Advancing Electric Vehicle Charging Ecosystems With Intelligent Control of DC Microgrid Stability

The increasing adoption of renewable energy sources (RES), such as solar photovoltaics and wind turbines, is transforming electricity generation. However, integrating RES within DC microgrids (DCM) for applications such as fast DC charging in electric vehicles (EVs) presents challenges, including low inertia, power fluctuations, and voltage instability. This study addresses these challenges with novel control strategies and optimization algorithms. A hybrid Firefly Algorithm-Particle Swarm Optimization (FA-PSO) approach is used to tune Takagi-Sugeno Fuzzy Inference Systems (TSFIS), Adaptive Neuro-Fuzzy Inference Systems (ANFIS), and Fractional Order Proportional-Integral-Derivative (FO-PID) controllers. This strategy optimizes power management within the DCM, ensuring faster convergence, superior accuracy, and reduced topological constraints. In addition, a comprehensive Small Signal Stability Analysis (SSSA) evaluates the impact of the proposed hybrid optimization techniques on DC microgrid stability. Crucially, a hardware prototype validates these strategies under real-world uncertainties, such as varying wind speed and solar insolation, demonstrating their effectiveness and feasibility for practical DC microgrid applications with integrated EV charging.


AC
I N RECENT years, a combination of renewable energy sources (RES) and energy storage technologies is transforming electricity generation.Sources like solar photovoltaic (PV) are increasingly used alongside energy storage options like solid oxide fuel cells (SOFC) and battery energy storage systems (BESS).This shift, driven by environmental concerns and the depletion of fossil fuels [1], [2], is enabling the growth of electric vehicles (EVs) that rely on fast DC charging solutions.EV charging stations, especially those integrated with DC microgrids (DCM), face challenges such as low inertia, unreliability, and the irregular nature of RES, which affects their operation and control [3].Integrating RES and energy storage within DCMs through DC/DC or AC/DC converters can address the challenge of stabilizing the DC bus voltage and reducing power consumption during standalone operations [4] [5].Strategies such as a three-level DC voltage control in a four-terminal DC microgrid using droop-based power-sharing, decentralized voltage control techniques [6], modified droop algorithms [7], and modified DCbus signaling methodologies for integrated systems have been proposed to enhance the quality, efficiency, and flexibility of the integration of RES in EV charging stations [8].
Research into stability, voltage regulation, and power management of DC microgrids is an active field, with significant contributions focusing on both AC/DC hybrid systems and pure DC microgrid configurations [9], [10], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26].However, there are persistent challenges regarding optimal controller performance, the need for more adaptive control strategies, and handling system uncertainties that create voltage fluctuations and other stability concerns.A novel non-linear disturbance observer-based control algorithm introduced in [9] aims to improve the power quality and voltage dynamics of the DC bus.The robust nonlinear control scheme equation presented in [10], based on the Hamilton-Jacobi-Bellman equation, is designed for effective power management in DC microgridoriented EV charging stations.Furthermore, a combination of current-and droop-based feedforward control strategies is proposed using an observer-based methodology to ensure robustness and stability of the DC microgrid system, while [10] suggests an adaptive droop control strategy with normalization and projection algorithm for improved voltage stability and current sharing.Research in [12] discusses an energy management control strategy for power balancing in multisource DC microgrids, and [13] proposes a series voltage regulator to control DC-bus voltage, with improved power management control strategies reported in [27], [28] for hybrid DC microgrids by combining voltage and SoC of energy storage devices, addressing the limitations of conventional PI-controllers during transient operations with variable system parameters.
In the realm of DC microgrids, various optimization algorithms and control methods are employed to address challenges of stability and power quality.The Firefly Algorithm (FA) is highlighted in [29] for its easy hardware implementation, fast convergence, precision, and low computational burden.However, FA exhibits limitations like slow convergence rates or becoming trapped in local optima.The Particle Swarm Optimization (PSO) method, noted for its rapid convergence and efficiency in finding better solutions in less time, is discussed in [30].PSO is respected in the optimization community for not requiring learning rates and initial parameter calculations, having been a popular metaheuristic swarm intelligent method for over two decades.Hybrid optimization approaches like FA-PSO show promise in addressing these shortcomings, leveraging the global exploration of FA and the rapid convergence of PSO.Intelligent fuzzy logic-based controllers such as the Takagi-Sugeno fuzzy inference system (TSFIS) and adaptive neuro-fuzzy inference systems (ANFIS) are introduced [31], prized for their robust voltage control, power balance, ease of implementation, and low-cost processor demands.However, these FLCs require expert knowledge and a rule-based system design, which presents a challenge [28], [32].Artificial Neural Networks (ANN), known for rapid voltage tracking, require extensive data for effective training and testing [33].ANFIS is recognized for combining the advantages of FLC and ANN but requires proper data training and updating for enhanced performance [33], [34].Integration of optimization techniques such as FA and PSO with ANFIS is seen as a promising approach to overcome the challenges of the DC microgrid [34].In [35], PSO and ANFIS are merged for photovoltaic power prediction, optimizing ANFIS parameters through PSO to achieve faster convergence, high accuracy, simplicity, and reduced topological constraints.
Small Signal Stability Analysis (SSSA) is used to scrutinize the behavior of DC microgrid (DCM)-oriented EV charging stations during minor disturbances like load or generation level changes, involving the linearization of the system and examination of eigenvalues of the resulting equations [36], [37], [38], [39], [40], [41], [42], [43].Integrating optimization techniques such as FA-PSO and intelligent fuzzy logic controllers (FLC) like TSFIS and ANFIS significantly influence the system's dynamic characteristics, particularly when using FLC to fine-tune the parameters of the Fractional Order Proportional-Integral-Derivative (FO-PID) controller.This integration, especially through hybrid optimization techniques applied to the control parameters of TSFIS, ANFIS, and FO-PID, can lead to a unique dynamic response of the system, improving its adaptability and robustness against uncertainties and nonlinearities.Thus, the impact of hybrid optimization techniques on SSSA is crucial, particularly in power system control applications, highlighting the significance of FO-PID controllers receiving input from FLCs in achieving more robust and adaptive control amidst system uncertainties.To ensure stability and meet performance requirements, meticulous analysis and testing of the resulting dynamic system response should be undertaken, aspects not underlined in [1].This paper addresses the identified shortcomings by: r Developing a comprehensive SSSA framework for DC microgrids, explicitly designed to enhance voltage stability across various operating conditions and uncertainties.
r Proposing a hybrid FA-PSO algorithm specifically aimed at improving DC-DC boost converter efficiency and adaptability within DC microgrids.
r Demonstrating the effectiveness of TSFIS and ANFIS Fuzzy Logic Controls, optimized with FA-PSO, in enhancing FO-PID controller performance.This approach offers the potential for faster convergence, precise voltage regulation, and adaptability to uncertainties in DC microgrids.This paper directly addresses the challenges of integrating fast DC charging for EVs by ensuring stable voltage conditions within the DC microgrid.This is a critical aspect for future power systems as EV adoption increases.Section II describes the SSSA for each subsystem within the DC microgrid.The control approaches for these individual subsystems are detailed in Section III.Section IV provides empirical validation along with related discussions.The work is summarized and concluded in Section V.

