Optimal Electrical Vehicle to Grid Integration: Three Phase Three Level AC/DC Converter with Model Predictive controller based Bidirectional Power Management Scheme

The control and modelling of an electric Vehicle charging station with a three-level converter are discussed in this study from both the grid side and the EV side. The primary subject of discussion is the control systems for charging stations with a bidirectional DC/DC charging regulator and a three-level AC/DC power conversion. In order to manage the duty cycle of the converter during the AC-to-DC conversion stage, three alternative controller techniques—proportional-integral, proportional-integral-derivative, and model predictive controller are developed in this study. The goal of the study is to understand how these controller techniques impact the battery's charging and discharging processes in a bidirectional charging system. To evaluate and compare the different controller schemes, the researchers use simulation results and assess their performance based on various criteria including charging/discharging e�ciency, voltage and current, battery state-of-charge regulation, and response time. The simulation results show that in terms of peak overshoot and settling time, the MPC controller performs better than the conventional Proportional-Integral and Proportional-Integral-Derivative controllers. The signi�cance of the controller selection in bidirectional charging systems, emphasizing the bene�ts of using Model Predictive Control for better battery charging and discharging outcomes.


Introduction
Electric vehicles (EVs) are in greater demand, and as a result, effective and cost-effective charging systems are required to both assist their adoption and address the problems associated with their incorporation into the power grid [1].It is vital to build charging systems that can meet EV needs because existing EV charging systems frequently experience inadequacies, high costs, and long charging times [2].One of the primary challenges in electric vehicle (EV) charging is the e cient conversion of AC electrical energy supplied by the grid to DC electricity required for charging the EV's battery.[3].The development of AC-to-DC converters that can function e ciently while avoiding losses is essential since the effectiveness of the conversion process directly affects energy losses, expenses, and long charging times.The control scheme of the converter is vital for guaranteeing that the output current and voltage are stabilized [4].The response time, accuracy, and complexity of the control system are all important considerations when choosing a controller.A crucial component of AC-to-DC converters, in addition to the controller, is the recti er, which transforms AC power into DC power [5].The e ciency of the recti er is crucial since losses during the conversion process can raise prices and lengthen charging periods.Depending on the desired output voltage and current as well as the input voltage and frequency, many recti ers, such as diode, thyristor, and bridge recti ers, can really be employed.Other crucial parts of AC-to-DC converters include lters, transformers, and DC-DC converters.Filters lower harmonic distortion and noise, transformers increase or decrease input voltage, and DC-DC converters control DC voltage and current.To guarantee safe and dependable operation, security and safeguarding systems, such as excessive current, voltage unbalance, and over-temperature prevention, are also essential [1].
The integration of EVs into the electrical grid is a di culty of EV charging in addition to recti cation e ciency [6].The stability of the grid, the control of peak demand, and the balance of power supply and demand can all be dramatically impacted by the charging of EVs.Hence, cuttingedge control and protection technologies are necessary to guarantee secure and effective charging operations while reducing the grid's impact.
One inventive approach to the problems associated with the integration of electric vehicle charging into the power grid is the use of bidirectional charging devices [7].When necessary, these technologies allow EVs to discharge electricity back into the grid in addition to charging from it as shown in Fig. 1.In addition to balancing power supply and demand, the capacity to discharge power back into the grid also makes it easier to integrate renewable energy sources into the grid.A bidirectional charge circuit, which is commonly based on a Buck-Boost converter, regulates the battery's charging and discharging modes.The control scheme of the Buck-Boost converter is essential for assuring secure and effective charging as well as discharge operations while safeguarding the battery from harm.The Buck-Boost converter works in the charging mode whenever grid power is accessible, transforming the grid's AC power to DC power and recharging the battery.To provide secure and effective battery charging, the Buck-Boost converter controls the output voltage and current of the DC power [8].Accurately controlling the output voltage and current of the converter depends on its control strategy, which may be based on a PI, PID, or MPC controller [9].The Buck-Boost converter shifts towards the discharging phase, turning the DC energy that the battery produces back to AC power and feeding it back to the grid, whenever the input power as from grid is inadequate.Once more, the control strategy of the converter is crucial for precisely regulating the output voltage and current and preventing battery damage during discharge [10].To increase e ciency and safety, bidirectional charging systems may also incorporate extra parts such lters, transformers, and DC-DC converters in addition to the bidirectional battery and Buck-Boost converter [11].To guarantee safe and dependable operation, safety and protection systems, such as over current, overvoltage, and over-temperature protection, are also essential [12].
