Multiobjective Neuro-Fuzzy Controller Design and Selection of Filter Parameters of UPQC Using Predator Prey Firefly and Enhanced Harmony Search Optimization

Tis research introduces a unifed power quality conditioner (UPQC) that integrates solar photovoltaic (PV) system and battery energy systems (SBES) to address power quality (PQ) issues. Te reference signals for voltage source converters of UPQC are produced by the Levenberg–Marquardt back propagation (LMBP) trained artifcial neural network control (ANNC). Tis method removes the necessity for conventional dq0, abc complex shifting. Moreover, the optimal choice of parameters for the adaptive neuro-fuzzy inference system (ANFIS) was achieved through the integration of the enhanced harmony search algorithm (EHSA) and the predator-prey-based frefy algorithm (PPFA) in the form of the hybrid metaheuristic algorithm (PPF-EHSA). In addition, the algorithm is employed to optimize the selection of resistance and inductance values for the flters in UPQC. Te primary objective of the ANNC with predator-prey-based frefy algorithm and enhanced harmony search algorithm (PPF-EHSA) is to enhance the stability of the DC-link capacitor voltage (DLCV) with reduced settling time amid changes in load, solar irradiation (G), and temperature (T). Moreover, the algorithm seeks to achieve a reduction in total harmonic distortion (THD) and enhance power factor (PF). Te method also focuses on mitigating fuctuations such as swell, harmonics, and sag and also unbalances at the grid voltage. Te proposed approach is examined through four distinct cases involving various permutations of loads and sun irradiation (G). However, in order to demonstrate the performance of the suggested approach, a comparison is conducted with the ant colony and genetic algorithms, i.e., (ACA) (GA), as well as the standard methods of synchronous reference frame (SRF) and instantaneous active and reactive power theory (p-q). Te results clearly demonstrate that the proposed method exhibits a reduced mean square error (MSE) of 0.02107 and a lower total harmonic distortion (THD) of 2.06% compared to alternative methods.