II. SMALL SIGNAL MODELING OF INTEGRATED DERS
In this Section II, a comprehensive description of the DC microgrid system designed for the Electric Vehicle (EV) charging station is provided.This system, depicted in Fig. 1, is seen to encompass a variety of subsystems including PV panels, a Wind Turbine powered by a Permanent Magnet Synchronous Generator (PMSG), a SOFC, a BESS, an Electrolyzer, and Nonlinear EV loads.The characteristics and capacities of these components, such as the power capacity of the PV panels (e.g., 6 kW), the size of the BESS (e.g., 10 kWh), and the EV charging power (e.g., 2 kW), are explicitly highlighted to ensure better clarity and understanding.Moreover, in this section, the dynamic modeling of each subsystem is delved into, with a state-space modeling approach being employed, complemented by relevant assumptions and simplifications.A deeper insight into the modeling process is provided to the readers through these elaborations.To ensure effective control of each energy source, small disturbance studies are conducted through the Small Signal Stability Analysis (SSSA) of each subsystem.The analysis of power electronics-based converters, crucial for understanding the dynamic and stability performance of voltage/current, is presented, with variations in system parameters and duty ratio being taken into account.

A. SSSA of the PV cell converter control
In this paper, a single-diode PV cell from SUNTECH Power Holdings Co. Ltd is considered with a module power rating of 290 W and a nonlinear current-voltage characteristic function [27].The series and parallel combination of this PV module is detailed in Table I.The operating solar irradiance values of the PV system is 100 W/m 2 to 1000 W/m 2 and further analyzed applying the appropriate Maximum Power Point Tracking (MPPT) techniques [27], [28].This characteristic behavior of the PV modules/systems significantly influences the design of the power converter and the control system.The small signal transfer functions of the converters are derived using small perturbations in the output voltage and/or current and duty ratio around their steady-state operating values, as illustrated in the closed-loop state-space equation of the PV boost converter with perturbated state variables { ĩpL , ṽpv , ṽ0 }, given in (1).
where L pv and C p are the inductance and capacitance of the boost converter, respectively.C pv is the capacitance of the PV cell.D pv is the pulse width modulation (PWM) duty ratio of the PV converter.R eq pv and R p are the equivalent resistance of the PV cell and the load resistance, respectively.V 0 and I pL are the rated output voltage and the load current of the converter, respectively.ĩpL , ṽpv , ṽ0 and d are the small signal inductor current, the output voltage of the PV system, the output voltage of the converter and the control variable duty ratio due to a small perturbation, respectively.To design the controller, the values of V 0 = V dc , L = 450V , I pL = 16A, L pv = 3.2mH, C pv = 100 μF , R eq pv = 4.5 Ω, R sh = 250.174Ω, R s = 0.221 Ω, C p = 2000 μF , and D pv = 0.78 are considered.Detailed specifications for the PV system are presented in Table I.
After putting the value of V 0 , I pv , L pL , C pv , D pv , R eq pv and R p , the small signal open-loop state-space equations of the boost converter system are derived as (2).Firstly, the inductor current (i pL ) to duty ratio transfer function is evaluated; followed by a PI-compensator with proportional and integral controller gains (i.e.k p1 and k i1 ) is designed to achieve the proper phase margin and bandwidth.Later, the transfer function of the PV voltage to the inductor current i pL is formed, and the corresponding controller is designed to obtain a minimum phase margin of 60 • due to low system gain.To achieve the desired phase margin of the system, the gains (k p2 and k i2 ) of the PI controller / compensator are designed to Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

