Optimized Power Management Approach for Photovoltaic Systems with Hybrid Battery-Supercapacitor Storage

Round 1

Reviewer 1 Report

The paper explores utilizing a hybrid battery-SuperCap for PV plants.

 

1. The abstract should be more concise and specific. The algorithm used and its benefits should be clearly and quantitatively introduced.

2. Keywords should be sorted alphabetically according to the template.

3. Mass citations like [1-5] and [10-19] are frowned upon. One reference seems to be adequate for such general statements.

4. The literature review should have explored many different algorithms proposed in the past for hybrid battery-supercap applications. Only four papers are briefly discussed without proper clarification of the research gap.

5. Section 2 is just page filler and could be removed as it does not seem to be directly adding much value to the main objectives of the paper. 

6. Based on Figure 2, battery charging signal is not impacted by the PV and load power, and only based on battery's measured current and voltage. That needs to be clarified or corrected.

7.  In some parts of the paper, spaces between words are missed. There are also several grammar and formatting errors. Proofreading is highly recommended.

8. IV and PV curves provided in Figure 4 are always provided in the datasheet. There is not much research value in section 4.1.

9. Details of simulation testbench are not provided.

10. It is not clear what scenario is simulated in Figure 7. Same story for Figure 10.

11. Use subscripts for symbols like Usc or R1.

12. Table 3 does not have any references. 

13. The exact model numbers for battery and supercap are not provided.

14. The algorithm presented in Figure 11 is too simplistic and does not include losses and optimum charging value. Based on the depicted algorithm, number of charging and discharging cycles are not optimized. Also, PI-based supercap-battery hybrid energy management systems have been presented in the past. The novelty and main benefits of this work is not clear to the reviewer.

15. Figures 17-31 are presented without much introduction and discussion. 

16. Comparison with other algorithms is missing. Also, it is not clear what advantages are gained using a hybrid system based on the simulation results.

17. Experimental pictures presented are misleading as the results are based on offline or real-time simulation.

18. Use of supercaps need to be justified by their advantage as they are relatively expensive and high maintenance. Such analysis is missing in the results. For example, multiple scenarios with and without SC could be simulated to show what advantages are gained using the hybrid approach.

As mentioned earlier, space is missing in many instances.

In many cases authors need to use subscripts (RLoad, Pload, etc.)

Figures should not be broken in multiple pages.

References need to be formatted based on the template.

There are several grammar and punctuation errors. Proofreading is must.

Author Response

Response to Reviewers

Response to Reviewer 1 Comments

We agree with the reviewer's evaluation. Therefore, we've made the changes they suggested in the manuscript. Below is a detailed list of these modifications.

Point 1: The abstract should be more concise and specific. The algorithm used and its benefits should be clearly and quantitatively introduced.

Response 1

As per the suggestion of reviewer, the abstract has been improved and the change can be found in the revised manuscript.

 

Abstract: The paper addresses the ongoing and continuous interest in photovoltaic energy systems (PESs). In this context, the study focuses on an isolated photovoltaic system with hybrid battery-supercapacitor storage (HBSS). The integration of supercapacitors (SCs) in this system is particularly important because of their high specific power density. In photovoltaic (PV) systems, multi-storage systems use two or more energy storage technologies to enhance system performance and flexibility. When batteries and supercapacitors are combined in a PV system, their benefits are maximized and offer a more reliable, efficient, and cost-effective energy storage option. In addition, effective multi-storage power management in a PV system needs a solid grasp of the energy storage technologies, load power demand profiles, and the whole system architecture. This work establishes a battery-supercapacitor storage system (HBSS) by combining batteries and supercapacitors. The primary objective is to devise a novel management algorithm that effectively controls the different power sources. The algorithm's purpose is to regulate the charge and discharge cycles of the HBSS, ensuring that the state of charge (SOC) of both batteries and supercapacitors remains within the desired rangebetween a minimal and a maximal SOC values (SOC_min and SOC_max).The used control technique is based on current regulation of two energy sourcesthrought the use ofproportional integral (PI)regulators. The proposed management algorithm is designed to be simple, efficient, and light on computational resources. It efficiently handles the energy flow within the HBSS, optimizing the usage of both batteries and supercapacitors based on real-time conditions and energy demands. The proposed method ensures their longevity and maximizes their performance by maintaining the SOC of these energy storage components within the specified limits. Simulation results obtained from applying the management strategy are found to be satisfactory. These results show that the proposed algorithm maintains the SOC of batteries and supercapacitors within the desired range,between SOC_min and SOC_maxleading to improved energy management and enhanced system efficiency.The finding swore verified by simulation with MATLAB/Simulink, and they we reals out to the test in real-time with the RT LAB simulation platform

 

The algorithm used and its details are explained in section 5.

 

Point 2:Keywords should be sorted alphabetically according to the template.

Response 2:Thank you for your exact remark. In the revised version of the manuscript, we have sorted the keywords alphabetically as per the template

 Keywords: Batteries; Hybrid energy storage; Photovoltaic; Power management control; Supercapacitor.

Point 3:Mass citations like [1-5] and [10-19] are frowned upon. One reference seems to be adequate for such general statements.

Response 3

Thank you for your exact remark. In the revised version of the manuscript, we have corrected it.

Point 4:. The literature review should have explored many different algorithms proposed in the past for hybrid battery-supercap applications. Only four papers are briefly discussed without proper clarification of the research gap.

Response 4

• We think this is a good suggestion. We have added a section (section 2) devoted to a Brief state of art by adding discussions based on other previously work. Also a paragraph in added in the introduction.

 

SCs are compared to other storage devices [20-22], and the benefits of hybrid PV-battery SCs systems are examined in the literature [23, 24]. In addition, some research [25-27] propose hybrid energy storage systems (HESS) such as PV-battery supercapacitors or fuel cells as a potential approach. Most studies focus on load control and demand sharing with these hybrid systems.

 

2. Brief state of art

Their inherent fluctuations generally limit the use of photovoltaic energy source, and demand changes often occur independently of the availability of such sources. A solution to overcome these limitations, particularly in remote locations, is to employ hybrid systems with multiple sources with storage or with multi storage [33]. The different components of these systems are interconnected using different architectures, and to obtain the maximum power output from the photovoltaic generator, the Maximum Power Point Tracking (MPPT) technique is applied. The MPPT controllers track the Maximum Power Point (MPP) of the electrical characteristic curve of the energy solar source, ensuring that the solar panels operate at their most efficient point, resulting in a higher overall power output from the system. Despite working towards the same objective of enhancing the power output, each controller behaves differently.  Power flow (PF), power management control (PMC), or energy management control (EMC) are used to manage the various powers. These techniques depend on the kind of energy system and its constituent parts. Additionally, it coordinates the various sources, making the power or energy generated controllable. These control strategies have been investigated in many publications. We cannot cite all the articles, but some have supported and contributed significantly to scientific research. While the technologies used in each differ, most applications remain around isolated systems for electrification [34, 35], microgrids [36, 37], as well as multi-storage in traction and electric vehicles [38, 39]. Also, most of the works focus on simulation, implementation, economic study, optimization, analysis, and environment. The focus is mainly on controlling the different sources' powers, while supplying the load and protecting the storage system.

Several algorithms can address this problem in the literature [38-43] and [44-54]. Some EMs methods use "if-else" statements in the decision algorithms [40] or on linear controllers as in [39]. Others use more intelligent [41] and predictive methods [36, 37], [42, 43]. But, all the energy management strategies (EMS) determine the output powers of each source that are sent to the control system comprising the different converters and follow the power flow while protecting the storage systems used. In their review paper, Olatomiwa, L et al. [44] have conducted a comprehensive review on Energy management strategies in hybrid renewable energy system, with some details on Energy management strategies based on fuzzy logic systems. In paper [45], authors have reviewed the various methods to use the excess energy in renewable systems, which generally are not used and can damage the battery or be sent to dump loads. They present the different methods for this purpose to improve operation without any additional cost. In another study [46] the EMS is developed as a non-linear model predictive control strategy to extract the optimal control signals. The application has been made to standalone DC Micro grids (Wind turbine/PV with battery storage). This method allows to obtain optimal values, a reasonable simulation time and increases battery life and by removing dump loads, the overall installation cost has been decreased. Meng et al. [47] have summarized the main control objectives of supervisors and the different energy management methods used for microgrids (MG) and conclude that the energy management of MGs is in fact a multi-objective and multi-disciplinary topic dealing not only with electrical aspects but also with economic and ecological considerations. Another study [48] revealed that energy management optimization is combined with sizing algorithms to minimize system cost. Artificial intelligence methods have been widely used in supervising renewable energy systems. For example, in [49], the authors propose a hybrid renewable energy system based on grid integrated storage systems. Fuzzy controllers have been considered in the methodology for optimizing and designing the control energy management strategy. And in [50], the purpose of the fuzzy logic control was to regulate the overall power supply of the flow system while maintaining the state of the charging battery. In our laboratory, an EMC strategy has been proposed in 2015. First, it was applied to electric vehicle (EV) [51-53] to manage hybrid storage (battery/PEM Fuel cells) without using power optimization but by taking account and manage the excess power by using a multi objective algorithm. Then, the strategy has been applied to multi-sources pumping system [54].

