002 seconds and a response time of 0.02 seconds for the transferred power. These results agree with the values described in S2 Table and S2 Fig.

10.1371/journal.pone.0309460.g020 Fig 20 Temperature profile under variation conditions.

10.1371/journal.pone.0309460.g021 Fig 21 Proposed solution under temperature variations at constant irradiance.

(a)Currents. (b)Voltage.

10.1371/journal.pone.0309460.g022 Fig 22 Proposed solution under temperature variations at constant irradiance.

(a)Powers. (b)powers zoom.

3.4 Comparison of proposed solution with HG-QBC

The proposed solution is compared to the high-gain quadratic boost converter (HG-QBC) proposed by [43] in order to appreciate its performances. The Figs 23–26 show that the proposed solution can operate in a wide voltage range.

10.1371/journal.pone.0309460.g023 Fig 23 (a) Irradiance profile. (b) Currents at constant irradiance.

10.1371/journal.pone.0309460.g024 Fig 24 (a)Voltages and (b)output power at constant irradiance.

10.1371/journal.pone.0309460.g025 Fig 25 (a)Currents and (b)Voltages under variable irradiance.

10.1371/journal.pone.0309460.g026 Fig 26 (a)Output Power and (b)output power zoom under variable irradiance.

Fig 26B show more the behaviors facing the different change of variations according to profile presented on Fig 23A. An analysis is made between the performances of the proposed solution and the performances of the HG-QBC proposed by [43] and is presented in Tables 4 and 5.

10.1371/journal.pone.0309460.t004 Table 4 Performance analysis of the proposed solution and the HG-QBC.

Type of MPPT	Type of converter	Setting time	V out	Voutripples	Efficacy	
Hybrid (PO&NN) [43]	HG-QBC	1.2 second	104.8 V	0.2%	97.5%	
Proposed	Multicellular	0.04 second	104.7 V	0.005%	99.08%	

10.1371/journal.pone.0309460.t005 Table 5 Performance analysis of the proposed solution and the HG-QBC under irradiance variation.

Irradiance	Hybrid (PO&NN) using HG-QBC [43]	Proposed MPPT using Multicellular	
V out	I out	P out	V out	I out	P out	
G = 500W/m2	75.78 V	1.316 A	99.79 W	74.39 V	1.348 A	100.1 W	
G = 750W/m2	90.79 V	1.578 A	143.1 W	90.91 V	1.646 A	149.7 W	
G = 1000W/m2	104.8 V	1.819 A	190.63 W	104.7 V	1.896 A	198.3 W	
Where Vout,Iout,Pout are respectively output voltage, output current and output power of the converter.

By analyzing values presented on Table 5 to values on S1 Table and S1 Fig for different irradiance values, we observe that the proposed solution presents best results in term of precision of tracking.

3.5 Comparison of proposed solution with IHGBC

Among the solutions for improving the performance of boost converters dedicated to PV applications, there is the interleaved high-gain boost converter (IHGBC) proposed by [44]. This converter has the capacity to increase the voltage gain with less ripple output. Fig 27A presents irradiance profile under variations; the currents, voltages and output power operate at constant irradiance are respectively show on Figs 27B and 28.

10.1371/journal.pone.0309460.g027 Fig 27 (a) Irradiance profile. (b) Currents at constant irradiance.

10.1371/journal.pone.0309460.g028 Fig 28 (a) Voltages and (b) output power at constant irradiance.

Under variable irradiance, currents are presented on Fig 29A, voltage on Fig 29B and powers on Fig 30. Fig 30B presents more in details the oscillations and response time of the power delivered by GPV (PPV) and the transferred output power (Pout). Table 6 presents the comparison made between the proposed solution and the IHGBC. In spite of slow response time of proposed solution facing the IHGBC, Table 6 show best performances of the proposed solution in term of ripples minimization and maximum transferred power to output.

10.1371/journal.pone.0309460.g029 Fig 29 (a) Currents and (b) voltages under variable irradiance.

10.1371/journal.pone.0309460.g030 Fig 30 (a) Powers and (b) powers zoom under variable irradiance.

10.1371/journal.pone.0309460.t006 Table 6 Performance analysis of the proposed solution and the IHGBC.