Introduction
In recent years, the integration of distributed generating sources such as wind, tidal, and solar power into the distribution network has been encouraged to reduce the load and strain on VSCs [1].Additionally, using the unit vector generation approach for UPQC with a solar system was recommended to address difculties related to voltage and current [2].Subsequently, it was proposed to use multilevel UPQC with neural network-based signal generation to address PQ problems and do away with intricate p-q transformations [3].To address the PQ problems and get rid of complicated p-q shifts, the UPQC in conjunction with the solar energy storage system with neural network-based signal production was developed [4].In order to reduce the voltage and current THD, the fuzzy-based back propagation approach was also used for DLCV and reference signal generation [5].
Te several algorithms that are now in use to regulate DLCV regulation, current control methods, harmonic separation approaches, and SHAPF functioning are described [6].In the meantime, ANFIS was used to manage the series flter in order to handle voltage-related troubles [7].Te distributed energy system, which mixes PV and wind, was constructed to minimize load fuctuations and enable a smooth transition between the grid and the island [8].In the meantime, the PV-connected UPQC was demonstrated to reduce the THD at voltage changes such as sag and swell by utilizing the neural network.Additionally, the suggested approach was contrasted with methods based on reactive power and SRF theories under various load scenarios [9].To efectively manage the power and reduce the imperfections in the current signal, a combination of the grey wolf with particle swarm metaheuristic algorithms was selected to obtain the PIC's ideal gain values [10].
A feed-forward ANN was created for the wind system and solar PV systems of UPQC to maintain the DLCV steady and regulate the electricity [11].To solve PQ issues, a novel neural network signal production method was proposed for the fuzzy controller-operated MPPT for PV-connected UPQC [12].In order to efectively handle PQ difculties, a UPQC custom device with a multilevel converter was connected to the fuel cell combined PV and wind systems based microgrid in the near future [13].In the meantime, a thorough examination of various phased synchronization approaches that work well for SHAPF control and operation was conducted [14].To minimize THD, the GWO-based PIC was recommended for diferent UPQC loading circumstances [15].A novel approach was put forth to UPQC to stabilize DLCV oscillations and enable prompt, accurate fault restructuring [16].Neuron-based controller was developed to efectively address load current THD and grid voltage issues such as swell, THD, and sag [17].
To solve the PQ problems, it was proposed to hybridize the Improvedbat and Mothfame metaheuristic optimization techniques for choosing the PIC's gain settings [18].It was recommended that series hybrid active power flter use a fuzzy control for local distribution systems in order to successfully reduce voltage fuctuations and current THD [19].To address PQ concerns in the distribution system, PV and SBES integrated UPQC were advised to use a soccer match optimization for the best ANNC design [20].Te PV-linked ninelevel UPQC was created using an adaptive hysteresis with FLC to get voltage signals [21].Te best choice of PIC gain settings for UPQC was suggested using a soccer league in order to efectively manage both voltage fuctuations and current distortions [22].For 5-level UPQC, the neural network pulse generation system was created to efectively handle current and voltage aberrations [23].A novel approach was introduced to assess the level of harmonic emissions, utilizing a piecewise probabilistic high-pass flter algorithm.To begin with, a piecewise probabilistic harmonic coupled model (HCM) is employed to examine the harmonic produced by residential loads [24].A stochastic scheduling methodology that integrates risk restrictions for an energy hub was introduced, taking into account uncertainties associated with renewable generation and load needs [25].Furthermore, based on the established HSS model, the primary parameters are identifed by analyzing the eigenvalues of the system state matrix, in conjunction with the participation factors [26].A hybrid-modifed GSA-PSO (MGSA-PSO) strategy was suggested to improve the load dispatch of a microgrid with electric vehicles by combining the gravitational search algorithm (GSA) and particle swarm optimization (PSO) algorithm [27].
A distributed optimization approach was presented that aims to reduce the overall generation cost in a dynamic economic dispatch problem (DEDP) for a hybrid microgrid network.Te hybrid microgrid model was built using a combination of conventional power sources, renewable energy sources, and energy storage batteries [28].Meanwhile, an overview of diferent decentralized control methods for MGs was recently published, based on research.Te methods used in each study are fully described, along with their results [29].Te approach that consists of two primary components was developed: global search and local search.Te global search, utilizing the modifed SCO method, combines the density peak clustering (DPC) algorithm and the cooling scheduling function [30].However, to address the issue of selecting an appropriate confguration from three available HP flter options for a specifc harmonic problem, three HP flters analytically were presented in contrast to traditional optimization-based flter research [31].Besides, a crucial concern regarding power management control in autonomous hybrid systems was suggested that there are difculties in improving the efciency of energy sources and backup systems, particularly when dealing with high demand or limited renewable energy production [32].
Te majority of research articles employing evolutionary algorithms focused solely on fne-tuning the parameters of the traditional PIC.Furthermore, it demonstrates how the UPQC's current traditional management plans incorporate both Clarke's transformations and the complex parks.In combination with photovoltaic (PV) systems and SBES, this work provides a unique ANN control technique for UPQC that determines the optimal ANFIS controller settings using PPF-EHSA.

2
International Transactions on Electrical Energy Systems Tis work's principal contributions are as follows: (i) Generation of reference signals for the SHAPF and SAPF of the UPQC, with LMBP-trained ANNC to prevent the usage for the complex abc to dq0 to shifting (ii) Design of optimal ANFIS controller with PPF-EHSA for DLCV balancing in SHAPF in addition to choosing the UPQC flter parameters for THD minimization and to handle PQ troubles such as harmonics, sag, unbalances, and swell efciently (iii) Additionally, in order to meet the demand, minimize the stress and rating of the VSCs, and keep stable DLCV, the PV with SBES is linked to the UPQCs (iv) Four separate test scenarios for various combinations of supply voltages, G, temperature, and load circumstances were used to validate the designed system and show how well it performed overall in terms of current THD and PF using waveform analysis (v) Performance evaluation with GA and ACA techniques and similarly with p-q and SRF approaches Section 1 provides an overview of the paper, followed by Section 2 outlining the UPVBSS design, Section 3 elaborating on the control scheme, Section 4 discussing the acquired results, and Section 5 concluding the paper.Here, the battery is linked to a DC capacitor via a buck-boost converter (B-B-C) and PV via a boost converter (B-C).Besides, V abc denotes the grid voltage, and V S_abc resembles the grid phase voltage.Te load voltage and current are denoted by the symbols V l and i l .L S stands for grid-side inductance, whereas R S stands for grid-side resistance.UPQC is the acronym for the combination of series and shunt VSCs.In order to address grid-side voltage-related problems, SAPF uses the injecting transformer to supply the proper compensating voltage V se .Te RL flter consists of two parts: the inductor L se and the resistor R se .Te SHAPF is connected to the grid by resistance R sh , which interfaces with inductance L sh .Te goal of SHAPF is to minimize the harmonics and to keep DLCV constant with a brief settling time by injecting a sufcient compensatory current through the point of common coupling (PCC).