When designing controllers for bidirectional converters in the context of vehicle-to-grid (V2G) applications, it is crucial to consider power quality standards to ensure the stability and reliability of the electrical grid.To control the injected current into the grid and maintain power quality, a suitable controller option is the Current Control Strategy.This strategy aims to regulate the grid current waveform to follow a sinusoidal shape while controlling the active and reactive power exchange between the vehicle and the grid.These controllers help maintain stability, improve the power factor, and minimize harmonics in the grid current.Lower-order harmonics in the current are the reason for the low power factor of the VA rating.The harmonic problem worsens as charging demand increases.The harmonics that can be introduced into the system are governed by some standards, including IEEE 519-1992, IEC 61000-3-12/2-4, and EN 50160:2000 [11][12][13][14][15][16].A controller designed for CC-CV charging regulates the DC/DC converter's switching and subsequently produces an output su cient for the EV battery.Battery voltage and current feedback are sent to the controller as input.
The choice of controller depends on the speci c requirements, system dynamics and available resources MPC offers advantages in terms of control performance, adaptability to complex dynamics and constraints, and the ability to handle multivariable systems.It optimizes control actions over a nite time horizon based on the predicted system response.On the other hand, PI and PID controllers are classical control strategies that rely on feedback control to adjust the control signal based on the error between the desired setpoint and the measured system response [17][18][19][20].
In this paper, we present the design and analysis of a bidirectional charging system for Electric Vehicles (EVs) using an AC grid.The system includes a recti er with three different controllers -Proportional Integral (PI), Proportional Integral Derivative (PID), and Model Predictive Control (MPC) -to regulate the duty cycles of the system.The DC output from the recti er is used to charge a bidirectional battery, which can also discharge to power the load when the grid input is unavailable.The bidirectional charging circuit is based on a Buck-Boost converter controlled by a PI or PID controller.The system is analyzed in three different scenarios: rst, when the grid input is available, the AC to DC converter curve, battery state of charge, and battery current and voltage are calculated.Second, after a time interval, when the grid input is unavailable then analyze the impact on state of charge, battery current and voltage, and the system's operation in discharging mode.As part of our research, we have analyzed the performance of three different controllers -PI, PID, and MPC -for the recti er module in the AC-to-DC conversion stage of a bidirectional charging system.

Electric Vehicle Charging Infrastructure Architecture
The grid-connected EV charging station consists of three primary components: EV chargers, a power converter for the grid, and a controller for system integration as shown in Fig. 2. The EV-side converter, which is a PWM DC/DC voltage source converter, is responsible for regulating each EV charging regulator.A three-phase, three-level recti er/inverter is used to convert the three-phase grid voltage to a DC voltage.
Connections are established between electric vehicles and the DC-bus through EV chargers.The charging station control system comprises the EVside controller, the grid-side interface controller, and the centralized charging controller.The EV-side controller manages the charging and discharging of EV batteries using a DC/DC power converter such as Buck boost converter.The grid-side controller regulates the three-level AC/DC inverter/converter, maintaining a constant DC-bus voltage and managing power exchange with the grid through the three-phase three-level recti er.The purpose of this control strategy is to determine the operating mode of the converter based on the charging state of the energy storage device, which is determined by the DC bus voltage (Vdc).The control strategy begins by evaluating the charging state of the energy storage device, which is represented by the DC bus voltage.If the DC voltage is below a certain threshold level, it indicates that the charging state is low, meaning that the energy storage device requires charging.
The integrated charging station controller ensures that the power reference signal from the centralized control system is met by the local EV-side controller.The central control system considers utility grid conditions, EV state of charge (SOC), and charge/discharge requirements to deliver power reference signals to each EV-side charge regulator.The control system enables the performance of grid-to-vehicle (G2V) and vehicle-to-grid (V2G) power management functions by determining the direction of power ow based on system conditions.