Magnitude	IHGBC using Hybrid (P&O-FP) MPPT [44]	Multicellular using Proposed MPPT	
Switching frequency	50 KHz	5 KHz	
V out	209.4 V	209.62 V	
Vout ripples	0.14%	0.001%	
I out	0.813 A	0.939 A	
P out	170.24 W	196.88 W	
Convergence time	0.05 s	0.1 s	

4. Conclusion

In this paper, the objective was to use the principle of current controlled voltage source and the parallel multicellular converter to improve the energy efficiency of a photovoltaic chain. A method by modification of the technics based on fraction of the short circuit current (FSCC) with the aim of generating a reference current to control the inductance current in order to control the static converter to follow the MPP has been proposed, this reference current was used as reference current in sliding mode control. The parallel multicellular converter integrating synchronous rectification through the advantages offered by the interleaving mode has been used to reduce power oscillations and switching losses in switches. The simulation results obtained show the effectiveness of the method by estimating the photocurrent as a reference current used for the pursuit of MPP, responds effectively whatever the environmental conditions, and the contribution of the multicellular converter in reducing oscillations of power around the MPP in steady state and the losses in the switches. The results show a response time of 0.04 s, power oscillations at maximum point around 0.05 W and efficiency of 99.08% facing the high-gain quadratic boost converter. Then by comparing with the interleaved high-gain boost converter the results show a response time of 0.1 s for the transferred power, a very low output voltage ripples of 0.001% and 98.37% as efficiency of the chain. Multicellular converter integrating synchronous rectification can be used in many power system, the control technique based on the control of inductance current is suitable for static converter which the inductance current should be control for its good functioning. The proposed solution can be connected to a grid by reducing the level of the inverter and active filter.

Supporting information

S1 Fig Characteristics (I-V and P-V) of Kyocera Solar KC200GT photovoltaic module at 25°C under irradiance variations.

(TIF)

S2 Fig Characteristics (I-V and P-V) of Kyocera Solar KC200GT photovoltaic module at 1000W/m2 under temperature variations.

(TIF)

S3 Fig Magnetics coupler behavior for cells connected in parallel.

(a) one cell. (b) 2 cells. (c) 4 cells. (d) 7 cells.

(TIF)

S1 Table Characteristics of Kyocera Solar KC200GT photovoltaic module at 25°C.

(DOCX)

S2 Table Characteristics of Kyocera Solar KC200GT photovoltaic module at 1000W/m2.

(DOCX)

10.1371/journal.pone.0309460.r001
Decision Letter 0
Bajaj Mohit Academic Editor
© 2024 Mohit Bajaj
2024
Mohit Bajaj
https://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Submission Version0
7 May 2024

PONE-D-24-09884Use of multicellular converter in PV chain for improving of energy efficiency and minimization of power oscillationsPLOS ONE

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Comments to the Author

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2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: No

Reviewer #2: Yes

Reviewer #3: Yes

Reviewer #4: Yes

Reviewer #5: Yes

Reviewer #6: Yes

Reviewer #7: Yes

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Reviewer #7: No

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5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: How does the proposed multicellular parallel boost converter compare to existing solutions in terms of efficiency and cost?

Given the environmental conditions' impact on photovoltaic (PV) generator performance, how does the proposed solution ensure consistent energy output across varying conditions?

The introduction mentions several maximum power point tracking (MPPT) techniques. Can you detail how the proposed solution improves upon these or integrates with them?

Can you elaborate on the specific challenges the multicellular converter addresses in non-linear load applications, such as harmonic currents and chaotic behavior?

How does the introduction of multicellular converters impact the overall lifecycle and maintenance costs of PV systems?

How does the modeling of the multicellular boost converter account for real-world inefficiencies, such as component losses and non-ideal behaviors?

The method section discusses the control of inductance current. Can you explain the advantages of this approach over voltage-based control methods in PV systems?

How does the proposed method ensure stability and robustness in the face of sudden changes in environmental conditions?

Can you discuss the scalability of the presented method? How does it perform when scaled up for larger PV installations?

Given the detailed mathematical modeling, how accessible is this method for practical implementation by engineers in the field?

The results show improved efficiency with multicellular converters. Can you quantify the impact on overall system cost and return on investment?

How do the simulation results compare with real-world testing and validations? Are there any discrepancies, and how were they addressed?