Modelling of Solar and Battery Systems.
By adding solar and batteries to the UPQC's DC-link, the utility's demand for converters is reduced, negating the need for high ratings.In this case, B-C is utilized to increase the solar system's and buck-boost converters' output.Te battery connected to the DC-link is charged and discharged using B-B-C to control the DLCV when loads vary.Te controller for the PV and batteries is described because the modeling of these systems is already accessible in the literature [5].Equation (1) provides the power demand () for the proposed approach.P PV ± P BSS � P L . (1) 2.1.1.PV System.Te solar radiation is converted into electrical power by the SPG structure.Te quantity of series and parallel connections made to these PV cells is a determining factor in the necessary solar generation.Te PV model used in this study is from the Simulink library.To extract the highest yield from modules, however, the MPPT algorithm (incremental conductance) was selected.Te PV system's (PPV) power is determined by the following equation: In this section, the terms "i PV " and "V PV " stand for the current and voltage that a solar panel produces, respectively.In this study, the P and O are ofered as MPPT to manage the B-C duty cycle (D) and generate the maximum output power.

SBES.
Te DLCV is stabilized by the SBES in support with B-B-C.Equation (3) expresses the state-of-charge-ofthe-battery (SOCB).
Te output generated by PV will determine whether a battery is in the charging or discharging state by meeting the top and bottom bonds given by the following equation: Te i ref dc is computed by minimizing the DLCV error V dc,err by a PIC.Te battery error reference current i BS,err * is calculated using PIC.Where i BS,err refects the mismatch between the reference current of battery i ref BS obtained from the flter and the i ref dc retrieved from it.Te controller of the developed system with the hybrid algorithm is given in Figure 2, and the graphical layout of the power fow is shown in Figure 3. Te power fow between grid, load, solar, and battery is clearly illustrated in the forms of waveforms in results and discussions as case studies.5) can be used for determining the C dc value [5].

DC Capacitance (C dc ). Equation (
Te V ref dc is selected within the range of ratings allowed by the recommended approach.Te selection of C dc is infuenced by shunt corrective current and voltage ripple (V r,pp ).

Inductor for Shunt
Converter.By shunt inductor (L sh ), the shunt converter is connected to the system.Equation (6) gives the frequency of switching, ripple current, and DLCV.

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Peak-to-peak ripple current (I r,pp ) determines the magnitude of L sh considering that the frequency of switching (f sh ) is 10 kHz, the modulation depth (m) is 1, and the overloading factor (a f ) is 1.5.

Inductor for Series Converter with Isolation Transformer.
Te series VSC is connected to the grid using a power injection transformer, and the design requirements are given in the following equations: with a 10 kHz frequency of switching, and the series inductance is dependent on the ripple current.

Artificial Neural Network Control
VLDC typically fuctuates in tandem with changes in the distribution side dynamic load.However, before the system can resume regular operation, it needs to swiftly revert to its initial condition (VLDC).Here, fring pulses are generated using the suggested ANNC to manage the PWM hysteresiscurrent of the shunt VSC.

Shunt VSC.
By introducing corrective current, SHAPF aims to eliminate current waveform distortions and stabilize DLCV in fault and transient loading conditions.