Proposed Control Strategy for charging station
MPC was developed in the 1960s and has become a widely used control strategy in various industries.The key advantage of MPC over other control strategies is its ability to handle constraints on states, inputs, and outputs, allowing for the incorporation of system limitations into the control process as shown in Fig. 3. Further, by considering constraints, MPC enables the operation of a system closer to its boundaries, which can enhance pro tability, particularly in industries like the chemical industry where process limitations are critical.MPC achieves this by optimizing the control actions over a prediction horizon, considering future system behaviour and constraints, thereby allowing for more e cient and effective control [21,22].
Additionally, MPC's optimization problem is solved at each time step, considering the current state and predictions of future behaviour.This characteristic of MPC prevents the control strategy from being short-sighted, as it takes into account the future evolution of the system.Three steps are included in the MPC algorithm: 1) Estimate future outputs using the system's dynamic model throughout the optimization horizon; 2) Assess the cost function for the set of the system's potential outputs 3) Implement the rst component of the control policy at the lowest possible expense.
For reference tracking and control effort, a typical objective function in MPC could be formulated as a weighted sum of terms that represent the tracking error and control effort.The tracking error term penalizes deviations between the system outputs and desired setpoints, while the control effort term penalizes excessive control actions or changes in control signals [23,24].By adjusting the weights and terms in the objective function, MPC can be expressed to achieve different control objectives, whether it is achieving reference tracking, controlling effort, optimizing fuel economy, or reducing emissions.
is the weights for the output y and control inputs u, N represent the prediction horizon length.
The MPC controller is a model-based controller that uses a mathematical model of the system to predict the system's future behaviour and optimize the control signal [25].In this application, the MPC controller regulates the duty cycle of the recti er based on the system's current state and the predicted future state.The MPC controller's equation is given by: 3 where J is the cost function, x(t) is the system's state at time t, and u(t) is the control signal.

Working Principle of EV integration to grid operation
The simulation model of an Electric Vehicle (EV) charger station built in MATLAB/Simulink R(2022b) as shown in Fig. 4. The model comprises several components, including a grid model, a three-level bridge converter, EV battery chargers, Buck boost converter and two controllers: the charging controller and the GSC (Grid-Side Converter) and controller.
The grid model is represented by a three-phase voltage source connected in series with an RL (inductive) branch.It is further connected to a 600/60 V isolating transformer in star delta con guration), which allows for voltage conversion.The short-circuit level of the grid model at the base voltage (presumably 60 V) is speci ed to be 60 MVA (Mega Volt-Ampere), indicating the maximum fault current capability of the grid.This battery model allows for simulating the charging and discharging processes, as well as the battery's response to different control strategies and operating conditions.The three-level converter is responsible for converting the AC voltage from the grid to the appropriate DC voltage for charging the EV batteries.It typically employs power electronic switches, such as insulated gate bipolar transistors (IGBTs), to regulate the power ow between the grid and the EV batteries.The charging controller is responsible for managing the charging process and monitoring the battery state of charge, controlling the charging current or power ensuring safe and e cient charging of the EV batteries.The GSC controller controls the operation of the Grid-Side Converter, which is responsible for the interaction between the charger station and the grid.

