A novel converter using MPPT algorithm and acceleration factor for standalone PV system

Solar power is an excellent alternative to existing power sources; standalone PV systems demonstrate its importance. PV panels are the energy source for connected loads, with storage systems or batteries necessary due to solar insolation’s intermittency. The present investigation uses a novel high-efficiency DC-DC converter to perform the maximum power point tracking (MPPT). This converter enables the connection of solar panels in series or parallel because it can step up or step down the PV voltage according to the DC link voltage. A bidirectional DC-DC converter is also used at the load side to maintain DC link voltage and charge/discharge the batteries. The second part of the paper discusses a modified Perturb and Observe (P &O) MPPT algorithm, which is vital in tapping the maximum power from PV panels. A fast solar MPPT is desired to track the operating point, which can be served by adding an acceleration factor to the existing P &O (hill climbing) solar MPPT algorithm. With the inclusion of the proposed converter and modification in P &O algorithm, the obtained system’s efficiency is approximately 96% and tracking time reduced from 7 sec to 3.7 sec. The detailed analysis of component efficiency provides valuable insights into the performance of the system. A comprehensive simulation and hardware results obtained for various irradiation (Ropp, sine, step, ramp, less, no, etc.), temperature, loads, and acceleration factors are presented.


Introduction
Presently, solar energy is being rapidly adopted compared to conventional energy sources.Solar energy is sustainable, one of the cleanest, and widely used because of its availability, short payback period, and installation.The energy produced can be used locally or fed to the electricity grid.The nature of power produced is DC and can be stored in the battery using DC-DC converters.There is intermittency in solar power generation, so the battery storage system is helpful to cater to the steady output requirement.Standalone solar PV system includes solar PV, batteries, and loads [1].Such systems are widely used in remote areas like islands, far-off B Shubham Agrawal shubhama1@iisc.ac.inLoganathan Umanand lums@iisc.ac.inSubba Reddy Basappa sreddy@iisc.ac.in 1 Interdisciplinary Center for Energy Research, Indian Institute of Science, Bangalore, Karnataka 560012, India villages, mountains, etc., where the grid supply is unavailable [2].The unpredictable load shedding also encourages the installation of standalone solar PV systems.The usage of solar PV systems reduces the dependency on diesel generators, leading to reduced emissions into the atmosphere.The solar panels can be connected in a series or a parallel arrangement.The parallel connected solar PV systems can address partial and rapidly fluctuating shadow conditions [3].
The combination of both series and parallel arrangement is widely used.The layout of the system depends on the converter system attached to it.The terminals of the PV array should be connected to a DC-DC converter through a PV capacitor.The PV capacitor filters out current harmonics.Generally, DC-DC converters [4] can broadly be classified under two categories.First, based on galvanic isolation, there are isolated and non-isolated types of converters.Secondly, based on the output-to-input voltage ratio, there are three types of converters: buck, boost, and buck-boost DC-DC converters.Many DC-DC converters [5] can be derived from the converters mentioned above; however, the essential characteristics remain the same.A DC-DC converter attached to the solar PV array tracks the maximum power point (MPP) on solar I-V characteristics [6,7].The range covered by the buck and boost converter is limited to a particular section on the I-V characteristics.However, the buck-boost converter and its derived topologies [8] can sweep through the entire range of I-V characteristics.At higher duty ratios, the inductor of the conventional buck-boost converter gets shorted, and the efficiency also reduces.The problem of shorting the inductor persists with Cuk [9] and SEPIC converters at higher duty ratios [10].The Watkins-Johnson converter [11] has reverse gain; nonetheless, the highest positive voltage that this converter may generate is the input voltage itself.The same problem prevails for the inverse Watkins-Johnson converter [12].The number of active and passive components also limits the efficacy of the converter [13][14][15][16].In a standalone system, the boost converter is widely used to increase the voltage at the output side [17][18][19][20]; however, if the PV array is connected in a series, the boost converter has to be replaced with a flyback or buck-boost converter [21][22][23][24][25].
MPPT is crucial in standalone solar PV systems [26].Several algorithms are available, including P&O, incremental conductance, neural network, fuzzy logic control, and adaptive algorithms.Among these, adaptive MPPT algorithms are particularly beneficial as they dynamically adjust control parameters based on changing parameters such as temperature and irradiance.This real-time adaptation enables improved energy efficiency, rapid tracking, and enhanced overall PV system performance.Adaptive MPPT algorithms effectively respond to varying conditions, ensuring optimal power extraction from the solar panels.
A fixed zone P&O MPPT technique [27] for a standalone distributed PV system is presented.The proposed MPPT method offers a simple and practical approach to tracking the MPP of PV modules in a distributed system configuration.By dividing the operating range into fixed voltage zones, the algorithm perturbs the voltage in small steps to determine the direction of the MPP.It then adjusts the operating point toward the identified zone for improved tracking accuracy.The fixed zone P&O MPPT technique reduces oscillations and steady-state tracking errors commonly associated with traditional P&O algorithms.When the PV system operates near the boundaries of the fixed voltage zones, frequent zone transitions may occur.These transitions can cause oscillations and instability in the MPPT algorithm, reducing tracking accuracy and potential power losses.There is dependence on the zone placement, and the fixed zone P&O may be unable to track the global MPPT.Sankar et