ANN-MILP Hybrid Techniques for the Integration Challenge, Power Management of the EV Charging Station with Solar-Based Grid System, and BESS

Abstract

Smart power management practices are needed for a sustainable EV charging infrastructure due to the fast use of renewable energy resources. An innovative power management structure for a small grid-connected solar PV system-based AC and DC charging station, combined with a backup purpose battery energy system (BESS), is demonstrated in this paper’s study. The sustainability transition is associated with integrating renewable energy resources with a battery storage system, providing a helpful solution for managing large power-demanding entities (EV, microgrid, etc.). In this study, a solar PV system takes 500 datasets (based on data availability or to prevent overfitting) of PV voltage, solar irradiance, and air temperature, and the performance of controlling for the maximum power point tracker by training these datasets using Levenberg–Marquardt (LM), which was implemented in the ANN toolbox and created this technique in MATLAB 2016 or Simulink. Also, using this technique for the estimation and forecasting of the datasets of solar PV systems and EVs obtains better results for achieving further targets. To enhance decision-making capability through optimized technique, we have to find it before forecasting PV power generation and EV datasets throughout the day (24 h). The optimized power flows among solar PV power generation, EV charging demand (including AC charging and DC fast charging), the BESS, and the utility/small grid under several priority operating scenarios. A famous technique for optimization, mixed-integer linear programming (MILP), is applied. In this technique, the objective function is used for the solution of problem formation and compliance with system constraints such as the power balancing equation, charging/discharging limits, SOC limits, and grid export/import exchange limits: basically, equality, inequality, and bounds limits. Optimized results show that the coordinated power flow operations are consented to by EV users, by prioritizing some key points, such as solar PV use at the maximum, reducing the grid power dependency, and the first power flow towards EV charging demand. The verified MILP-based solutions boost the maximum utilization of renewable energy resources, feasible EV charging demand, and scaling power flow among these entities. The key contribution of this study is suitable for different powered EV charging stations based on both AC and DC, with different ratings of EVs (including fast and slow charging). Most solar PV-based generation supports the EVCS and backup for ranking-wise BESS, and grid support for the EVCS. Also, the key contribution of hybrid techniques in this article is divided into two stages: in the first stage, an artificial neural network (ANN) is utilized for estimating the PV voltage at the maximum point and forecasting, while in the second stage, mixed-integer linear programming (MILP) employs optimal power management.

1. Introduction

The widespread penetration of electric vehicles (EVs) has grown due to the world’s shift towards automobile sustainability and low-carbon transportation, while the manufacturing of the battery is also associated with the environment, such as the use of materials, extraction, and carbon emissions from the manufacturing process. But battery-based vehicles will be integrated with a solar-powered charging system that reduces our dependency on the fossil fuel-based grid and charging stations. Overall, the impact of the environment during integration is reduced compared to the initial effect, and the environmental benefits increase. The PV-based grid is integrated with an EV charging station and a storage battery setup that provides a sustainable combination of renewable resource use and electrical energy storage, thereby increasing the EV adaptability [1]. Although EVs have a lot of issues presenting in the power system, especially rising electricity demand, maximum load demand stress, and grid resilience, especially during peak EV demand times, power infrastructure based on grid-dependent systems may result in voltage instability, power stress, etc. That is why a combination of intelligent power flow management techniques and renewable energy resources in EV charging stations has become a crucial domain of research.

The abstract illustrates the comprehensive configuration of the proposed PV-based grid-connected EV system, which utilizes on-grid solar energy for EV charging. Based on the availability of renewable energy, this integrated system decides the smart EV charging allocation by adjusting the power flow. In the case of solar energy, a high amount of power is generated in a day, which increases the available demand for EV charging and grid supplies. Conversely, in low-renewable energy generation, EVs will receive less energy for charging or will intelligently use available power flow between EVs and the grid.

Sudden power demand by EVs can disrupt the grid, the battery converter’s stability, and reliability. Effective optimal power management is needed for PV-based EV charging stations to ensure battery longevity as well as handle small grids’ loads [2]. The intermittent behavior of solar PV power generation and uncertain or varying EV demand is addressed by the integrated model of the PV-grid system, with BESS-based EV charging stations for both AC and DC charging available [3,4]. EV charging scheduling in a renewable resource-based integrated grid system has two advantages. One is the maximum use of renewable energy resources for charging EVs, which is the best combination of sustainability and clean environmental energy. Second, it mitigates the grid stress due to extra power flow for charging EVs and fixes the variability of renewable energy resources. Also, this clearly explains the control mechanism for every power entity, although a lot of significant unresolved research gaps still exist regarding the advancement in solar PV–grid integrated systems with BESS-based EV charging stations. To boost the effective impact of EVCS (charging station) and improve the switching mechanism in the control system, loop optimization techniques are crucially needed. The existing planning infrastructure for PV-grid-BESS-based EVCS integrated systems often disregards various EV demand behaviors and handling uncertainties. Ref. [5] proposed the control algorithm for power flow management through adaptive least mean square (LMS) and logarithmic normalized least mean square (LN-LMS).

Mostly, research regarding EV integrated with PV/grid or both is concerned with other power entities of EV. Ref. [6] proposed for the study to support the distribution grid by integration with EVCS, and solved it using a conventional method. Mathematical equations are made from datasheets from manufacturers and are finally simulated in MATLAB to present the results. Ref. [7] optimized the problem formation by (PSO + GWO), which accurately resolves the management, but these are complex to understand, whereas the other techniques or methodologies, such as ARIMA (autoregression integrated moving average), LSTM (long short-term memory), PSO (particle swarm optimization), GA (genetic algorithm), and machine learning methods, are sophisticated optimization techniques to handle large, realistic data samples and uncertainty; time-series forecast for the datasets to change in a linear pattern; and fast convergence. Additionally, these complexity-based techniques will create a suitable benchmark comparison analysis for our future work, which involves multiple forecasting and optimization methods with system-level performance. The present study primarily focuses on the suggested forecast-based optimization framework.

The need for forecasting in uncertain variables is important, as explained in [8,9]. Forecasting of the solar PV power generation and EV charging demand is crucial for the best possible power management in combined PV-EV-BESS-grid connected systems. The MILP optimizing technique is a look-ahead capability for optimal power scheduling for battery charging and maximum utilized solar PV generation, based on the forecast data for predicting future power accessibility for EV charging demand and grid requirements. Without the forecasted data, inputting into MILP will generate inaccurate results. The previous day’s datasets are required for finding the forecasting value, then deciding the input and target data in the ANN approach (the target value is always forecasted data) [10,11]. Also, data have to be converted into a normalized form for easy data handling and accurate results. Several AI-based techniques can be implemented in this application, such as deep learning, machine learning, etc., but hybrid AI-based optimizing frameworks deal with the best approach and accurate outcomes, scalability into high-powered applications, and processing efficiency that cannot be achieved by a single AI-based technique used [12]. The main tackling problem of solar PV systems is their intermittent nature, which has to be addressed. A single ANN approach is sufficient to manage power from it at the maximum power point (MPP) and its variable power generation, so that it will not affect the optimal goal of this study [13,14]. Every system in an integrated model has an important role, such as BESS, which will support the whole system by checking the limit of SOC and the capacity of BESS, as presented in this study [15]. Electric vehicles (EVs) are charged in two ways: slow and fast charging in inductive types of EV charging. Slow EV charging is mostly preferred for residential areas, and fast EV charging for public and in the parking lots of workplaces [16]. Fast EV charging creates extra stress on the grid when the grid is based on non-renewable energy resources, but when it is based on the full utilization of renewable energy resources, it will be beneficial. But the use of renewable energy resources also has drawbacks, such as an intermittent nature and having to forecast the solar PV datasets. The EVs have the same problem of the random or unpredictable nature of the EV arrival time in the charging station and EV power demand, which has to be fixed and dealt with based on the explanation given in this article [17,18].

The proposed integrated system has several important subsections, and each of the individual parts has its own importance, such as the solar PV system; EVCS, both AC-and DC-based; BESS; and grid loads. Every individual system has its own power limitations/constraints, and an optimal solution has to be an integer value, which is why the mixed integer linear programming (MILP) technique is used, as the MILP has one or more objective equations and constraints, as explained in this article [19,20].

This study proposes a completely comprehensive design of EV with both AC- and DC-type charging stations, together with an integrated solar PV-based grid system and BESS, which will be associated with novelty in this paper’s research. In this study, various datasets are uncertain in nature, such as solar PV power generation (which is intermittent in nature), EV power demand patterns, and EV users’ arrival and departure times in charging stations. These uncertain datasets can be resolved by both neural networks and the MILP approach, but more preferable results are obtained from using the neural network approach. In this approach, first decide the input and target. Target nodes will give the forecasted value with complete or regular datasets that will be beneficial for further use in optimization purposes. The optimal solution for this integrated system is to maximize the utilization of the solar PV system for fulfilling the EV charging demand, store excess power, and, finally, transfer the remaining power into the grid to meet the grid loads and reduce the dependency of the EV charging demand on the grid. An optimal MILP approach sets constraints for the BESS to provide backup support during low solar PV power generation or at night, and to reduce grid dependency. The grid system is imported into EV charging stations when both solar PV and BESS are unable to fulfill the EV power demand, resulting in continuous, uninterrupted power flow from an emergency perspective. Also, when solar PV, BESS, and the grid are involved, these three power entities cannot maintain the power flow; in that condition, V2G operation will be enabled under several circumstances developed by the MILP technique. The communication part in this integrated system plays a role as a backbone and relay-assisted communication technique, as presented in this article [21], which increases the level of the integrated system. A two-way communication system among EV owners, grid operators, EV charging stations, and aggregators is needed to respond to the demand side and schedule EV charging. The basis of the smart grid has several algorithms to understand the demand response, as discussed in the previous article. In advanced EV charging allocation, automakers play an intelligent part in integrating communication permissions.

There are some research gaps related to the same application, such as previous studies that mainly focus on the grid-side benefits and achieving the goal to improve the grid’s stability, and optimizing the model with complex hybrid techniques, which are complex and difficult to understand [1]. The article focused on load-side benefits with integrated EVs, such as improved power quality and power factor of the grid, PV, and battery converter. Basically, it focused on the energy system’s power quality, so earlier studies did not prioritize the people who have EVs. In contrast, this study will be framed for the benefits of EV users first, with a very easy-to-handle hybrid technique for optimization.

Simulating the hybrid AC-DC EV charging station feed with a solar PV system, BESS, and utility grid, along with an ANN-MILP hybrid optimizing technique framework, makes this paper novel. This study shows a combined power flow management approach that emphasizes the maximum utilization of the solar PV system and power balancing among the integrated system, and tackles the dependency of EVs on the utility grid. The novelty of this suggested article develops the hierarchical optimal power management for the EV-based integrated model.

The key novel contributions are explained as follows:

• Two-stage optimized structure.
  The recommended approach presents a two-stage framework instead of a single-stage power management optimized technique. In the first stage, this is targeted for solar PV-generated voltage at the maximum power point and forecasted data samples for estimating the solar PV power generated, EV demand, and its arrival patterns, whereas in the second stage, the power demand of EVs for both types of charging (AC and DC) is optimally allocated using an optimized technique. The machine learning-based forecasting estimation and optimization are separated to improve the computational time and increase versatility in operation.
• Peak demand reduction on the utility grid via the EV charging coordinated allocation and V2G technique.
  The peak demand of the grid is reduced by another source of power supply synchronized with an optimal coordination relationship in an EV-based integrated system. The synchronization among the solar PV system, BESS, and EVCS (EV-charging station) explicitly creates benefits for the grid’s load, such as reducing the grid dependency and mitigating the peak load demand on it. This will be achieved by the EV coordinating charging scheduling with a solar PV system and backup purpose storage, BESS. This combined task was addressed individually in a previous study; in this article, we will tackle it combined.
• Coordinating balanced power flow: both types of AC and DC EV charging loads in the integrated system.
  The suggested optimal framework explicitly embodies a structured approach for both types of EV charging with different power demand levels and load profiles, which makes the EVCS more realistic. Such depth infrastructure can improve the load balancing in an integrated system.
• Get the EV charging scheduling top-prioritized and maximum use of the solar PV system in the hierarchical allocation system.
  The power distribution from the available power resources is planned based on the priority of the EV demand—firstly fulfilled—and the maximum utilization of the renewable energy resources. Firstly, the solar PV-generated power is transferred to fulfill the EV power demand, followed by the extra power stored in the BESS for the backup purposes of the EV, as well as the grid’s load. The optimal allocation of power for reducing the grid dependency and reducing its peak load demand is done by using the grid as a secondary backup resource for power in an integrated system.