 

Point 5: Section 2 is just page filler and could be removed as it does not seem to be directly adding much value to the main objectives of the paper. 

Response 5

The reviewer is right, and we have made the suggested modification bydeleting the section2.

It is replaced by section 2 and 3

3. Outline of paper

In this regard, this research aims to enhance the performance of a standalone photovoltaic system with multi storage (batteries/Supercapacities). The strategy considers the state-of-charge (SOC) and charging/discharging current of the batteries and SCs for SOC balancing-based power sharing through power converters. The batteries and SCs and PV systems are linked to DC bus via DC-DC converters, which enable improving the dynamic efficiencies of the system through the regulation of batteries and SCs charging/discharging as a function of the EMS provided when the system is exposed to variable perturbations. This paper's main contribution is providing simple implementations of power flow management regarding optimal energy flow between PV system, batteries and SCs system, and load. Balancing between minimal energy flows through the connecting line with minimal requirements of batteries and SCs capacity is kept. The real-time simulation/experimentation that uses Matlab/Simulink and RTlab is realized to validate the effectiveness of the developed EMS and control approach by comparing the results with other authors.

The rest of this article is organized as follows: Proposed PV hybrid storage system are defined in Section 4. Section 5 presents parameters identification and modelling of the different subcomponents. Section 6 is devoted to the proposed power management strategy. The studied system is simulated under MATLAB/Simulink to verify the suggested control and energy management technique. The findings are presented in section 7. On a real-time simulator (RT Lab), a number of experimental tests were carried out to assess the suggested control algorithms. The step description is described in section 8, and the results are presented and compared to the simulation ones, showing the effectiveness and performance of the proposed system. Finally, the conclusion summarizing the contributions of this article is reported in Section 9.

.

Point 6: Based on Figure 2, battery charging signal is not impacted by the PV and load power, and only based on battery's measured current and voltage. That needs to be clarified or corrected.

Response 6

This figure justa bloc diagram representing the different subcomponents of the studied system. Of course, batteries are impacted by PV and load power, especially on voltage and state of charge. All this is controlled and managed in the proposed power management control (PMC). The proposed PMC's initial goal is to supply the load power requirement, and the second goal is to keep the storage charged in order to avoid blackouts and prolong battery life. The simple method enables us to manage the various sources quickly and easily and doesn’t include heavy computations.This allows us a substantial increase in PV power and reduced battery and SCs stress. Also, the association of MPPT controllers with the proposed management method and the accuracy of the sizing method used leads to improve the global system.

To make sure the system runs smoothly and effectively, these converters regulate the Flow of power. These are the load power requirements:

                                                                                                (10)

Where ∆P is the power demand variation

                                                                                            (11)

 

Point 7:  In some parts of the paper, spaces between words are missed. There are also several grammar and formatting errors. Proofreading is highly recommended.

Response 7

We have carefully revised the WHOLE manuscript and tried to avoid grammar or syntax errors. In addition, we have asked several colleagues who are skilled authors of English language papers to check the English. The modification is yellow highlighted.

Point 8:IV and PV curves provided in Figure 4 are always provided in the datasheet. There is not much research value in section 4.1.

Response 8

Thank you for your exact remark. This part is added only to validate the PV mathematical model chosen. Indeedvarious mathematical models of photovoltaic generators were developed to represent their nonlinear behavior which results from the semiconductors junctions. Thesemodels are usedto compute PV panel electrical curves, and theiraccuracy and complexity varies. Wehaveappliedtheone-diodemodel in ourresearch. Although simple, itisusefulforcharacterizingtheelectricalpropertiesof a solar generator .

Figure 2. Onediodemodel.

Thesingle-diodemodel'selectricalcurrentis [3], [25]:

                                                      (1)

   (2)

I_ph, I_d, I_sh are respectivelythephotocurrent, diodecurrent and shunt current, R_shthe shunt resistance, R_sthe serial resistance.

In fact, we have found the characteristics of the simulation and those found to be expertly close to those of the datasheets.

Point 9:Details of simulation testbench are not provided.

Response 9

Thank you for this remark. Indeed, reviewer’s comment is true and constructive.

The established experimental bench is highlighted in Fig.4. It is composed bya 80W_p panel (Table 2.), a voltmeter and an amperemeter with a variable load. The ambient temperature and solar irradiance are measured by using measurements devices.

Table.2. Parameters of the Photovoltaic Panel 80 Wp

Parameters	Values
photovoltaic power  Ppv	80 Wp
maximum current at PPM Impp	4.65 A
maximum voltage at PPM Vmpp	17.5V
short circuit currentIsc	4.95A
open circuit voltage Voc	21.9V
temperature coefficient of short-current αsc	3 mA/°C
voltage temperature coefficient of short-current Βoc	-150mV/°C

A measurement acquisition equipment was used in the lab to measure the sun radiation, and temperature(Fig.5). It is essentially composed of sensors in order to transfer the different signals to a data processing interface and then to a PC where they will be displayed using ACQUIsol software in real-time.

To test the effectiveness of the proposed energy management strategy, extensive numerical simulations were carried out under Matlab/Simulink environment. Runge Kutta of 4th order is used as a solver with a step of 1e-5. The table 3 below summarizes the used simulation details

Table.3. Parametrs simulation details

Parameters	Value
D	96 days
Ts	1e-4
Solver	RK-ode4
Solver type	Fixed

 

Figure 3. Experimental test bench.

(a) I_pv=f(V_pv)

(b) P_pv=f(V_pv)

Figure 4. Electrical characteristics.

Figure.5 Measurement acquisition device at the laboratory

The fpur days corresponding to different periods of the year (winter, spring,  summer and automn) are given in the fllowing figure (Fig 6).

• day 1 (b) day 2
• day 3 (d) day 4

Figure 6.Measured four profiles during 2022 year

 

 

Point 10:. It is not clear what scenario is simulated in Figure 7. Same story for Figure 10.

Response 10

Thank you for your interesting comment. In figures 7 and 10, we have identified supercapacitor equivalent series resistance and its capacitance.Measured values have been incorporated in the simulation to obtain more realistic results.

Point 11:Use subscripts for symbols like Usc or R1.

Response 11

Thank you for this remark. It is corrected.

U_scand R₁.

Point 12:. Table 3 does not have any references. 

Response 12

Thank you for this remark. It is added.

Point 13:. The exact model numbers for battery and supercap are not provided.

Response 13

We have used 12 panels of 80 Wp (table 1), 02 batteries in series of 12 V, 110 Ah and 01 supercapacitor.

Point 14:. The algorithm presented in Figure 11 is too simplistic and does not include losses and optimum charging value. Based on the depicted algorithm, number of charging and discharging cycles are not optimized. Also, PI-based supercap-battery hybrid energy management systems have been presented in the past. The novelty and main benefits of this work is not clear to the reviewer.

Response 14

Thank you for this remark. More details and explanations on the proposed algorithm have been added in section 5.

5. Proposed Power management control

Two DC/DC convertersthat are set up as buck-boostconverters are employedbythepowermanagementsystem, whichalsoemploys a powerflow control method. Tomakesurethatthesystemrunssmoothly and effectively, theseconvertersregulatethe Flow ofpower. These are the load powerrequirements:

                                                                (10)

Where ∆P is the powerdemand variation

                                                                                     (11)

The system operation is as follow The two storage batteries and SCs can generally function in either charge or discharge mode, depending on the state of power availability-requirement between the PV and load. The prolonged power unbalancing in the PV-storage system may allow the storage deep discharging or over-charging. To extend the lifetime of the storage system and fully utilize the PV power generation, the operating modes of the PV with batteries/SCs system can be divided into three modes: the operation with fully charged mode, the operation with normal-charging/discharging of batteries and SCs (normal mode) and operation with full-charge/discharge of batteries and SCs (transient mode).

1-Fully charged mode (FCM):

In this scenario, appear only two modes M1 and M2.

M1: We disconnected the batteries because they are fully charged.

                                                                                (12)

M2: We disconnected the supercapacitors because they are fully charged.

                                                                                     (13)

2-Normal mode:

In this scenario, there is two cases. The first one is the charge mode where appear three modes M4, M5 and M6, where the excess power is used to charge the batteries and SCs. The second case is a discharge mode with only two modes M3 and M11, where the batteries and supercapacitors are disconnected to protect them as the load is powered by PV power.

a-Charge mode(CM):PV power output is higher than the power load requirement. We have three modes M4, M5 and M6.

M4: The generated photovoltaic power will be used to supply the load since it is greater than what is needed by the load. The extra power is used to charge the batteries.