B. SSSA of the wind system converter control
In this study, a variable speed PMSG-based wind turbine is considered in the microgrid system.The P&O based control methodology is employed for extracting the maximum power from the wind turbine [27].The generalized structure of the wind turbine generator (WTG) with converter control is given in Fig. 1.A buck converter is employed to control the DC output voltage of the WTG at the desired level.The small signal analysis is used to design the PI-controller, as in [44].The open-loop small signal/linearized state-space equations of the buck converter are obtained as (3) [45].
The small signal transfer function can be evaluated as (4).
where R s and L s are the stator resistance and inductance of PMSG, respectively.p is the number of magnetic poles of PMSG, J and f are the moment of inertia and coefficient of friction of PMSG, respectively.D w is the duty ratio of the wind-based converter.L w and C w are the inductance and capacitance of the wind turbine converter, respectively.i dcW , i qW , ω m and d denote the small signal rectifier current, quadrature-axis current, rotor speed, and duty ratio due to small perturbations, respectively.In this study, the value of R s = 0.39 Ω, L s = 0.0082 mH, C w = 1500 μF, L w = 10 mH, C d = 1000 μF, p = 10, J = 0.01197, f = 0.001189 and the rated rotor speed (ω r = 153 rps) are chosen to design the controller parameter and the modeling.The detailed modeling data of the wind system is taken from [27].In this study, the cut-in and cut-out wind speeds of the PMSG-based wind turbine system are taken as 6 m/s 2 and 15 m/s 2 , respectively.The PI controller parameter of the wind-based converter is obtained by a similar approach to that discussed in Section II-A.The design value of the PI controller parameters of the PMSG-based wind system is indicated in Table II.

C. SSSA of electrolyzer converter control
In this work, the empirical current-voltage relationship is used to model the electrode kinetics of the electrolyzer cell.The detailed modeling of the electrolyzer is taken from [27], [28].The detailed modeling specifications of the electrolyzer system are obtained from [27].The corresponding open-loop state-space equations of the converter can be derived as ( 5) and the corresponding small signal transfer functions are evaluated as (6).
where V e is the operating output voltage of the electrolyzer, V e1 is the output voltage of the inner converter, V 0 is the output voltage of the outer converter, L e and C e are the inductance and capacitance of the converter, respectively.R e is the load resistance of the electrolyzer and the duty ratio of the electrolyzer converter is D e .The small signal inductor current, electrolyzer output, capacitor output voltage, and duty ratio due to small perturbations are taken as i L2 , v e1 , v 0 and d, respectively.The values of V e = 86 V, V e1 = 86 V, L e1 = 10 mH, C e1 = 100 μF, L e2 = 20 mH, C e2 = 500 μF, D e = 0.2 and R e = 0.08 Ω are taken to design the controller/converter in this study.The operating voltage of the electrolyzer is 86 V.The main objective of the PI controller is to improve the performance of the system and follow the reference voltage signal.The design value of the electrolyzer PI control parameters is given in Table II.

D. SSSA of battery energy storage system converter control
The modeling of the battery is realized by using a controlled voltage source in series with a constant resistance [27], [28].The detailed modeling data of the BESS are taken from [27].In BESS, to obtain the PI control parameters, the same methodology is followed as discussed in Section II-A.The small signal state-space equations of the BESS converter are represented as ( 7)- (8). where

E. SSSA of fuel cell converter control
In this study, a generic SOFC model is taken into account [27], [28].The small signal/linearized state-space equations of the converter can be written as (10).
where V f is the operating output voltage of the fuel cell, L f and C f are the inductance and capacitance of the boost converter, respectively.C fc is the capacitance of the fuel cell.R f is the load resistance, V o is the output voltage of the converter, and the duty ratio of the fuel cell converter is D f .Fuel cell current, output voltage, converter output voltage, and duty ratio of the small signal caused by small perturbations are ĩf ,ṽ f and ṽ0 and d, respectively.In this study, the operating voltage of the fuel cell is 300 V.After putting the following converter parameters of (10), the small signal transfer function of the fuel cell-based converter is derived as (11).

F. SSSA of Central MG Converter
From the literature survey, it is observed that the performance of the micro-grid relies on the application of power electronics converters/inverters; controller structure, proposed control techniques and the objective function to design a controller [1][2].Hence, recommending and implementing new controller practices using high-performance techniques/algorithms are always welcome.Because of the above discussion, a preliminary effort has been made to implement the FA-PSO based control method for designing the controller of the central boost converter in the DC micro-grid.Hence, in this paper, the standard value has been used with reference to which the maximum ±5% deviation V dch (i.e., 630V to 690V) is considered while designing the controller, for a stable and reliable operation of the DC micro-grid.The generalized controller structure is given in Fig. 2. The design parameters of the system are taken as: where The dynamics equation can be written as ż = Az + Bv + Bv.Further linearizing this relation at the operating point z = 0 yields ż = Az + Bv.The Lyapunov linearization method implies that the original non-linear system is stable as long as the linearized system is stable.

G. SSSA of EV Charging Station
The EV charger employs a regulated rectifier and a chopper in the design modeling of the electric vehicle charging station [46].The utility grid is connected to the rectifier input through the inductive filter, and the output voltage is maintained at a level that permits efficient dynamic control while minimizing unnecessary switching losses.The output dc voltage can be evaluated as follows (13).
where μ i is the modulation index taken as 0.9 to avoid the over modulation effect and V L−L is the line voltage assumed to be 415 V.As a result, V dc is evaluated as 652 V and selected as 650 V.The rectifier output voltage has ripples that are eliminated by the filter capacitor (C f o ).Therefore, the appropriate value of the C f o can be evaluated as follows (14).
where P r dc is the nominal DC power, which is taken to be 14 kW, f is the grid frequency, which is 50 Hz, and Vdc is assumed 1.5 percent of the rectifier terminal voltage.Thus, C f o is chosen Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
as 3300 μF as it's computed value is 2862 μF.The battery is connected to the output terminals of the rectifier through the chopper.It generates the appropriate voltage and current for charging the battery while regulating the rectifier's output voltage.The inductor (L ch ) and capacitor (C ch ) of the chopper can be evaluated by the following expressions as (15).
where ΔV b o , ΔI b o represent ripple voltage and current respectively.f sw is the switching frequency, α is the duty ratio and V b o is the battery voltage.