The key aims of this study are as follows:

• To propose a simulation of an integrated solar PV–grid-based EV charging station for both AC and DC types in Simulink/MATLAB.
• To design a control mechanism that is AI-based, such as an ANN-based MPPT controller for a solar PV system, and a control mechanism for the phase shift controller for bidirectional and power flow control.
• To estimate the datasets, an ANN algorithm was used to define each dataset in 24 h for accurate optimization results at the last step.
• To make a priority list or scenarios for implementing balanced power management.
• To create an optimized approach using the MILP technique by setting an objective function to tackle the problem formation, and setting equality and inequality equations for the limits of the energy entities.
• To create feasible and resilient power management by dealing with non-linear relations using ANN and optimal solutions, using the MILP approach.
• To achieve a dynamic optimal power flow by a hybrid technique, which becomes an advanced optimal learning approach.

2. Literature Review

Smart EV charging means properly scheduling the use of power/energy from the solar PV-based grid for EV charging demand, which is also called the allocation of EV charging, to maximize the renewable energy resources. Basically, this is balancing the power demand that occurs for EVs charging and getting power from renewable energy resources and the grid.

Table 1. The summary of the literature on the same topics.

Year	Authors	Hybrid System				Key Finds	Methodology	Limitation
2025	Sithambaram, M. et al. [1]	PV	EV	BESS	GRID	Improved power quality and power factor of the grid, PV, and battery converter. Basically, focused on the energy system’s power quality	Hybrid technique (SWO-MHFAN)	Difficult to understand, complex learning
		√	√	√	√
2025	Sharma, J. et al. [2]	PV	EV	BESS	GRID	Power management for grid stability and EV longevity	PSO algorithms for MPPT + evaluation in MATLAB/simulation + dSPACE DS1202 platform	Complex learning skills/programming, high-cost
		√	√	√	√
2025	Ali. et al. [3]	PV	EV	BESS	GRID	Maximum RES utilized, grid stability maintained, better power flow	Neural network- based ANFIS for MPPT	Not express the optimal EV scheduling properly in a graph or tabular form
		√	√	√	√
2025	Alok Jain, et al. [4]	PV	EV	BESS	GRID	Grid power quality, DC bus voltage regulation, BESS to grid operation	Perturb and observe (P&O) MPPT + LMS algorithm for control strategy	LMS algorithm has slow convergence compared to the machine learning approach
		√	-	√	√
2025	Alok J., et al. [5]	PV	EV	BESS	GRID	Sudden variation in PV solar irradiance and EV power demand effect on the grid quality and stability	LMS-based controller	Not uncertainty—discuss for the EV datasets and PV, and forecast to resolve the uncertain nature. For a low-power system
		√	√	-	√
2025	Mehmood, A. et al. [6]	PV	EV	BESS	GRID	Power quality improved by the grid-connected EV charging station	Conventional method—mathematical equations, datasets from manufacturers and simulated proposed model in MATLAB	Low power application
		-	√	-	√
2025	Adiguna, S. et al. [7]	PV	EV	BESS	GRID	Optimal combination of BESS and the grid-connected solar PV power generation with EVCS	Particle swarm optimization (PSO) and gray wolf optimization (GWO) algorithms	Very complex learning approaches
		√	√	√	√
2020	Ghotge, R. et al. [8]	PV	EV	BESS	GRID	Dealing with uncertainty in EV datasets for optimal scheduling	MATLAB simulation + model predictive control (MPC) control technique	Time-taking controlling
		√	√	√	√
2025	Alguhi, A. et al. [22]	PV + DG	EV	BESS	GRID	Renewable energy resources with BESS integration enhances the EV penetration and grid stability	MATLAB + AI-based (Combine ANN, LSTM) control and optimizer technique	Uncertain datasets of EV and solar PV power generation are not modeled
		√	√	√	√
2024	Fan, P. et al. [23]	PV	EV	BESS	GRID	Voltage and frequency regulation of the grid with EVs, optimal EVs charging scheduling	MATLAB Simulink + MILP technique = deep reinforcement learning algorithm	Predictive model of EV arrival time, EV owners’ preferences are mixing and advancing, known in the study
		-	√	-	√
2025	Tiburtini, F. M.et al. [24]	PV	EV	BESS	GRID	Power balance in between PV and EV by BESS sizing	Non-dominated sorting genetic algorithm-2	Assume uncertainty is negligible or fixed, datasets of EV and PV
		√	√	√	√
This study	_	PV	EV	BESS	GRID	Maximum utilized PV solar power, peak power reduction export from the utility grid, EV charging allocation in integrated system, maintain the constant power on the DC buses	MILP + AI-based control mechanism = hybrid optimization techniques for hybrid system	Easy to understand every step, estimated, forecasted model and explained optimal EV allocation in tabular form
		√	√	√	√

shows the literature review table with the same application.

3. Methodology

Figure 1 represents the hybrid model, which combines a PV solar system, BESS, a large number of electric vehicles, and two types of loads connected to the AC grid. Here, two types of EV charging are discussed: AC charging and DC charging, also called fast charging. This model combines a solar PV system with a unidirectional DC/DC converter and BESS with a bidirectional DC converter. Also, an AC utility grid is connected to the DC link through a power electronics-based inverter to fulfill local utilities’ loads. DC EV charging or fast charging stations are connected to a constant-powered DC bus with a power electronic-based DC converter, and AC EV CS is connected to the AC grid with a suitable power level by a transformer. This setup will supply solar PV power production to EVCS, store extra power in BESS, and balance the grid’s loads. The PV power generation uncertainty depends upon the weather conditions, and it can handle the problems caused by this lack of power by forecasting this variable. The big frame problem can be resolved by setting an objective function for this study. Objective functions are solved by mixed-integer linear programming (MILP) algorithms, with AI-based control schemes for accurate optimization. Basically, we must make a hybrid optimized technique (MILP + AI) to solve the hybrid model that definitely tackles the energy management in this system. ANN/Fuzzy logic is ideal for predicting and forecasting PV generation power, handling real-world scenarios with large datasets, load forecasting, and the arrival of EVs, as well as solving complex and nonlinear system issues. On the other hand, MILP is used generally in optimal decision-making applications and load balancing. Both techniques are evolving this integrated system for the problem-solving formation, because this system has non-linear components, uncertain behaviors, and demanding discrete optimal decision-making.

3.1. EV Integrated Model with Solar PV-Based Grid System

This paper aims to take advantage of the EV–PV–grid connected integrated system with BESS backup storage and propose this model with various datasets, including photovoltaic modules, the converter, the inverter, BESS, EVs, both types of charging, and all types of control mechanisms that are essential for model design.

3.1.1. PV System

Solar photovoltaic (PV) modules transform sunlight into electrical energy by using solar photovoltaic cells under the photovoltaic effect. This phenomenon occurs when light energy that has photons collides with the semiconductor-made cell, and the photon’s energy is higher than the electrons in the semiconductor-made cell [3]. In this occurrence, the electrons jump from the valence band to the conduction band and generate electron–hole pairs in this whole phenomenon. A PV cell generates a direct current (DC) with the movement of charge carriers towards the DC loads. Due to the required output voltage and current values for the grid and storage electrical energy, solar PV modules are often arranged in parallel and series configurations. P_PV(t) is the total output power generated from Solar PV modules, and it depends upon solar irradiance, the air temperature of the individual solar cells, other weather conditions, and the physical states of solar panels.

For the reference PV module, we simulated a PV module in MATLAB, using a publicly available dataset of the solar irradiance data hosted by Vikram Solar Hypersol VSMDH.66.AAA.05 715 W module, 132 cells. The characteristics table of the PV module is shown in

Table 2. Characteristics of a PV module.

Parameters	STC (Irradiance- 1000 W/m2, 25 °C)	NOCT (Irradiance- 800 W/m2, 20 °C)
Maximum power from PV per module (PPV_(DC))	715 W	539 W
At maximum power point, voltage (VPV_MPP)	40.6 V	37.6 V
At maximum power point, current (IPV_MPP)	17.63 A	14.28 A
Open circuit voltage (VPV_OC)	48.1 V	45.4 V
Short circuit current (IPV_SC)	18.64 A	15.03 A
Cells per module of solar PV panel	132	132
Number of series modules per string	15	15
Number of strings in parallel	280	280
Max efficiency	23.02%	23.02%
Temperature coefficient of VPV_OC	−0.26%/°C	−0.26%/°C
Temperature coefficient of IPV_SC	0.046%/°C	0.046%/°C

. The maximum efficiency of this PV module is 23.02%. G shows solar irradiance. The standard testing condition means 1000 W/m², and nominal operating condition air temperature means 800 W/m², as established by this [25] reference. Solar energy generation requires three main subsystems: solar modules, an MPPT controller for the control phase shift, and a DC-DC converter (switching subblock). In this research, the implementation of an ANN-based MPPT controller is presented. Several algorithms are used for ANN to work on 3 MW power generation from a solar PV system. The maximum solar power generation is 3 MW at 800 V constant DC bus voltage. P_PV(t) is the total power generated from PV modules at time ‘t’ (kW), V_PV voltage, and the I_PV current from the total number of PV modules. V_PV is 609 V at STC, which is out of the converter. In this study, the Dual Active Bridge DC/DC converter is used for bidirectional operation and isolates every large powered system by controlling the phase shift angle (δ). Eventually, bidirectional or unidirectional flow is done by control enforcement, not through designing the structure. The power flow is proportional to the phase shift angle. The DC converter near the PV modules in this study is a unidirectional DAB, and the phase shift angle control remains in a positive value. Solar PV module specification datasets are shown in Table 2, and module arrangement in Figure 2.

Total no. of modules = 4200

Modules in series and make a string = 15

Total Maximum power point voltage at STC = 609 V

Total Maximum power point voltage at STC = 563 V

Maximum power point, current per string = 17.63 A

Total number of strings = 280

Total maximum power point current, I_PV = 4936.4 A

Total maximum power point current, I_PV = 3997.4 A

Total maximum power point PV generation at STC 3.003 MW

Total maximum power point PV generation at NOCT 2.263 MW

The PV-modules’ voltage is typically around 600–609 V, and for integration, the DC BUS must maintain the voltage at 800 V.

3.1.2. Industrial Load and Distribution Transformer Through AC Bus

An AC bus supplies power to the industrial loads and the utility through a distribution transformer. The distribution transformer has a rating of 1000 kVA, 11 kV/415 V, and 3-phase, 1 MW industrial load. For the distribution required, the Delta-Star (Delta-wye) connection is the most commonly used for stepping down the high 11 kV voltage to the low 415 V Delta-Star (Delta-wye) connection, and is the most commonly used for stepping down the high 11 kV voltage to the low 415 V. The details about the transformer needed and the industrial load in MATLAB Simulink are summarized in

Table 3. Domestic transformer datasets.