al. [28] utilize a novel perturbation technique that allows larger voltage steps for the MPPT process.Due to this process, the MPP is achieved quickly under rapidly changing environmental conditions; however, the module can overshoot the MPP and require additional converging iterations.A modified and efficient P&O technique [29] is incorporated to address dynamic and varying irradiation conditions.The buck-boost converter is used to perform extensive experimentation to validate the proposed algorithm.However, due to the sensitivity in the voltage and current measurements, filtering techniques are essential.A dual-discrete model predictive control [30] enhances the tracking accuracy and efficiency of the MPP under dynamic temperature and irradiance levels.It is to be noted that the buck converter is not capable of PV curve sweep, and the used algorithm involves solving optimization problems at each control step.A state-plane direct MPPT technique [31] utilizes a two-dimensional statespace representation of the operating conditions of a PV system, including both voltage and current.By monitoring and analyzing the states in real time, the algorithm determines the operating point corresponding to MPP.The algorithm is adaptive and very fast in nature to track the dynamic operating irradiation levels; however, it has limited pertinency to stable irradiance conditions.A two-stage-based PV standalone system is used with virtual synchronous generator control [32] strategy to regulate the power flow between the PV stage, battery stage, and load.The system efficiency reduces with the number of stages present in the system.In the coarse tracking stage [33], the algorithm quickly searches the voltage range to estimate the approximate GMPP.This estimation is based on mapping PV characteristics obtained during offline calibration, such as voltage and power.Once the approximate GMPP is determined, the fine tracking stage refines the tracking by employing a P&O algorithm.The systems work with grid-connected [34] PV systems.A further investigation is required to test the same algorithm in standalone conditions (Table 1).
A detailed literature survey is performed, and several papers related to the work are discussed below.The shortcomings of the literature are as follows: • One of the issue encountered with the boost converter is the tendency to obtain only higher gain, which can lead to potential challenges in maintaining stability and controlling the output voltage.Similarly, in the case of the buck-boost converter, there is a risk of inductor shorting, which can disrupt the operation and impact the overall performance of the system.These issues highlight the importance of careful design and control strategies to mitigate such drawbacks and ensure proper functionality of the converters.• The algorithms employed for MPPT can be complex and are associated with certain limitations.Some algorithms may not perform to track the MPP under normal irradiation conditions, leading to suboptimal performance.Additionally, when operating at boundary conditions, there can be challenges in achieving convergence, resulting in reduced tracking accuracy.These drawbacks highlight the need for further research and development to address the issues and improve the effectiveness of MPPT algorithms.
In the present investigation, a novel converter [35] is proposed to overcome the issue of obtaining only higher gain and inductor shorting with the boost converter and buck-boost converter, respectively.This modified converter can act as a buck-boost converter in the duty ratio range between 0 and 0.5.At the duty ratio near 0.5, the efficacy of the converter reduces; however, it eliminates the issue related to the inductor short at the higher duty ratios.The MPPT is done with the help of this converter.A simple P&O algorithm may be used with either the current or voltage reference method; however, the current control method is less complex and faster than the voltage reference method.The conventional P&O algorithm takes a long time to reach the point where maximum power is tapped from the solar PV array.In the present work, an acceleration factor is introduced in the existing P&O algorithm to make it faster by recording the power values at two previous time instances.After reaching the MPP, the role of the acceleration factor ceases, and the conventional P&O algorithm continues.The system has the following key characteristics to realize a standalone solar PV, battery storage, and DC load system: • The proposed converter enables both lower and higher output voltage than the input PV voltage.• The same hardware system applies to the series (high input voltage) and parallel (low input voltage) connection of PV panels.• A modified MPPT algorithm with an acceleration factor reduces the time taken to track the MPP.
The paper is further structured into seven sections, each focusing on different aspects of the investigation.Section 2 of the paper presents a comprehensive explanation of the proposed system through the use of a block diagram.The block diagram illustrates the different components and their interconnections, providing a clear overview of the system's architecture and functionality.Sections 3 and 4 delve into the details of the proposed converter, with specific emphasis on its integration with a PV source and the implementa-tion of the MPPT technique.These sections elaborate on the key features and functionalities of the converter, showcasing how it optimizes power extraction from the PV source.Section 5 discusses the efficiency of the system with several non-idealities associated with the components in the system.In Sect.6, a comprehensive simulation study is conducted to evaluate the performance of the proposed system.In sect.7, hardware results are presented, providing empirical evidence of the system's functionality and effectiveness.These results serve to validate the theoretical concepts and demonstrate the practical feasibility of the proposed solution.Finally, in Sect.8, the paper concludes with a comparative analysis of existing literature, highlighting the strengths and advantages of the proposed system in relation to other approaches.This comparative analysis offers valuable insights into the potential impact and significance of the research findings, emphasizing the contributions made by the present investigation.