Working Principle of AC/DC converter operation
In the control of a three-phase bidirectional AC/DC converter using Model Predictive Control (MPC), the power ow is regulated based on the discrete behaviour of a static power converter.The MPC scheme utilizes a nite set of possible switching states to govern the converter's operation.One important aspect in the MPC algorithm for this converter is the utilization of the discrete characteristics of the lter inductances (Ls).These inductances play a role in managing the power ow through appropriate switching actions.By controlling the switching states, the converter can control the direction and magnitude of power transfer between the AC and DC sides.To determine the appropriate switching state, a selection criterion is de ned to quantify the error between the desired references and the expected values.This criterion can be based on the tracking error, control effort, or other performance criteria speci c to the power ow control objectives.The MPC algorithm then evaluates the cost function associated with each possible switching state for the next sample interval.The cost function incorporates the desired control objectives and penalties for deviations from reference values, control effort, and other constraints.The switching state as shown in Table 1 that minimizes the cost function is selected as the optimal choice for activating the converter switch during the next sample interval.
Switches operated in complementary mode, hence the gating signal in three phase AC/DC converter decide switching states: Switching vector can be expressed as: -7 The output space vector for AC/DC converter is given as: -8 9 where, , is the phase to neutral voltage of a, b, c phase, is the DC bus voltage.
where, unityvector After applying KVL at the AC side of the recti er equation will be: - where, and is the space vector model of 3-phase ac voltage and current.are phase voltage and are phase current.
Rate of change of input current during recti er operation can be evaluated from Eqs. 12 and 14. 13 In inverter operation, Eq. 17 becomes same but it is 180 degrees out of phase with output voltage.
The recti cation module is controlled by a duty cycle generated by three control strategies: PI, PID, or MPC.These control strategies adjust the duty cycle to regulate the DC voltage and maintain a constant output voltage.The output voltage of the recti er circuit has a signi cant amount of ripple.To obtain a smooth DC voltage, a smoothing capacitor is used.However, the capacitor is not enough to provide a constant voltage.The voltage ripple is still present, and it is proportional to the load current.To minimize the voltage ripple, a controller is used to generate the duty cycle of a pulse width modulation (PWM) signal that controls the power switch.The controller adjusts the duty cycle to maintain a constant DC voltage output.The control scheme described utilizes direct-quadrature-zero (dq0) transformation equations, lter circuit, and a phase-locked loop (PLL) algorithm to achieve synchronization with the utility grid voltage.The phase currents , as well as the utility voltages are converted from abc coordinates to a dq frame using Park transformation, with the angle generated by the PLL.The dq0 transformation converts the phase currents and utility voltages from the a-b-c coordinate system to a d-q coordinate system, where d represents the direct axis and q represents the quadrature axis.The transformation is given by the following equations: - The PLL algorithm is used to synchronize the phase angle of the inverter output voltage with the utility grid voltage.The PLL algorithm generates an estimate of the grid voltage angle using the following equation: where is the time constant of the PLL lter, where is the estimated grid voltage angle generated by the PLL algorithm.and are the measured quadrature and direct components of the utility voltage, respectively.
Once the PLL algorithm has generated an estimate of the grid voltage angle ωt, it can be used to transform the phase currents and utility voltages to the d-q coordinate system using the Park transformation: Finally, the low-pass lters are used to lter out high-frequency components of the signals, and the active and reactive power calculations are used.The instantaneous active power and reactive power can be calculated using the following equations: To regulate the DC bus voltage, we have used individual controller separately.Controller is used to generate the duty cycle of the PWM signal.The output of the controller is compared with the voltage in the outer voltage loop to generate the current reference for the inner current loop.The inner controller's current loops are established by comparing the actual measured line currents obtained using the Park transformation matrix with the current reference.The output of the current loop controller is used to modulate the PWM signal, which is used to control the switching of the GSC converter.To obtain the duty ratios in the d-q coordinate system, the results of the Park transformation, speci cally the components ed and eq, are combined with decoupling terms. 19 To obtain d q ratio in a, b, c coordinates: -20