Rated Voltage (HV) kV	Rated Voltage (LV) kV	Rated Capacity MVA, kW	Rated Current (HV) A	Rated Current (LV) A	Turn Ratio	Voltage Regulation	No Load Loss	Load Loss	Short Circuit Current	Connection Type	No Load Current I0
11 kV	415 V	1 MVA, 900 kW	52.49 A	1392.2 A	26.51:1	4.3%	1.8 kW	11 kW	41 kA	Dyn11	13.92 A

and

Table 4. Industrial load dataset’s specifications.

Voltage Levels	Rated Frequency Hz	Active Power MW	Reactive Power MVAr	Load Current (A)
11 kV	50 Hz	1	0.6197	61.75

.

The complex power is supplied by the industrial load, which is a 3-phase, 11 KV system at a rated voltage. The load current depends on the complex power it draws. An AC bus has two types of loads, namely industrial and domestic loads and AC EV charging, and DC bus loads are through a bidirectional DC-AC inverter. The rating of the AC BUS is V_{_AC BUS} 11 KV (L-L voltage), I_{_AC BUS} 1779.9 kA, P__{AC BUS} 3 MW, PF_{_AC BUS} 0.88, and Q__{AC BUS} 0.528 MVAr.

3.1.3. BESS (Battery Energy Storage System)

The idea of having a battery bank near each power plant is shown as a function of balancing the demand and supply of power flow. This EV–PV integrated model is a combinational model of power balancing that employs the proper and appropriate charging–discharging patterns and power-flow balancing, in which BESS plays a vital role, enabling the whole system to run without conventional energy resources and to support EV charging for both charging types. BESS has an optimal capacity and takes part in the backup power flow. The charging/discharging behaviors of the BESS or the priority level of this charging and discharging depend upon the availability of solar power generation, the grid’s responsibility, and EVs’ load profiles [7]. The main importance of BESS in this integrated system is support during fluctuating PV power generation for a backup power source for loads, maintaining consistency to fulfill the EV charging demand, mitigating peak demand on the grid, and also maintaining a constant DC voltage at the DC bus. The mathematical relationship of the BESS-related state of charge (SOC) at each capacity and ${ E}^{BESS}$ is the battery capacity in MWh. Here, ${\eta }_{charging,}{ \eta }_{discharging}$ are the battery charging and discharging efficiencies. In BESS, SOC at a subsequent time is equal to the present SOC with the total stored energy in the given time period, given in Equation (1).

$${\mathrm{S}\mathrm{O}\mathrm{C}}_{\mathrm{B}\mathrm{E}\mathrm{S}\mathrm{S}}\left(\mathrm{t}+1\right)={SOC}_{BESS}\left(t\right)+\left( {\displaystyle \frac{1}{E^{BESS}}}\right)\ast \left({\eta }_{charging }{P}_{BESS}^{charging}\left(t\right)-{\displaystyle \frac{P_{BESS}^{discharging }\left(t\right)}{{\eta }_{discharging}}}\right)\ast ∆t$$

(1)

Here is a description of an important point that is the difference between EV’s battery and batteries in BESS. This can be cleared before dealing with the fact that both have the same chemistry: Li-ion type. But batteries used in BESS remain in a stationary position, and those of EVs, vice versa. Therefore, dealing with these is not simple, as they are used for both battery storage and load purposes. In many searches, these have different designs and management approaches (different generalized ways). In this research, both batteries are similar in their application.

The establishment of BESS in this proposed model is structured to run to 20%, meaning minimum discharging till 20% and maximum charging at 90%, with all safety points of view. Lithium-ion batteries are used for a stationary BESS model. The total rating of BESS is 2 MW, and the BDC rating is just over that, at 2.2 MW. Both are working at the same voltage with a transformer turn ratio of 0.75:1.

3.1.4. EVs

An electric vehicle (EV) uses electricity to run instead of conventional energy resources and is a sustainable automobile, using electricity generated by renewable energy resources. Different types of charging methods are available for EVs, like inductive charging, wireless charging, and battery swapping. The two ways of charging are charging by DC (direct current) or AC (alternating current) in inductive types of EV charging [26,27]. $P_{EV\left(AC+DC\right)}^{charging}\left(t\right)$ is the total active power demanded by the AC and DC EV charging station (AC-EVCS + DC-EVCS).

Table 5. EV charging specifications table.

Types of EV Charging	AC Charging	DC Charging
No. of EVs	100	100
Total demanded voltage at EVCS	400 V	600–800 V, 80 A Proposed
Total demanded current at EVCS	1760.96 A	6250 A
Total station power demand by EVCS	1.1 MW	5 MW
Total apparent power demand by EVCS	1.22 MVA	5 MW
Connected transformer rating	11 KV/400 V, 1.22 MVA	-----
Rating of bidirectional DC-DC Converter	-------	5.5 MW

shows the specifications of both types of EV charging that are used in this proposed model. The EV charging stations are associated with vehicle-to-grid (V2G) operation, which requires important systems such as transformers and converters. These systems need isolation from large power entities and small rating EVs and lower the large power accordingly for every commercial and domestic EV rating. These specifications have been decided based on the rating of the solar PV system, the rating of the DC bus constant rating, the AC grid rating, and the estimated EV rating from their specifications in the real world, and the rest of the ratings are based on the large system’s power rating. Basically, a step-down transformer at the medium power grid level is used for transferring to the low power needed for the EV charging demand and V2G operation. The proposed article does not use individual EV users’ personal data in the forecasted model to avoid privacy problems and maintain research ethics. The generalized EV datasets (power rating, arrival/departure time, and charging demand in a day) are used.

In this paper, there is proper charging–discharging allocation for both types of EV charging: slow and fast. The charging time for the AC is predominantly that of the DC. $E^{EV}$ is the battery capacity in MWh. Here, ${\eta }_{charging,}{ \eta }_{discharging}$ are the battery charging and discharging efficiencies. In EVs, SOC at a subsequent time is equal to the present SOC with the total stored energy in the given time period, shown in Equation (2).

$${\mathrm{S}\mathrm{O}\mathrm{C}}_{\mathrm{E}\mathrm{V}}\left(\mathrm{t}+1\right)={SOC}_{EV}\left(t\right)+\left( {\displaystyle \frac{1}{E^{EV}}}\right)\ast \left({\eta }_{charging }{P}_{EV}^{charging}\left(t\right)-{\displaystyle \frac{P_{EV}^{discharging }\left(t\right)}{{\eta }_{discharging}}}\right)\ast ∆t$$

(2)

3.1.5. Bidirectional DC-AC Inverter

The direct current (DC) from the PV’s output at the DC bus is converted into an alternating current (AC) with a specific voltage and frequency. This is also called an inverter [28,29]. The inverter is connected between the DC link and the AC link. This inverter is called a PV inverter because the output of solar PV modules is connected to the input of the PV inverter. In this application, a high-powered inverter is required (specifications shown in

Table 6. Bidirectional inverter specifications.

Types	VSI–Multilevel Inverter–NPC + LCL Filter
Ratings	2.5 MW
DC input voltage, AC output	800 V/689 V
AC-Bus voltage	11 kV, 3-phase, 50 Hz
Transformer ratio (n)	689/11,000 V

) from a voltage source inverter (VSI)–multilevel inverter–NPC (neutral-point-clamped). VSI is used mostly because of its high reliability and no complexity, and it is also used in high-powered solar PV applications.

3.1.6. Unidirectional DC-DC Converter and Bidirectional DC-DC Converter (BDC)

A power electronic model that supports unidirectional/bidirectional DC power flow between the two links, like between the solar PV module and DC bus connection and between the DC bus and BESS storage system, is called a unidirectional/bidirectional DC converter (BDC). This setup ensures efficient power flow management in both directions by appropriating the charging and discharging activities inside a converter architecture. In this application, involving PV-generated power stored in EVs, battery energy storage systems, and utility grid integration systems, such as V2G and G2V systems, both types of DC converters are very advantageous for power flow management and the development of optimal EV charging/discharging allocation. The BDCs are of two types: non-isolated bidirectional converter (NBDC) and isolated bidirectional converter (IBDC) [30,31,32]. For these two types of converters, the primary difference lies in their power level, voltage range, performance, efficiency, and cost. In this paper, a unidirectional and bidirectional DC power flow by a dual active bridge DC converter will be utilized to benefit.

Ref. [33] shows all types of DC converters, application areas, and ratings, also. The dual active bridge BDC is structured by two full bridges surrounding a single high-frequency transformer [34]. Isolates converters are typically used to provide the distinction between the input and output in high-power-level applications for the safety purposes of both types of equipment.

An isolated dual active bridge (DAB)DC converter is designed with two identical full bridge converters, and these are separated by a high-frequency transformer with an LC filter for ripple-free output at the DC bus. The DAB converter has a control mechanism with a phase modulation approach. EVs with both types of chargers (AC, DC) comprise an important subsystem of DC-DC and AC-DC converters and have a role in vehicles-to-grid (V2G) and grid-to-vehicles (G2V) technology/operation [35]. Basically, the DAB converter uses the phase modulation technique in the control strategy that will create a phase shift between the outputs of two full bridges. A transformer leakage inductance is for transferring energy between two circuits, which demonstrates the importance of transformer leakage inductance in converter applications. The squared waveform is obtained from both types of active bridge, and the final output waveform at the DC bus is constant-valued (in this paper, the value is 800 V). The placement of the converters in the integrated system is shown in Figure 3 and the data specification is in

Table 7. Converter types and specifications.

Types of Bidirectional DC-DC Converter with Battery	Dual Active Bridge BDC
Types Of DC-DC converters	Dual Active Bridge BDC
Types Of bidirectional DC-DC converter with EVs	Dual Active Bridge BDC
Specifications of DC-DC converter near PV modules (unidirectional)
Capacity	2.5 MW
Number of parallel converters	5
Per converter capacity	500 kW
Transformer ratio (n) per converter	609/800 = 1.35:1
Control strategy	Phase-shift angle control
Specifications of the BDC near the battery
Capacity	2.2 MW
Numbers of parallel converter	5
Per converter capacity	500 kW
Control strategy	Phase-shift angle control
Transformer ratio (n)	600/800 = 0.75:1
Specifications BDC near DC/fast charging EVCS
Total Capacity	5.5 MW
Maximum no. of EVs	100
Single parallel DC converter	5, 1.1 MW
Control strategy	Phase-shift angle control
Transformer ratio (n)	800/(600–800) ≈ 1.30

.

3.2. Problem Formation

A coordinated power management control system utilizing renewable energy resources, handling a large number of electric vehicles, and for backup using the BESS, plays a pivotal role because it is independent of traditional power resources. Intelligent control mechanisms are implied before each power entity, such as BESS, and for the best EV owners’ satisfaction, which also allows for handling the invariable nature of solar power generation, the unpredictable nature of the coming EVs for charging, and the discharge to manage demand and fluctuations on the grid load side. Each of the primary components of this integration system has a specific reference dataset that is obtained through control or management signals via an AI-based control mechanism. This section will discuss the problem formation, certain objectives’ functions based on the problem formation, and some constraints in that path. Some subsystems in this integrated system have a separate control system, but their control-based decision variable datasets are related to these. This study addresses the proper power management of an integrated solar PV-connected grid–EV–BESS system combined on both DC and AC buses.

The problem formation of this paper is based on these factors, namely:

• Maximum utilization of solar PV system-generated power to supply the required load, such as charging EVs, storing electrical energy in BESS, etc., and mitigating reliance on the grid power.
• Optimal charging/discharging scheduling/allocation of the EV and BESS for ensuring the power management under a specific objective function and limits/constraints of each subsystem’s function, such as SOC limits on the BESS, EV power demand limits/constraints, EV users’ contentment-based limits, power limits of solar PV power generation, converter, etc.
• Reducing peak load at the AC Bus by controlling power flow distribution among power entities.
• The power flow regulatory system maintains a constant power at the AC and DC buses, which improves the stability.

