A hybrid optimization and graph network for sustainable electric vehicle charging using a dual active bridge converter and renewable energy

Abstract

The Hybrid Renewable Energy (HRE) in Electric Vehicle (EV) charging involves combining power from Photovoltaic (PV), Fuel Cell (FC), and batteries, as well as charging batteries for upcoming charging cycles. However, power conversion efficiency and grid stability are required for reliable, smooth charging of EVs. The problems at hand necessitate a hybrid approach to the economic assessment of the EV Charging System (EVCS) implemented with a Dual Active Bridge (DAB) converter and Hybrid Renewable Energy Sources (HRES). The proposed method integrates the Pelican Optimization Algorithm (POA) and Attributed Multi-order Graph Convolutional Network (AMOGCN); therefore, it is called the POA-AMOGCN technique. The objective is to reduce the Levelized Cost of Energy (LCOE) in order to enhance the economic performance of the EVCS combined with HRES. The POA optimizes power management by balancing power generation from RES and battery storage with the demand of EVCS while generating control signals for the DAB converter. The AMOGCN predicts the optimal control signal for the DAB converter to enhance resource distribution, facilitating the integration of EVs with RES. Accordingly, the proposed method is implemented in the MATLAB environment and its performance is assessed against several existing approaches, including the Gorilla Troop Optimizer (GTO), Hybrid Crow Search Algorithm-Particle Swarm Optimization (HCSA-PSO), Neural Network with Improved PSO (NN-IPSO), Forensic Investigation Algorithm-Archimedean Optimization Algorithm (FBIAOA), and conventional PSO. The proposed POA-AMOGCN approach achieves the lowest LCOE of $0.0549/kWh, demonstrating a substantial improvement in cost-effectiveness compared to other optimization methods.

Introduction

Background

The charging infrastructure for EVs is being rapidly transformed with integration of HRE sources^1,2. This helps to reduce conventional power grids, lowers carbon emissions, and enhances energy sustainability^3,4. The main problem arises due to fluctuating Renewable Energy (RE) production; thus, Energy Management (EM) frameworks are necessary for providing stable and continuous power supply to EV charging stations^5,6. The DC converter plays a significant role in voltage regulation, increased power converging efficiency, and efficient energy transfer between RES, Energy Storage Systems (ESS), and EVs^7,8. In addition, combining Battery Energy Storage (BSS) with pieces of training from RESs will make the safety of the system by lowering fluctuations in availability of energy, thus ensuring smooth delivery of energy supply. However, many challenges still remain in optimizing energy flow, power conversion, and overall system stability in EV charging networks integrated with HRE sources^9,10. The rapid and intermittent EV charging demand overlaps with fluctuations generated by RE. This necessitates advanced EM strategies^11,12. Price-Based Demand Response can be employed to balance energy supplies reducing operational costs and alleviating the peak load impact on the grid¹³. This is coupled with choosing the appropriate converter topologies to enable efficient transfer of energy while minimizing losses and enhancing overall system efficiency¹⁴. The addition of the multiple RES with EV charging infrastructure has added to the idea of system scalability, interoperability, and reliability while opening up further avenues for innovative research in adaptive and efficient EM frameworks¹⁵.

Challenges

Certain challenges emerge on account of EM, power conversion, and reliability of the system when combining HRE sources with EV charging infrastructure. Buildings intermittent RE systems like utilities from solar and wind imply variability in available power. Such a supply of stable and continuous energy for EV charging requires efficient ESS and controls that balance the supply with the demand. The variability of demand in EV charging also adds to the complexity in that the demand patterns are often unpredictable and might invoke peak loads that influence the energy distribution system. Topologies of DC converters must also be selected and optimized effectively so as to meet conversion efficiency, voltage regulation, and system stability. Following that, high-efficiency DC converters facilitate bi-directional energy flow between the renewable sources, ESS, and EVs with minimum loss and other compatible charging standards. Additionally, the scalability and interoperability of the EV charging stations integrated with HRE sources pose another major challenge. With the increasing adoption of EVs, charging infrastructure needs to be designed such that it also meets the increase of energy demand without compromising performance. The design should incorporate grid integration strategies with energy distribution criteria that must address issues concerning power quality, harmonics, and voltage stability to allow for seamless operation. Moreover, such stations require advanced monitoring and control systems for optimized energy flow, avoiding instances of overload or under-utilization of resources. Issues related to cyber security and data privacy can also not be overemphasized; for instance, unauthorized access to EM by entities that predispose cyber-attacks could paralyze the process of charging. This has brought about the necessity for adaptive EM frameworks and reliable power conversion techniques and communication protocols to make the charging infrastructure not only reliable but also sustainable.