Working Principle of EV side converter operation
This paper combines both CC and CV control strategies to ful l the requirements of the EV battery charge and discharge process.This combination is often used in advanced charging systems for EV batteries.The electric vehicle side converter consists of a control loop i.e., voltage loop.The dc link voltage (Vdc) is measured, and it is compared with a reference voltage (Vref*).The result of the voltage comparison, which indicates the difference between the dc link voltage and the reference voltage, is passed to a voltage loop controller.In this case, the controller is referred to as PIv, which stands for Proportional-Integral (PI) controller for voltage control.Then, if battery current is positive, the battery is charging; otherwise, then it is discharged.Current reference in CC mode and Iref(soc) in the centre.However, depending on the SOC and sign, the system can function in one of the following modes.
Case 1 If the voltage reference is less than dc link voltage, the switch is in the bottom position and the below circuit as shown in Fig. 5 to operate in discharge mode.To maintain the voltage signal within a desired range and avoid non-linear modulation states, a voltage signal is generated by the current control loop.This voltage signal is then regulated to stay between + Vtri and -Vtri using a saturation block.Here, Vtri represents the magnitude of the triangle carrier waveform used for pulse width modulation (PWM).

Case 2
If the voltage reference is more than dc link voltage, the switch is in the top position and the below circuit as shown in Fig. 5 to operate in charge mode.The voltage controller loop is responsible for generating a reference current.This reference current is then passed to the current-loop controller.The purpose of the current-loop controller is to regulate the operation of a DC/DC power converter in order to charge the battery at the desired current level.
In order to protect the EV battery during charging, it is important to ensure that the charging current does not exceed the maximum current limit.This can be achieved by utilizing a saturation block, which imposes upper and lower limits on the current reference signal generated by the voltage-loop controller.By applying upper and lower limits to the signal, it prevents the charging current from surpassing the maximum allowable value, thereby protecting the EV battery from potential damage.As the battery gets charged, the required current decreases in order to maintain the battery voltage.To achieve this, an output voltage regulation (OVR) controller generates a current reference signal, which is then passed to the output current regulation (OCR) controller.The range of the current reference signal is determined as a function of the DC bus voltage.The upper limit of the current reference is set based on the maximum current that the EV battery can safely handle.when the DC bus voltage drops below the predetermined limits, the power converter will start supplying energy to the DC bus instead of drawing from it.This enables bidirectional power ow, allowing the charger to effectively transfer energy between the DC bus and the battery, depending on the charging or discharging requirements.In the Simulink model, the charging current reference and the corresponding duty ratio for each PWM converter are determined.The controller model also controls the power switches to determine when to turn them on or off for charging and discharging the EV battery.The charge controller regulates the voltage during the charging process.It monitors the battery voltage and adjusts the charging parameters to maintain the desired voltage levels.It also regulates the charging currents based on a continuous charge current scheme.Furthermore, the charge controller decides when to terminate the charging process.It monitors the charging currents and voltages and determines when the battery has reached its full charge capacity.