Proposed system
Figure 1 shows the block diagram of the proposed system along with the control scheme for associated power electronics converters.The proposed system consists of solar PV connected with the proposed converter, a DC link capacitor, a bidirectional buck-boost converter, battery storage, and a DC load, as shown in Fig. 1a.The solar PV panels can be connected in series or parallel according to the design requirements.The proposed converter tracks maximum power and acts as a power interface between the PV source and the load.The battery storage system is interfaced with the PV panels and the DC load at the DC bus through a bidirectional buck-boost converter.The bidirectional buck-boost converter maintains the DC bus voltage and charge/discharge the battery accordingly.
Figure 1b shows the control scheme required to generate the appropriate gate pulses to turn O N and O F F the power electronic switches (MOSFETs/IGBTs) in the proposed converter.The voltage v PV and current i PV at the PV output are measured and fed to the MPPT controller block along with parameters like small change in current I and acceleration

Proposed converter with PV source
The proposed converter is analyzed in non-ideal conditions.The non-ideal analysis is of prime importance because it Non-idealities such as on-state resistance R DS for MOS-FETs, forward voltage drop V d0 for diodes, DC resistance R L for inductor are taken as non-idealities in the proposed converter.The total time duration for mode-I and mode-II is T S , which is the inverse of the operating frequency F S of the converter.
Mode-I: in the mode-I, The MOSFETs S 1 and S 2 are turned O N using gate driver circuits.The diodes D 1 and D 2 are in reverse bias due to the voltage polarity across them.During this mode, the loop consists of a DC source V g , MOS-FET S 1 , inductor L, MOSFET S 2 , capacitor C, and the load R as shown in Fig. 3a.The non-idealities for MOSFETs and inductor are included in the circuit diagram.The equation for the voltage across inductor v L , the current through capacitor i C , and source current i g is formulated using Kirchhoff's laws and presented in Eqs. ( 1)- (3).
Mode-II: in the mode-II, the MOSFETs S 1 and S 2 are turned O F F. The voltage across inductor L reverses as the current through it reduces; hence, diodes D 1 and D 2 become forward biased.During this mode, the loop consists of diode D 1 , inductor L, diode D 2 , capacitor C, and the load R as shown in Fig. 3b.The non-idealities for diodes and inductor are included in the circuit diagram.Similar to mode-I, the voltage v L , current i C , and current i g are presented in Eqs. ( 4)- (6).4)-( 6) are valid for (1 − d)T S time duration.The relationship between input and output voltages can be obtained using the volt-second balance, which implies the area under the inductor voltage curve in a complete cycle of T S time duration will be null.Equations ( 1) and ( 4) are used to nullify the area under the inductor voltage curve.
Equation (7) shows the relationship between input and output voltage in terms of non-idealities, duty ratio d, and inductor current i L .The relationship between input and output currents can be obtained using the charge balance across the capacitor, implying that the area under capacitor current in a complete cycle of T S time duration will be null.Using Eqs. ( 2) and ( 5), the following relationship is obtained as mentioned in Eq. (8).
The output current i 0 can be expressed in terms of output voltage v 0 and load resistor R using Ohm's law.Equation ( 8) can be rewritten as following Eq.( 9).
The relationship between input and output voltage can be explicitly written if the current i L is removed from Eq. ( 7).The value of the inductor current i L from Eq. ( 9) is inserted in Eq. ( 7) to obtain the direct relation between input and output voltage, as mentioned in Eq. (10).
Equation (10) shows that the ratio of output voltage to the input voltage is a variable of duty ratio d, input voltage V g , load resistance R, and non-idealities of the converter.In the case of an ideal converter, all the non-idealities vanish, and the gain ratio results in Eq. (11).
Taking the average of input current i g in mode-I and mode-II, Eq. ( 12) is obtained.
Inserting the value of the inductor current i L from Eq. ( 9) into above Eq.( 12), the average input current in terms of load voltage v 0 is obtained as mentioned in Eq. (13).

MPPT with proposed converter
Figure 4 shows the general I-V characteristics of solar PV panel.There are infinite points on the curve where it can be operated.In other words, if the terminal resistance R T of a PV panel is changed, the operating point can be changed.A DC-DC converter with a solar PV as an input source can have a variable terminal resistance seen from the terminals of the PV panel, as shown in Fig. 5.
To operate the PV at the MPP, the terminal resistance should be equal to the ratio of V mp and I mp , where V mp is the terminal voltage at the MPP, and I mp is the current flowing from solar PV while operating at the MPP.The maximum

Proposed converter with PV input
Figure 6 shows that a PV source is connected to the proposed converter.An input capacitor filter with a capacitance of C PV is connected across the solar PV.The capacitor ensures the continuous current from the solar PV; however, the average current across the capacitor in a cycle of one time period T S will be null.Thus, the average solar PV current i PV will equal the current i g as mentioned in Eqs. ( 14) and (15).
i PV avg = i g avg (14) Equation ( 11) can be rewritten as following Eq.( 16) in terms of terminal PV voltage v PV .
The resistance seen from the terminal of solar PV R T can be calculated through terminal voltage v PV and current  15) and ( 16): It is inferred from Eq. ( 17) that the I-V characteristic curve's load line will depend on the duty ratio and the load resistance.The variation of the load line with respect to the duty ratio is shown in Fig. 7.
If the duty ratio d is equal to zero, the terminal resistance R T will tend to infinity.Hence, the inverse of the resistance or slope of the I-V characteristic curve will tend to be zero.Similarly, if the duty ratio d is equal to 0.5, resistance R T will be zero, and the slope of the I-V characteristic curve will tend to be infinity.The highlighted portion of the curve in Fig. 7 shows that every point on the I-V characteristic can be covered with the duty ratio range between 0 and 0.5.