3.3. Control Mechanism

The integrated system will be optimized by an AI-based control mechanism and a mixed integer linear programming (MILP) technique that combines to nullify several issues. This new type of intelligent/smart optimization methods (hybrid optimization techniques) will handle the unpredictable nature of solar PV systems, and the complexity of integrated systems will be better in terms of decisions made than individual optimization techniques like MILP, GA, and PSO. These techniques are easy to use, but they require accurate modeling and higher computational power to achieve the best solution. Smart optimization involves a simulation model in Simulink MATLAB with complex constraints, and yields discrete solutions. This is also called hybrid optimization (machine learning + optimization algorithm). Machine learning is also utilized for forecasting purposes so that the optimization algorithms can be used for optimal scheduling or energy management. With the aim of making the appropriate power use, stable bus operations, and fixing the power demand of EVs with the unpredictable behavior of solar PV power generation and fewer grid dependency conditions, a hierarchical and appropriate type of control mechanism will be needed. Every subsystem in the integrated model requires an individual control mechanism that will be explained in this section in detail, one by one. Also, the currently proposed study deals with a hybrid optimization technique for power flow management among the PV system, BESS, EV, and grid; accordingly, the forecasted model is established by a neural network. But if the errors occur in the forecasted model, the controller will be compensated by using feedback-based updated measurements to rectify the errors and maintain system stability.

Sometimes it is difficult to find sophisticated energy management techniques that satisfy all linear and non-linear constraints. That application requires hybrid techniques that are used in a very linear way, which we have tried to explain in Figure 4.

3.3.1. AI-Based MPPT (Maximum Power Point Tracking) Controller with Unidirectional DC Converter

Power balancing in PV-grid-connected-EV-BESS systems is necessary because of their flexible nature. An important part of the solar PV system is the maximum power point tracking (MPPT) controller. It works like the maximum power theorem’s application. Refs. [36,37] show 40 old and recent methods for tracking the maximum power from PV solar generation. Power generation by a solar PV system can be achieved by a DC/DC converter power electronic system. A dual active bridge DC-DC converter is normally controlled by a phase shift angle or a control signal, which plays a crucial role in its operation. An artificial neural network (ANN)-based MPPT controller is implemented, training, validating, and testing the datasets from the solar PV modules system, and a further traditional control loop generates the converter’s duty-cycle output. In summary, an MPPT controller with AI (ANN) will improve the system reliability. Conventional methods for measuring MPP in PV systems will be associated with the slow tracking, instability around MPP, etc. [38]. That is why the ANN technique will be used in this paper, because it handles the nonlinearity in power due to uncertain datasets of irradiance and air temperature, and it also defines the missing datasets so that there is not a gap in the research.

The solar PV modules’ output generation does not directly connect to the EV load or batteries because of instability in the maximum power points. That is why the DC/DC converter, with its maximum power point (MPP)-based controller operational setup, which is called a maximum power point tracking (MPPT) system, is required to manage the property. The MPP operating setup will modify the essential phase shift angle of the DC converter. Generated I-V characteristics of solar PV or the input of the DC/DC converter will be changed to function until the setup gets MPP, basically pushing the converter to operate at MPP. Intelligent-based MPP carries the maximum power point datasets and creates a converter’s maximum solar PV voltage (v_{PV_ MPP}), maximum power (P_{PV_ MPP}), and control signal of the phase shift angle for the converter to get the utilized power flow with a traditional control loop system. In the whole solar PV power generation system, only the MPPT implies the novel control algorithms for increasing the popularity of the PV generation. PV modules’ power generation is mainly influenced by fluctuations in solar irradiance (G) and air temperature (T) throughout the day. That is why the position of the maximum power point (MPP) in V-I characteristics varies dynamically with changes in the atmospheric weather conditions throughout the day. If the solar PV system operates under an operating point other than the MPP, the system will incur power losses. An efficient and intelligent maximum power point tracking (MPPT) algorithm or setup will continuously modify the PV system dataset to get the maximum power extraction under all changing solar irradiance and air temperatures throughout the day. This research determines the MPP using calculation and ANN technique models. The AI-based MPPT controller technique (based on machine learning) requires the measurement of the input of PV modules (solar irradiance and air temperature) and the output of PV modules (voltage and current) at MPP.

In AI-based MPPT techniques, as shown in Figure 5, this paper has studied the neural network-based trained datasets of the solar PV model. This ANN model has three layers: input, hidden, and output layers. The performance depends upon the number of nodes in particular layers. The inputs of the ANN are the throughout-day variation in solar irradiance and air temperature (G(t), T(t) for t = 0 to 24 h’ time period) (morning to evening). The output layer displays the numerical value of the voltage at the maximum power point. The hidden layer deals with nonlinear changes in the input parameters using various algorithms. In this layer, the control action motivates the operating characteristic to move towards the maximum power point, adjusting for changes in solar irradiance and air temperature throughout the day. Therefore, the maximum benefits from this EV–PV integrated system are achieved with a proper MPPT algorithm, i.e., the operating system of the DC/DC converter, which will initiate for optimal power utilization. The non-linear output behavior comes from a solar PV system that will also be managed intelligently. In this paper, researchers will work on the Levenberg–Marquardt (LM) algorithm, which is constructed in artificial neural networks (ANN). A basic idea related to the AI-based methodology for PV operation at the maximum point is perfectly explained in these articles [39,40].

The proposed PV solar system has been simulated in MATLAB/Simulink, illustrated in Figure 2. This proposed simulated model consists of three main subsystems: a PV Solar power generation array, an ANN-based MPPT Controller (based on the ANN algorithm), and a control mechanism for the DAB converter (for the changing phase-shift that is beneficial in this integrated system). The solar PV system voltage at MPP obtained from the ANN algorithm will be further utilized in the proposed control mechanism for the DC/DC converter to maintain a constant voltage at the DC bus.

In ANN, the datasets of PV input are classified into three parts—training, validation, and testing—and three layers. The ANN structure has three layers, such as the input, hidden, and output layers with 2-6-1 neurons, shown in Figure 6. Using the ANN feedforward network designed toolbox, the suggested study is established. The Levenberg–Marquardt (LM) backpropagation algorithm is chosen to train the network because the LM is used for fast convergence and stable results. The activation functions are used for the hidden layer, which is the tansig (tangent sigmoid), and for the output layer, a linear activation function that is purelin. The total number of layers in the input, hidden, and output layers is three (an individual has a single layer). The weights for the network are initialized randomly in MATLAB via the Randon function to improve the training process. The ANN algorithm is presented by a flow chart, as shown later in Figure 7. The solar irradiance and air temperature datasets could be considered in several ways, such as the Solcast provider website accessed by [41], and a formula based on sunrise and sunset times, etc. These ways are used in cases when the measured data is not available. Both are ways of estimating the dataset’s curve, which is bell-shaped. The continuous value or time-varying values of both datasets are required to capture an accurate dataset, and the dynamic behavior variations in the system parameters/variables are achieved to ensure an optimized model. These datasets are directly used in PV solar system simulation and have physical significance, but more advantageous results are obtained from the randomization of variation on these data by the rand function. The Levenberg–Marquardt algorithm is used for efficient training of the neural network by minimizing prediction error. Under low- or no-sunlight conditions, the PV output approaches zero, and the algorithm adjusts the network weights accordingly based on the input–output relationship. This ensures accurate prediction across varying solar irradiance conditions.

Equation (3) shows the randomized solar irradiance datasets formula. Randomization will consider all the operating power points. The rand function is a uniform distribution of random numbers in the interval of [0, 1] or [Min, Max], explained in MathWorks and the MATLAB Documentation Help Center, and accessed from [42]. The datasets used in this article have been partially obtained from the Solcast website, with the basic idea of low to high solar irradiance and air temperature. This information is used for randomizing the solar PV datasets, using the ‘rand’ function. The dataset’s time range is 24 h. The normalization of the datasets is done in the preprocessing of this methodology to improve the system operations and performance, and is divided into training, validation, and testing data samples (75%, 15%, and 10%, respectively). Before training in ANN, all input–output data samples have to be normalized to enhance the convergence process time. This will be done by scaling these data into a fixed range of [1, 0].

G = [(G_Max − G_Min) ∗ rand] + G_Min

(3)

Equation (4) shows the randomized air temperature dataset formula:

T = [(T_Max − T_Min) ∗ rand] + T_Min

(4)

Equation (5) shows that the voltage at MPP is a function of the solar irradiance and air temperature. An ANN can handle or learn about non-linear functions. Randomization of samples of solar irradiance and cell temperature is recommended for ANN testing, training, and validation because the parameters at MPP depend only on the air temperature and solar irradiance and not on the time samples. Continuous value of these samples is found by the location or morning/evening time, which does not handle sudden changes in weather conditions. But in ANN-randomization, sampling can handle unexpected changes, cover the whole operating region, and determine the generalized datasets of output from the ANN.

V_PV__MPP = f (G(t), T)

(5)

3.3.2. Bidirectional Dual Active Bridge DC Converter (BDA) with BESS

This basic idea implies a control mechanism with BESS for implementing bidirectional power flow at the time of need; backup power for the load demand is shown in Figure 8. The role of the control mechanism for proper operation should maintain a constant DC bus voltage for steady purposes. The supervisory control algorithm is made for controlling some main functions, such as simultaneously maintaining a steady DC voltage, bidirectional power flow by BESS, and the phase shift angle limits for the DC converter. For the phase angle controlled by a traditional control loop, such as a PI control loop system, we consider the error signal as the difference between the reference DC bus voltage and the actual DC bus voltage.

3.3.3. BDA with DC Fast EV Charging

A diagram of the control mechanism of the EV fast DC charging system is shown in Figure 9.

3.3.4. Bidirectional DC-AC (Inverter) with Grid Loads

A three-phase inverter is connected between the DC and AC buses, using a nonlinear PID (NPID) droop control loo and, a traditional control loop with a harmonic filter (LCL filter), and is connected to the point of common coupling (PCC), as shown in Figure 10. The voltage source inverter and three-phase inverter convert DC bus power into three-phase AC voltage with control using pulse width modulation (PWM) and the LCL filter is for harmonics suppression to place before the AC grid (bus).

3.3.5. AC EV Charging Through AC Grid

An 11 kV/400 V step-down transformer is installed before the EV AC charging station, with a 1 MVA rating. AC CS (off-board EVCS) is connected through the AC bus/grid by linking an 11 kV/400 V AC line via a step-down transformer. The control mechanism is done by the NPID closed-loop system (LCL-filter bidirectional converter + PLL + PI controller), as shown in Figure 11.