Formulation of MPC and conventional controller
A model predictive controller (MPC) can be bene cial in managing the charge and discharge rates of electric vehicles (EVs) in distribution networks.MPC are particularly useful in this context due to the non-linear nature of EV chargers and distribution networks.MPC typically consists of three main components: a prediction horizon, a control horizon, and a weight.The prediction horizon refers to the length of the future time horizon over which the system's behaviour is predicted such as state of charge of EV, voltage and current level.It represents the number of future steps for which the controller calculates predictions.The control horizon, on the other hand, refers to the length of the future time horizon over which the control actions are determined.It represents the number of future steps for which the controller calculates optimal control actions.The control horizon is typically equal to or shorter than the prediction horizon.Using MPC, the charge and discharge rates are managed.The charging controller's input factors in this situation include EV's SOC and the voltage level at the node to which the charging station is connected.The EV battery will charge if SOC is low and the node voltage is high, while the EV battery will discharge if SOC is greater and the node voltage is lower.
The node voltages and SOC can, however, be high or low simultaneously in various circumstances.In certain circumstances, a particular charging/discharging rate is used.In order to sustain the voltage variations at the distribution node, the MPC must be tuned to handle crucial scenarios as well.
Figure 6 displays the block diagram of the generated Simulink model's GSC controller.The controller has a PLL, a VDC regulator, a current regulator, and measurements block.Based on the current references Id and Iq it calculates the necessary reference voltages for the inverter.The current regulatory system uses MPC controller as shown in Fig. 7.The Iq reference is initialised to zero in case of G2V and has a predetermined value.The necessary active current Id reference for the current regulator is established.For grid synchronisation and current/voltage measurements, respectively, the PLL & measurements block is needed.For the reference voltages, the PWM Generator generates the gate signals for the active switches.
The discrete time domain is used to formulate the MPC controller.As a result, it is necessary to convert the dynamic system of the bidirectional AC-DC converter shown in Eq. ( 13) into a discrete time model at a certain sampling time Ts for both the charging and discharging modes of operation.From the measured currents and voltages at the kth sample instant, a discrete time model is used to predict the future values of currents and voltages in the following sampling interval (k + 1).The system model derivative from the Euler approximation is denoted by the following formula:

23
The bidirectional AC-DC converter's discrete time model of predicted currents and voltages for the following (k + 1) sampling instant can be created using the above approximation.The discrete time model of predictive input currents at the following sampling moment (k + 1) for the charging and discharging modes of the bidirectional AC-DC converter can be assessed from (13).24

Cost function
MPC has two main functions, in the rst step, the objective is to determine a voltage vector that will closely follow a reference current pro le.In the second step, a cost function is constructed based on the error between the calculated voltage vector and the possible voltage vectors that can be applied by the VSI.The cost function is designed to capture the deviation between the desired and actual motor responses.The goal is to nd the optimal voltage vector that minimizes this cost function.The cost function evaluates the performance of each candidate voltage vector, and the MPC algorithm searches for the one that provides the best control action to reduce the error between the reference voltage and the actual voltage.
To obtain discrete form of model, Euler method has been employed therefore Eq. 13 can be written as: - For next sampling time (k + 1) the direct and quadrature axis voltage can be calculated as: -27 28 To achieve voltage reference, prediction of the current at the next sampling time replaced with current reference: -29 30 The control action (voltage vector) that results in the least difference with the desired voltage vector is given as: -

31
Where: -J is the objective function.
i represents the discrete time index.
N is the prediction horizon, which determines the number of future time steps considered in the optimization.
Let's take an example of conventional controller PI, and its output equation is given by: - The controller generates the output signal u(t) based on the error signal e(t), which is the difference between the reference voltage ( ) and the actual voltage ( ).

32
The output voltage of the 3-phase recti er circuit is then given by: 33 Where is the DC voltage output of the recti er circuit, D is the duty cycle of PWM signal 34 35 Similarly, for PID Controller,

37
Where and are the proportional, derivative and integral gains of the controller, respectively, and de(t)/dt and ∫ e(t) dt is the derivative and integral of the error signal over time.

Control Algorithm
Figure 8. shows the control algorithm of Model Predictive Controller that control the charging and discharging of energy storage system.
1.The control algorithm begins by measuring and sampling the three-phase AC current for the kth sampling period.This involves capturing the instantaneous values of the current waveform at regular intervals.
2. By using this equation, the control algorithm can estimate or predict the future value of the current based on the current value and other relevant information available at the current sampling period (k). 3.After predicting the future value of the three-phase AC current, the control algorithm calculates and sets the reference currents.These reference currents are determined based on the desired power ow in the system.4. Then cost function (e) is calculated by comparing the predicted values of the grid current with the reference values.The cost function serves as a measure of the deviation between the predicted and reference grid currents.5.After calculating the cost function, the control algorithm selects the switching state associated with the minimum cost function for ring the converter in the next sampling time period (k + 1). .The PI and PID control algorithm compare the DC-link voltage (Vdc link) with a reference voltage (Vref).This comparison is made to determine whether the buck or boost operation should be implemented in the buck-boost converter.7. If the DC-link voltage (Vdc link) is found to be less than the reference voltage (Vref), it indicates that the DC-link voltage is lower than the desired level.In this case, the control algorithm selects the buck operation, otherwise it selects boost operation based on the switching signal and duty cycle of PWM.