Literature survey

Some research studies examine quite a number of other aspects and techniques for EV Charging via HRE Integration. These are discussed in the following review.

GTO algorithm has been introduced by A. Eid et al.¹⁶. The chosen fitness functions reduce overall voltage variation and power loss. By reducing the suggested fitness functions, BES units are designed to improve performance of distribution system and regulate power flow within them. The power generated by any BES was mostly determined by State of Charge (SoC) and system limitations. P. Ray et al.¹⁷ have recommended a HCSA-PSO was used to maximize the installation and running costs of the charging station. The efficacy of the proposed strategy was compared to the PSO, CSA and hybrid genetic pattern search algorithm. G. Anjinappa et al.¹⁸ have presented a NN-IPSO control algorithm was developed. It establishes an isolated converter topology for PHEVs to preserve battery charging functions through a lesser number of power electronic devices over the existing topology. For the PHEV, this isolated converter architecture was controlled by NN-IPSO, which interfaces with the battery. R. Ilango et al.¹⁹ have presented the combination of FBI and AOA; thereafter referred to as the FBIAOA technique. By strategically allocating parking lot for EVs, the suggested technique aims to reduce both real and reactive power loss while simultaneously lowering costs. The recommended method was applied to evaluate the reliability of the smart grid (SG), when the random parameters of the EV are added to the state matrix. K. El. Mezdi et al.²⁰ have presented a new algorithm for EM. The algorithm considers many operational modes to achieve network stability, good energy quality, and optimal power supply among different sources and EV. To do so, the recommended fuzzy logical controllers, which are known for flexibility, easy to implement, and resistant to uncertainties, are used. The fuzzy logic control parameters are tuned using PSO to ensure maximum performance.

H. U. R. Habib et al.²¹ have presented a JO for the best design and operation of grid-connected residential, rural microgrid (MG) that was integrated with EVs and RE in light of DRPs. This study combines aspects of residential household energy efficiency under various DRPs and RER integration. Innovative hybrid control system strategies that improve the energy efficiency of electronic converters in power electronics have been introduced by S. Sodagudi et al.²². To enhance the energy efficiency of the control system, a hybrid energy storage electric converter has been employed to provide a synergetic battery reference adaptive controller set to supplement the control system. A plug-in hybrid EV with PV module was used in a performance assessment of the control approach that was represented that allows on-grid control of the electric power by discharging batteries during peak times and charging during off-peak times to reduce load at converter and enable EV charging faster. A hybrid approach to optimizing the size of HRE systems in the presence of EVs has been presented by T. Ramesh and K. Balachander²³. The hybrid approach was developed by combining the deep attention dilated residual convolutional neural network (DADRCNN) with the light spectrum optimizer (LSO). It was often called the LSO-DADRCNN approach. Maximizing system dependability, reducing system costs, and guaranteeing an adequate power supply for EVs and other electrical loads were the main objectives of the suggested technology. The LSO approach was used to optimize the size of the RE system and it put into consideration factors like load demand, solar power, wind turbine power, and battery capacity. The DADRCNN approach was used to predict the future energy consumption of EVs. A methodology of the integration of RE sources (RES) and EV charging stations into radial distribution networks has been demonstrated by V. K. Paravasthu et al.²⁴ using Hybrid Whale Optimization Algorithm (HWOA). The approach synergistically combines Genetic WOA (GWOA) and Thermal Exchange Optimization (TEO) to optimize the placement and sizing of RESs and EVCSs. The usage of the method was adapted to address the intricate optimization issues in a distribution network, such as the allocation of resources efficiently, the improvement of stability of the network, and the strategic coverage of EVCSs and was presented on IEEE 33- and 69-bus networks. R. T. Kumar and C. C. A. Rajan²⁵ proposed a Hybrid Energy System (HES) integrating PV and wind sources with the grid for reliable EV charging. The key contribution is a high-gain bidirectional modified Zeta converter that enhances PV efficiency through voltage boosting. A Social Spider Optimization Algorithm (SSOA)-based fuzzy Maximum Power Point Tracking (MPPT) controller optimizes energy extraction, while a Proportional Integral (PI)-controlled Doubly Fed Induction Generator (DFIG) ensures stable wind power operation and voltage regulation.

The subsequent Table 1 articulates the Comparison of EM in SG under PBDR.

Table 1.

Literature comparison of EV charging with HRE integration.