MPPT algorithm with acceleration factor
MPPT is required to tap the maximum power of a solar PV panel.A DC-DC converter is used to operate the PV at the point where it can generate the maximum power.If the load resistance R of the converter is fixed, the terminal resistance R T seen by the PV terminals is set by the duty ratio.In the controller design to generate the required duty ratio d, the MPPT algorithm is executed.There are many MPPT algorithms available in the literature.Among the various algorithms, the most simple and used algorithm is P&O method.The P&O algorithm can be classified into two categories: the current reference method and the voltage reference method.There are specific pros and cons to each method over another; however, the current reference method is faster and less complex.
The current reference-based P & O algorithm is initialized with parameters like initial reference, minimum, and maximum current values.If the initial reference current is very low or high than the actual reference current, it takes a long time to reach the actual reference point.An acceleration factor can be associated with the existing P&O algorithm to quickly track the MPP.The detailed algorithm with relevant initializations, measurements, calculations, conditions, and updations is shown in Fig. 8.The algorithm is initialized with current through PV terminals I PV (t − 1), Reference current I r (t − 1), PV power at two subsequent time instants P(t − 1) and P(t − 2), incremental factor α 1 , acceleration factor α 2 , and a small change in the reference current δ.After the initializations, the PV terminal current I PV (t) and voltage V PV (t) are measured through the respective current and voltage sensors.The instantaneous PV power P_PV (t) is calculated with the multiplication of the instantaneous current I PV (t) and voltage V PV (t).The change in two subsequent powers is defined as P 1 , which is the difference between recent instantaneous power P(t) and previous instantaneous power P(t − 1).Similarly, P 2 is the difference between power P(t − 1) and power P(t − 2).The difference of the PV current is defined as I , which is the difference between recent instantaneous current I PV (t) and previous instantaneous current I PV (t − 1).Now the conditions for various logic are checked to update the reference current I r (t).If the change in power P 1 is zero, it is inferred that the power is the same at two points on the PV panel I-V characteristic curve; hence, no change in the reference current.The new reference current I r (t) will be equal to the previous reference current I r (t −1).If the change in power P 1 is nonzero, the algorithm enters into a nested loop.The next condition is to check P 1 , P 2 and I .If the subsequent changes in the power P 1 and P 2 are of the same nature (either positive or negative).In that case, the change in the reference current will be through the acceleration factor α 2 .On the other hand, if the subsequent changes in the power P 1 and P 2 are opposite nature, the change in the reference current will be through just incremental factor α 1 .
Condition-1: if the subsequent changes in the power P 1 and P 2 and the change in current I are of the same nature as mentioned in Fig. 9a, b, the acceleration factor α 2 is multiplied to the small change in the reference current δ.This factor α 2 δ is added to the reference current.Equation (18) shows the modified reference current.
Condition-2: if the power P 1 and P 2 are of the same nature and the change in current I is of a different nature as mentioned in Fig. 9c, d, the factor α 2 δ is subtracted from the reference current.Equation (19) shows the modified ref- Condition-3: if power P 1 is less than zero, power P 2 is greater than zero, and current I is less than zero as mentioned in Fig. 9e, the incremental factor α 1 is multiplied to the small change in the reference current δ.This factor α 1 δ is added to the reference current.Equation (20) shows the modified reference current.
Condition-4: if power P 1 is less than zero, power P 2 is greater than zero, and current I is greater than zero as mentioned in Fig. 9f.The factor α 1 δ is subtracted from the reference current.Equation (21) shows the modified reference current.
It is inferred that in condition-1 and condition-2, the acceleration factor α 2 plays a role in determining the modified reference current I r (t), whereas in the rest of the conditions, the incremental factor α 1 is significant.If any of the abovementioned conditions are not followed, the reference current remains the same as in Eq. (22).
The above-described process completes a cycle of the MPPT algorithm with the acceleration factor.The same cycle is repeated with the measurements of the PV terminal current I PV (t) and voltage V PV (t).

Calculation and analysis of efficiency
The efficiency of a system is influenced by power losses occurring in its components, with the power circuit being a major contributor.In Fig. 10a, the schematic of the system without a control structure is depicted.The light green highlighted portion of the circuit is the proposed converter, and the light blue highlighted portion of the circuit is the bidirectional buck-boost converter.It is important to note that no component is perfect, and each introduces a certain level of loss when current passes through it or when it blocks voltage.Figure 10b illustrates the non-ideal characteristics of components such as the MOSFET, diode, inductor, and capacitor.Within the MOSFET, a drain-to-source resistance R DS can be considered as a lossy element.The diode exhibits a prevalent loss due to forward voltage drop V d0 .Similarly, the inductor possesses a DC resistance (DCR), and the capacitor possesses The following subsections discuss the proposed and bidirectional buck-boost converter efficiency calculation.The loss calculation and its effect on the efficiency are presented through curves and equations.A DC source and a resistive load can be considered to calculate the losses in the converters.

Proposed converter
The proposed converter incorporates various non-idealities, including the on-state resistance of the switch R DS , the forward voltage drop of the diode V d0 , the DCR of the inductor R L , and the ESR of the capacitor R C .Among these, the losses in the capacitor are negligible compared to the losses in the other elements, allowing us to treat the capacitor as an ideal component.Equation ( 10) is utilized to determine the efficiency of the proposed converter, and the corresponding formula is presented as Eq. ( 27).