                                                                             (14)

M5 : The generated photovoltaic electricity will be used to supply the load because it is greater than the load power. The extra power is used to charge the SCs.

                                                                   (15)

M6: PV powers the load, and any extra power is sent to charge the batteries and supercapacitors

                                                    (16)

b-Discharge mode (DM):

M3: When the batteries and supercapacitors are discharged, the algorithm intervenes to avoid the batteries and SCs deep discharging, and the low-priority load can be disconnected them to preserve power balance and DC bus stability as the load is powered by PV power.

                                                                    (17)

M11: The PV could not supply the load, which can be very low or null, and we disconnected the batteries and SCs because of their low levels of SOC.

                                                                    (18)

3-Transient mode (TM): We have four modes M7, M8, M9, M10 and M11.

M7: The batteries are charged; the load is supplied since  and the photovoltaic power is zero.

                                                                     (19)

M8: As long as the batteries are charged, since the PV power is not zero, they will fill up the power gap and supply the load by compensation.

                                                                    (20)

M9: Since there is no PV power in this scenario, charged SCs will be used to fed the load.

                                                                          (21)

M10:Since the , SCs can, provide energy compensating the deficit of the PV power which not sufficient to supply alone the load.

                                                                           (22)

Recharging/discharging of the batteries and supercapacitors stops when they are fully charged/discharged. The eleven possible modes are shown in Table 7. The flowchart (Fig. 13) shows how it works.

Table 7. The different possible modes.

M1	M2	M3
M4	M5	M6
M7	M8	M9
	M10	M11

 

 

Figure 13. Photovoltaic system energy management flowchart.

It is worth mentioning that the proposed energy management strategy has eleven different modes and this increases the HESS system reliability and reduces the stress applied on the batteries.

Point 15:. Figures 17-31 are presented without much introduction and discussion. 

Response 15

As suggested by the reviewer, the results and discussion sections have been improved to better express the results obtained.

7. Simulation results

The studied system is simulated under MATLAB/Simulink to verify the suggested control and energy management technique. The simulation's findings have been presented and analysed. The measured profiles of solar irradiation and ambient temperature are respectively given in Fig.14 and Fig.15. DC bus voltage tracks well its reference (Fig.16). It is regulated in the desired value and remains at its reference (V_DCref=24 V); with low fluctuations ((ΔV=0.98<1%). In conclusion, the voltage V_DCreffulfills the load demands with high control efficiency. The well-performing V_DCref enables correct functioning in the PV/Batteries/SCs system, where the power balance is achieved. This result demonstrates the voltage loop effectiveness in DC bus regulation and indicate the effectiveness of DC bus voltage regulation that contributes to the optimal performance of the suggested PMC. Figure.17 presents the simulated voltage profiles of the battery and supercapacitor over time. The batteries and SCs voltage vary in accordance with the power absorbed/injected into the DC bus. Monitoring these voltage profiles is crucial to ensure that the energy storage components are appropriately charged and discharged. Proper voltage control helps maximize the efficiency and lifespan of the energy storage system.The study demonstrates the practical application of the proposed control and energy management technique by presenting these simulation results and profiles. Analysing these outcomes allows researchers to evaluate how well the suggested approach performs under varying environmental conditions and dynamic system behaviour. It also provides insights into the system's response to different inputs and perturbations, helping validate the effectiveness of the control strategy and its ability to manage the energy storage system efficiently.

It is shown in Fig.18 that battery SOC is well controlled and maintained between 82.85%and 90% while supercapacitor SOC varies between 58.05 % and 90 %. The batteries and SCs SOCs are kept within bounds, regardless of the variations in PV and load power profiles. We have conducted a simulation comparing two scenarios: one with only battery storage and another with a hybrid storage system incorporating both batteries and supercapacitors (SCs). Based on your simulation results (specifically shown in Figure 19a and 19b), we have observed that introducing supercapacitors in the storage system led to a reduction in stress on the batteries. In the scenario with only battery storage, the SOC started at 75% and decreased over time.However, when supercapacitors and a well-implemented control loop were introduced in the system, the battery SOC remained relatively constant and reached a minimum value of 82.85%. This suggests that adding supercapacitors helped regulate the battery SOC and prevent it from dropping significantly.In the battery-only scenario, the battery voltage likely fluctuated as the SOC decreased, which is typical behavior for batteries.The battery voltage remained relatively stable with some fluctuations with the hybrid storage setup including supercapacitors and a control loop. This stability indicates that the supercapacitors might be assisting in maintaining a steady voltage level, contributing to more consistent system performance.

Figure 20 shown below points out the battery and supercapacitor currents. The different resulting modes are given in the Fig.21. During each cycle, batteries and SCs are discharged and then rapidly recharged at M4 and M6 modes (for batteries and at M5 and M6 for SCs). The only cases of disconnection are during M3 where P=0 but the load is supplied entirely by the PV, and during M11 where the load is disconnected.

The battery, supercapacitor and the PV powers are simultaneously depicted in Fig.22. The power per day of all power sources corresponding to four distinct days are shown in Fig.23. The PV power varies in accordance with the solar irradiance profile. The curve of maximum available PV power coincides with solar irradiance variation, despite the fluctuations of load requirements, which validates the proposed MPPT. Battery and SC powers are shown in negative to better illustrate their discharges with regard to PV and load variations.It is worth noting that the negative sign of the batteries and SCs powers means that they are recovering the power and the positive sign impliesthat they are supplying the load. They change its path (sign) from charging mode to discharging mode to assist the PV source in meeting the load power during the load increase. During the first day (Fig.23 a), when solar irradiance is very low and does not exceed 200W/m², the battery is highly stressed and is supported by the SC during sudden changes in load (at t=6, 7, 11 and 18 h). The most frequent modes are M7, M8, M9 and M10, as DP is always negative. On the second day (Fig.23 b), when maximum solar irradiation is around 460 W/m², the same observations were made, with slightly less stress on the batteries, assisted by the Sc, at times of abrupt load changes (t=31 and 41 h). On the third day (Fig.23 c), solar irradiance reached 620 W/m², and up to 740 W/m² on the fourth day. On these last two days, we note less stress on the batteries and the presence of modes M4 and M5, corresponding to battery and SC charging.

We can conclude that the proposed control strategy distributes the load power dynamically effectively between different system units. PMC approach correctly ensures the power-sharing between the various sources (PV, batteries and SCs) and load demand. Furthermore, the proposed PMC technique is very efficient in terms of mode changes in accordance with the operating constraints. The reference load power and the sum of power developed by all the power sources are respectively shown in Fig 24. The zoom of this last-mentioned figure for four distinct days is shown in Fig 25.

 

Point 16:. Comparison with other algorithms is missing. Also, it is not clear what advantages are gained using a hybrid system based on the simulation results.

Response 16

As suggested by the reviewer, comparisons with other works and algorihms are added.

There are several algorithms that can address this problem in the literature [38-43] and [44-54]. Some EMs methods use "if-else" statements in the decision algorithms [40] or on linear controllers as in [39]. Others use more intelligent [41] and predictive methods [36, 37], [42, 43]. But, all the energy management strategies (EMS) determine the output powers of each source that are sent to the control system comprising the different converters and follow the power flow while protecting the storage systems used. In their review paper, Olatomiwa, L et al. [44] have conducted a comprehensive review on Energy management strategies in hybrid renewable energy system, with some details on Energy management strategies based on fuzzy logic systems. In paper [45], authors have reviewed the various methods to use the excess energy in renewable systems, which generally are not used and can damage the battery or be sent to dump loads. They present the different methods for this purpose to improve operation without any additional cost. In another study [46] the EMS is developed as a non-linear model predictive control strategy to extract the optimal control signals. The application has been made to standalone DC Micro grids (Wind turbine/PV with battery storage). This method allows to obtain optimal values, a reasonable simulation time and increases battery life and by removing dump loads, the overall installation cost has been decreased. Meng et al. [47] have summarized the main control objectives of supervisors and the different energy management methods used for microgrids (MG) and conclude that the energy management of MGs is in fact a multi-objective and multi-disciplinary topic dealing not only with electrical aspects but also with economic and ecological considerations. Another study [48] revealed that energy management optimization is combined with sizing algorithms to minimize system cost. Artificial intelligence methods have been widely used in supervising renewable energy systems. For example, in [49], the authors propose a hybrid renewable energy system based on grid integrated storage systems. Fuzzy controllers have been considered in the methodology for optimizing and designing the control energy management strategy. And in [50], the purpose of the fuzzy logic control was to regulate the overall power supply of the flow system while maintaining the state of the charging battery. In our laboratory, an EMC strategy has been proposed in 2015. First, it was applied to electric vehicle (EV) [51-53] to manage hybrid storage (battery/PEM Fuel cells) without using power optimization but by taking account and manage the excess power by using a multi objective algorithm. Then, the strategy has been applied to multi-sources pumping system [54].

 

Point 17:Experimental pictures presented are misleading as the results are based on offline or real-time simulation.