The paper mentions rapid pursuit of the MPP despite irradiance variations. How does this rapid tracking affect the system's longevity and reliability?

Can you detail any specific challenges encountered during the simulation, particularly with modeling environmental variations?

How does the efficiency and performance of the proposed system compare to leading commercial systems currently available on the market?

The conclusion mentions the effectiveness of the method under various environmental conditions. Can you provide more details on limitations or conditions where the proposed solution might not perform optimally?

Given the conclusion's claims about reducing power oscillations and switching losses, what are the anticipated impacts on the broader adoption of PV systems?

Can you elaborate on potential future research directions suggested by the findings of this paper?

How do the authors envision the integration of their solution with existing PV infrastructure, particularly in urban settings?

The conclusion suggests improved energy efficiency. Can you discuss any potential environmental impacts, positive or negative, that might arise from the widespread adoption of this technology?

Reviewer #2: This article discusses the role of multicellular converters in enhancing the quality of electrical energy in photovoltaic systems, aiming to maximize power output with minimal oscillations around the maximum power point and reduced switching losses. Through modeling and simulation in Matlab/Simulink, the proposed solutions demonstrate effective performance under irradiance and temperature fluctuations. The subject matter is intriguing, yet there are minor suggestions for improvement. The specific points to address are outlined below:

Clearly articulate the novelty of the proposed control algorithm in the abstract. It remains ambiguous which aspect of the design is innovative.

The derivation of the control design lacks sufficient explanation. Clarification is needed regarding how the control law was derived, including the steps involved.

Justification for the selection of controller gains is necessary.

Provide further elucidation on the advantages and enhancements of the proposed method and technology. Additionally, compare these findings with existing literature. Acknowledge that the control design techniques employed here are akin to those in other studies, but highlight and discuss the challenges encountered in this research to demonstrate that it is not merely an incremental extension of existing methodologies.

I understand that hardware realization may not be possible due to lack of hardware resources. However, please include a critical discussion on what could be anticipated challenges if the proposed algorithm is realized on a real quadrotor system.

Integrating additional performance indices could offer a more comprehensive verification of the controller's performance.

Enhance the discussion on existing control algorithms in the introduction with recent references, such as those available at https://doi.org/10.1371/journal.pone.0293878, https://doi.org/10.1371/journal.pone.0298093, https://doi.org/10.1109/ACCESS.2023.3344451, https://doi.org/10.3389/fenrg.2023.1293267.

Incorporate a discussion on the limitations of the control law in the conclusions section.

Address the issue of chattering inherent in sliding mode control variants. Reference the ' Maximum Power Extraction from a Standalone Photo Voltaic System via Neuro-adaptive Arbitrary Order Sliding Mode Control Strategy with High Gain Differentiation ' and explore potential mitigation strategies in detail.

Conduct a thorough proofreading of the paper to rectify any typos and enhance linguistic clarity.

Ensure that all abbreviations are defined and explained within the text.

Reviewer #3: My review comments are below:

1. Please consider that the presented boost and interleaved boost converters are conventional converters that cannot transfer high powers and work under limited values of power. The presented parallel cell type application of the boot converter is not a novel idea and has been pesented aleady in detail. Therefore I suggest the authors to focus on the control process and reflex this topic on the title of the paper.

2. The calculation of the efficiency for the proposed converter should be presented in detail. By considering the paper at https://www.sciencedirect.com/science/article/pii/S0142061520313958, authors should present the converter efficiency under different working conditions. Compare your results with this paper.

3. The state of the active and passive components under the proposed controller system should be presented in detail. See the paper at https://link.springer.com/article/10.1007/s00202-024-02295-x, and draw your voltage and current graphics according to figures 4 and 6 of this paper. Compare your results with this apper.

4. The voltage and currents under different duty ratios and dynamic loads should be considered and presented by Matlab Simulink.

5. A table should be presented, and advantages and disadvantages of the proposed controller compared with other conventional controllers. Different parameters like the complexity of the control process in practice, cost of the system, efficiency, etc., can be compared.

6. Present several graphics based on the table in comment 5 and present your results. Readers can understand better the advantages of the suggested controller graphically.