Optimal Selection of ANFIS Parameters for DLCV Stability.
It is advised that the ANFIS keeps the DLCV constant.Te proposed ANFIS combines the capabilities of an ANNC and FLC to create a smart combination controller.However, to keep the DLCV steady, the acquired DLCV and the selected reference DLCV are compared, and the variation in error (CE) and its output error (E) are taken into account as inputs.As seen in Figure 4, the inputs given into the neural network are frst trained based on the triangular membership to yield optimal results.Te ANFIS is primarily composed of fve layers: fuzzifcation is the frst layer, and its outputs are fuzzy MSF, which are determined by the following equation: Here, μ Ai μ Bj resembles the memberships received as the output from the 1st layer.
Te triangular membership is expressed by the following equation: where b i is the fuzzy set i's point of greatest support and x min , x max (lower and upper bonds) is the range (world of discourse) of x.Under normalization, − 1 and 1 are regarded as lower and upper bonds in this work.Te subsequent items are classifed as inputs and outputs: positive small (POSS), positive big (POSB), positive medium (POSM), negative small (NEGS), negative big (NEGB), negative medium (NEGM), and zero (ZERO).Te MF's inputs and outputs are shown in Figure 5.
Where the AND operator is used in the second layer (weighting of fuzzy rules) to determine the strength of fring  International Transactions on Electrical Energy Systems by using the MSF in the frst layer, the output of which is determined by the following equation: In the third layer, which receives data from the preceding layer, values are normalized.By calculating the ratio of the fring strength (true values) for the k th rule to the total fring strength of all rules, every node achieves normalization, as shown by the following equation: By using the inference variables (p k , q k , r k ) in the fourth layer (defuzzifcation), the ANNC can adapt to itself.Te output of this process is provided by the following equation: Finally, in equation ( 14), at the ffth layer, all the inputs are added to generate the necessary total ANFIS output.
Figure 6 displays the layout of ANFIS.Te goal of the hybrid algorithm that combines PPFA and EHSA is to optimize the a i , b i , and c i of membership in order to Three phase Non-Linear and unbalanced Loads  International Transactions on Electrical Energy Systems minimize learning errors and enhance the overall performance of the ANFIS controller.Te goal of the problem is to evaluate the ftness function provided by equation ( 15) in order to achieve the objective (obj), which is expressed as MSE.
MaximizeF � Here, o is the desired result, o is the output that was obtained, and m is the number of instances.Te fundamental and harmonic components of current are resembled by I n , I 1 .A detailed discussion of the suggested hybrid algorithm is given.