Response 17

Thank you for this remark

A comparison has been made to validate that the proposed mathematical model is correct and of course to show that the suggested system is feasible under various solar irradiance variations and load power variations.

 

Point 18:. Use of supercapsneed to be justified by their advantage as they are relatively expensive and high maintenance. Such analysis is missing in the results. For example, multiple scenarios with and without SC could be simulated to show what advantages are gained using the hybrid approach.

Response 18

Thank you for this remark

The various scenarios are explained in table 7. The SCs are solicited only during the modes M9 and M10.

For more details a simulation is made in the two cases with and without the introduction of the SCs and the obtained results are as follows:

We have conducted a simulation comparing two scenarios: one with only battery storage and another with a hybrid storage system incorporating both batteries and supercapacitors (SCs). Based on your simulation results (specifically shown in Figure 19a and 19b), we have observed that introducing supercapacitors in the storage system led to a reduction in stress on the batteries. In the scenario with only battery storage, the SOC started at 75% and continued to decrease over time.However, when supercapacitors and a well-implemented control loop were introduced in the system, the battery SOC remained relatively constant and reached a minimum value of 82.85%. This suggests that the addition of supercapacitors helped regulate the battery SOC and prevent it from dropping significantly.In the battery-only scenario, the battery voltage likely exhibited fluctuations as the SOC decreased, which is typical behavior for batteries.The battery voltage remained relatively stable with some fluctuations with the hybrid storage setup including supercapacitors and a control loop. This stability indicates that the supercapacitors might be assisting in maintaining a steady voltage level, contributing to more consistent system performance.

(a) Battery SOC

(b) Voltage battery

Figure 19. Battery SOC and voltage with and without introduction of supercapacitors

 

Comments on the Quality of English Language

 

Response

We have revised the WHOLE manuscript carefully and tried to avoid any grammar or syntax error. In addition, we have asked several colleagues who are skilled authors of English language papers to check the English.

 

As mentioned earlier, space is missing in many instances.

Response

It was corrected

In many cases authors need to use subscripts (RLoad, Pload, etc.)

Response

It was corrected

Figures should not be broken in multiple pages.

Response

It was corrected

References need to be formatted basedon the template.

Response

It was corrected.

References

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There are several grammar and punctuation errors. Proofreading is must.

Response

All spelling and grammatical errors pointed out by the reviewers have been corrected.

 

We look forward to hearing from you in due time regarding our submission and to respond to any further questions and comments you may have.

Sincerely,

 

Author Response File: Author Response.pdf

Reviewer 2 Report

This paper basically has attempted to investigate Optimized Power Management Approach for Photovoltaic Systems with Hybrid Battery-Supercapacitor Storage. Following are some my suggestions for the improvement of this submission!

1. The introduction part can be made more comprehensive and a detailed information regarding the subject can be provided so the readers can have a better idea regarding this subject of research. The authors can take help and cite the following papers to enhance the quality of this submission!

a)https://doi.org/10.3390/en16020609 b) https://doi.org/10.1177/0734242X221127175

2. The line 1 of the introduction, citation style is not according to the Journal guidelines.

3. A research gap should be identified clearly and should be mentioned accordingly in the submission.

3. Explanation of results requires a detailed check to explain the results well for the understanding of the readers, it can be read again and corrected. Multiple sentences does not make a clear meaning.

4. A detail conclusion should be given, multiple concluding remarks are missing. Future research directions can also be incorporated. 

5. English of this manuscript can be improved. 

English of this manuscript can be improved particularly in the result explanation part of the submission.

Author Response

Response to Reviewer 1 Comments

We agree with the reviewer's evaluation. Therefore, we've made the changes they suggested in the manuscript. Below is a detailed list of these modifications.

Point 1: The abstract should be more concise and specific. The algorithm used and its benefits should be clearly and quantitatively introduced.

Response 1

As per the suggestion of reviewer, the abstract has been improved and the change can be found in the revised manuscript.

 

Abstract: The paper addresses the ongoing and continuous interest in photovoltaic energy systems (PESs). In this context, the study focuses on an isolated photovoltaic system with hybrid battery-supercapacitor storage (HBSS). The integration of supercapacitors (SCs) in this system is particularly important because of their high specific power density. In photovoltaic (PV) systems, multi-storage systems use two or more energy storage technologies to enhance system performance and flexibility. When batteries and supercapacitors are combined in a PV system, their benefits are maximized and offer a more reliable, efficient, and cost-effective energy storage option. In addition, effective multi-storage power management in a PV system needs a solid grasp of the energy storage technologies, load power demand profiles, and the whole system architecture. This work establishes a battery-supercapacitor storage system (HBSS) by combining batteries and supercapacitors. The primary objective is to devise a novel management algorithm that effectively controls the different power sources. The algorithm's purpose is to regulate the charge and discharge cycles of the HBSS, ensuring that the state of charge (SOC) of both batteries and supercapacitors remains within the desired rangebetween a minimal and a maximal SOC values (SOC_min and SOC_max).The used control technique is based on current regulation of two energy sourcesthrought the use ofproportional integral (PI)regulators. The proposed management algorithm is designed to be simple, efficient, and light on computational resources. It efficiently handles the energy flow within the HBSS, optimizing the usage of both batteries and supercapacitors based on real-time conditions and energy demands. The proposed method ensures their longevity and maximizes their performance by maintaining the SOC of these energy storage components within the specified limits. Simulation results obtained from applying the management strategy are found to be satisfactory. These results show that the proposed algorithm maintains the SOC of batteries and supercapacitors within the desired range,between SOC_min and SOC_maxleading to improved energy management and enhanced system efficiency.The finding swore verified by simulation with MATLAB/Simulink, and they we reals out to the test in real-time with the RT LAB simulation platform

 

The algorithm used and its details are explained in section 5.

 

Point 2:Keywords should be sorted alphabetically according to the template.

Response 2:Thank you for your exact remark. In the revised version of the manuscript, we have sorted the keywords alphabetically as per the template

 Keywords: Batteries; Hybrid energy storage; Photovoltaic; Power management control; Supercapacitor.

Point 3:Mass citations like [1-5] and [10-19] are frowned upon. One reference seems to be adequate for such general statements.

Response 3

Thank you for your exact remark. In the revised version of the manuscript, we have corrected it.

Point 4:. The literature review should have explored many different algorithms proposed in the past for hybrid battery-supercap applications. Only four papers are briefly discussed without proper clarification of the research gap.

Response 4

• We think this is a good suggestion. We have added a section (section 2) devoted to a Brief state of art by adding discussions based on other previously work. Also a paragraph in added in the introduction.

 

SCs are compared to other storage devices [20-22], and the benefits of hybrid PV-battery SCs systems are examined in the literature [23, 24]. In addition, some research [25-27] propose hybrid energy storage systems (HESS) such as PV-battery supercapacitors or fuel cells as a potential approach. Most studies focus on load control and demand sharing with these hybrid systems.

 

2. Brief state of art

Their inherent fluctuations generally limit the use of photovoltaic energy source, and demand changes often occur independently of the availability of such sources. A solution to overcome these limitations, particularly in remote locations, is to employ hybrid systems with multiple sources with storage or with multi storage [33]. The different components of these systems are interconnected using different architectures, and to obtain the maximum power output from the photovoltaic generator, the Maximum Power Point Tracking (MPPT) technique is applied. The MPPT controllers track the Maximum Power Point (MPP) of the electrical characteristic curve of the energy solar source, ensuring that the solar panels operate at their most efficient point, resulting in a higher overall power output from the system. Despite working towards the same objective of enhancing the power output, each controller behaves differently.  Power flow (PF), power management control (PMC), or energy management control (EMC) are used to manage the various powers. These techniques depend on the kind of energy system and its constituent parts. Additionally, it coordinates the various sources, making the power or energy generated controllable. These control strategies have been investigated in many publications. We cannot cite all the articles, but some have supported and contributed significantly to scientific research. While the technologies used in each differ, most applications remain around isolated systems for electrification [34, 35], microgrids [36, 37], as well as multi-storage in traction and electric vehicles [38, 39]. Also, most of the works focus on simulation, implementation, economic study, optimization, analysis, and environment. The focus is mainly on controlling the different sources' powers, while supplying the load and protecting the storage system.