Reviewer #4: This article proposes a method to improve the efficiency of photovoltaic (PV) systems by controlling the current through the inductance of a boost converter. Here's a breakdown of the key points and some suggestions for improvement:

1-While the combination of current control and multicellular converters might be interesting, the novelty of the approach compared to existing methods isn't clearly highlighted.

2-The specific algorithm used for Particle Swarm Optimization (PSO) is not mentioned.

3-The switching frequency isn't explicitly stated, which can impact efficiency.

4-Compare the proposed method with existing MPPT (Maximum Power Point Tracking) techniques in terms of efficiency, response time, and complexity.

5-Discuss the limitations of the proposed method and potential areas for future work.

6- Specify the PSO algorithm used and its parameters.

7- Mention the switching frequency used in the simulations.

8- Consider including simulations with more realistic scenarios like partial shading.

Reviewer #5: The paper is readability.

- the all figures should be high quality.

- to cite the reference such as "described by [[44]-[45]]", please check there are double []!.

- check the journal format

- Fig. 17-21 should be explained in more details.

Reviewer #6: Comments to the Author:

The manuscript is well presented with use of multicellular converter in PV chain for improving efficiency and to reduce power oscillations. The paper can be accepted with minor revision and grammatical corrections. The following points can be followed to update/strengthen the manuscript:

1. The manuscript has some grammatical mistakes - Please check it.

2. Literature review is shallow

3. Authors mentioned thaat the efficiency is 99.65% for Inductance current and 99.6% for sliding method which is not convincing due to the passive components involved in the boost converter.

4. The analysis of traditional DC/DC converters can be presented with respect to various duty cycle with the suggested MPP.

5. Novelty of the proposed work should be established by comparing the same with comparable work. Authors can justify or compare the following MPPT based boost converter and justify how the presented MPP technique is superior to other MPPT approaches.

i. Nagaraja Rao, S., Anisetty, S. K., Manjunatha, B. M., Kiran Kumar, B. M., Praveen Kumar, V., & Pranupa, S. (2022). Interleaved high-gain boost converter powered by solar energy using hybrid-based MPP tracking technique. Clean Energy, 6(3), 460-475.

ii. Veerabhadra, & Nagaraja Rao, S. (2022). Assessment of high-gain quadratic boost converter with hybrid-based maximum power point tracking technique for solar photovoltaic systems. Clean Energy, 6(4), 632-645.

6. In the abstract and conclusion, the results performances should be reflected which helps to improve the quality of the manuscript. Add the results values in the abstract.

Reviewer #7: The authors presented “Use of multicellular converter in PV chain for improving energy efficiency and minimization of power oscillations,” which is very interesting. However, it requires a few suggestions to improve. The suggestions and comments are as follows:

1. The presented work is very good. The title of the paper needs to reflect the work that is presented.

2. The abstract needs to highlight some significant results. It should include 1-2 lines of gaps, authors' contributions, and advantages of the work.

3. The introduction section needs to be improved. Try to avoid bulk referencing (ex: ) [[1]-[4]]) , also, the references should be in chronological order.

4. The literature survey can be improved by adding more related papers. It is advised to add the following papers to improve the introduction section.

https://doi.org/10.1002/oca.2773, https://doi.org/10.1007/s12667-021-00465-5, https://doi.org/10.1007/s40435-023-01274-7,

5. The authors should add more results to show the speed of tracking and the accuracy of tracking.

6. The simulation results should be shown in good-quality figures.

7. In simulation results, to highlight the effectiveness of the proposed MPPT, the authors are recommended to compare their method with other methods that also target fast MPPT convergence to provide a fair comparison. This can highlight the paper's contribution to already existing fast methods for MPT.

8. Detailed circuit parameters should be included in the manuscript.

9. The paper requires further English revision as it has many grammatical mistakes.

**********

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Reviewer #1: No

Reviewer #2: Yes: Dr. Safeer Ullah

Reviewer #3: No

Reviewer #4: No

Reviewer #5: No

Reviewer #6: Yes: Dr. S. Nagaraja Rao

Reviewer #7: No

**********

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Attachment Submitted filename: Comments to the Author_PLOS.docx

10.1371/journal.pone.0309460.r002
Author response to Decision Letter 0
Submission Version1
17 Jun 2024

Response to Reviewers comments

Reviewer #1:

How does the proposed multicellular parallel boost converter compare to existing solutions in terms of efficiency and cost?