A. Control Architecture and Objective Function
By utilizing a fractional-order PID (FO-PID) controller, all the DC-DC boost converter can potentially exhibit improved performance, robustness, and stability compared to a classical PID controller, particularly when dealing with complex dynamics, time-varying parameters, or system uncertainties.The control structure for all DC-DC boost converters using a fractional-order PID controller is as follows and is shown in Fig. 2.
Step-1: Measure the output bus voltage v o,n of the n th target converter.
Step-3: Apply the fractional-order PID controller to the FLC output signal u f,n and find the control output (u n ) as where k p,n , k i,n , and k d,n are the proportional, integral, and derivative gains, respectively.Variables σ n and μ n are fractional orders of the integral and derivative terms that satisfy the conditions σ n , μ n > 0.
Step-4: Convert the control output u n into a duty cycle signal (d) for the boost converter switch S n using where d min and d max are the minimum and maximum allowable duty cycle values, typically 0 and 1, respectively.min and max ensure that duty d n stays within the specified limits.
Step-5: Apply the duty cycle signal d to control the boost converter switch S, adjusting the energy transfer from the input to the output to regulate the output voltage.
When using a fractional-order PID controller for DC-DC boost converter control, proper tuning of the controller param- crucial for achieving optimal performance.Optimization algorithms, such as PSO, FA, or hybrid versions like FA-PSO, can be employed to find the optimal controller parameters that meet the desired performance criteria (e.g., transient response, output voltage ripple, efficiency, etc.).The two variants of FA-PSO based optimization are designed using fuzzy and ANFIS techniques, which are elaborated as FA-PSO-Fuzzy and FA-PSO-ANFIS optimization schemes.For such optimization, the multi-objective function J n for the n th targeted DC-DC boost converter, considering efficiency and transient response, can be defined as min where η c,n (=P o,n /P i,n ) is the efficiency of the target converter, typically represented as a ratio of output power (P o,n ) to input power (P i,n ).The transient response of a boost converter is the measure of its ability to respond quickly to load changes, typically quantified by the settling time (t s,n ) or the peak overshoot (M p,n ).{w 1,n , w 2,n , w 3,n } are the weighting factors to balance the importance of efficiency and transient response in the overall objective function.These values can be adjusted depending on the design priorities.When optimizing a DC-DC boost converter using an optimization algorithm such as FA-PSO, the objective function J n is used to evaluate the performance of candidate solutions in the search space.By minimizing or maximizing the objective function, the algorithm seeks to identify the best design parameters for the converter that meet the desired performance goals.

B. FA-PSO Optimization Algorithm
The Firefly Algorithm (FA) and Particle Swarm Optimization (PSO) are two popular swarm intelligence-based optimization algorithms.When combining them into a hybrid algorithm, referred to as FA-PSO, the goal is to take advantage of the strengths of each algorithm to improve the overall optimization process.The strategic solution for the FA-PSO hybrid algorithm is as follows: Step-1: Initialize the swarm with a mixture of fireflies and particles, each representing a candidate solution in the search space.
Step-2: The position of each firefly i toward a more attractive firefly j can be formulated using the FA movement equation as where the relative position x ji (= x j (t) − x i (t) ) is the vector sum of the position of firefly i (x i ) and j (x (t) j ) at a time t, respectively.β 0 is the attractiveness at distance 0, γ is the light absorption coefficient, α is the step size, and λ() → rand(0, 1) are the random variables U ∈ [0, 1].Similarly, the velocity and hence the position of each particle i in the swarm can be addressed using the PSO update equations as Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.where v (t) i represents the velocity of particle i at time t, w is the inertia weight, c 1,n and c 2,n are the cognitive and social acceleration constants, x (t) pb,i is the personal best position of particle i, and x (t) gb is the global best position in the swarm.By combining the FA and PSO positions, the position vector can be updated using FA-PSO as ( 22)-( 23).
Further simplifications yield the position vector as, gb,j are given in (24).
Step-3: Evaluate the fitness of each candidate solution in the swarm.
Step-4: Update the best personal position x pb,i and the best global position x (t) gb based on the new fitness values.
Step-5: Repeat steps 2-6 until a termination criterion is met, such as a maximum number of iterations or a desired level of solution accuracy.
From Fig. 3, the hybrid FA-PSO, represented by the continuous line, showcases a faster and higher convergence rate than its counterparts.This underlines the assertion that, by combining the global exploration capability of the FA with the local exploitation efficiency of the PSO, the FA-PSO hybrid technique enhances convergence speed, solution quality, and robustness when confronting intricate optimization challenges.Comparatively, the PSO, depicted by the dashed line, demonstrates a slower convergence rate than FA-PSO, but eventually approaches similar fitness values as iterations progress.The FA, marked by the dotted line with star markers, shows a gradual increase in fitness value but does not reach the levels of FA-PSO or PSO within the illustrated iterations.In conclusion, Fig. 3 quantitatively emphasizes the superiority of the hybrid FA-PSO method in terms of convergence over the traditional FA and PSO approaches.This suggests that FA-PSO might be a more  effective tool for complex optimization problems, ensuring better results in fewer iterations.