PPFA.
Te frefy algorithm is motivated by the illuminated habits of the collection of frefies.First, an arbitrary set of frefies is generated in the space.Each frefy here represents the required solution, which is entirely dependent upon the parameters chosen for control.Each frefy (y) represents the control parameters whose limits are expressed as follows: where nd � total variables Te frefies' bioluminescent communication is used by this program to control their movement.Every frefy is drawn to the illumination of the opposing frefy and tries to move in that direction.Te frefy's illumination function (F) provides the ideal solution for the selected issue.Tis approach computes the illuminating function iteratively and modifes their placements accordingly.Equation (17) represents the attraction between the i th and j th frefies.
where r ij is the Cartesian distance, as calculated by equation ( 18) between the frefy i th and j th .
Te i th frefy moves toward the other j th frefy in the group and changes its position if BF j is bigger than BF i according to the following equation:   International Transactions on Electrical Energy Systems Firefies (prey) encounter challenges in remaining at their desired locations when pursued by predators.Instead, they seek new locations that are devoid of predators and potentially more favorable.Te predatory behavior aids frefies in efciently exploring the search area.Te predation by predators is regulated by a modest hunting probability factor η, and the predators are characterized based on the least optimal solutions.
Te frefies consistently distance themselves from predators, a behavior that can be represented through modeling.
Te improved frefy algorithm prevents the swarm from converging to a suboptimal point in the search space.Instead, it enhances exploration capabilities and compels the population to settle at the globally optimal solution.
International Transactions on Electrical Energy Systems 3.1.3.EHSA.Tis metaheuristiciterative strategy, which takes inspiration from artists' improvisational approach to music, explores problem space to fnd the best global solution thatmaximizes the chosen ftness function (F) while meeting the problem constraint.Te problem space is defned by a harmony memory (HM), which consists of several candidate solutions, each representing a harmony, as outlined in the following equation: Te goal of the optimization is to minimize error by optimally selecting the MSF parameters a i , b i , and c i in the ANFIS.Te harmony ftness function (F), which is derived from the goal as the selected problem as shown in equation (15), evaluates the quality of each harmony.As stated in equation ( 23), an improvised harmony is produced by comparing a random number with the HM adjusting rate (HMAR) value.
if(rand ( ) < HMAR) Here, 0∼1 is a random number and rand ().Equation ( 24) modifes the pitch of every variable in the improved harmony according to the pitch tuning rate (PTR).if(rand ( ) < PTR) Here, BW stands for bandwidth.Te poorest harmony in the HM is substituted by the new harmony h ′ if the improved harmony vector h ′ is better than the worst harmony.
Te conventional harmony search optimization may fall into suboptimal traps during problem-solving due to the absence of a jumping mechanism.To address this issue, this section introduces a mechanism utilizing poorly composed music that induces dissonance.Referred to as the dissonance-avoiding mechanism, it draws inspiration from the predator-prey optimization concept, enabling the newly generated harmony to jump away from unfavorable harmonies.If the spontaneous combination of musical tones resembles the unpleasant combination of tones in the harmonic minor scale, the newly created combination of tones may result in discord.Te new harmony must be altered to ensure its dissimilarity from bad harmony by augmenting the Euclidean distance (c) between them using the following equation: Here, α resembles the dissonance factor.Te process of generating new harmony is iterated until convergence.Every fy modifes its location, HMAR, and PTR in HSA based on the F value, which helps the convergence to accurately signify the global optimal solution.Te process is executed until it reaches the maximum number of iterations (T max ).Te HS method ofers notable benefts such as fast convergence, minimized parameter changes, and straightforward implementation.Nevertheless, it exhibits other shortcomings, such as suboptimal convergence speed and premature convergence.Table 1 presents the parameters chosen for the suggested optimizations and their subsequent comparison.
Step 2. Assess the Brightness function F.
Step 3.While t < T max Arrange the frefies based on their brightness; for i � 1: Give value for i th frefy (all frefies) do Execute simulation and obtain THD using equation (17) for j � 1: Give value for j th frefy (all frefies) do Execute simulation and obtain THD using equation (17) if (F j < F i ) then By calculating equation ( 19), move frefy j toward i using equation ( 22

Neural Network for Reference Signal Production.
Figure 7 illustrates the proposed artifcial neural network (ANN) controller for the shunt flter.Te ANNC confguration includes the input layer (IPL), hidden layer (HIL), and output layer (OPL).Te objective of IPL is to collect the given data and transmit it to the HIL.Te weights on the interconnected linkages between the IPL and HIL are subsequently multiplied by this quantity.At this location, mathematical calculations are carried out with a preestablished inclination towards HIL.Ultimately, the OPL is employed to resolve the discoveries.To ensure accurate results, the link weights are modifed during training through an evaluation of the error.Tus, the LMBP training strategy is employed to achieve expedited convergence.
Figure 7 designates the reference currents (i ref sh_a , i ref sh_b , i ref sh_c ) as the desired data, while the load currents (i l_a , i l_b , i l_c ) and DC loss component (Δi dc ) are treated as the input.Figure 8 illustrates the expected BP structure for the 200 neurons in the HIL system, which is utilized to generate the reference current signal.Te shunt VSC is believed to generate the required gating signals through the operation of a hysteresis controller within the ±0.25 A and ±0.5 A range.

Series Converter.
Te principal function of a SAPF is to reduce grid voltage disruptions and ensure a constant load voltage by generating compensating voltages.Figure 9 illustrates the suggested control system for the VSC series.Te supply voltage signal (V s_a , V s_b , and V s_c ) is considered as input data for generating the reference voltage signals (V ref se_a , V ref se_b , and V ref se_c ), which are considered as target data for the neural network.Figure 10 provides the confguration of a neural network with 200 neurons in the HIL.PWM is employed to generate the sequence of VSC gating pulses.