3.3.6. Forecasting PV Power Generation, EV Demand, and EV Customers’ Arrival Time by ANN (AI) Tool

The forecasting modeling system has evolved, including data estimation, dataset processing, and sample normalization. The estimated datasets or input are used to normalize, firstly, for efficient ANN-trained dataset operations. In our article, a feedforward artificial neural network (ANN) technique is used to train the neural network using the Levenberg–Marquardt algorithm. The ANN creates an appropriate implementation of a power flow management application with computational accuracy compared to other modern hybrid techniques. An AI (ANN)-based technique is applied for forecasting three parameters: PV power generation, EV charging demand, and EV customer arrival time. These parameters are non-linear because they depend on the weather and the behavior of EV customers (behavior pattern). Why will only these parameters be forecasted [43,44]? These quantities are uncertain in nature and have an impact on the future. The total PV power generation depends upon previous PV power generation, solar irradiance, and air temperature changes throughout the day. EV power demand depends on the time EV owners spend in charging stations (arrival time), previous EV power demand, and customers’ satisfaction. The control mechanism controls the remaining variables. The forecasting datasets are inputs for MILP techniques. The estimation of EV datasets is required for forecasting these three parameters. Various methods, including probability distributions and MATLAB coding, determine the estimation of EV datasets. The synthetic datasets with the consideration of research-based standard model and distribution statistical datasets have been used for analysis because of the unavailability of standard or real-time datasets, and also the public datasets of EV users are not correct for use in terms of safety, or against research ethics. This suggested methodology with statistical datasets makes a model that is a scope implementation and can be proven in real applications for future purposes. The normal distribution function has been used for determining the EV users’ arrival time by the ‘normrnd’ function, in which the mean arrival time is 18:00 peak, and the standard deviation is 2 h. The uniform distribution has been used for determining the EV power demand and the SOC of arrival EV users, within which the preprocessing set of the maximum to minimum charging power level (for both AC and DC) and the EV users’ arrival SOC level are, with the number of EV users. Synthetic data samples have a wide range of coverage with full input space, including different and extreme situations. The extreme situations mean noise, shading real solar irradiance transients, which impact the output of the solar PV system. These datasets also handle real-world challenges, and training coverage improved after the ANN. The randomized/synthetic data is devoid of missing data and mistakes during measurement, which occur in real-world samples. The synthetic data samples are also created by a generated solar PV mathematical system instead of being totally arbitrary random numbers. These synthetic data samples are reproducible by specific pre-defined equations and can be replicated with real data sample implementations, which are challenging. Earlier research with the parameters of distribution, like the mean and standard deviation, are chosen based on general EV users’ patterns of arrival and power demand (e.g., mostly power demand at evening after the end of working hours). Small modifications/adjustments are required for aligning this earlier research with realistic applications.

This paper estimates EV datasets using a normal/Gaussian distribution and a uniform distribution in MATLAB coding 1, which is presented below.

MATLAB_coding 1.

Important pre-processing is discussed here, such as the normalization of datasets. The need for this application is to properly clean samples for consistency checks in several scenarios. So, we have to normalize the datasets before the training, testing, and validation process. All inputs for training in the neural network have to be normalized to avoid numerical instability. This will be done using scaled datasets between the minimum and maximum normalization, meaning between 0 and 1. Through this preprocessing, the appropriate model is obtained while avoiding overfitting. The algorithm structure is shown in Figure 12.

Intelligence making solar PV-connected grid-EVCS with BESS has to deal with uncertain datasets of intermittent PV nature, EV owners’ behavior of arrival in EVCS, and their power demand. For an optimal solution, these variables have to be forecasted. In this study, the forecasting is applied in the short-term and a day ahead. The short-term forecasting determines the power equation balancing of the whole system, based on minutes to 24 h and a day ahead for optimal charging allocation in advance. Various objectives from forecasting can be achieved, such as already knowing about the upcoming EV demand from EVCS, which will avoid component overloading and lower the stress on grid suppliers, and also avoid delayed EV charging or peak demand shifting. This study is based on two stages or a hybrid technique-based study. The first stage is dedicated to the estimation and forecasting of data samples by a neural network, such as estimating the solar PV voltage at MPPT and forecasting the solar PV power generation and EV demand power for charging, whereas the second stage is dedicated to getting an optimal solution by using the MILP technique, with forecasted datasets as inputs.

3.4. Mixed-Integer Linear Programming (MILP)

Mixed-integer linear programming (MILP) is a mathematical optimization technique applied in linear applications. In this article, the entire system’s parameters, such as solar PV power generation, EV power demand, EV arrival time, BESS conditions, etc., are used as linear relations inside the MILP framework. Solar PV power generation is not treated as a non-linear input because nonlinearity is estimated and it passes through the normalization and forecasting methods. Normalization supports the linearization handling operation for reducing the nonlinearity impacts on a linear methodology. That is why the MILP technique does not deal with the nonlinear term or introduce nonlinearity by solar PV power generation. Although this article does not use any high-order equations or nonlinear formulas, EV power demand, arrival, and BESS operation are incorporated into the system with a linear power-balancing equation and constraints, and are forecasted from Gaussian and uniform distributions. However, the human behavior term or physical pattern terms are assumed approximately as being linear with linear restrictions. That technique requires objective functions, equality constraints, inequality constraints, and outcomes that will produce continuous or integer-valued solutions. The MILP technique cannot control the switch control tendency in this application; however, it is used to achieve an optimal power transfer/allocation solution finder. MILP finds the optimized future scheduled power from PV, planned demand for EV charging, backup of stored power in BESS, and grid power exchange over a full day. This optimization will answer many essential questions: for example, how to have maximum utilization from a PV solar system, when the battery should be charged or discharged, and how to create grid stability, etc. Why is this technique used in this paper? Integration systems have multiple constraints, one or more objective functions, and satisfactory decision-making scenarios, balancing the power flow in the integrated system. That is a condition that only the MILP technique can manage in an optimal way. The final output from MILP will be numerical values as well as graphical values, and optimal future EV/BESS charging allocation, optimal power balancing, and grid scheduling. The suggested MILP-based optimal framework is a standard optimal solver method that executes within the computational time. This proposed application is for the allocation throughout the day (24 h). The computational time depends upon many factors, such as the number of EVs, the number of decision variables and constraints, and the choice of the defined step size for execution (for example, 10 min intervals in-stead of 24 h for ahead-of-time power planning). In this study, the ideal executing time of the optimal solver meets the optimal charging allocation solution between a few seconds and a few minutes for the application of day-ahead allocation of power. The computational time reduces in the two-stage optimal technique as compared to single large-scale-based optimization by using sequentially solving application. In the current study, the computational time of the proposed framework for the integrated application has been found under 24 h allocation-

• Number of EVs: 200
• Decision variables: 14
• Operational constraints: 26
• Time frame: 24 h
• Total Computational time: 0.42–2.06 s;
• (0.4–2.0 s) for ANN forecasting and (0.02–0.06 s) for MILP optimal solution.

The computational time seems very low in this integrated application because a large number of EVs are loaded in an aggregated or grouped manner, with very small decision and constraint numbers. The decisions and constraints variables are across the model level, not based on individual EVs. The fast convergence is achieved by the absence of any huge rule combinations, and simplified MILP by ANN. The low computational time has good scalability and is easy to implement in real-time. Additionally, the suggested two-stage framework shows excellent scalability with low computational time and complexity because EVs are dealt with as a grouped load and with small variables. However, in real-time implementation, incorporating the real detailed variables and constraints may increase system complexity and computational time. This will be studied using sophisticated hybrid techniques in future work. Below is a priority list for the optimal solutions from the MILP technique.

Performing scenarios (priorities listed from one to seven):

• (PV→EV(DC/AC)): The PV modules generated enough power to first fulfill the demand of EV charging with both types in two ways: PV modules → DC Bus → DC EV charging station, and AC Bus → transformer → AC EV charging station (on-board charging) → control mechanism → Off-board charging. In this case, a PV array will satisfy only the EV demand, not other sources of energy. The priority decides between AC/DC charging by checking the SOC conditions, arrival time of customers, etc.
• (PV → (BESS+ EV)): When there is not sufficient energy generated by PV modules (they have some but not zero). In that scenario, the battery energy storage system (BESS) supplies the remaining power to the EV charging station, allowing it to continue meeting the EV demand if the PV power is insufficient to meet the EV charging demand.
• (PV → 0, (BESS + Grid → charging of EV): There is no PV power generation for that case; both BESS and the grid will support the EV charging demand.
• (PV → Surplus power generation, PV power → (EV₁ + BESS₂ + Grid): In this case, PV power generation will be sufficient to manage the whole system’s loads. The “1” shows that the priority number means that one will be the first to get power.
• (EV demand → 0, (PV power generation → BESS₁ + Grid): In this case, power from PV is stored for backup purposes in BESS and reduces the grid’s dependency on non-renewable power sources. The “1” shows that the priority number means that one will be the first to get power.
• (Only PV power generation → Grid): This case is rare, but it is an example of the curtailment of traditional energy resource generation and the benefits of optimal allocation of power distribution. The EV demand is zero, and BESS are fully charged.
• (PV power generation → 0, BESS fully discharged, EV →Grid loads at emergency and show independence on conventional power resources.)

3.4.1. Objective Function

The objective function is the mathematical formula that represents the main motive of the proposed integrated system with an energy management strategy, and it has to maximize and minimize to achieve the target or optimize the system. The multi-objective function is shown in a single equation, Equation (6), for optimal charging allocation and maximum utilization of solar PV. The objective function of the proposed model is based on all key appropriate power drivers of the system, such as the first to last terms related to the maximum utilization of renewable energy resources for charging EVs, enhancing the PV system, EV best charging/discharging allocation, and making the charging station less dependent upon the grid supply. Here, Equation (7) shows the objective function of the integrated system based on this study.

Minimized (Objective 1, Objective 2, Objective 3)

(6)

Objective 1: Maximum utilization of the solar PV system power generation.

Objective 2: Mitigate the grid dependency.

Objective 3: Optimal EV charging and discharging allocation.

The proposed study framework mainly focuses on EV balanced charging, maximum utilization of the solar PV output, and reducing the dependency on the grid that is powered by conventional resources: in short, on technical significance and operational optimization aspects. The main controller in the control mechanism is the PID controller that maintains the stability of every subsystem using the voltage and current datasets, and that way it reduces the harmonics injection by all non-linear loads. This conventional NPID controller’s help will support the three objective functions in terms of stable voltage and proper working of the system’s operations, and this article discusses the three main objective functions’ operational aspects.

Assumptions:

• The communication delay is ignored to make a stable approach and study for the ideal application.
• Limits in SOCs and in power to avoid battery degradation or to ensure battery-safe operations.
• The PID controller mechanism supports the integrated system.

The communication delays are not considered in this proposed study, as the simulation model looked at perfect connectivity between grid operators and EV owners, mainly concentrating on ideal power flow management and power dispatch performance, rather than two-way communication aspects, which can affect the system stability. The repeated vehicle-to-grid (V2G) operations do not affect the battery’s life (battery degradation) because the BESS and EV system incorporates the limits into the SOC and charging/discharging demand-related constraints to ensure the safe implementation of this application.

$$\min Objective function=min\sum _{t=1}^N[a\left(P_{Grid}^{E{V}_{DC}}(t)+P_{Grid}^{E{V}_{AC}}(t)\right)+b\left(P_{BESS}^{{EV}_{DC}}(t)+P_{BESS}^{{EV}_{AC}}(t)\right)+c\left(P_{EV\left(AC+DC\right)}^{V2G}\left(t\right)\right)-d\left(P_{PV}^{E{V}_{DC}}\left(t\right)+P_{PV}^{E{V}_{AC}}\left(t\right)+P_{PV}^{BESS}\left(t\right)+P_{PV}^{Grid}\left(t\right)\right)+\mathrm{e}[P_{Grid}^{import}\left(t\right)+P_{BESS}^{charging}\left(t\right)-P_{BESS}^{discharging}\left(t\right)-P_{EV\left(DC+AC\right)}^{V2G}\left(t\right)+P_{EV\left(DC+AC\right)}^{charging}(t)]]$$

(7)

where a > b > c > d > e.

3.4.2. Power Balance Equations

The power balance equation represents the stability that will be maintained or created in the power system, as given in Equation (8). Equation (8) for power balancing has terms such as the forecasted values of the solar PV power and EV power demand. These datasets are obtained with an ANN and incorporated as the inputs in the MILP technique-based power balancing constraint equation for an optimal solution.

$$P_{PV}^F(t)+P_{Grid}^{import}\left(t\right)+P_{EV\left(AC+DC\right)}^{V2G}\left(t\right)+P_{BESS}^{discharging}\left(t\right)=P_{EV\left(AC+DC\right)}^{F\_charging}\left(t\right)+P_{BESS}^{charging}\left(t\right)+P_{Indus}\left(t\right)+P_{Resi}\left(t\right)+P_{Loss}(t)$$

(8)

3.4.3. Operational Constraints

The objective function of this study is minimized with each subsystem’s equality and inequality constraints set, based on operational characteristics. This proposed study is considering operational limits such as SOC limits, transfer power limits, arrival/departure EV time limits for protected charging/discharging operations, means for the V2G operation through bidirectional converter’s controllers limits, and feedback systems. This type of safety should be ensured to ensure the power transfer between the grid and EV items, to keep people safe in the EV car, and also in terms of overvoltage and overcurrent.