Result and Discussion
In the a simulation was conducted for a duration of 1 seconds to examine the transient behaviour of the system and how controllers affect recti er duty cycle regulation and provide effective charging and discharging operations.In order to examine the performance of the three controllers PI, PID, and MPC for the recti er module in the AC-to-DC conversion stage of a bidirectional charging system, a simulation was carried out in MATLAB Simulink R2022b, the simulation parameters and controller tuning parameters are given in Table 2 and Table 3 and used in the simulation with the sampling time of 5µsec.In the simulation, the DC link voltage curve, battery voltage, current, and state of charge were all analysed.Also, the effect of the charge state with regard to time was investigated.The model operates at a voltage of 600 V rms and the AC power from the grid is fed into a recti er, which converts the AC voltage into DC voltage.
The DC voltage obtained from the recti er is then fed into a controlled DC-DC converter.This converter regulates the DC voltage and supplies it to the vehicle battery.It is designed to maintain a constant current output.A controller is employed to regulate the output voltage of the DC-DC converter.It adjusts the ring pulses to the bidirectional power converter, which is responsible for switching and controlling the output voltage.It compares the actual battery voltage level to the desired battery voltage level and adjusts the ring pulses accordingly to maintain the desired output voltage.
The Table 4 and Table 5 presents a comparison of different control systems based on their settling time, undershoot, overshoot, rise time, fall time.The conventional PID and PI system shows a relatively high overshoot and settling time, indicating that it may have slower response characteristics and signi cant oscillations before reaching the desired output.where initially the grid input is given, and after a simulation of 0.5 seconds, the voltage drops.The three controllers are evaluated and analysed based on their performance in this scenario.In Fig. 9 (b), the charging and discharging voltage curves are plotted for the three controllers.As the input voltage drops, the output voltage at the charging point also drops to around 30 volts for all three controllers.In Fig. 14, 15, and 16, the charging current curves are plotted for the three controllers.As the input voltage drops, the charging current starts to rise for all three controllers.The MPC controller has the highest discharging current, followed by the PID and PI controllers.The SOC curve is plotted for the battery as the input voltage drops, the SOC of the battery starts to drop, indicating that the battery is discharging.The PI controller has the signi cant drop in SOC, followed by the PID and MPC controllers.The curves in Figs. 13, 14 and 15 show that the PI controller has the highest drop in charging voltage and current.The PID and MPC controllers have a better performance in terms of voltage, current and SOC drop, also overshoot, undershoot and preshoot of MPC controller is far better than the PI and PID controller.Overall, the results from the gures indicate that the MPC controller is a promising control approach for charging stations operating in charging and discharging mode, providing better performance in terms of stability, e ciency, and power regulation compared to the conventional PI controller.