Results and Discussion
Te proposed UPVBSS with ANNC was implemented using MATLAB 2016a.Te appendix provides the system's and UPQC's confgurations.Four test cases were selected to show the functionality of the proposed ANNC-controlled PPF-EHSA.Tese test cases involved diferent rectiferbased nonlinear loads, balanced and unbalanced, as well as varying source voltages.Additionally, the test cases included circumstances such as swell, disturbance, and sag, which were infuenced by changing irradiation (G).
Te test cases are presented in Table 2.In case 4, V S is selected as an unbalanced phase supply, while, for cases 1-3, it is chosen as a balanced phase supply.Te investigation focused on cases 1 and 2, specifcally examining concerns related to balanced sag and swell.Besides, the unbalanced condition is assessed in case 3. Tis study focuses on minimizing THD by optimizing the selection of flter parameters R se , R sh , L se , and L sh .Te limits for these parameters are chosen as (0-10), (0-0.5),(0.01-10), and (0.01-10), respectively.Te major objective is to improve PF and ensure a constant DLCV by optimizing the selection of parameters for the ANFIS.Te performance of the proposed ANN-based PPF-EHSA is demonstrated by comparing the results with GA and ACA approaches.Figure 11 presents the convergence plot of MSE for the suggested technique, genetic and ant colony algorithms in relation to case 1. Te PF is determined by applying equation (26) to the obtained THD.
For the frst case study, the balanced voltage source is used to analyze the behavior of the SAPF.According to Figure 12(a), 30% of balanced sag and swell occurred in the range of 0.2 to 0.3 seconds, and another occurrence happened between 0.4 and 0.5 seconds in the VS system.ANNC accurately detects and responds to changes in voltage, effciently providing the necessary compensating voltage to provide a constant load terminal voltage.To assess the performance of the suggested approach's SHAPF, we examined load 1 and load 4. Te load current shape in Figure 12(b) is nonsinusoidal and balanced due to the presence of harmonics.Te proposed solution rectifes the defciencies in the existing waveform, resulting in a reduction of the THD of the current waveform from 17.74% to 2.06% and an increase in the PF to 0.9898.In addition, as illustrated in Figure 12(c), the proposed approach regulates the constant DLCV under a fxed 1000 W/m 2 light and a constant temperature of 25 °C.Figure 12(d) demonstrates that the suggested system adequately meets the load demand

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In case study 2, which is similar to Case 1, the V S is chosen to be balanced.To verify the functionality of the series flter, a disturbance is introduced from 0.6 to 0.7 seconds.Nevertheless, as depicted in Figure 13(a), ANNC accurately identifes the disruption in the grid voltage and resolves it by introducing the required compensatory voltage.As a result of the simultaneous operation of loads 1, 2, and 3, the i l waveform was determined to be  International Transactions on Electrical Energy Systems    In the third case study, the V S is deliberately adjusted to achieve a balanced state.Tis balanced state is then subjected to a 30% increase in sag and swell, as well as an external disturbance, in order to verify its performance.Nevertheless, as depicted in Figure 14(a), ANNC accurately identifes the asymmetrical phase voltage fuctuation, voltage increase, and disruption and resolves it by introducing the required compensatory voltage.Furthermore, in order to assess the efciency of the SHAPF, loads 1 and 4 were consolidated, and at the 0.7-second mark, load 3 was added.Consequently, the resultant waveform exhibited signifcant contamination, imbalance, and amplifed magnitude, as depicted in Figure 14(b).Te proposed method rectifes the disparities in the current signal.Te PF rises to 1, and the THD of the current signal decreases from 3.76% to 27.44%.Furthermore, Figure 14(c) demonstrates that the proposed controller efectively keeps the DLCV constant while   International Transactions on Electrical Energy Systems simultaneously meeting the load requirements specifed in Figure 14(d).
In the fourth case study, it is believed that the V S is unequal in phases.However, the system identifes the imbalances and efectively rectifes them, as depicted in Figure 15(a).In this case, loads 1 to 3 were sequentially connected by incrementally applying to the existing load at time intervals of 0.1 seconds to 0.4 seconds, 0.4 seconds to 0.6 seconds, and 0.6 seconds to 0.7 seconds, respectively.Consequently, the i l waveform was determined to be contaminated and lacking equilibrium, as depicted in Figure 15(b).Te THD decreased from 25.86% to 3.43%, and the PF rose to a value of 1. Furthermore, as illustrated in Figures 15(c Figures 16 and 17 present a comparison of the THD and PF between the suggested methodology and other commonly used methods such as GA, ACA, p-q method, SRF, and other controllers mentioned in the existing literature.Te data demonstrate that the suggested approach has much lower THD and higher PF in comparison to existing techniques.Te PPF-EHSA optimized ANFIS enhances the system's efciency by minimizing error and improving the adjustment capability of the UPQC.Table 3 presents the comparison of the MSE values obtained from the algorithms.Te data demonstrate that the proposed approach yields   4. Figure 11 demonstrates that the proposed PPF-EHSA achieves a lower MSE in a smaller number of iterations (22), indicating faster convergence compared to GA (45) and ACA (39). Figure 18 depicts the FFT analysis of the proposed system for case study 4. Furthermore, based on the fndings presented in Figure 19, the implemented strategies demonstrate their ability to rapidly stabilize the DCLV in a brief duration (almost less than 0.1 seconds) amidst changes in both load and irradiation.Tis is signifcantly lower compared to the efectiveness of alternative methods.