Operational Constraints of PV Solar Module

The goal of solar PV modules is to utilize the maximum. The constraints related to solar PV power generation are considered by the forecast and charging of the BESS for support in terms of power, charging of EVs, and feeding the load of the grid-connected AC.

A.

Equality Constraint Equations

$$P_{PV}^F(t)=P_{EV\left(AC+DC\right)}^{F\_charging}\left(t\right)+P_{BESS}^{Charging}(t)+P_{Grid\_Loads}(t)‘\mathrm{OR}’ P_{Grid}^{export}(t)$$

(9)

“+” for charging EV and “−”for EV discharging for V2G technology in Equation (9).

B.

Inequality Constraint Equations

$${0\le \mathrm{P}}_{\mathrm{P}\mathrm{V}}\left(\mathrm{t}\right)\le P_{PV}^F\left(t\right) (\mathrm{Forecast} \mathrm{Value})$$

(10)

$$P_{PV}^F(\mathrm{t})\le P_{PV}^{Maximum}\left(\mathrm{t}\right)$$

(11)

C.

Bounds

$$0\le P_{PV}^{EV\left(AC+DC\right)}\left(\mathrm{t}\right)\le P_{EV\left(DC+AC\right)}^{Ma{x}_{charging}}\left(t\right)$$

(12)

$$0\le {\mathrm{P}}_{PV}^{BESS}\left(\mathrm{t}\right)\le P_{BESS}^{Maxi\_charging}(t)$$

(13)

$$0\le P_{PV}^{Grid}(\mathrm{t})\le P_{Grid}^{Maxi\_export}(t)$$

(14)

Equation (9) shows the PV-generated power utilized in various subsystems at a specific period of time, t. This power needs to be allocated among the grid, the various EV charging types (onboard and offboard charging types), and BESS to achieve the maximum distribution of renewable energy resources. The BESS stores the remaining power from the grid and the EV load that is utilized to feed these two loads in the event of an emergency or for improved power management. The power generated by PV varies from the minimum to the maximum, depending on factors such as solar irradiance, air temperature, the quality of the PV module (efficiency), and the average wind speed.

The solar PV power generated fluctuates with respect to solar irradiance, air temperature, and other factors, and also needs to forecast solar power generation to avoid a power shortage, which is limited by Equations (10) and (11), which give the relationship between the forecast and the maximum solar PV power generation.

Equation (12) shows the supply of PV power to EVCS.

Equation (13) presents the supply of PV power to be stored in BESS.

Equation (14) presents the supply of the PV power to the loads of the AC grid.

Operational Constraints for the AC Grid

The power will be available at the AC grid in terms of export and import in two different cases of charging and discharging modes: Equation (15) and Equation (16). The main agenda will be to feed the EV charging station, as well as take a step toward beneficial power/energy management. The grid and EV operator set a limitation for both entities to exchange power more efficiently, as shown in the equations given below. Several subsections are connected to a grid with operational limits, and the import/export grid power are explained in Equations (17)–(20). MILP will be considered the curtailment in terms of power drawn by the grid to mitigate grid dependency.

A.

Equality Equations

$$P_{Grid}^{export}\left(t\right)=(\left(P_{EV\left(AC+DC\right)}^{F_{charging}}\left(t\right)\right)+P_{Indus}\left(t\right)+P_{Resi}(t))-\left(P_{PV}^F\left(t\right)+P_{BESS}^{discharg}\left(t\right)\right){-(P}_{Grid}^{Curtailment}\left(t\right))$$

(15)

$$P_{Grid}^{import}\left(t\right)=P_{PV}^F\left(t\right)+P_{EV\left(AC+DC\right)}^{V2G}\left(t\right)-{(P}_{BESS}^{charg}(t)+P_{EV\left(AC+DC\right)}^{charging}\left(t\right))$$

(16)

B.

Inequality Equations

$${\mathrm{P}}_{EV(DC+AC)}^{F\_charging}(\mathrm{t})\le P_{Grid}^{export}(\mathrm{t})$$

(17)

$${\mathrm{P}}_{EV(DC+AC)}^{discharging}(\mathrm{t})\ge P_{Grid}^{import}(\mathrm{t})$$

(18)

C.

Bounds

$$0\le {\mathrm{P}}_{Grid}^{import}(\mathrm{t})\le P_{Grid}^{\mathrm{M}\mathrm{a}\mathrm{x}\_import}(\mathrm{t})$$

(19)

$$0\le {\mathrm{P}}_{Grid}^{export}(\mathrm{t})\le P_{Grid}^{\mathrm{M}\mathrm{a}\mathrm{x}\_export}(\mathrm{t})$$

(20)

Operational Constraints for the BESS

Equality, inequality, and bound constraints of the BESS model are considered in the MILP optimization frameworks shown in the constraint equations. The SOC value at (t + 1) is given by the previous value and other terms, as shown in Equation (21). Equation (22) sets the SOC limit within a range to avoid overcharging and deep discharging. Equations (23) and (24) present the lower to upper limits for the charging and discharging power from BESS.

A.

Equality Equations

$${\mathrm{S}\mathrm{O}\mathrm{C}}_{\mathrm{B}\mathrm{E}\mathrm{S}\mathrm{S}}\left(\mathrm{t}+1\right)={SOC}_{BESS}\left(t\right)+\left( {\displaystyle \frac{1}{E^{BESS}}}\right)\ast \left({\eta }_{charging }{P}_{BESS}^{charging}\left(t\right)-{\displaystyle \frac{P_{BESS}^{discharging }\left(t\right)}{{\eta }_{discharging}}}\right)\ast ∆t$$

(21)

B.

Inequality Equations

$$0.2\le {\mathrm{S}\mathrm{O}\mathrm{C}}_{\mathrm{B}\mathrm{E}\mathrm{S}\mathrm{S}}(\mathrm{t})\le 0.9$$

(22)

Avoid deep discharging and overcharging.

C.

Bounds

$$0\le {\mathrm{P}}_{BESS}^{charging}\left(\mathrm{t}\right)\le P_{BESS}^{\mathit{Max}\_charging}\left(\mathrm{t}\right). w_{BESS}$$

(23)

$$0\le {\mathrm{P}}_{BESS}^{discharging}\left(\mathrm{t}\right)\le P_{BESS}^{\mathit{Max}\_discharging}\left(\mathrm{t}\right).(1-w_{BESS})$$

(24)

$w_{BESS}$ $\in${0, 1} represents a binary state for avoiding simultaneous discharging and charging.

Operational Constraints for EVs

The EV-related constraints are related to the EV power demand and SOC because, in this study, these parameters regulate the charging and discharging process in the whole model, as given in Equations (25), (27) and (28). For the longevity of the battery of EVs, the SOC remains within a predetermined range, from a minimum to a maximum, to prevent the problems of overcharging and deep draining, as shown in Equation (26). The amount of power taken by the EV during charging has to be reduced by an MILP optimal solution, which is defined by this term: $P_{EV}^{Curtailment}\left(t\right)$.

A.

Equality Equations

$${\mathrm{S}\mathrm{O}\mathrm{C}}_{\mathrm{E}\mathrm{V}}\left(\mathrm{t}+1\right)={SOC}_{EV}\left(t\right)+\left( {\displaystyle \frac{1}{E^{EV}}}\right)\ast \left({\eta }_{charging }{P}_{EV}^{charging}\left(t\right)-{\displaystyle \frac{P_{EV}^{discharging }\left(t\right)}{{\eta }_{discharging}}}\right)\ast ∆t$$

(25)

B.

Inequality Equations

$$0.2\le {\mathrm{S}\mathrm{O}\mathrm{C}}_{\mathrm{E}\mathrm{V}}(\mathrm{t})\le 0.9$$

(26)

Equation (26) shows the SOC limits of the battery energy storage system. The SOC limits are defined as the limits under which the battery operates in BESS for avoiding overcharging and deep discharging, which are basically for safe operation purposes.

C.

Bounds

$$0\le {\mathrm{P}}_{EV}^{charging}(\mathrm{t})\le P_{EV}^{F\_charging}(t) (\mathrm{Forecast} \mathrm{value}). w_{EV}$$

(27)

$$0\le {\mathrm{P}}_{EV}^{discharging}(\mathrm{t})\le P_{EV}^{\mathrm{M}\mathrm{a}\mathrm{x}\_\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{i}\mathrm{n}\mathrm{g}}(\mathrm{t}).(1-w_{EV})$$

(28)

$w_{EV}\in${0, 1} represents consent of the EV users.

Equations (25)–(28) show the operational limits of the SOC need and charging demand; these limits must be satisfied before the EV users depart from the charging station in the optimization model. Additionally, grid stability is a key consideration in the objective of this optimization model for EV user benefits and the safety of the battery. This balance between grid stability and EV users’ benefits shows fairness for EV users.

V2G Operation Enabling

Vehicle-to-grid (V2G) operation enables helping the emergency load requirements in the integrated system, with some constraints being different from those of the constraints of EV at the charging state. V2G operation also regulates with the SOC and battery power level for discharging purposes. Equation (29) shows the required SOC level of EVs for V2G operation enablement.

SOC_EV(t) > (0.2 + SOC_incapacity(t))

(29)

t_plugging < t_departure

(30)

In EV, t_plugging is the plug-in time period in the charging station for V2G operational activity in an integrated system that will be more than the time leaving the charging station, as shown in Equation (30). Also, the permission of EV owners is necessary for this type of support in this integrated model.

Owner_consent = 1, $w_{EV\_V2G}\in${0, 1}, presented like that in Equation (31).

$$o_{EV}^{charging}(\mathrm{t})+o_{EV}^{discharging}(t)\le 1$$

(31)

The power level limits are shown in Equations (32) and (33).

$$P_{EV}^{{F\_}_{charging}}\left(t\right),P_{EV}^{discharging}(t) \ge 0$$

(32)

The power limit by V2G operation is as follows:

$${\mathrm{P}}_{EV}^{\mathit{discharging} }(t)\le P_{EV}^{\mathit{Maximum\; rating} }(t). o_{EV}^{\mathit{discharging} }(t)$$

(33)

Algorithm 1, shown as complete execution in two stages with the ANN and MILP approach.

Algorithm 1. MATLAB coding

Stage 1: Artificial neural network (ANN) for solar PV power generation. Input: Solar PV system datasets such as solar irradiance, air temperature, time, and solar PV power generation. Target: Forecast solar PV generation for 24 h. Stage 2: Artificial neural network (ANN) for EV Datasets. Input: EV known datasets such as EV charging demand, previous EV arrival time in CS, arrival SOC states, charging station capacity, and time. Target: 24 h forecast, EV charging demand, EV arrival time, and charging station. Stage 3: MILP for optimal EV charging/discharging, solar PV power generation, maximum utilization, and reduced grid dependency. Input: Forecasted solar PV datasets and EV datasets from Stage 1 and Stage 2. Objective Function: $min\sum _{t=1}^N[Object1,Object2,Object3]$ Power Balance: $P_{PV}^F(t)+P_{Grid}^{import}\left(t\right)+P_{EV\left(AC+DC\right)}^{V2G}\left(t\right)+P_{BESS}^{discharging}\left(t\right)= P_{EV\left(AC+DC\right)}^{F\_charging}\left(t\right)+P_{BESS}^{charging}\left(t\right)+P_{Indus}\left(t\right)+P_{Resi}\left(t\right)+P_{Loss}(t)$ Constraints: Operational constraints of every subsystem. Decision Variables: Optimal allocation. $P_{Grid}^{export}\left(t\right)$, $P_{Grid}^{import}\left(t\right)$, $P_{PV}^{Grid}\left(t\right)$, $P_{PV}^{BESS}\left(t\right),P_{PV}^{E{V}_{AC}}\left(t\right)$, $P_{PV}^{E{V}_{DC}}\left(t\right){,P}_{BESS}^{{EV}_{AC}}\left(t\right){,P}_{EV\left(AC+DC\right)}^{V2G}\left(t\right)$, $P_{BESS}^{{EV}_{DC}}\left(t\right)$, $P_{Grid}^{E{V}_{AC}}(t)$, $P_{Grid}^{E{V}_{DC}}(t)$, ${\mathrm{P}}_{\mathrm{P}\mathrm{V}}\left(\mathrm{t}\right)$, $P_{EV\left(AC+DC\right)}^{charging}\left(t\right)$, ${\mathrm{P}}_{\mathrm{B}\mathrm{E}\mathrm{S}\mathrm{S}}^{\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{i}\mathrm{n}\mathrm{g}/\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{i}\mathrm{n}\mathrm{g}}\left(\mathrm{t}\right)$. Output: The satisfying objective function and decision variables, optimal solutions throughout the day, are shown graphically.