C. Fuzzy Logic Control Algorithms
The two types of Fuzzy Logic Control (FLC) algorithms discussed, Takagi-Sugeno Fuzzy Inference System (TSFIS) and Adaptive Neuro-Fuzzy Inference Systems, are essential in efficiently managing the dc-link voltage error in several systems, as outlined in Section II, by providing a robust and adaptive mechanism to cope with uncertainties and non-linearities inherent in these systems.The Takagi-Sugeno Fuzzy Inference System (TSFIS) excels in handling non-linear systems with its capability to approximate any real continuous function, while Adaptive Neuro-Fuzzy Inference Systems integrate the learning capabilities of neural networks, allowing for the fine-tuning of fuzzy systems through a data-driven approach.The following sections provide a detailed discussion on these algorithms.
1) Takagi-Sugeno Fuzzy Inference Systems: In this research, the primary focus is on the use of TSFIS for improved control in independent DC microgrids.The TSFIS uses output DC-link voltage error signals as input, as presented in Fig. 5.This allows it to effectively manage the non-linearities and uncertainties inherent in these power systems.Unlike traditional Fuzzy Logic Controllers, which require specialized knowledge to define membership functions and rules, the TSFIS parameters can be optimized through a less cumbersome method.The hybrid FA-PSO algorithm serves as the optimization engine to tune the TSFIS parameters.Although FA is known for its thorough exploration of the search space, PSO offers the advantage of rapid convergence and reduced computational effort.When these two methods are combined, the hybrid FA-PSO algorithm efficiently fine-tunes the TSFIS parameters y k,n , leading to faster convergence and higher precision.With optimized TSFIS parameters, the system achieves superior DC-link voltage tracking and minimizes computational load.This eliminates the need for operator-dependent trial-and-error methods to set controller gains, making the system more robust and versatile for handling complex and non-linear control problems in DC microgrids.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

TABLE III VALUE OF CENTRAL CONVERTER PARAMETERS USING FA-PSO
As discussed earlier, ṽo,n is the DC-link voltage and vo,n is the change in the DC-link voltage deviation.The threshold limits for ṽo,n and vo,n are ±10% and ±5%, repectively, i.e., the variables M and L can be defined as 0.1 pu and 0.05 pu, respectively.Now, μ P (ṽ o,n ) and μ N (ṽ o,n ) are the membership functions (MF) assigned to the variable ṽo,n , while μ P ( vo,n ) and μ N ( vo,n ) are the membership functions (MF) assigned to the variable vo,n , respectively.
where P (positive) and N (negative) are the linguist variables for the MFs, as shown in Fig. 5.The TSFIS is represented by four simplified fuzzy rules as (27).
where k is the k th iteration; the variables Z 1,n , Z 2,n , Z 3,n and Z 4,n indicate the consequent of the TSFIS.The FA-PSO optimized values of the fuzzy constants a 1,n , a 2,n , a 3,n , a 4,n and a 5,n are presented in Table III.This mechanism is used to obtain the output of the TSFIS (u f ) by evaluating the generalized defuzzifier mechanism, which is assessed as (28).
To track the voltage of the DC link with precision and minimal computational effort, the value of u f,n is dynamically modified and used in conjunction with a fuzzy controller.This results in improved stability and overall dynamic performance of the DC microgrid.
2) Adaptive Neuro-Fuzzy Inference Systems: The design of ANFIS controller requires a close conformity with the system identification methodology.The functional architecture of the ANFIS control algorithm is presented in Fig. 5.The nodes in a square (adaptive nodes) carry parameters, contrasting with the circle nodes (fixed nodes), which bear no parameters.Assuming that an adaptive network comprises L layers and within the m th layer there are l nodes, the number of nodes depends on the linguistic labels of TSFIS, denoted as (N , P ), i.e., l = 2 per input variables.The node situated at the i th position in the m th layer can be symbolized by (m, i), with its node function (or node output) expressed as O m i .The current model includes five layers (i.e., L = 5), comprising an input layer, an output layer, and three hidden layers.In ANFIS, TSFIS if-then rules are employed where each rule's output is a linear blend of input variables, augmented by a constant term, with the final output being the weighted average of the outputs from each rule.A detailed description of each layer is illustrated below.
Layer 1: This layer receives the primary input variables {ṽ o,n , vo,n } and computes the fuzzy sets of the output matching as follows: where O 1 i,n is the output Bell-shaped membership function of μ N (ṽ o,n ), μ P (ṽ o,n ), μ N ( vo,n ) and μ P ( vo,n ), which are the linguistic degrees of the i th node with i ∈ {1, 2, 3, 4}.The number of MFs significantly affects the performance of the model, which evaluates the computation period, the data collection of DC microgrid events such as load fluctuation, change in irradiance, change in wind speed, and nonlinear load conditions.The mathematical expressions of these MFs can be expressed as (30).
where α i,n , β i,n , and χ i,n are the parameters of the MFs.Layer 2: The output signals from layer 1 are multiplied by the signals in this layer.The layer 2 output (O 2 i,n ) nodes are circles and can be stated as (31).
where ω i,n stands for every node's firing terminal.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.Layer 3: This layer's nodes are typically like circles.The layer 3 output (O 3 i,n ) can be characterized as (32).
Layer 4: The output node functionalities in this layer would be determined as (33).Now, the operational rules of Takagi-Sugeno ANFIS for the signal ṽo,n and vo,n can be stated as follows where r i,n , s i,n , and i,n are the constants.Layer 5: The overall output of the ANFIS is computed in this layer by adding up all of the received signals from earlier layers, and it can be expressed as (34).
The core aim of the proposed control algorithm is to accurately track DC-link voltage with minimal computation time, enhancing the DC microgrid's performance during varied system events like changes in PV irradiance, wind speed, and load power.The effectiveness of fuzzy controllers is dependent on MFs and rules, but designing an FLC requires expert knowledge.The ANFIS controller addresses these challenges by reducing fuzzy calculations and uncertainties, albeit with training and update limitations.To overcome this, the FA-PSO algorithm tunes the ANFIS model parameters, simplifying hardware implementation and speeding up convergence, thus efficiently managing system uncertainties by pre-training with actual data, and validating the FA-PSO optimized ANFIS performance in the DC microgrid through comparison of real and training data.