Effect of DCR R L
When considering a DC source and resistive load, the power loss in the DCR (R L ) of the inductor plays a substantial role in the overall losses of the converter.This power loss P R L Fig. 11 Efficiency variation with DCR R L can be calculated using Eq. ( 9).
In Eq. ( 28), the output voltage (v 0 ) will remain relatively constant if the output capacitor is sufficiently large.As a result, the power loss in the DCR of the inductor becomes directly proportional to the DCR value (R L ).In Fig. 11, a family of efficiency curves is plotted for different values of DCR (R L ) as a function of the duty ratio, while keeping the values of other non-idealities constant.It is observed that lower values of R L lead to better efficiency.Therefore, when designing the inductor winding for higher current values, it is advisable to use parallel wires with a higher Standard Wire Gauge (SWG) rather than a single wire with a lower SWG.

Effect of on-state resistance of switch R DS
When MOSFETs are in conduction mode, they can be approximated as resistances.The datasheets specify the value of this resistance as the on-state switch resistance R DS .How-Fig. 12 Efficiency variation with on-state resistance R DS ever, MOSFETs are not conducted throughout the entire switching cycle.They are turned ON for a duration of dT S , while diodes conduct for the remaining period of (1 − d)T S .The power loss P R DS in the MOSFET over a complete cycle can be calculated using Eq. ( 29).
In Eq. ( 29), the presence of a factor of d in the numerator indicates that the switches are conducting for a duration of dT S .Since the proposed converter consists of two switches, the power loss P R DS is multiplied by a factor of two in the efficiency calculation.Figure 12 displays a range of efficiency curves, each corresponding to a different value of R DS , plotted as a function of the duty ratio while keeping the other non-idealities constant.Selecting the switch with a lower on-state resistance R DS for improved efficiency is recommended.

Effect of forward voltage drop of diode V d0
When a diode carries a large current, the forward voltage drop V d0 across the diode becomes significant.The power loss across the diode, denoted as P V d0 , can be calculated using Eq.(30).
In Fig. 13, a set of efficiency curves is depicted, showing the relationship between the duty ratio and efficiency for various values of the forward voltage drop V d0 across the diode.The other non-idealities are kept constant.If the diodes are replaced with MOSFETs, the power loss calculation can be performed using Eq.(31).Consequently, the efficiency

Bidirectional buck-boost converter
An extensive analysis of power losses and efficiency is conducted for the bidirectional buck-boost converter, following a similar approach outlined in the previous section.The DCR of the inductor and the on-state resistance of the switches are identified as the primary contributors to power losses in the bidirectional buck-boost converter.The efficiency of the bidirectional buck-boost converter is represented by Eq. ( 32).Examining Eq. ( 32) reveals that larger values of R DS and R L lead to a decrease in converter efficiency, making smaller values desirable.Notably, it is important to mention that the efficiency of the converter is not affected by the duty ratio d.

Effect of DCR R L
The average inductor current I L equals the average output current I 0 in the bidirectional buck-boost converter.As a general guideline, the inductor is typically designed such that the ripple in the inductor current does not exceed 5% of the average inductor current.For loss calculations, the inductor current can be approximated as constant.Equation (33) provides the relationship for the power loss in the DCR (R L ) over a complete switching cycle.

Effect of on-state resistance of switch R DS
During a complete switching cycle in the bidirectional buckboost converter, one MOSFET is turned ON for a duration of dT S , while the other MOSFET conducts for the remaining period of (1 − d)T S .The power loss P_R DS in both MOSFETs can be calculated using Eq. ( 34).