4. Results and Discussion

A hybrid optimized technique could be a good concept to resolve the observational problems. In this article, a combined ANN and MILP technique is used to tackle non-linearity, the basic idea of the problems with next-day power demand for the grid, and additional load management, and to also deal with EVs’ benefits. The operational mechanism in the solar PV system and dealing with getting enough output from it have been solved by a neural network-based MPPT controller, the forecasted datasets have been optimized by MILP, and the remaining mechanism is still of a conventional type. ANN-related mechanisms and programming make the input–output structure of a neural network to train the non-linear datasets and reduce the error through the backpropagation algorithm. In the MILP model, the objective function, power balanced equation, and constraints are programmed to get optimal solutions.

4.1. PV Modules

The I-V curve of PV is affected by air temperature and solar irradiance. Figure 13 and Figure 14 show the curves under 1000 W/m² and 25 °C. ANN-based MPPT is designed to track the predicted maximum power points without measuring them, enabling fast operation. Your ANN target (maximum power point voltage, V = 40.6 V) is extracted from this single PV module curve.

Figure 15 and Figure 16 show the whole day variations in irradiance and atmospheric air temperature, and the corresponding voltage with a constant cell temperature (25 °C).

Table 8. Total voltage from the PV system at MPP (V_PV__MPP) through the ANN-based MPPT controller that covers the whole operating region.

S. No	Solar Irradiance (W/m2)	Air Temperature (°C)	VPV_MPP
1.	980	35.9	493.8
2.	982.7	25.6	598.5
3.	601.1	34.9	490.0
4.	210.3	30.8	518.2
5.	910.2	24.2	569.2
6.	955.2	31.8	515.4
7.	50.2	27.9	533.2
8.	927.2	32.5	608.9
9.	788.2	28.9	535.2
10.	425.0	30.5	522.2
11.	189.2	27.8	532.9
12.	45.2	29.8	525.8
13.	69.3	28.6	592.5
14.	789.1	19.8	506.2
15.	425.02	28.6	529.5
16.	49.3	34.8	494.1
17.	398.2	25.7	461.3
18.	825.2	30.5	518.9
19.	506.8	19.8	556.8
20.	678.2	25.0	525.1
21.	759.2	28.4	487.4
22.	780.2	21.7	533.9
23.	250.3	28.3	508.5
24.	497.3	19.9	498.3
25.	398.2	33.5	605.2
26.	298.3	26.8	493.8
27.	278.7	31.5	525.3
28.	789.2	25.5	552.9
29.	988.3	33.9	602.5
30.	158.7	29.8	547.8
31.	298.7	18.2	496.3
32.	289.2	32.9	566.6
33.	278.8	31.8	509.5
34.	398.5	35.2	515.8
35.	289.7	19.5	497.4
36.	489.2	28.2	592.3
37.	869.4	23.2	458.4
38.	568.7	27.9	592.2
39.	289.4	33.4	552.3
40.	769.5	30.2	499.9

contains 40 rows, each representing a specific operating characteristic among 500 datasets. The value of the voltage at MPP, solar irradiance, and air temperature are determined by Equations (3)–(5) in a random way. Then, these data samples were applied in a neural network system for training, validation, and testing.

Figure 17 presents the performance plot under the LM, which shows the mean squared error (MSE) of trained dataset samples in an artificial neural network (ANN) with 569 training iterations (epochs). Therefore, this trained dataset sample indicates the best train and validation performance after 569 epochs. The MPPT controllers’ result indicates that the validation performance of 1.5141 × 10⁻¹⁰ at 569 epochs shows the optimal voltage at the MPP value. In the estimation of the solar PV voltage at MPP by an ANN-based MPPT controller found by the LM algorithm in ANN, the MSE had a near-zero value in the trained, validation performance plot, which means that the solution was good enough. Figure 18 shows the training and validation dataset sample plot in the ANN. The dataset sample is split into training, validation, and testing for ANN performance checking. In this study, 75% training, 15% validation, and 10% testing datasets were used. According to the results, the gradient is 9.9804 × 10⁻⁸ at 569 epochs. Basically, during training, convergence is reached, and the training error is reduced and stabilized. The network was found at 569 epochs, and from this point, the result does not have significance. For example, in epochs up to 850 or after 569 epochs, the learning process became unstable, the validation check increased, and the MSE did not increase gradually. This plot has negligible deviations from the training data samples. The lower value of the gradient, Mu, and the validation check of the training data samples are found with a suitable LM algorithm-based ANN MPPT controller. During the training process or learning process, convergence was reached, performance error was reduced, and the network had stabilized. At this point, the training of the neural network was ended.

In the finalized results, the trained network has achieved a very minimal value of gradient (9.9804 × 10⁻⁸) and perfect MSE validation performance (1.5141 × 10⁻¹⁰), based on stable convergence. The training process stopped early in the 569 epochs. Presenting early halting means that there is no need for further improvement to avoid overfitting. The key contribution of the LM algorithm is the automatic adjustment of the damping factor (Mu) and weights to get a stable trained optimized network, and a constant/fixed learning rate is not needed. Setting the random number generator seed controlled by the rng function corroborates the reproducibility of the outcomes of the neural network. For other implementations, the rng random generator function will replicate the same outcomes.

The nature of the solar PV-generated power is fluctuating or unpredictable. So, accurately predicting the solar PV power generation has to be found to primarily support the MILP optimal power management approach and improve EV and BESS charging/discharging allocation. This study used an ANN coding approach to avoid the unpredictable nature of solar PV power generation for forecasting this data sample. Firstly, in ANN coding, the solar irradiance, air temperature, time, and actual PV power are loaded as the deciding input and target datasets. The next steps are to normalize these datasets, split into a percentage of train–validate–test samples, model an ANN model with some layers and an activation function, and train the model. The last step, ANN coding for forecasting, is used, and finally, the numerical values of the forecasted solar PV power generation are represented in graphical form, as shown in Figure 19, by a combined graph of forecasted and real solar PV power generation.

4.2. EVs Discussion

Like PV-generated power, EVs have unpredictable data. The process for determining the forecasted EV datasets from ANN coding is the same as previously explained, as shown in Figure 20 and Figure 21.

4.3. MILP Optimized Result (Optimal EV Charging/Discharging Allocation + Maximum Utilization of PV Power Generation + BESS Backup Power + Grid Dependency Reduced)

The MILP approach gives the suggested optimal power flow management, scheduling BESS charging/discharging and mitigating grid dependency, and also the curtailment in terms of power shown in

Table 9. Scenario 1 ((PV → EV(DC/AC) charging).

Hours	PV (MW)	EV_DC (MW)	EV_AC (MW)	Charging BESS(MW) (Fully Charged)	Discharging BESS (MW)	Grid (MW)
12:00	3	1.9	1	0	0	0

,

Table 10. Scenario 2 (PV → EV charging but insufficient to fulfill full EV load, BESS discharging → EV) (curtailment of grid dependency that is suggested by MILP approach).

Hours	PV (MW)	EV_DC (MW)	EV_AC (MW)	Charging BESS (MW)	Discharging BESS (MW)	Grid (MW)
24:00	0	0.55	0.17	0	0.72	0
2:00	0	0.60	0.19	0	0.62	0.17

,

Table 11. Scenario 3 ((PV → 0, ((BESS discharging + Grid export) → EV charging).

Hours	PV (MW)	EV_DC (MW)	EV_AC (MW)	Charging BESS (MW)	Discharging BESS (MW)	Grid (MW)
15:00	1.96	2.4	1.05	0	1.49	0
16:00	1.49	2.1	0.520	0	1.13	0

,

Table 12. Scenario 4 ((PV → (EV charging + BESS charging + Grid import)).

Hours	PV (MW)	EV_DC (MW)	EV_AC (MW)	Charging BESS (MW)	Discharging BESS (MW)	Grid (MW)
11:00	3	1.6	0.88	0.52	0	0

,

Table 13. Scenario 5 (EV charging → 0 Curtailment EV demand), (PV → (BESS charging + Grid import)).

Hours	PV (MW)	EV_DC (MW)	EV_AC (MW)	Charging BESS (MW)	Discharging BESS (MW)	Grid (MW)
6:00	0.08	0	0	0.08	0	0

,

Table 14. Scenario 6 ((PV → Grid import) + BESS fully charged) (also suggested by MILP).

Hours	PV (MW)	EV_DC (MW)	EV_AC (MW)	Charging BESS (MW)	Discharging BESS (MW)	Grid (MW)
6:00	0.08	0	0	0	0	0.08

and

Table 15. Scenario 7 ((PV → 0, BESS → 0) (V2G Enable) (EV → Grid import).

Hours	PV (MW)	EV_DC (MW)	EV_AC (MW)	EV_V2G (MW)	Charging BESS (MW)	Discharging BESS (MW)	Grid (MW)
3:00	0	0.5	0.76	2.52	0	0	1.26

: scenarios 1 to 7 are tabular solutions.

Table 16. Baseline performance.

Scenarios	Scenario 1	Scenario 2	Scenario 3	Scenario 4	Scenario 5	Scenario 6	Scenario 7
1. RUR%	96.67%	Undefined. No available solar PV power	100%	82% 0.52 MW power curtailed	0% 0.08 MW power curtailed	100%	Undefined. No available solar PV power
2. Met EV demand	Not met	Partially fulfilled	Not met by 1.260 MW, demand unfulfilled	Fulfilled	No EV required power	No EV required power	EVs work in V2G operation and fulfill the system’s demand
3. Grid load reduction with respect to baseline grid load demand	Overloaded with the 1.162 MW and increased by 92%	Not reduced. Grid loaded with 57% and 62% because of no proper allocation with BESS	Overloaded	Demand within limits	Demand within limits	Demand within limits	Take power from EVs
4. Peak load	Peak load reached 2.422 MW	Extra load demand 0.472 MW 0.542 MW	Extra load demand	No peak load occurred	No peak load occurred	No peak load occurred	No peak occurred

shows the system-level performance.

The system-level performance is represented by several terms, which are explained in Table 16 and

Table 17. Improved system-level performance.