Several algorithms can address this problem in the literature [38-43] and [44-54]. Some EMs methods use "if-else" statements in the decision algorithms [40] or on linear controllers as in [39]. Others use more intelligent [41] and predictive methods [36, 37], [42, 43]. But, all the energy management strategies (EMS) determine the output powers of each source that are sent to the control system comprising the different converters and follow the power flow while protecting the storage systems used. In their review paper, Olatomiwa, L et al. [44] have conducted a comprehensive review on Energy management strategies in hybrid renewable energy system, with some details on Energy management strategies based on fuzzy logic systems. In paper [45], authors have reviewed the various methods to use the excess energy in renewable systems, which generally are not used and can damage the battery or be sent to dump loads. They present the different methods for this purpose to improve operation without any additional cost. In another study [46] the EMS is developed as a non-linear model predictive control strategy to extract the optimal control signals. The application has been made to standalone DC Micro grids (Wind turbine/PV with battery storage). This method allows to obtain optimal values, a reasonable simulation time and increases battery life and by removing dump loads, the overall installation cost has been decreased. Meng et al. [47] have summarized the main control objectives of supervisors and the different energy management methods used for microgrids (MG) and conclude that the energy management of MGs is in fact a multi-objective and multi-disciplinary topic dealing not only with electrical aspects but also with economic and ecological considerations. Another study [48] revealed that energy management optimization is combined with sizing algorithms to minimize system cost. Artificial intelligence methods have been widely used in supervising renewable energy systems. For example, in [49], the authors propose a hybrid renewable energy system based on grid integrated storage systems. Fuzzy controllers have been considered in the methodology for optimizing and designing the control energy management strategy. And in [50], the purpose of the fuzzy logic control was to regulate the overall power supply of the flow system while maintaining the state of the charging battery. In our laboratory, an EMC strategy has been proposed in 2015. First, it was applied to electric vehicle (EV) [51-53] to manage hybrid storage (battery/PEM Fuel cells) without using power optimization but by taking account and manage the excess power by using a multi objective algorithm. Then, the strategy has been applied to multi-sources pumping system [54].

 

Point 5: Section 2 is just page filler and could be removed as it does not seem to be directly adding much value to the main objectives of the paper. 

Response 5

The reviewer is right, and we have made the suggested modification bydeleting the section2.

It is replaced by section 2 and 3

3. Outline of paper

In this regard, this research aims to enhance the performance of a standalone photovoltaic system with multi storage (batteries/Supercapacities). The strategy considers the state-of-charge (SOC) and charging/discharging current of the batteries and SCs for SOC balancing-based power sharing through power converters. The batteries and SCs and PV systems are linked to DC bus via DC-DC converters, which enable improving the dynamic efficiencies of the system through the regulation of batteries and SCs charging/discharging as a function of the EMS provided when the system is exposed to variable perturbations. This paper's main contribution is providing simple implementations of power flow management regarding optimal energy flow between PV system, batteries and SCs system, and load. Balancing between minimal energy flows through the connecting line with minimal requirements of batteries and SCs capacity is kept. The real-time simulation/experimentation that uses Matlab/Simulink and RTlab is realized to validate the effectiveness of the developed EMS and control approach by comparing the results with other authors.

The rest of this article is organized as follows: Proposed PV hybrid storage system are defined in Section 4. Section 5 presents parameters identification and modelling of the different subcomponents. Section 6 is devoted to the proposed power management strategy. The studied system is simulated under MATLAB/Simulink to verify the suggested control and energy management technique. The findings are presented in section 7. On a real-time simulator (RT Lab), a number of experimental tests were carried out to assess the suggested control algorithms. The step description is described in section 8, and the results are presented and compared to the simulation ones, showing the effectiveness and performance of the proposed system. Finally, the conclusion summarizing the contributions of this article is reported in Section 9.

.

Point 6: Based on Figure 2, battery charging signal is not impacted by the PV and load power, and only based on battery's measured current and voltage. That needs to be clarified or corrected.

Response 6

This figure justa bloc diagram representing the different subcomponents of the studied system. Of course, batteries are impacted by PV and load power, especially on voltage and state of charge. All this is controlled and managed in the proposed power management control (PMC). The proposed PMC's initial goal is to supply the load power requirement, and the second goal is to keep the storage charged in order to avoid blackouts and prolong battery life. The simple method enables us to manage the various sources quickly and easily and doesn’t include heavy computations.This allows us a substantial increase in PV power and reduced battery and SCs stress. Also, the association of MPPT controllers with the proposed management method and the accuracy of the sizing method used leads to improve the global system.

To make sure the system runs smoothly and effectively, these converters regulate the Flow of power. These are the load power requirements:

                                                                                                (10)

Where ∆P is the power demand variation

                                                                                            (11)

 

Point 7:  In some parts of the paper, spaces between words are missed. There are also several grammar and formatting errors. Proofreading is highly recommended.

Response 7

We have carefully revised the WHOLE manuscript and tried to avoid grammar or syntax errors. In addition, we have asked several colleagues who are skilled authors of English language papers to check the English. The modification is yellow highlighted.

Point 8:IV and PV curves provided in Figure 4 are always provided in the datasheet. There is not much research value in section 4.1.

Response 8

Thank you for your exact remark. This part is added only to validate the PV mathematical model chosen. Indeedvarious mathematical models of photovoltaic generators were developed to represent their nonlinear behavior which results from the semiconductors junctions. Thesemodels are usedto compute PV panel electrical curves, and theiraccuracy and complexity varies. Wehaveappliedtheone-diodemodel in ourresearch. Although simple, itisusefulforcharacterizingtheelectricalpropertiesof a solar generator .

Figure 2. Onediodemodel.

Thesingle-diodemodel'selectricalcurrentis [3], [25]:

                                                      (1)

   (2)

I_ph, I_d, I_sh are respectivelythephotocurrent, diodecurrent and shunt current, R_shthe shunt resistance, R_sthe serial resistance.

In fact, we have found the characteristics of the simulation and those found to be expertly close to those of the datasheets.

Point 9:Details of simulation testbench are not provided.

Response 9

Thank you for this remark. Indeed, reviewer’s comment is true and constructive.

The established experimental bench is highlighted in Fig.4. It is composed bya 80W_p panel (Table 2.), a voltmeter and an amperemeter with a variable load. The ambient temperature and solar irradiance are measured by using measurements devices.

Table.2. Parameters of the Photovoltaic Panel 80 Wp

Parameters	Values
photovoltaic power  Ppv	80 Wp
maximum current at PPM Impp	4.65 A
maximum voltage at PPM Vmpp	17.5V
short circuit currentIsc	4.95A
open circuit voltage Voc	21.9V
temperature coefficient of short-current αsc	3 mA/°C
voltage temperature coefficient of short-current Βoc	-150mV/°C

A measurement acquisition equipment was used in the lab to measure the sun radiation, and temperature(Fig.5). It is essentially composed of sensors in order to transfer the different signals to a data processing interface and then to a PC where they will be displayed using ACQUIsol software in real-time.

To test the effectiveness of the proposed energy management strategy, extensive numerical simulations were carried out under Matlab/Simulink environment. Runge Kutta of 4th order is used as a solver with a step of 1e-5. The table 3 below summarizes the used simulation details

Table.3. Parametrs simulation details

Parameters	Value
D	96 days
Ts	1e-4
Solver	RK-ode4
Solver type	Fixed

 

Figure 3. Experimental test bench.

(a) I_pv=f(V_pv)

(b) P_pv=f(V_pv)

Figure 4. Electrical characteristics.

Figure.5 Measurement acquisition device at the laboratory

The fpur days corresponding to different periods of the year (winter, spring,  summer and automn) are given in the fllowing figure (Fig 6).

• day 1 (b) day 2
• day 3 (d) day 4

Figure 6.Measured four profiles during 2022 year

 

 

Point 10:. It is not clear what scenario is simulated in Figure 7. Same story for Figure 10.

Response 10

Thank you for your interesting comment. In figures 7 and 10, we have identified supercapacitor equivalent series resistance and its capacitance.Measured values have been incorporated in the simulation to obtain more realistic results.

Point 11:Use subscripts for symbols like Usc or R1.

Response 11

Thank you for this remark. It is corrected.

U_scand R₁.

Point 12:. Table 3 does not have any references. 

Response 12

Thank you for this remark. It is added.

Point 13:. The exact model numbers for battery and supercap are not provided.

Response 13

We have used 12 panels of 80 Wp (table 1), 02 batteries in series of 12 V, 110 Ah and 01 supercapacitor.

Point 14:. The algorithm presented in Figure 11 is too simplistic and does not include losses and optimum charging value. Based on the depicted algorithm, number of charging and discharging cycles are not optimized. Also, PI-based supercap-battery hybrid energy management systems have been presented in the past. The novelty and main benefits of this work is not clear to the reviewer.

Response 14

Thank you for this remark. More details and explanations on the proposed algorithm have been added in section 5.

5. Proposed Power management control

Two DC/DC convertersthat are set up as buck-boostconverters are employedbythepowermanagementsystem, whichalsoemploys a powerflow control method. Tomakesurethatthesystemrunssmoothly and effectively, theseconvertersregulatethe Flow ofpower. These are the load powerrequirements:

                                                                (10)

Where ∆P is the powerdemand variation

                                                                                     (11)

The system operation is as follow The two storage batteries and SCs can generally function in either charge or discharge mode, depending on the state of power availability-requirement between the PV and load. The prolonged power unbalancing in the PV-storage system may allow the storage deep discharging or over-charging. To extend the lifetime of the storage system and fully utilize the PV power generation, the operating modes of the PV with batteries/SCs system can be divided into three modes: the operation with fully charged mode, the operation with normal-charging/discharging of batteries and SCs (normal mode) and operation with full-charge/discharge of batteries and SCs (transient mode).