Simulation results
Simulations are conducted on the proposed circuit in the Simulink environment of MATLAB.Figure 14 illustrates the Simulink schematic diagram, showcasing the main structure with the proposed converter and bidirectional buck-boost converter as subsystems.The explicit representation of the converters is displayed below the main circuit.The simulation parameters adopted are mentioned in Table 2. Five solar PV panels, each of maximum power P M P 213 W, current at MPP I M P 7.35 A, and voltage at MPP V M P 29 V are connected in parallel.The mentioned ratings of the solar PV correspond to the solar insolation of 1000 W/m 2 .The filter capacitor of 1000 µ F is connected in parallel to the solar PV panels.A total of four MOSFETs are used, out of which two MOSFETs are used in proposed converter and two are used in bidirectional buck-boost converter.Inductors of 15 and 5 mH are used in the proposed converter and bidirectional buckboost converter, respectively.A DC link capacitor of 4700 μ F and a variable resistive load are connected at the common coupling point between the proposed converter and the bidirectional buck-boost converter.Battery storage is connected to the output of the bidirectional buck-boost converter.Figure 15a, b shows a series of reference currents and currents at PV terminals for different acceleration factors in the solar MPPT algorithm at fixed solar insolation of 500 W/m 2 .It can be inferred that the acceleration factor α increases the speed of the reference current to reach the MPP.After reaching the MPP, the role of the acceleration factor ceases, and it continues with the conventional P&O algorithm.Particularly, the acceleration factor is significant when there is a sudden change in solar insolation.
Figure 15c shows curves for the DC bus voltages of 24 V and 48V .The proposed converter can step up and step down the PV terminal voltage of 29V , and a desired DC bus voltage can be obtained.Figure 15d indicates the battery current when the load is either connected or not connected at the common coupling point.The negative current in the figure represents that the battery is getting charged.The battery charging current is higher when no load is connected at the DC bus terminals.The charging current reduces with the increment in the resistive load at the DC bus terminals.A couple of curves for PV currents for different solar insolation levels of 1000 and 500 W/m 2 are shown in Fig. 15e.As the number of solar PV panels is five, the curve corresponding to the solar insolation level of 1000 W/m 2 shows that the steady-   Figure 15f shows the battery current for different solar insolation levels of 1000 and 500 W/m 2 .It is evident from the curves that with the increase in solar insolation level, the charging current of the battery increases if there is no change in the load.
The system undergoes testing under various climatic conditions, including temperature and solar irradiation.The system is subjected to multiple solar irradiation profiles to validate its versatility, such as step, ramp, sine.One specific profile used for testing is the Ropp profile [29], which incorporates both increasing and decreasing ramp and step functions.Figure 16 illustrates the simulation results for the solar irradiation corresponding to the Ropp profile.In the simulation, the generated solar power P_PV is directly proportional to the solar irradiation.The load is maintained at a fixed resistance of 10 .Regardless of the solar power generated, the load should consistently receive the same amount of power.To achieve this, a Proportional Integrator (PI) controller regulates the voltage at the Point of Common Coupling (PCC) or the DC bus, maintaining it at approximately 48 V.
Consequently, the power consumed by the load P_Load remains constant at approximately 384 W. It is important to note that the voltage at the DC bus may exhibit slight variations around 48 V due to the continuous operation of the MPPT algorithm.Thus, the term 'approximately' denotes the slight deviations from exactly 48 V.The impact of solar power variations is reflected in the battery charging power.Negative power values in the P_Batt curve indicate that the batteries are being charged.When solar irradiation is sufficient, the PV system supplies power to the load, charges the batteries, and compensates for losses.However, the batteries are discharged during inadequate solar PV power periods to compensate for the power deficit.
In the subsequent analysis, a sine profile of solar irradiation is applied to the system, as depicted in Fig. 17.The solar irradiation profile is configured with a DC offset and sine amplitude, designed to trigger the charging and discharging modes of the batteries and demonstrate the system's adaptability to sine variations in solar irradiation.The DC offset of the solar irradiation is set at 400 W/m 2 , while the peak-topeak variation is 400 W/m 2 .As a result, the solar irradiation oscillates between 200 and 600 W/m 2 .Correspondingly, the generated PV power P_PV follows the same curve as the solar irradiation, as does the battery power P_Batt.This alignment occurs because the power the load P_Load consumes remains relatively constant.It is worth noting that the power consumed by the load P_Load exhibits slight variations.This phenomenon arises due to the high frequency of the solar irradiation variation in the simulation.In practical scenarios, solar irradiation variations are not as rapid, lead-Fig.20 Simulation results for temperature variation ing to more stable load power consumption.However, in this simulation, the quick changes in solar irradiation contribute to slight fluctuations in the load power.
As depicted in Fig. 18, the system simulation is conducted under low or no solar irradiation conditions.The generated PV power aligns with the solar irradiation profile.Under low or no solar irradiation, the PV power output decreases accordingly, reflecting the reduced or absent solar power generation.Consequently, the load draws power from the batteries to meet energy requirements.This demonstrates the system's capability to seamlessly transition to the battery power supply without sufficient solar irradiation.Overall, the simulation results illustrate the dynamic behavior of the system, showcasing the interplay between solar power generation, load consumption, and battery charging/discharging under varying solar irradiation conditions.
An important simulation scenario is illustrated in Fig. 19, where different loads are applied to the system at various time intervals.The solar irradiation is maintained at a constant value of 500 W/m 2 .At the beginning of the simulation, no load is connected to the DC bus.Consequently, the power generated by the PV source is wholly utilized for charging the batteries and serving the non-idealities.After 5 s, a load of 30 is connected to the DC bus, causing the load current I l oad to reach approximately 1.6 A. Subsequently, at every 5-second interval, an additional 30 load is connected in parallel to the existing load.This parallel connection results in an overall increase in the load current.The stepped drop in the power consumed by the battery can be observed in the P_Batt curve.As more loads are connected, the power demand from the PV system increases, leading to a decrease in the power supplied to the battery for charging purposes.
The temperature of the PV panel plays a significant role in its efficiency and power generation capabilities.In Fig. 20, a simulation is conducted to observe the impact of temperature variations on the power generation of the solar panel.The temperature of the solar panel is gradually increased from 25 to 50 • C over a duration of 500 s.It results in a reduction in the power generated P_PV .This decrease in power generation is evident in the simulation results.The power consumed by the batteries P_Batt also reflects this decrease, as the power generated by the PV system decreases.On the other hand, the power consumed by the load P_Load remains relatively constant, indicating that the load is being served with a consistent power supply.
A simulation study is conducted to examine the impact of non-idealities or model uncertainties on the system's performance.Referring to Fig. 10a, various non-idealities mentioned in Table 3 are considered.
In the simulation results shown in Fig. 21a, the power generated by the PV panels is measured at 1040 W when operating at the MPP.The load connected to the system consumes a constant power of 395 W. The remaining power is either used to charge the battery (430 W) or dissipated across the circuit (215 W).According to Table 3, the power dissipation across the capacitors is minimal, allowing us to neglect their contribution when calculating the system's efficiency.The primary sources of power dissipation are the DCRs R L PC and R L B B of both inductors, as well as the diodes D 1 and D 2 .By varying these parameters, changes in the power profiles of the PV system, load, and battery can be observed.It is evident that the power dissipation across the non-ideal components significantly affects the overall system performance.Therefore, optimizing these components and minimizing their losses can greatly improve the efficiency  and effectiveness of the system.By reducing the DCR R L PC of the inductor in the proposed converter by a factor of 10, the new value becomes 1 m .As a result, the power loss across this non-ideality decreases from 87 to 9 W.This significant reduction in power loss is achieved by modifying the component.In Fig. 21b, which corresponds to the simulation using the new parameters, it can be observed that the charging current in the battery has increased, leading to additional losses due to the presence of R L B B .The total losses attributed to the non-idealities amount to 148 W.However, despite the increased losses in the non-ideal components, the system's overall efficiency improved from 79 to 85%.In the next step, the circuit is modified by replacing the diodes with MOSFETs, where the on-state resistance of the MOSFETs is 1 m .This alteration results in a reduction of power loss in the diodes/switch to 5.5 W. As a result, the efficiency of the system improves further to 92%, as depicted in Fig. 21c.Continuing the optimization process, the resistance of R L B B is further reduced to 10 m .This improvement contributes to enhanced efficiency of up to 96%, as shown in Fig. 21d.The results obtained through the proposed method are compared against two established techniques documented in existing literature.The authors [36] employed a bidirectional buck-boost converter as an interface between PV systems and Fig. 22 Comparative analysis of the simulation results with literature for Ropp irradiation profile, sine irradiation profile, low irradiation profile, load variation, temperature variation batteries.To enhance the tracking speed, a momentum-based P&O algorithm is employed.The authors [37] focused on a simple buck-boost converter and proposed a modification to the conventional MPPT algorithm.The authors introduced specific alterations to the existing MPPT algorithm to enhance its effectiveness in the context of the buck-boost converter.
The comparative analysis involved replacing the conventional buck-boost converter and MPPT algorithm with the proposed converter and modified MPPT.The graphical comparison in Fig. 22 showcases the outcomes obtained from the proposed technique in contrast to the techniques presented [36,37].
The graphical representation clearly illustrates the advantages of the proposed technique across various scenarios, such as Ropp, sine, low irradiation, load variation, and temperature variation.Notably, the proposed technique exhibits faster tracking speed, reduced rise and fall times, and relatively lower noise in power profiles when the solar irradiation remains constant.The comprehensive analysis of the graphs highlights the superior performance and efficacy of the proposed technique in comparison with the other approaches presented in the cited research papers.