Scenarios	Scenario 1	Scenario 2	Scenario 3	Scenario 4	Scenario 5	Scenario 6	Scenario 7
1. RUR%	96.67%	Undefined	100%	100%	100%	100%	Undefined
	Almost entirely utilized. Efficient solution	Not available renewable energy (sunlight). Utilization cannot be measured	Fully utilized to feed the EV demand	Fully utilized to feed EV charging and BESS charging (surplus power)	All solar PV-generated power is fully utilized in BESS storing	All solar PV-generated power is fully utilized in the Grid’s loads	Not available: renewable energy (sunlight)
2. Met EV demand	Total EV demand is fulfilled by PV-generated power	EV power demand is satisfied by BESS stored surplus/backup power + grid supply	EV demand is fulfilled by PV-generated power + BESS backup power	EV demand is fulfilled by PV-generated power only	No EV required power	No EV required power	EV power demand is supplied to the grid’s loads and fulfills their demand
3. Grid load reduction	100% Do not use the grid power supply because the BESS supplies the EV with stored extra power	86% Suggested MILP optimal allocation, the grid supplies a little bit of power to the EV and mitigates the 86% grid’s load demand	100% Total grid power is reduced by optimal allocation, and power demand is handled by PV and BESS backup power	100% Total grid power is reduced by optimal allocation, and power demand is handled by PV only	100% Total grid power is reduced by optimal allocation	Not applicable to this condition because the grid power load is supported by PV-generated power	Not applicable grid load reduction factor, because it is a V2G operation
4. Peak load shaving on grid	100%	78%	43%	100%	100%	This case is not applicable because PV is fed to the grid	This case is not applicable because of its V2G operation

, before and after the application of the optimized technique.

• The renewable utilization ratio (RUR) is known as the effective use of the renewable energy resources being fed to the grid loads, EV charging demand, and BESS charging during the extra generated solar power, based on this study. In technical terms, RUR % is defined as the use of renewable energy to feed all types of loads mentioned in this article to the total renewable power generated.
• The EV demand met is defined as the difference between the total needed EV demand and the demand served to EV users by any sources of power in this article, and a difference of zero means fully satisfying the EV users. Additionally, the MILP optimal charging scheduling will fulfill the EV demand to improve the satisfaction level of the EV users by adjusting the power level among power entities.
• Grid load reduction with respect to the baseline grid load demand is estimated by comparing the total load demand occurring on the grid before and after applying the proposed optimization methodology by adjusting the power demand.
• Peak load shaving on the grid means mitigating the peak load power demand of the grid by optimizing the allocation of EVs’ power demand and BESS.

The baseline is a reference criterion for comparing the optimized solution to show improvement. These baselines are based on such key points, as shown in Table 16.

• Prioritize the grid power demand.
• Solar PV power generation is used without strategic planning (extra power is curtailed and not stored in BESS, the EV power demand is met by the grid during no available solar PV power, and the power is directly taken from the solar PV system without planning).
• Unplanned BESS and EV allocation.

The peak load on the grid is a maximum of 0.17 MW instead of 1.262 MW after optimizing the allocation of EV charging and discharging. Additionally, the MILP optimal solution for EV charging scheduling achieved the maximum solar PV utilization and ensured the satisfaction of EV users. The improvement is illustrated in Table 17 in terms of system performance after applying the MILP-optimized technique.

4.4. Sensitivity Analysis for Forecasted Datasets

The system’s performance after optimization is affected by errors in the forecasted solar PV power, EV demand power, and other factors across all forecasted datasets. This is measured by the sensitivity analysis (S). The forecasting errors can impact the grid’s total power loads, or grid dependency increases with a reduction in the utilization of the solar PV power generation, whereas increased solar PV power generation can curtail the power or destroy the system performance. Small changes in the EV demand and other EV-related data samples can impact the power distribution and power flow management, but even defined mild variations in datasets can also have good system-level performance for the MILP optimization technique. The variations in the solar PV power and EV demand are ±20%, for EV SOC at arrival time ±5%, and for EV arrival time ±2 h cannot impact the system-level performance. Additionally, sensitivity is calculated by the change in outcomes due to forecasting errors/variations in the change in input forecasted datasets.

Table 18. Sensitivity analysis.

Forecasted Parameters	Solar PV Power Increased +20%	Solar PV Power Decreased −20%	EV Demand Increased +20%	EV Demand Decreased −20%	EV SOC Increased +5%	EV SOC Decreased −5%	EV A. T Increased +2 h	EV A. T Decreased −2 h
Outcome	RUR, +15%	RUR, −10%	Entire System Demand, +5%	Entire System Demand, −10%	Charging Pattern, +2%	Charging Pattern, −3%	Scheduling duration, +1 h	Scheduling duration, −1 h
Sensitivity	0.75, Moderate	0.5, Moderate	0.25, Low	0.5, Moderate	0.4, Low	0.6, Moderate	0.5, Moderate	0.5, Moderate

shows the sensitivity analysis. In addition, ±20% change in solar PV power can also impact the RUR, and the results demonstrate values such as 0.75 and 0.5 for moderate sensitivity to solar PV power. Furthermore, the model-level performance is significantly influenced by the solar PV power. But ±20% change in EV demand presents less impact on the entire system load. So, it has low sensitivity. The outcome of the sensitivity suggests that the MILP optimized technique handles the power demand changes by optimal allocation of power flow. The changes in EV SOC show low to moderate sensitivity and less impact on the charging pattern and the system’s performance. The ±2 h changes in EV arrival time in EVCS suggest an impact on the scheduling duration and have moderate sensitivity.

Figure 22 represented the optimal solution through the optimization technique to mitigate the grid export power distribution in the integrated system and also to reduce the grid import power distribution because, after applying the optimization method, the best utilization of solar PV power generation was stored in batteries in the BESS for power flow in the backup power needed. Reducing the peak load on the grid is done by proper EVCS charging/discharging allocation, maximum PV power utilization, and V2G technology.

Throughout the day, the MILP optimizing approach identifies a better method for power distribution among the solar PV generation, EVCS (AC/DC), the BESS, and the AC grid, alongside the minimizing objective function and operational constraints shown in Figure 23 and

Table A1. Simulation Results.

Time (Hours)	Solar PV Power (MW)	EV Demand (MW)	BESS SOC %	Grid Exchange (MW)
1	0	1.68	98%	0.02
2	0	1.380	75%	0.17
3	0	1.52	35%	−1.26 (V2G)
4	0	1.25	32%	0.27
5	0	1.380	31%	0.38
6	0.15	0.4	90%	0
7	0.31	2.3	98%	0
8	0.69	2.02	60%	0.01
9	1.23	3.4	70%	0
10	1.92	4.75	55%	0
11	2.54	5.9	48%	0
12	2.85	2.6	100%	0
13	3	3.35	75%	0
14	2.99	3.70	98%	0
15	2.08	3.1	98%	0
16	1.56	2.7	80%	0
17	0.78	3.9	75%	0.07
18	0.38	5.0	74%	0.6
19	0.05	6.1	64%	0.098
20	0.1	5.7	60%	0.258
21	0	4.65	50%	0.587
22	0	3.4	55%	0.02
23	0	1.5	60%	0
24	0	0.75	85%	0

. This graph shows the satisfaction of the objective function within the limits of every subsystem by the optimizing approach. This study is compared in Table 1 in the literature review, and it presents a comparative analysis.

5. Conclusions

This research study described the power management among grid-connected EV charging stations (off-board and on-board) and a solar PV power-generated system with BESS for storing extra power for backup supply power. An AI-based maximum power point tracking (MPPT) controller found the PV voltage at the MPP with train, validate, and test datasets without measuring, which was a fast approach to determine the PV voltage at the MPP. In short, an AI-based MPPT controller predicted the solar PV voltage at the MPP for further processing in the MILP. The outcomes from the ANN seem to be accurate because of the reduced MSE value (1.514 × 10⁻¹⁰), the fact that convergence was reached, and a stabilized model. An optimization technique, mixed-integer linear programming (MILP), was established to optimize the combined system power flow management involving AC and DC EV charging stations’ demand, charging/discharging of BESS, mitigate the use of a traditional grid-based power supply, and deal with the intermittent nature of the solar PV. The proposed coordinated approach successfully prioritizes the utilization of renewable energy resources, reduces dependence on the grid, and reduces peak demand. These results show different scenarios for solving using the MILP technique, by a set objective function and constraints. Coordinated EV charging/discharging scheduling prevents energy waste by storing it in BESS, and the system becomes flexible in managing the power flow. This integrated system includes the bidirectional power entities, bidirectional converters, and the AC/DC bus (links), which enable smooth power exchange and enhance the operational efficiency of charging stations. Also, this proposed integrated model is scalable for high-powered EV charging/discharging scenarios.

Significance of This Research

This study has significance in the real world because it envisions both off-board and on-board EV charging station infrastructures with renewable energy resources and a traditional energy-based AC grid, which means multiple energy resources and the optimal solution in terms of the numerical value of the power allocation among these power entities. Several significant points are as follows:

• Peak load demand mitigation on the grid and reduced dependency on the grid.
• Integrated system power flow management.
• Concentrated renewable energy resource use.
• A scalable optimization approach (ANN + MILP).

This hybrid technique is a scalable property and can be applied to large-scale power systems with proper computational aspects. The MATLAB platform shows the small-scale power flow system feasibility, and for future working states, this approach will be extended for large-scale power implementations. Table 16 represented the quantitative system-level performance with a suggested optimal power management framework, using an optimized technique. Also, the efficacy comparison of the seven scenarios is established. Scenarios 3 to 6 have achieved a full renewable utilization ratio (100%), showing the effective use of solar PV power generation to feed power to the EV, grid, and extra power stored in BESS for backup purposes. Scenario 1 illustrates the almost utilization of the solar PV power generation, and in scenarios 2 and 7, the RUR is not applicable because there is no available solar power/sunlight. The EV demand is fully satisfied in all different scenarios and becomes a versatile system, except in scenario 2, where the EV demand depends upon the grid, and scenario 7 is dedicated to V2G operation. The grid load reduction with respect to the EV power load is 100% in the majority of scenarios, except for scenario 2, which used 14% of the grid’s power by EV power demand, and scenarios 6–7 are not applicable to find this performance because the grid takes the power from the solar PV system and EV in V2G operation. The peak load demand shaving performance depends on the power demand condition, shaving 100% when there is substantial power available from the solar PV system and BESS, whereas peak shaving is reduced when the grid’s support is essential, as seen in scenarios 2 and 3 (78% and 43% reduction). Overall the outcomes show that the framework built by the optimized technique achieves optimal power management and maximum utilization of the solar PV system, and mitigates grid dependency.

6. Future Scope

Although this proposed integrated solar PV–grid-connected EVCS with a BESS offers the optimal solution for power allocation among the systems, several new techniques in the research can further improve its implementation.

• A fast, reliable system.

AI-based MPPT can directly focus on a phase shift for controlling the DC/DC converter without using a PID controller, i.e., traditional controllers for speed and stability purposes.

2.

Deal with uncertain datasets.

A combined optimization technique will be needed for dealing with the optimal solution of EV charging allocation with uncertain datasets simultaneously, such as solar PV power generation, random EV power demand, and arrival time at the charging station. For future work, research will be needed on these combined optimization techniques.

3.

Ancillary services provider.

Future expansion of this proposed research into a frequency and voltage stability checker by bidirectional power flow in V2G technology, which also sees EV as an ancillary provider in an integrated system, is required.

4.

Multi-timescale optimization technique.

The currently proposed study presents a decisive hybrid optimization for better power dispatch. But the multi-time scale stochastic optimization can be a further promising approach for improving performance under non-linear behaviors, and will also be explored in future work.

5.

Battery throughput and battery deterioration/aging modeling approach in an integrated system.

The objective function can include battery degradation and the aging effect of the batteries in the V2G repeating operation. The battery throughput term will be checked by the number of charging/discharging cycles. This crucial part can be incorporated into further work in the future, and it also includes the economic cost related to every subsystem.

6.

Real-world data sample implementation.

Future research on this same topic should be done with realistic data samples to further validate their resilience. Also, a real-world study with respect to cost and emission can further expand this EV-based integrated application. Additionally, in the current study, the communication delays among model entities are assumed to be zero delay(negligible). In a real-time application, this assumption can impact the day-ahead allocation. That’s why, for future work/study will be based on dealing with communication delays among all entities.