D. Stability Evaluation of Test microgrid
The Fig. 6 presents an in-depth frequency domain analysis of a proposed controller using the Bode plot, the Nyquist plot and the Pole-Zero plot.In the Bode plot (Fig. 6(a)), the magnitude and phase are plotted against the frequency in rad / s.Observing the magnitude plot, it appears that the system's gain drops as the frequency increases, and the phase plot shows the phase shift.Crucially, the system details highlight a phase margin of 50.5 degrees and a delay margin of 0.246, both taken at a frequency of 3.58 rad/s.The positive phase margin and the absence of any magnitude crossing the 0 dB line in the vicinity of the phase crossing of −180 degrees are indicative of the closed-loop system's stability.Turning to the Nyquist plot (Fig. 6(b)), it graphically represents the system's frequency response.The curve plots the imaginary part against the real part of the system's transfer function over a frequency range.In particular, the Nyquist plot does not encircle the critical point (−1,0), suggesting a stable system according to the Nyquist stability criterion.The plot further confirms the system's stability, echoing the findings from the Bode plot.Lastly, in the Pole-Zero plot (Fig. 6(c)), the system's poles and zeros are plotted in the complex plane.All poles of a stable system must lie in the left half of this plane (with negative real parts).The plot showcases this trait, as all poles are found on the left side, further corroborating the system's stability.In summation, on the basis of the displayed plots, the proposed controller for the DC microgrid demonstrates stability.This stability is confirmed by the positive phase margin in the Bode plot, the behavior of the Nyquist plot around the critical point, and the location of poles in the Pole-Zero plot.

A. System Description
The DC microgrid prototype is developed in the laboratory, as shown in Fig. 7.The prototype consists of a PV emulator, a PMSG-based wind power emulator, a SOFC, an electrolyzer, and a BESS unit.The details of the modeling and control of each subsystem are discussed in Section II.The study is limited to Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.a 13 kW system due to the limitations of laboratory facilities, which are only equipped for this nominal load capacity, preventing experiments at higher capacities.In the study, the dSPACE MicroLabBox-based real-time digital controller with 4 cores (i.e., the latest generation of FPGA processor card) is considered to realize / establish the proposed controller performance.The complete microgrid system controllers are developed in MAT-LAB/SIMULINK and built with the dSPACE DS1202 platform, considering a sample time of 50 μs.The duty cycle is generated from the dSPACE controller and fed to the individual converter subsystem through the built-in Digital to Analog converter, as shown in Fig. 7.In addition, these duty cycles are converted into pulses using the internal DSP processors of the converter.

B. Test Scenarios
The effectiveness of the proposed optimization technique with the FO-PID controller is assessed through three distinct scenarios: r Scenario-1: Variations in solar irradiance and wind speed.r Scenario-2: Fluctuations in EV charging demand.r Scenario-3: Unpredictability in supply and demand.