In terms of efficiency, the multicellular parallel boost converter offers a better reduction in conduction losses in switching switches and oscillations reduction at steady state (Fig 2 page 4).

The cost is slightly higher than the single cell boost converter.

Given the environmental conditions' impact on photovoltaic (PV) generator performance, how does the proposed solution ensure consistent energy output across varying conditions?

The reference current is automatically generated by a light sensor. Thus, depending on the level of illumination detected, a reference current value will be provided; Through to the PI regulator, the inductor current will be controlled to follow this value. Depending on the current value, the corresponding voltage value will be imposed. (Fig 19 page 19, Figs 21 and 22 page 21).

The introduction mentions several maximum power point tracking (MPPT) techniques. Can you detail how the proposed solution improves upon these or integrates with them?

The proposed solution is a direct improvement of the short circuit method technique where the current at the power point was given by Eq 21 (page 10):

I_OPT=K_I I_SC (21)

Where the proportional constant K_I depends on the PV cell technology, meteorological conditions

and the fill factor, mainly. However, in many cases, K_I is determined by performing a PV scanning every several minutes. After K_I is obtained, the system remains with the approximation of Eq 21, until the next calculation of K_I.

Eq 21 has been modified taking into account certain parameters to obtain the reference current given by Eq 24 (page 11):

I_ref= I_(ph,ref)=K_G I_OPT (24)

Où K_G=G/G_r

The coefficient K_G depends only on the illumination, unlike

K_I which depends on the PV cell technology, meteorological conditions and the fill factor, mainly.

The solution presented offers speed and precision in the search for the maximum point, a reduction in oscillations around the maximum power point.

Ease of implementation, automatic update depending on irradiance

Can you elaborate on the specific challenges the multicellular converter addresses in non-linear load applications, such as harmonic currents and chaotic behavior?

The multicellular converter, through its rapid dynamic response, improves the spectral content, hence reducing ripples (Fig 2). Through to the magnetic coupler used, the harmonic currents are attenuated depending on the number of cells used; because the magnetic coupler considerably reduces the currents therefore the harmonic content is not multiple of the number of cells, in other words the harmonic currents not multiple of the number of cells put in parallel will cross a resistance of very high value unlike the harmonic current multiple of the number of cells in parallel (Fig 5 page 7). According to the authors [56,57] chaotic phenomena were more observed with low switching frequency values. Concerning chaotic phenomena, we have not yet carried out the chaotic analysis with our converter, we plan to do so in perspective.

How does the introduction of multicellular converters impact the overall lifecycle and maintenance costs of PV systems?

Multicellular converters provide better current regulation, enable low current operation in power switches, at low switching frequency. These advantages reduce the heating and oscillation that were once responsible for the destruction of semiconductors. Good energy quality will ensure a good lifespan of the system.

How does the modeling of the multicellular boost converter account for real-world inefficiencies, such as component losses and non-ideal behaviors?

Certain aspects have been neglected in order to facilitate modeling.

The method section discusses the control of inductance current. Can you explain the advantages of this approach over voltage-based control methods in PV systems?

This method uses a reference current generated by the illumination to control the inductor current. Its advantages are the rapid pursuit of the maximum power point and the precision in the search for the maximum power point during rapid changes in conditions climatic. It is easily adaptable compared to other techniques.

How does the proposed method ensure stability and robustness in the face of sudden changes in environmental conditions?

Stability is ensured by a low presence of oscillations around the maximum power point in steady state, robustness for its part is translated by a rapid search for the power point during change. (Fig 19 page 19, Figs 21 and 22 page 21, Fig 26 page 23, Fig 30 page 25)

Can you discuss the scalability of the presented method? How does it perform when scaled up for larger PV installations?

The method works well in a large installation, just set the maximum current value and the reference current is generated automatically. Which makes the approach integrable into any type of photovoltaic system.

Given the detailed mathematical modeling, how accessible is this method for practical implementation by engineers in the field?

To the extent that the inductor current can be measured through a current sensor, the entire control approach can be integrated into a microcontroller in order to control the photovoltaic system in real time. This method is therefore accessible for practical implementation.

The results show improved efficiency with multicellular converters. Can you quantify the impact on overall system cost and return on investment?