1-Fully charged mode (FCM):

In this scenario, appear only two modes M1 and M2.

M1: We disconnected the batteries because they are fully charged.

                                                                                (12)

M2: We disconnected the supercapacitors because they are fully charged.

                                                                                     (13)

2-Normal mode:

In this scenario, there is two cases. The first one is the charge mode where appear three modes M4, M5 and M6, where the excess power is used to charge the batteries and SCs. The second case is a discharge mode with only two modes M3 and M11, where the batteries and supercapacitors are disconnected to protect them as the load is powered by PV power.

a-Charge mode(CM):PV power output is higher than the power load requirement. We have three modes M4, M5 and M6.

M4: The generated photovoltaic power will be used to supply the load since it is greater than what is needed by the load. The extra power is used to charge the batteries.

                                                                             (14)

M5 : The generated photovoltaic electricity will be used to supply the load because it is greater than the load power. The extra power is used to charge the SCs.

                                                                   (15)

M6: PV powers the load, and any extra power is sent to charge the batteries and supercapacitors

                                                    (16)

b-Discharge mode (DM):

M3: When the batteries and supercapacitors are discharged, the algorithm intervenes to avoid the batteries and SCs deep discharging, and the low-priority load can be disconnected them to preserve power balance and DC bus stability as the load is powered by PV power.

                                                                    (17)

M11: The PV could not supply the load, which can be very low or null, and we disconnected the batteries and SCs because of their low levels of SOC.

                                                                    (18)

3-Transient mode (TM): We have four modes M7, M8, M9, M10 and M11.

M7: The batteries are charged; the load is supplied since  and the photovoltaic power is zero.

                                                                     (19)

M8: As long as the batteries are charged, since the PV power is not zero, they will fill up the power gap and supply the load by compensation.

                                                                    (20)

M9: Since there is no PV power in this scenario, charged SCs will be used to fed the load.

                                                                          (21)

M10:Since the , SCs can, provide energy compensating the deficit of the PV power which not sufficient to supply alone the load.

                                                                           (22)

Recharging/discharging of the batteries and supercapacitors stops when they are fully charged/discharged. The eleven possible modes are shown in Table 7. The flowchart (Fig. 13) shows how it works.

Table 7. The different possible modes.

M1	M2	M3
M4	M5	M6
M7	M8	M9
	M10	M11

 

 

Figure 13. Photovoltaic system energy management flowchart.

It is worth mentioning that the proposed energy management strategy has eleven different modes and this increases the HESS system reliability and reduces the stress applied on the batteries.

Point 15:. Figures 17-31 are presented without much introduction and discussion. 

Response 15

As suggested by the reviewer, the results and discussion sections have been improved to better express the results obtained.

7. Simulation results

The studied system is simulated under MATLAB/Simulink to verify the suggested control and energy management technique. The simulation's findings have been presented and analysed. The measured profiles of solar irradiation and ambient temperature are respectively given in Fig.14 and Fig.15. DC bus voltage tracks well its reference (Fig.16). It is regulated in the desired value and remains at its reference (V_DCref=24 V); with low fluctuations ((ΔV=0.98<1%). In conclusion, the voltage V_DCreffulfills the load demands with high control efficiency. The well-performing V_DCref enables correct functioning in the PV/Batteries/SCs system, where the power balance is achieved. This result demonstrates the voltage loop effectiveness in DC bus regulation and indicate the effectiveness of DC bus voltage regulation that contributes to the optimal performance of the suggested PMC. Figure.17 presents the simulated voltage profiles of the battery and supercapacitor over time. The batteries and SCs voltage vary in accordance with the power absorbed/injected into the DC bus. Monitoring these voltage profiles is crucial to ensure that the energy storage components are appropriately charged and discharged. Proper voltage control helps maximize the efficiency and lifespan of the energy storage system.The study demonstrates the practical application of the proposed control and energy management technique by presenting these simulation results and profiles. Analysing these outcomes allows researchers to evaluate how well the suggested approach performs under varying environmental conditions and dynamic system behaviour. It also provides insights into the system's response to different inputs and perturbations, helping validate the effectiveness of the control strategy and its ability to manage the energy storage system efficiently.

It is shown in Fig.18 that battery SOC is well controlled and maintained between 82.85%and 90% while supercapacitor SOC varies between 58.05 % and 90 %. The batteries and SCs SOCs are kept within bounds, regardless of the variations in PV and load power profiles. We have conducted a simulation comparing two scenarios: one with only battery storage and another with a hybrid storage system incorporating both batteries and supercapacitors (SCs). Based on your simulation results (specifically shown in Figure 19a and 19b), we have observed that introducing supercapacitors in the storage system led to a reduction in stress on the batteries. In the scenario with only battery storage, the SOC started at 75% and decreased over time.However, when supercapacitors and a well-implemented control loop were introduced in the system, the battery SOC remained relatively constant and reached a minimum value of 82.85%. This suggests that adding supercapacitors helped regulate the battery SOC and prevent it from dropping significantly.In the battery-only scenario, the battery voltage likely fluctuated as the SOC decreased, which is typical behavior for batteries.The battery voltage remained relatively stable with some fluctuations with the hybrid storage setup including supercapacitors and a control loop. This stability indicates that the supercapacitors might be assisting in maintaining a steady voltage level, contributing to more consistent system performance.

Figure 20 shown below points out the battery and supercapacitor currents. The different resulting modes are given in the Fig.21. During each cycle, batteries and SCs are discharged and then rapidly recharged at M4 and M6 modes (for batteries and at M5 and M6 for SCs). The only cases of disconnection are during M3 where P=0 but the load is supplied entirely by the PV, and during M11 where the load is disconnected.

The battery, supercapacitor and the PV powers are simultaneously depicted in Fig.22. The power per day of all power sources corresponding to four distinct days are shown in Fig.23. The PV power varies in accordance with the solar irradiance profile. The curve of maximum available PV power coincides with solar irradiance variation, despite the fluctuations of load requirements, which validates the proposed MPPT. Battery and SC powers are shown in negative to better illustrate their discharges with regard to PV and load variations.It is worth noting that the negative sign of the batteries and SCs powers means that they are recovering the power and the positive sign impliesthat they are supplying the load. They change its path (sign) from charging mode to discharging mode to assist the PV source in meeting the load power during the load increase. During the first day (Fig.23 a), when solar irradiance is very low and does not exceed 200W/m², the battery is highly stressed and is supported by the SC during sudden changes in load (at t=6, 7, 11 and 18 h). The most frequent modes are M7, M8, M9 and M10, as DP is always negative. On the second day (Fig.23 b), when maximum solar irradiation is around 460 W/m², the same observations were made, with slightly less stress on the batteries, assisted by the Sc, at times of abrupt load changes (t=31 and 41 h). On the third day (Fig.23 c), solar irradiance reached 620 W/m², and up to 740 W/m² on the fourth day. On these last two days, we note less stress on the batteries and the presence of modes M4 and M5, corresponding to battery and SC charging.

We can conclude that the proposed control strategy distributes the load power dynamically effectively between different system units. PMC approach correctly ensures the power-sharing between the various sources (PV, batteries and SCs) and load demand. Furthermore, the proposed PMC technique is very efficient in terms of mode changes in accordance with the operating constraints. The reference load power and the sum of power developed by all the power sources are respectively shown in Fig 24. The zoom of this last-mentioned figure for four distinct days is shown in Fig 25.

 

Point 16:. Comparison with other algorithms is missing. Also, it is not clear what advantages are gained using a hybrid system based on the simulation results.

Response 16

As suggested by the reviewer, comparisons with other works and algorihms are added.

There are several algorithms that can address this problem in the literature [38-43] and [44-54]. Some EMs methods use "if-else" statements in the decision algorithms [40] or on linear controllers as in [39]. Others use more intelligent [41] and predictive methods [36, 37], [42, 43]. But, all the energy management strategies (EMS) determine the output powers of each source that are sent to the control system comprising the different converters and follow the power flow while protecting the storage systems used. In their review paper, Olatomiwa, L et al. [44] have conducted a comprehensive review on Energy management strategies in hybrid renewable energy system, with some details on Energy management strategies based on fuzzy logic systems. In paper [45], authors have reviewed the various methods to use the excess energy in renewable systems, which generally are not used and can damage the battery or be sent to dump loads. They present the different methods for this purpose to improve operation without any additional cost. In another study [46] the EMS is developed as a non-linear model predictive control strategy to extract the optimal control signals. The application has been made to standalone DC Micro grids (Wind turbine/PV with battery storage). This method allows to obtain optimal values, a reasonable simulation time and increases battery life and by removing dump loads, the overall installation cost has been decreased. Meng et al. [47] have summarized the main control objectives of supervisors and the different energy management methods used for microgrids (MG) and conclude that the energy management of MGs is in fact a multi-objective and multi-disciplinary topic dealing not only with electrical aspects but also with economic and ecological considerations. Another study [48] revealed that energy management optimization is combined with sizing algorithms to minimize system cost. Artificial intelligence methods have been widely used in supervising renewable energy systems. For example, in [49], the authors propose a hybrid renewable energy system based on grid integrated storage systems. Fuzzy controllers have been considered in the methodology for optimizing and designing the control energy management strategy. And in [50], the purpose of the fuzzy logic control was to regulate the overall power supply of the flow system while maintaining the state of the charging battery. In our laboratory, an EMC strategy has been proposed in 2015. First, it was applied to electric vehicle (EV) [51-53] to manage hybrid storage (battery/PEM Fuel cells) without using power optimization but by taking account and manage the excess power by using a multi objective algorithm. Then, the strategy has been applied to multi-sources pumping system [54].