7.
The main focus of the research is on developing and evaluating three different controller strategies: Proportional-Integral (PI), Proportional-Integral-Derivative (PID), and Model Predictive Control (MPC).These controllers are designed to manage the duty cycle of the converter during the AC-to-DC conversion stage, which is crucial for e ciently charging and discharging the EV battery.The effects of several controller techniques, including PI, PID, and MPC, on the charging process, battery state of charge, and voltage and current pro les through simulation and analysis are shown in this paper.The simulation results are analysed to compare the different controller schemes and their effects on the battery's charging and discharging processes.MPC performs better than PI and PID in tracking the required output voltage and reducing overshoot and settling time.
The research nds that the MPC controller outperforms the traditional PI and PID controllers in terms of peak overshoot and settling time.This indicates that the MPC controller provides improved control performance, resulting in reduced deviations from the target values and faster response times.In order to facilitate the integration of electric vehicles into the smart grid, the results of this study can help in the design and optimization of bidirectional charging systems for general use.Future work in this eld will focus on creating bidirectional charging systems that are more dependable and e cient as well as integrating cutting-edge control techniques for AC-to-DC converters.Bidirectional charging systems' energy e ciency might be enhanced, and their performance could be optimized for different grid circumstances, according to future research.The control and optimization of bidirectional charging systems may also be improved by the use of arti cial intelligence and machine learning methods.

Declarations Figures
Page 16/ and integral constant for charging current, is the proportional and integral constant for voltage regulation, and I are the voltage and current of EV battery.and are the reference current and charging voltage of EV battery.

Fig. 9 (
Fig.9(a) and 9 (b) shows the recti ed DC voltage of charging and discharging of bidirectional AC-DC converter.During the charging mode the three phase AC voltage transfer to DC bus with controlled input current in which the output DC voltage is xed at 48 V.And in discharging mode bidirectional AC-DC converter allows power transfer from DC link voltage to AC side by keeping 180-degree phase shift.In this gure the X and Y axis represent the time and DC link voltage.From g. 9 (a) it is seen that the settling time of MPC, PI and PID controller are 5.839 ms, 8.762 ms, very large for one second duration whereas overshoot of MPC, PI and PID controller are 4.737%, 2.371% and 5.86% and undershoot of MPC, PI and PID controller are 2.000%, 3.059% and 1.999% respectively.Similarly, from g. 9 (b) it is seen that when converter acts as a discharging mode after

Table 1
Bidirectional Converter AC-DC voltage space vectors Switching States Voltage Space Vectors

Table 2
Description of Variables and System Parameters 9 (a)it is seen that the settling time of MPC, PI and PID controller are 5.839 ms, 8.762 ms, very large for one second duration whereas overshoot of MPC, PI and PID controller are 4.737%, 2.371% and 5.86% and undershoot of MPC, PI and PID controller are 2.000%, 3.059% and 1.999% respectively.Similarly, from g. 9 (b) it is seen that when converter acts as a discharging mode after 0.5 sec the settling time of MPC, PID and PI controllers are 10.9775 ms, 11.565 ms and 11.679 ms.Overshoot and undershoot of MPC, PID and PI controllers are 1.996%, 1.997% ,1.997% and 0.578%, -0.115%, -0.189% whereas rise time and fall time of MPC, PID, PI controllers are 48.106ms, 47.755 ms, 44.821 ms and 15.925 ms, 16.258 ms, 16.196 ms.

Table 4 Comparative
Performance of the Proposed Controllers (Charging) effectively than traditional controllers like PI and PID, which may lead to better SOC characteristics.The MPC controller has the highest charging voltage and current among the three controllers.The simulation results indicate that the MPC controller provides the most stable and consistent charging characteristics for the EV battery.Figures 13, 14 and 15 presents the curves of charging voltage, current, and SOC of the battery during a scenario The model predictive controller showed improved performance compared to the conventional PI and PID controllers in different aspects such as voltage stabilization, state of charge, charging and discharging current and voltage.The MPC controller achieved a stable DC voltage of 48V at 0.45 sec while the conventional controller reached the same value at 0.6 sec in case of PI for charging state as shown in Fig.9(a).In Figs. 10, 11 and 12 presents the MPC controller exhibits a stable charging voltage and current, resulting in a smooth SOC curve.The PI controller has a slightly higher charging current and lower charging voltage than the PID controller, whereas the SOC curve of PID shows a slight overshoot and oscillation.MPC controller can achieve better SOC characteristics compared to PI and PID controllers in the same charging period.MPC can handle nonlinearities more