Our control approach with a multicellular converter is in line with energy efficiency, allowing it provides to the load the power necessary for its functioning. Although the overall cost of the system will be relatively high, the efficiency obtained can already guarantee the return on investment.

How do the simulation results compare with real-world testing and validations? Are there any discrepancies, and how were they addressed?

We have not yet carried out an experimental validation test on our approach. As we mentioned at the conclusion of our manuscript, we plan to carry out an experimental study of our approach.

The paper mentions rapid pursuit of the MPP despite irradiance variations. How does this rapid tracking affect the system's longevity and reliability?

The rapid pursuit of the MPP in the face of variations in irradiation allows the system to exploit the maximum energy produced by the photovoltaic generator. The performance is therefore improved. Furthermore, the reduction of switching losses in the switches, which will improve the overall lifespan of the system.

Can you detail any specific challenges encountered during the simulation, particularly with modeling environmental variations?

During the simulation a signal generator was used to generate environmental variations. With this approach, the difficulties initially encountered regarding the convergence of the entire PV system were wiped out.

How does the efficiency and performance of the proposed system compare to leading commercial systems currently available on the market?

The proposed approach presents a very high robustness to the variation of environmental conditions and system parameters. Compared to the approaches available on the market, the proposed approach presented presents a better performance.

The conclusion mentions the effectiveness of the method under various environmental conditions. Can you provide more details on limitations or conditions where the proposed solution might not perform optimally?

One of the hypotheses for developing the method was based on the weak influence of temperature on the current; faced with a strong temperature variation, the current continues its reference value but the voltage is very sensitive due to the strong influence of the temperature on the voltage.

Given the conclusion's claims about reducing power oscillations and switching losses, what are the anticipated impacts on the broader adoption of PV systems?

The expected impacts are the reduction in the complexity of the filtering system, the increase in the lifespan of the components, the improvement in the quality of the energy produced, and the reduction in maintenance costs.

Can you elaborate on potential future research directions suggested by the findings of this paper?

Potential future research directions that may arise are:

- Study of an autonomous photovoltaic system;

- Photovoltaic systems with multicellular converter connected to the grid;

- Heating systems.

How do the authors envision the integration of their solution with existing PV infrastructure, particularly in urban settings?

The solution presented will be used as an interface between the photovoltaic generator and the load.

The conclusion suggests improved energy efficiency. Can you discuss any potential environmental impacts, positive or negative, that might arise from the widespread adoption of this technology?

Improving energy quality will help reduce noise caused by harmonics and reduce the number of fires resulting from overheating in electrical systems.

Thank you Sir for your comments and suggestions.

Reviewer #2:

This article discusses the role of multicellular converters in enhancing the quality of electrical energy in photovoltaic systems, aiming to maximize power output with minimal oscillations around the maximum power point and reduced switching losses. Through modeling and simulation in Matlab/Simulink, the proposed solutions demonstrate effective performance under irradiance and temperature fluctuations. The subject matter is intriguing, yet there are minor suggestions for improvement. The specific points to address are outlined below:

Clearly articulate the novelty of the proposed control algorithm in the abstract. It remains ambiguous which aspect of the design is innovative.

The derivation of the control design lacks sufficient explanation. Clarification is needed regarding how the control law was derived, including the steps involved.

Justification for the selection of controller gains is necessary.

Provide further elucidation on the advantages and enhancements of the proposed method and technology. Additionally, compare these findings with existing literature. Acknowledge that the control design techniques employed here are akin to those in other studies, but highlight and discuss the challenges encountered in this research to demonstrate that it is not merely an incremental extension of existing methodologies.

I understand that hardware realization may not be possible due to lack of hardware resources. However, please include a critical discussion on what could be anticipated challenges if the proposed algorithm is realized on a real quadrotor system.

Integrating additional performance indices could offer a more comprehensive verification of the controller's performance.

Enhance the discussion on existing control algorithms in the introduction with recent references, such as those available at https://doi.org/10.1371/journal.pone.0293878, https://doi.org/10.1371/journal.pone.0298093, https://doi.org/10.1109/ACCESS.2023.3344451, https://doi.org/10.3389/fenrg.2023.1293267.

Incorporate a discussion on the limitations of the control law in the conclusions section.