 

Point 17:Experimental pictures presented are misleading as the results are based on offline or real-time simulation.

Response 17

Thank you for this remark

A comparison has been made to validate that the proposed mathematical model is correct and of course to show that the suggested system is feasible under various solar irradiance variations and load power variations.

 

Point 18:. Use of supercapsneed to be justified by their advantage as they are relatively expensive and high maintenance. Such analysis is missing in the results. For example, multiple scenarios with and without SC could be simulated to show what advantages are gained using the hybrid approach.

Response 18

Thank you for this remark

The various scenarios are explained in table 7. The SCs are solicited only during the modes M9 and M10.

For more details a simulation is made in the two cases with and without the introduction of the SCs and the obtained results are as follows:

We have conducted a simulation comparing two scenarios: one with only battery storage and another with a hybrid storage system incorporating both batteries and supercapacitors (SCs). Based on your simulation results (specifically shown in Figure 19a and 19b), we have observed that introducing supercapacitors in the storage system led to a reduction in stress on the batteries. In the scenario with only battery storage, the SOC started at 75% and continued to decrease over time.However, when supercapacitors and a well-implemented control loop were introduced in the system, the battery SOC remained relatively constant and reached a minimum value of 82.85%. This suggests that the addition of supercapacitors helped regulate the battery SOC and prevent it from dropping significantly.In the battery-only scenario, the battery voltage likely exhibited fluctuations as the SOC decreased, which is typical behavior for batteries.The battery voltage remained relatively stable with some fluctuations with the hybrid storage setup including supercapacitors and a control loop. This stability indicates that the supercapacitors might be assisting in maintaining a steady voltage level, contributing to more consistent system performance.

(a) Battery SOC

(b) Voltage battery

Figure 19. Battery SOC and voltage with and without introduction of supercapacitors

 

Comments on the Quality of English Language

 

Response

We have revised the WHOLE manuscript carefully and tried to avoid any grammar or syntax error. In addition, we have asked several colleagues who are skilled authors of English language papers to check the English.

 

As mentioned earlier, space is missing in many instances.

Response

It was corrected

In many cases authors need to use subscripts (RLoad, Pload, etc.)

Response

It was corrected

Figures should not be broken in multiple pages.

Response

It was corrected

References need to be formatted basedon the template.

Response

It was corrected.

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There are several grammar and punctuation errors. Proofreading is must.

Response

All spelling and grammatical errors pointed out by the reviewers have been corrected.

 

We look forward to hearing from you in due time regarding our submission and to respond to any further questions and comments you may have.

Sincerely,

 

Author Response File: Author Response.pdf

Reviewer 3 Report

This paper deals with the ongoing and continuous interest in photovoltaic energy systems.  The manuscript is well organized and includes interesting and useful results. In the reviewer's opinion, the contents of this paper are valuable and the paper only need some following minor revisions:

 

1.      The formula (1) may wrong. Please check it.  

2.      The authors should clarify how to choice of  in (1). How is it reflected in the experimental and simulations?

3.      Discuss the computational complexity and the potential use of secondary function (5) involving secondary capacity terms as of in (5) in conservatism reduction. How the feasibility of the developed conditions in proposed power management control are ensured?

4.      Please provide the qualitative and quantitative comparison with existing works, together with simulations examples.

5.      In the simulation Fig. 16, the comparative studies between proposed method and other methods should be discussed in detail to demonstrate the effectiveness of the proposed method. How the authors selected the comparative methods and what are the reasons to select such methods?  

6.       The introduction of the manuscript should be proposed in a better way. Sometimes, adjacent phrases are not well connected. For example, " The algorithm's purpose is to regulate the charge and discharge cycles of the  HBSS, ensuring that the state of charge (SOC) of both batteries and supercapacitors remains within the desired range" is detached from previous or successive phrases. Is it a drawback to be tackled in some way?

 

7.      It seems that objective of the manuscript should be showing how to extract more performed to determine the battery impedance method. Please explain it? 

The authors should read and check the full article very carefully to correct possible grammar and spelling mistakes

Author Response

Reviewer 3

Comments and Suggestions for Authors

This paper deals with the ongoing and continuous interest in photovoltaic energy systems.  The manuscript is well organized and includes interesting and useful results. In the reviewer's opinion, the contents of this paper are valuable and the paper only need some following minor revisions:

 

Point 1:The formula (1) may wrong. Please check it.  

Response 1

Thank you for this remark. Indeed, reviewer’s comment is true and constructive.

Eq.1 is correct according to Fig.2, and we have added details in Eq.2

A.. Photovoltaic pannel modeling

A multitudeofmodels are usedto compute PV panel electrical curves. Theirlevelofaccuracy and complexity varies. Weappliedtheone-diodemodel in ourresearch [1]. Although simple, itisusefulforcharacterizingtheelectricalpropertiesof a solar generator (Fig. 2).

Figure 2. One diode model.

Thesingle-diodemodel'selectricalcurrentis[3], [25]:

                                                   (1)

            (2)

 

I_ph, I_d, I_sh are respectivelythephotocurrent, diodecurrent and shunt current, R_shthe shunt resistance, R_sthe serial resistance.

 

Point 2:The authors should clarify how to choice of ???? in (1). How is it reflected in the experimental and simulations?

 

Response 2

Thank you very much for the comment:

Theparameterrequestedbythereviewerdidnotappear. So theonlyparameters in equation 1 are thefollowing:

I_phisthephotocurrent,Itiscreated in a photovoltaiccellisproportionaltothesurfaceareaofthejunctionexposedto solar radiation;I_disdiodecurrent, I_sh is shunt current, R_shthe shunt resistance, R_sthe serial resistance.

In simulation, theusedanalytical method to find the different parametersis as follow [Ref]:

[Ref] D Rekioua, E Matagne,  Optimization of photovoltaic power systems: modelization, simulation and control,  Springer Science & Business Media,2012.

I_pv(V_pv) characteristicofthis model is given by:

ForV_pv=V_oc, I_pv=0, we have:

ForV_pv=0, I_pv=I_sc, wehave:

ReplacingIph in thisequation  byitsvalueextractedfromthepreviousone, wehave:

 

Thus

 

ForV_pv=V_ocwedefined

ForI_pv=I_sc ,wedefined:

At maximumpowerpoint, we have

As ,

weassumefortheparametersdeterminationthat

           

 we assume also:

weassume:

Finally, , we assume:

oftheremainingterms.

With these simplifications, we get:

Fromtheselastfour equations, we obtain an analytic expression of A. For that, , we have:

wehave:

 

    

Finally, we obtain the expression of A

and I₀, R_s and I_ph are obtainedby

 

Once theseparameters (A, I_ph, Rs, and I₀) are determined, theI_pv-V_pvcharacteristicwill be calculated by Eq.2usingthe Newton Raphson method.

Point 3:Discuss the computational complexity and the potential use of secondary function (5) involving secondary capacity terms as of in (5) in conservatism reduction. How the feasibility of the developed conditions in proposed power management control are ensured?

Response 3

Thank you very much for the comment:

There was an error in equation, it was corrected

                                                                     (7)

1. Bonert and L. Zubeita [Ref] developed the supercapacitor behavioral model using energy considerations. This model, known as the two RC branches, is based on dividing the electrostatic energy of supercapacitors into two parts:
   • A quickly stored or readily available energy ;
   • A slowly stored or readily available energy.

As shown in Fig. 10, the R₁C₁ branch determines the supercapacitor's immediate behavior during rapid charge and discharge cycles that last only a few seconds, where the slow branch is the R₂C₂ cell. It ends the first cell in a few minutes and describesthe internal energy distribution at the end of the charge (or discharge).