C. Scenario-1
Scenario-1 (S-1) presents the test case considering the varied solar irradiance and wind speed, as shown in Fig. 8. Fig. 8(a) presents the variable time series data for solar irradiance, modeled using the Beta function.The base value of the irradiance and the temperature of the PV cell are set at 1000 W/m 2 and 25, • C, respectively.These data are crucial for evaluating the performance of various control strategies applied to the PV cell.In contrast, Fig. 8(b) illustrates the time series data for wind speed, modeled using the Weibull probability function, as cited in [47].The base wind speed for the Permanent Magnet Synchronous Generator (PMSG) is maintained at a maximum of 12 m/s.These variations in wind speed are essential to evaluate the effectiveness of different control strategies in the context of PMSG.
Fig. 9(a) shows the power sharing responses between the various generation, storage, and load units considering the proposed FO-PID controllers, shown as various colored lines, representing the power flow in kilowatts (kW) over time in seconds (s).The associated powers (p L : EV-based non-linear load; p pv : PV Power; p w : wind power; p fc : SOFC power; p b : BESS power; p e : electrolyzer power) are maintained in a more stable manner with the proposed controllers.During this scenario, Fig. 9(b) focuses on the dynamic responses of the DC-link voltage v dch ,  measured in volts (V), over time.It compares the performance with various optimization techniques (ANFIS/TSFIS-FA-PSO, ANFIS-PSO and TSFIS-FA) based FO-PID controller.Among these, the proposed ANTIS-FA-PSO-based FO-PID controller is shown to have a tighter clustering of voltage levels over time, indicating a lower deviation in DC-link voltage.This implies that the proposed ANTIS/TSFIS-FA-PSO-based optimization techniques were able to maintain a voltage level more consistent than that for the other optimization, which is desirable for stable microgrid operation.The reduced peaks and dips reflect a more stable and reliable control strategy, which is essential in power system applications to prevent voltage spikes or drops that could damage equipment or cause reliability issues.
During the time interval t = 1 − 2 s, the combined power generated by solar PV and wind is inadequate to meet demand, since the DC load is fixed at 10 kW.This discrepancy is partly due to the solar irradiance falling to a low level of 150 W/m 2 at t = 1 s, 4 s, and 9 s, resulting in decreased solar power, as shown in Fig. 8(a).Consequently, the BESS is discharged to compensate for the gap between generation and demand.As depicted in Fig. 10(a), the lower side DC bus voltage drops below the permissible limit due to rapid changes in solar irradiance and wind speed, which employs the proposed FA-PSO triggered ANFIS-FO-PID controller for converters connected to the generationa and storage units.Various optimization algorithms with the proposed FO-PID controller are employed to stabilize the voltage on the higher side, as demonstrated in Fig. 10(b).When the load surges from 10 kW to 13 kW during t = 2 − 4 s, the BESS discharges more power to equalize the DC microgrid power requirement, detailed in Fig. 10(b), while the fuel cell and the electrolyzer do not share any power.the proposed FA-PSO-based FO-PID controller.This controller not only achieves the smallest deviation in DC-link voltage but also maintains it within the permissible limits of ±5%, outperforming the other mentioned control techniques.
Fig. 11 shows the hardware results for the dynamic power responses of the different subsystems of the DC microgrid, utilizing an FO-PID controller with various optimizers.The plots illustrate how each control strategy manages the power flow within the system components.Throughout the operation, the Pv and wind power dynamically interact to balance supply and demand as necessary.For example, as the load (P L ) intensifies from 10 to 14 kW between t = 2 s and t = 4 s, the wind supplies additional power, while PV power continues to fluctuate according to solar irradiance.Conversely, during t = 4 s to t = 5 s, the load demand is reduced to 13 kW with an increase in photovoltaic power and a decrease in wind power.Fig. 11 also captures moments such as between t = 6 s and t = 7 s when the demand peaks due to the simultaneous connection of non-linear EV loads, prompting the PV to supply to cover the demand because of better solar irradiance.The data in Figs.11(c) and 11(d) also underscore the efficacy of the proposed TSFIS/ANFIS-FA-PSO-based FO-PID controller to maintain power stability and minimize power fluctuations, demonstrating its improved power tracking ability and voltage stability under various system conditions.

D. Scenario-2
Scenario-2 (S-2) evaluates the dynamics involved in the nonlinear EV loads which comprises PMDC drive.The dynamic  Furthermore, the comparative dynamic power performances of each subsystem of the DC microgrid for different control strategies are plotted in Fig. 13.The DC resistive / lighting load (P L ) is considered to be fixed at 5 kW during 1-2 s.During this period, net power demand is less than net power generation.As a result, BESS received extra power to maintain the power balance Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.shown in Fig. 13.During 2 − 4 s, the load value (P L ) increases from 5 to 9 kW; as a result, the BESS discharges more power during that period to maintain the power balance.However, during 4 − 6 s, the load power (P L ) decreases to 5 kW and the photovoltaic power increases (i.e., solar irradiance increases) with a decrease in wind power (i.e., wind speed decreases) as shown in Fig. 13.Consequently, the extra energy is taken by the BESS (i.e., the battery charges/receives power) to balance the power during this period, as shown in Fig. 13.However, during 7 − 8 s, the net power demand is higher when both resistive (i.e., 8 kW) and the non-linear load of the PMDC motor (i.e., 1.5 kW) are connected in Fig. 13.As a result, the BESS discharges more energy to mitigate the power deficiency during this period.The observations clearly illustrate that the proposed TSFIS/ANFIS-FA-PSO-based FO-PID controller has contributed to a better power tracking ability (i.e., less swell/sag) and voltage stability under different system events compared to the other three controllers.

E. Scenario-3
Scenario-3 (S-3) case study is verified under constant solar irradiance (i.e., 1000 W/m 2 ), wind speed (i.e., 12 m/s) and step variations of load (P L ).The dynamic power sharing response of each microgrid subsystem for the proposed ANFIS-FA-PSObased FO-PID controller is illustrated in Fig. 14(a).The power generation is greater than the load (P L = 500 W).Therefore, the excess power is received by the battery for charging.For power balancing, SOFC initiates to supply power.Due to its slow dynamics for proper coordination, it operates at a slower rate, as shown in Fig. 14(a).Consequently, with FC participating in the power balance, the battery power decreases and eventually comes to zero after t = 2 s when FC supplies the required power under steady state conditions.Therefore, it indicates that there is proper coordination between the FC and the battery for power sharing during system events.At t = 5 s, the load decreases from 17 kW to 8.5 kW, the FC restricts the power supply and the battery consumes power.At t = 6.7 s, the battery is fully charged (i.e., the SOC is above 80%) to electrolyze and receives the unutilized/excess power, since the generated power is greater than the load power.Furthermore, the corresponding comparative DC-bus voltage responses for the controllers specified above are plotted in Fig. 14 IV, it is observed that the deviation of the DC-link voltage of the proposed FA-PSO-based controller is minimal over the other controllers discussed.