Hardware results
Figure 23 illustrates the hardware setup of the proposed system.Due to space limitations, the solar PV panels, batteries, and load are not shown in the diagram.The experimental setup consists of various components as specified in Table 4.The solar PV panels are connected to the proposed converter using a shared solar PV filter capacitor.The converter is then connected to the DC link capacitor and load.The connection between the converter and the batteries is established through a bidirectional buck-boost converter.To measure the appropriate currents and voltages at different nodes, measurement boards equipped with current sensor LEM LA 55-P and voltage sensor LV 25-P are incorporated into the system.The switching of the MOSFETs in both converters is achieved using gate driver circuits.These circuits include an isolated gate driver IC ISO5451 and a PWM IC SG3525.To ensure a stable power supply to the measurement and gate driver boards, voltage regulators based on the voltage regulator IC LM350 are employed.Metal oxide varistors (MOVs) are utilized across each MOSFET to safeguard against voltage surges.Additionally, four diodes are connected in parallel to provide the necessary current rating in the proposed converter.The microcontroller, TMS320F28379D, receives input from the measurement boards and generates suitable gate pulses for the gate drivers.This enables efficient control and coordination of the system components.As depicted in Fig. 23, the system is interconnected, and various hardware results are presented to demonstrate the effects of changing the acceleration factor, insolation levels, and load.Figure 24 clearly indicates that an increase in the acceleration factor (α) results in a faster response of the PV current to track the MPP.When α is set to 1, the MPPT operates conventionally, with a time of approximately 4.5 s to reach the MPP.However, when α is increased to 3, the time is reduced to 2 s.Further increments in α lead to a reduced time of 1.2 s to reach the MPP.In the hardware results, it is important to note that the time to reach the MPP may differ from the simulation results due to the influence of the sampling time considered.The sampling time plays a crucial role in the observation of results in the digital storage oscilloscope (DSO).If the sampling time is relatively large, the variations and transitions in the system behavior will be more clearly observable in the DSO measurements.
Figure 25a, b illustrates the relationship between battery charging current and PV current with changes in solar irradiation.It can be observed that as solar irradiation increases, both the input PV current and battery charging current also increase.Conversely, when solar irradiation decreases, the PV current follows a similar trend.In the case of a constant load, a decrease in solar irradiation leads to a decrease in battery charging current.Figure 26a, b presents the variation in battery charging current with changes in load.When no load is connected at the point of common coupling, the battery charging current is approximately 17 A.However, when a load of 20 is connected, the charging current reduces to 12 A.These results demonstrate the impact of the load on the battery charging current, highlighting the inverse relationship between load impedance and charging current.Under ideal conditions, the battery charging current should be 17.2A when the solar PV is operating at the MPP.However, due to losses in the system, there is a reduction in the charging current and a corresponding decrease in efficiency.In the absence of a load, there is a loss of 18 W, resulting in an  efficiency of 95.77%.When the load is connected, the battery charging current further reduces, leading to a loss of 22.8 W and an efficiency of 94.61%.The slight reduction in efficiency can be attributed to higher losses in the DCR of the bidirectional buck-boost converter when the load is not connected.These losses contribute to the overall reduction in system efficiency.