Conclusion
Tis study presents an innovative LMBP-trained ANNC method for producing the reference signals for SBES and battery-associated UPQC to avoid the complex abc to dq0 conversions.Additionally, the PPF-EHSA algorithm is used to design the optimal MSF of ANFIS and flter parameters, with the multiobjective of decreasing both the MSE and THD.Besides, the suggested UPVBSS ensures a consistent DLCV under various conditions such as loads, sun irradiation, and temperature fuctuations.It also efectively reduces current harmonics, enhances the current waveform, hence improving the PF, and eliminates voltage fuctuations.In the future, the approach can be extended to incorporate advanced metaheuristic algorithms for the implementation of multilevel UPQC.

Figure 1
Figure 1 displays the suggested UPVBSS schematic diagram.Here, the battery is linked to a DC capacitor via a buck-boost converter (B-B-C) and PV via a boost converter (B-C).Besides, V abc denotes the grid voltage, and V S_abc resembles the grid phase voltage.Te load voltage and current are denoted by the symbols V l and i l .L S stands for grid-side inductance, whereas R S stands for grid-side resistance.UPQC is the acronym for the combination of series and shunt VSCs.In order to address grid-side voltage-related problems, SAPF uses the injecting transformer to supply the proper compensating voltage V se .Te RL flter consists of two parts: the inductor L se and the resistor R se .Te SHAPF is connected to the grid by resistance R sh , which interfaces with inductance L sh .Te goal of SHAPF is to minimize the harmonics and to keep DLCV constant with a brief settling time by injecting a sufcient compensatory current through the point of common coupling (PCC).

Figure 2 :
Figure 2: Controller system with hybrid algorithm.

Figure 5 :
Figure 5: Fuzzy MSF for E and CE.(a) Membership for E. (b) Membership for CE.

Figure 13 :Figure 14 Figure 14 :
Figure 13: Waveforms for case study two.(a) V S , V se , and V l .(b) i l , i sh , and i s .(c) G, temperature, P PV , V PV , and V dc .(d) Grid power, PV power, battery power, and load power.
) and 15(d), the proposed controller efectively ensures a consistent DLCV despite changes in load, variations in irradiation, and a constant temperature of 25 °C.It successfully fulflls the required demand.

Figure 15 :
Figure 15: Waveforms for case study four.(a) V S , V se , and V l .(b) i l , i sh , and i s .(c) G, temperature, P PV , V PV , and V dc .(d) Grid power, PV power, battery power, and load power.

Figure 16 :
Figure 16: THD comparison for case studies.

Table 3 :
MSE comparison.Bold values indicate and highlight the best as well as the proposed model result.
Figure 19: Time in sec taken for DLCV to reach stable.Figure 17: PF comparison for case studies.International Transactions on Electrical Energy Systems current at output: 5.58 A; open circuit voltage: 64.2 V; short circuit current: 5.96 A. Battery: nickel metal hydrate; nominal voltage: 500; SOC: 60%; full charge voltage: 588.983; rated capacity: 100 Ah; cut-of voltage: 37 V