Themodelisdescribedbytheequationsbelow:

                    (6)

The secondary capacity C₂'s secondary voltage V₂ is determined by:

                                                                     (7)

Q₂ is the instantaneous charge of C₂, we have:

                                                                      (8)

The current i₁ in the main capacitor C₁ is given as:

                                                                    (9)

[Ref] Zubieta, L., Bonert, R.: Characterization of double-layercapacitors (DLCs) for power electronics applications. IEEE Transactions on Industry Applications 36(1),199-205 (2000)

Point 4:Please provide the qualitative and quantitative comparison with existing works, together with simulations examples.

Response 4

Thank you very much for the comment

We have added a text in the introduction to present existing works:

SCs are compared to other storage devices [20-22], and the benefits of hybrid PV-battery SCs systems are examined in the literature [23, 24]. In addition, some research [25-27] propose hybrid energy storage systems (HESS) such as PV-battery supercapacitors or fuel cells as a potential approach. Most studies focus on load control and demand sharing with these hybrid systems.

In [28] propose a hybrid energy storage system that combines batteries and supercapacitors to create a solution that optimizes electric vehicle operation across a wide range of ambient temperatures. This hybrid system likely utilizes the inherent strengths of both technologies–batteries for higher energy storage capacity and supercapacitors for quick energy delivery and management of power spikes. HBSS systems are increasingly used in various applications to combine the advantages of both technologies, such as the high energy density of batteries and the fast charge/discharge capability of supercapacitors. To optimize the performance of these hybrid systems, advanced control strategies like model predictive control are employed [29].

 

We have conducted a simulation comparing two scenarios: one with only battery storage and another with a hybrid storage system incorporating both batteries and supercapacitors (SCs). Based on your simulation results (specifically shown in Figure 19a and 19b), we have observed that introducing supercapacitors in the storage system led to a reduction in stress on the batteries. Here's a breakdown of our observations:

1. State of Charge (SOC) Behavior:
• In the scenario with only battery storage, the SOC started at 75% and decreased over time.
• However, when supercapacitors and a well-implemented control loop were introduced in the system, the battery SOC remained relatively constant and reached a minimum value of 82.85%. This suggests that the addition of supercapacitors helped regulate the battery SOC and prevent it from dropping significantly.
2. Battery Voltage Behavior:
• In the battery-only scenario, the battery voltage likely fluctuated as the SOC decreased, which is typical behavior for batteries.
• The battery voltage remained relatively stable with some fluctuations with the hybrid storage setup including supercapacitors and a control loop. This stability indicates that the supercapacitors might be assisting in maintaining a steady voltage level, contributing to more consistent system performance.

 

Point 5:In the simulation Fig. 16, the comparative studies between proposed method and other methods should be discussed in detail to demonstrate the effectiveness of the proposed method. How did the authors select the comparative methods, and what are the reasons for such methods?  

Response 5

Thank you very much for the comment:

 

Fig.16 represents the SOC variations of battery and SCs It is shown in Fig.18 shows that battery SOC is well controlled and maintained between 82.85%and 90% while supercapacitor SOC varies between 58.05 % and 90 %. The batteries and SCs SOCs are kept within bounds, regardless of the variations in PV and load power profiles. 

The introduction of supercapacitors to the storage system appears to have positively impacted the battery's performance and longevity. By providing an additional energy buffer and optimizing their usage through the control loop, you were able to keep both the SOC and voltage of the battery at more desirable levels.

It's worth noting that supercapacitors are known for their rapid charge and discharge capabilities, which can help mitigate some of the stress on batteries during high-power demand periods. The findings align with this advantage and demonstrate the potential benefits of hybrid storage systems in improving overall system reliability and performance.

 

Point 6:The introduction of the manuscript should be proposed in a better way. Sometimes, adjacent phrases are not well connected. For example, " The algorithm's purpose is to regulate the charge and discharge cycles of the  HBSS, ensuring that the state of charge (SOC) of both batteries and supercapacitors remains within the desired range" is det4ached from previous or successive phrases. Is it a drawback to be tackled in some way?

Response 6

Thank you very much for the comment. We think this is a good suggestion. We have rewritten the introduction according to the reviewer's recommendations. The sentence has been rewritten as:

 The algorithm is designed with the objective of managing the charge and discharge cycles of the Hybrid Battery-Supercapacitor Energy Storage System (HBSS), thereby guaranteeing that the State of Charge (SOC) for both batteries and supercapacitors is maintained within the specified range.

 

Point 7:It seems that objective of the manuscript should be showing how to extract more performed to determine the battery impedance method. Please explain it? 

Response 7

Thank you very much for the comment:

This study uses a 12 V-100 Ah battery as a storage device as shown in Fig.8. Identification is performed to determine the battery impedance (Z_Batt). The battery model is based on the calculation of the terminal voltage , and state of charge (SOC). The model includes the battery's open circuit voltage, the capacity and internal resistance . For this, the battery was identified to determine the impedance value and then   was deduced to be used in simulation. An excitation voltage or current is imposed on the battery in order to determine an ohmic representation of its internal state. The low-frequency measurement provides more details on the electrochemical operation of the battery.

Figure 8. Battery identification test bench.

The phase shift of these two signals gives the impedance Z_Batt. And then internal resistance R_Batt, and the capacitive reactance X_Batt

Figure 9 shows the different curves obtained while proceeding to the identification of the battery. It shows that there exists a phase shift of 3 degrees between voltage and current (voltage is lagging)

Figure 9. Battery voltage and current curves.

The signal 1 in pink color indicates the battery voltage, while signal 2 in orange is a direct image of the AC current. The battery operates as complex impedancewith resistance and reactance . The ratio of these two signals (voltage and current) and their phase-shift provides the absolute value of the internal impedance of the battery.

                                                                                        (4)

                                                                                                         (5)

With: ƒ the frequency, (Hz)

The different calculated results are:

R_Batt=0.795 Ω, X_Batt=0.07 Ω and C_Batt=44.96 mF

All of these identified variables were included in simulation models to establish realistic mathematical models that were as near to the experiment as possible.

 

Comments on the Quality of English Language

The authors should read and check the full article very carefully to correct possible grammar and spelling mistakes

Response

The manuscript was revised several times to correct all errors relating to the language and we have provided an acceptable one

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Thank you for applying the suggestions.

1. Figure 1 is still misleading. It seems that EMS only controls the SC and not the battery. How is the reference V_dc of battery set?

2. Sections 2 and 3 are too small for a separate section. I suggest adding them to section 1 as subsections.

3. Figure 6 is not clear at all. Please provide better resolution for these figures. Are these results obtained from measurements or a PV simulator? 

4. Equation editor used in the paper is outdated. I suggest using a better equation editor.

5. Spaces are missing in many parts of the paper, for example lines 278-281, 311, 402-403, 466, ...

6. Figures should be displayed soon after they are referenced. This is not the case for some figures. Please move some of the figures close to where they are referenced in the text. 

7. Please comment on the transients and glitched observed in Figures 20-23 (for example M9 and M11).

8. Add a legend for Figure 24.

9. Are Figures 21 and 27 presenting the same scenario? Why are the results different?

Major proofreading is still a big requirement for the paper. 

1. Please add spaces when needed.

2. It seems that different authors used different formats. Some parts of the paper is not consistent (for example look at the reference list).

3. Equations could be presented with more clarity.

4. The number of pages is rather excessive. Irrelevant figures could be omitted, and some images can be grouped together as one figure.

Author Response

Thank you for giving us the opportunity to submit a second revised draft of the manuscript “Optimized Power Management Approach for Photovoltaic Systems with Hybrid Battery-Supercapacitor Storage” for publication in Journal of Sustainability. We appreciate the time and effort that you and the reviewers dedicated to providing feedback on our manuscript and are grateful for the insightful comments on and valuable improvements to our paper. We have incorporated most of the suggestions made by the reviewers. Those changes are highlighted within the manuscript. Please see below, in blue, for a point-by-point response to the reviewers’ comments and concerns. 
The replies for the comments made by the reviewers are as follows:
Response to Reviewer 1 Comments
We agree with the reviewer's assessment. Accordingly, throughout the manuscript, we have made the suggested changes. The following is a point-by-point list of detailed modifications:
Thank you for applying the suggestions.

Author Response File: Author Response.pdf

Reviewer 2 Report

The author modified the manuscript according to the reviewer's suggestions. 

The author modified the manuscript according to the reviewer's suggestions.

Author Response

Thank you for giving us the opportunity to submit a second revised draft of the manuscript “Optimized Power Management Approach for Photovoltaic Systems with Hybrid Battery-Supercapacitor Storage” for publication in Journal of Sustainability. We appreciate the time and effort that you and the reviewers dedicated to providing feedback on our manuscript and are grateful for the insightful comments on and valuable improvements to our paper. We have incorporated most of the suggestions made by the reviewers. Those changes are highlighted within the manuscript. Please see below, in blue, for a point-by-point response to the reviewers’ comments and concerns. 
The replies for the comments made by the reviewers are as follows:
Response to Reviewer2 Comments
We thank you for accepting the modifications from the first stage

Here are some modifications for the first reviewer

Author Response File: Author Response.pdf