Discussion and important conclusions
The paper presents a highly efficient converter and a modified MPPT algorithm with an acceleration factor.The performance of the proposed system is extensively tested under dynamic conditions, including varying DC bus voltage, different insolation levels (such as Ropp, Sine, Ramp, step), variable loads, and various acceleration factors.Additionally, the system is evaluated with different configurations of solar The simulation and experimental results demonstrate that the proposed system is capable of achieving both lower and higher output voltages than the input PV voltage.This versatility allows for integration into series or parallel PV arrays with the appropriate rating of switches and passive components.Furthermore, the modified MPPT algorithm with the acceleration factor significantly reduces the time required to track the MPP.The proposed paper discusses the efficiency of the system with loss in every component contribution to be taken.Efficiency turns out to be around 95.77%.In the conventional P&O algorithm, it takes approximately 7 s to reach the MPP when there is a step change in solar irradiation from 300 to 1000 W/m 2 .However, in the proposed system with an adaptable step size, the time taken to reach the same level of MPP is reduced to around 3.7 s.This improvement in tracking speed is achieved by dynamically adjusting the step size of the MPPT algorithm based on the changing conditions.Similarly, the proposed system also adapts the step size of the MPPT algorithm when there is a negative step change in solar irradiation level.This adaptation ensures efficient and responsive tracking of the MPP, allowing the system to quickly adjust to changes in the environmental conditions and optimize power generation from the solar PV panels.
To validate the work, a comparative study, mentioned in Table 5, is conducted with the available literature to control standalone PV and storage systems with the proposed system.Overall, the findings of the paper highlight the effective-ness and adaptability of the proposed converter and MPPT algorithm, showcasing their potential for enhancing the performance and efficiency of solar PV systems.
Despite the excellent performance of the proposed system compared to existing PV standalone systems, there are areas for further improvement that are currently being researched and will be reported in the near future.The ongoing research activities focus on the following points: • Partial shading: the issue of partial shading in solar fields is being addressed by developing a global MPPT algorithm.This algorithm aims to optimize power generation even under conditions of partial shading.The inclusion of an acceleration factor remains important in this global MPPT algorithm to enhance its performance.• Galvanic isolation: to ensure the galvanic isolation between the input and output sides of the system, an isolated topology for a highly efficient DC-DC converter is being investigated.This topology will help address any potential issues related to electrical isolation and improve the overall system efficiency and safety.• AC load integration: to connect AC loads to the proposed system, a three-phase inverter is being explored for integration at the point of common coupling.This will enable the system to supply power to AC loads efficiently and effectively, expanding its applicability in various applications.The research activities on these aspects aim to further enhance the performance, functionality, and applicability of the proposed system, providing solutions to existing challenges and improving its overall efficiency and effectiveness.

Fig. 1
Fig. 1 Block diagram of the proposed system.a Power stages.b Control scheme for proposed converter.c Control scheme for bidirectional buckboost converter

Fig. 2
Fig. 2 Schematic diagram of proposed converter

Fig. 3
Fig. 3 Operation of proposed converter in non-ideal conditions.a Mode-I.b Mode-II

Fig. 4
Fig. 4 Solar I-V and P-V characteristics

Fig. 6
Fig. 6 Proposed converter with PV source

Fig. 8
Fig. 8 Flowchart for MPPT algorithm with acceleration factor

Fig. 10
Fig. 10 Schematic diagram of the proposed system's power circuit.a Power circuit.b Non-idealities/uncertainties

Fig. 13
Fig. 13 Efficiency variation with forward voltage drop of diode V d0

Fig. 15
Fig. 15 Simulation results.a Reference currents for different acceleration factors.b PV currents for different acceleration factors.c DC bus voltages for fixed PV input voltage.d Battery charging current with and

Fig. 18
Fig. 18 Simulation results for low or no solar irradiation

Forward voltage drop of D 1 ( 7 RFig. 21
Fig. 21 Simulation results with variations in non-idealities.a Parameters are as per Table 3. b Change of R L PC to 1 m .c Change of diodes to MOSFETs with R DS = 1 m .d Change of R L PC to 1 m

Fig. 23
Fig. 23 Hardware setup of the proposed system

Fig. 25 aFig. 26
Fig. 25 a Variation of battery charging current.b Variation of PV terminal current with variable solar insolation

Table 1
Some literature review

Table 2
Parameters adopted for simulation study

Table 4
Hardware setup specifications

Table 5
Comparative studies of the proposed scheme with existing PV standalone systems