F. Parameter Uncertainty with Eigenvalue Sensitivity
Within the context of the capacitor central boost converter, the performance of the proposed FO-PID controller under varying conditions has been thoroughly evaluated.This subsection details the response of the system when subject to uncertainty, particularly in capacitance (C d ), while maintaining a reference irradiance of G = 1000 W/m 2 is maintained.The control strategy employed is a closed-loop FO-PID controller with an optimized ANFIS-FA-PSO algorithm, designed to uphold system stability and assure convergence to the desired output despite variations in system parameters, such as changes in capacitance or inductance values.
The robustness of the controller is tested against a 10% deviation in C d .The resultant DC-bus voltage responses are presented in Fig. 15.The graph depicts two distinct voltage response trajectories over a span of 10 s: one under the influence of uncertainty ("With Uncertainty"), and the other in its absence ("Without Uncertainty").On the vertical axis, the high-side DC-bus voltage is measured V and the horizontal axis records time in s.The trajectory labeled "With Uncertainty" shows more fluctuation than the one labeled "Without Uncertainty," with both starting at approximately 663 V and stabilizing close to 659 V.The variations observed in the "With Uncertainty" plot highlight the controller's ability to manage uncertainties.Moreover, the impact of uncertainty on the eigenvalues is reflected in the voltage responses.Despite the induced deviations, the response remains within ±1% of the nominal value, which is consistent with the stability requirements.
The investigation extends to the frequency domain, examining the behavior of the loop transfer function L e (s) under the specified uncertain and nominal conditions of C d .The comparisons are visually represented in Figs. 6 and 9.In control systems, gain margin (GM) and phase margin (PM) are critical indicators of robustness, where ideally, a GM of over 6 dB and a PM of more than 30 • are desired.However, under uncertain conditions, there is a noticeable, albeit slight, reduction in the phase margin.This is illustrated in Fig. 16, a Bode plot showing the frequency response where the phase margin measures 40.9 • at 700 rad/s, suggesting a stability compromise due to C d variability.
In conclusion, even with the marginal impact on the phase margin in the presence of capacitance uncertainty, the system demonstrates considerable robustness.The controller is thus validated as effective in managing uncertainties, affirming its suitability for practical applications.

V. CONCLUSION
This study addressed the challenges of integrating RES with DC microgrids for applications such as fast DC charging of EVs.A novel control strategy was proposed, using a hybrid FA-PSO approach to tune the TSFIS and ANFIS controllers.This combined approach optimizes power management within the DC microgrid for faster convergence, better accuracy, and reduced topological constraints.The effectiveness of the proposed control strategy was validated through two key aspects: 1) Comprehensive SSSA assessed the impact of FA-PSO optimization on the DC microgrid's stability and 2) hardware prototype was developed to validate the control strategies under real-world uncertainties, including varying wind speed and solar insolation.This validation demonstrates the feasibility and effectiveness of the proposed approach for practical DC microgrid applications with integrated EV charging.The results showcased the superiority of the FA-PSO optimized ANFIS-PID control algorithm compared to traditional methods such as PID and fuzzy PI control.This superiority was evident in the DC-link voltage transient response during system disturbances, achieving a minimal deviation and a faster settling time.
L b and C b are the inductance and capacitance of the converter, respectively.The duty ratio of the bidirectional converter is D b , the internal battery resistance is R b .V b and I b are the battery voltage and current, respectively.The converter output voltage is V 0 .ĩb , ṽ0 and d are the small signal battery current, converter output voltage, and duty ratio due to small perturbation, respectively.The values of R b = 0.064285, D b = 0.4, V o = V dcl = 450 V, L b = 7.2 mH, C b = 88.1 μF and I b = 27.78A are considered in this work for the design of the BESS controller / converter.The operating voltage of the BESS is 450 V .Now, the open-loop transfer function of the BESS converter can be derived by neglecting external disturbances, such as variations in battery voltage and load current.After putting the numerical values in (7)-(8), the small signal open loop transfer function can be derived as (9).
6000 μF, D d = 0.32, L d = 0.8 mH and I d = 16 A.The input capacitor filter at the low-voltage side DC bus C e is 3750 μF.The small-signal average state model of the converter can be derived as follows:

Fig. 6 .
Fig. 6.Analysis of the proposed controller in frequency domain.

Fig. 9 .
Fig. 9. Hardware results for scenario-1: (a) Power sharing responses and (b) v dch response with various optimization techniques-based FO-PID controller.

Fig. 11 .
Fig. 11.Hardware results: Dynamic power responses of different subsystems with FO-PID controller.

Fig. 12 .
Fig. 12. Comparative response of DC-link voltage with FO-PID controller considering various optimizers.

Fig. 14 .
Fig. 14.Hardware results for scenario-3: (a) Power sharing responses and (b) v dch response with various optimization techniques-based FO-PID controller.
(b).From Fig.14(b), it shows that the proposed TSFIS/ANFIS-FA-PSO-based FO-PID controller contributes to a better DC-link voltage dynamics compared to

TABLE I PARAMETERS
OF THE DC MICROGRID SYSTEM 59 × 10 −12 s 2 − 10 9 s − 6.667 × 10 9 s 3 + 2003s 2 + 2.276 × 10 6 s + 1.022 × 10 8 ) where the distance (d pb,i ) between x Table IV presents the DC-link voltage settling time and the maximum percentage of peak-to-peak voltage deviation (Δv dc ) for various optimization strategies, highlighting the superior performance of

TABLE IV COMPARATIVE
PERFORMANCE CONSIDERING FO-PID CONTROLLER.