Address the issue of chattering inherent in sliding mode control variants. Reference the ' Maximum Power Extraction from a Standalone Photo Voltaic System via Neuro-adaptive Arbitrary Order Sliding Mode Control Strategy with High Gain Differentiation ' and explore potential mitigation strategies in detail.

Conduct a thorough proofreading of the paper to rectify any typos and enhance linguistic clarity.

Ensure that all abbreviations are defined and explained within the text.

Thank you Sir for these comments and suggestions, we have improved the manuscript by making many modifications, while also taking your suggestions into account. The references added in the introduction are references [38-41]

Reviewer #3:

My review comments are below:

1. Please consider that the presented boost and interleaved boost converters are conventional converters that cannot transfer high powers and work under limited values of power. The presented parallel cell type application of the boot converter is not a novel idea and has been pesented aleady in detail. Therefore I suggest the authors to focus on the control process and reflex this topic on the title of the paper.

Thank you Sir for your clarification, your suggestion has been taken into account and integrated into the manuscript.

2. The calculation of the efficiency for the proposed converter should be presented in detail. By considering the paper at https://www.sciencedirect.com/science/article/pii/S0142061520313958, authors should present the converter efficiency under different working conditions. Compare your results with this paper.

The calculation of the efficiency is presented on pages 14-15 of the manuscript, the efficiency of the converter in different working conditions according to reference [49] are presented on page 19 (Fig 19), page 21 (Figs 21 and 22).

3. The state of the active and passive components under the proposed controller system should be presented in detail. See the paper at https://link.springer.com/article/10.1007/s00202-024-02295-x, and draw your voltage and current graphics according to figures 4 and 6 of this paper. Compare your results with this paper.

Thank you Sir for your clarification, your suggestion has been taken into account and integrated into the manuscript.

4. The voltage and currents under different duty ratios and dynamic loads should be considered and presented by Matlab Simulink.

The voltage and currents under different duty cycles are shown in the figures (Figs 10-12) on pages 16-17. Thank you for this remark.

5. A table should be presented, and advantages and disadvantages of the proposed controller compared with other conventional controllers. Different parameters like the complexity of the control process in practice, cost of the system, efficiency, etc., can be compared.

Thank you for this remark. The comparisons are presented in tables 3 and 4 of the manuscript on page 20.

6. Present several graphics based on the table in comment 5 and present your results. Readers can understand better the advantages of the suggested controller graphically.

Thank you for this remark, several graphs have been added to present the results.

Reviewer #4:

This article proposes a method to improve the efficiency of photovoltaic (PV) systems by controlling the current through the inductance of a boost converter. Here's a breakdown of the key points and some suggestions for improvement:

1-While the combination of current control and multicellular converters might be interesting, the novelty of the approach compared to existing methods isn't clearly highlighted.

2-The specific algorithm used for Particle Swarm Optimization (PSO) is not mentioned.

3-The switching frequency isn't explicitly stated, which can impact efficiency.

4-Compare the proposed method with existing MPPT (Maximum Power Point Tracking) techniques in terms of efficiency, response time, and complexity.

Thank you for your comments, the document has been revised and we have incorporated the shortcomings that you highlighted. The comparisons were made and presented in tables 3 and 4 (page 20).

5-Discuss the limitations of the proposed method and potential areas for future work.

The control technique is more applicable to boost converters and its derivatives, as well as to the converter requiring control of the inductor current for their proper operation.

The proposed method can be used in battery storage systems, for connection to the electrical network.

6- Specify the PSO algorithm used and its parameters.

The PSO algorithm used is presented in Figure 8 as well as its parameters on page 12.

7- Mention the switching freq

10.1371/journal.pone.0309460.r003
Decision Letter 1
Bajaj Mohit Academic Editor
© 2024 Mohit Bajaj
2024
Mohit Bajaj
https://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Submission Version1
13 Aug 2024

A modified fractional short circuit current MPPT and multicellular converter for improving power quality and efficiency in PV chain

PONE-D-24-09884R1

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10.1371/journal.pone.0309460.r004
Acceptance letter
Bajaj Mohit Academic Editor
© 2024 Mohit Bajaj
2024
Mohit Bajaj
https://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
23 Aug 2024

PONE-D-24-09884R1

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==== Refs
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