References	Technique	Objectives	Limitations
A. Eid et al.16	GTO	Minimizes voltage variations and power loss; optimizes BES operation for power flow regulation in distribution systems	Optimization can be computationally active; it is effective based on system limitations
P. Ray et al.17	HCSA-PSO	Minimizes installation and operational costs of EV charging stations	Computational complexity increases due to hybridization; may not generalize well to varying grid conditions
G. Anjinappa et al.18	NN-IPSO	Optimizes battery charging with fewer power electronic devices	Additional validation of converter topology might need work with operating conditions
R. Ilango et al. 19	FBIAOA	Optimizes parking lot allocation for EVs; reduces real and reactive power loss while lowering costs	Effectiveness depends on accurate EV state matrix modelling; may face challenges in large-scale SGs
K. El. Mezdi et al.20	PSO	Improves EM, network stability, and quality; optimizes energy distribution between sources and EVs	Requires fine-tuning of fuzzy logic parameters; resilience to large-scale uncertainties needs further testing
H. U. R. Habib et al.21	JOA	Optimizes grid-connected residential MG architecture with EVs and RE	Its effectiveness depends on the various penetration levels of DRPs and RE
S. Sodagudi et al. 22	Hybrid Energy Storage Electric Converter with Synergetic Battery Reference Adaptive Controller	Improves the power electronics control system; facilitates efficient EV charging and decreases the peak-hour electricity consumption	Requires integration of hybrid ESS; grid dependency may impact performance
T. Ramesh and K. Balachander23	LSO-DADRCNN	Optimizes sizing of hybrid renewable systems; improves reliability; ensures adequate EV and load supply	Prediction accuracy depends on training quality; computational effort increases due to deep learning integration
V. K. Paravasthu et al.24	HWOA (GWOA + TEO)	Minimizes power loss; maximizes stability in voltages; optimizes locations and size of RESs and EV charging station	The performance can be dependent on the scale of the network; the hybrid optimization brings an increase in the complexity of the computations
R. T. Kumar and C. C. A. Rajan25	SSOA-Fuzzy-controlled HES with HGBMZ converter	Enhances energy harvesting; ensures reliable EV charging; enables bidirectional grid interaction	Converter design complexity; controller tuning required under varying operating conditions

Research gap and motivation

Even though the EV charging, EM, and optimization have been improved, there are still gaps in research. Present researches mainly concentrate on cost optimization, power loss minimization, and energy efficiency, with algorithms such as GTO, HCSA-PSO, NN-IPSO, FBIAOA, and PSO, but they do not usually address the problem with a comprehensive method of integrating PBDR, EV charging, EM, and HRE systems. Other issues, including flexibility to changing RE generation, energy uncertainty, and validation in various circumstances, are yet to be resolved. Other problems such as computational complexity, slow convergence, vulnerability to local optima, and lack of scalability also impede the use of optimization techniques in large-scale EVCS. There is a lack of research on the integration of holistic RES to ensure the best EM, particularly in market-based pricing schemes. Also, the adaptive approaches to dealing with RE volatility, scalability, interoperability, and cyber security risks remain underreported. Absence of sophisticated fault management solutions, including multi-level fault management and predictive maintenance, also constrain resilience of EVCS operations with the help of hybrid RESs. These shortcomings underline the necessity of this study.

Contribution

The primary contributions of this manuscript are summarized as follows:

• The introduction of the POA-AMOGCN technique offers a new hybrid approach to the economic evaluation of an EVCS connected to a DAB converter and HRES that can be used to overcome the shortcomings of conventional optimization approaches.

• The study is able to reduce the energy costs by focusing on minimizing the LCOE, increasing the economic feasibility of the RE-powered EV charging.

• POA optimizes power management, balancing RE generation, battery storage, and EVCS demand leading to better energy efficiency and stability.

• The AMOGCN forecasts optimal measures of control of the DAB converter, which translates to better resource allocation and EV-RES integration.

• Performance of POA-AMOGCN method is rigorously evaluated against a wide variety of existing optimization techniques to establish that its superiority lies in delivering lowest LCOE and improved overall cost-effectiveness of EV charging stations.

Novelty

This study’s novel hybrid technique, which combines the POA and the AMOGCN for the economic evaluation of an EVCS integrated with a DAB converter and HRES. The limitations to grid stability, power conversion efficiency and cost optimization are addressed by this unique method as a way to balance the generation, storage, and optimal control signal prediction to make resource allocation. The proposed POA-AMOGCN technique increases the economic feasibility and reliability of RE-powered EVCS; it shows the potential for a remarkable development in sustainable EM and optimization techniques.

Organization

The paper’s remaining section is arranged as below: Part 2 shows the configuration of EVCS using DAB converter and HRE. Part 3 demonstrates the Proposed POA-AMOGCN Approach of EVCS. Part 4 presents the findings and a discussion. Part 5 is the conclusion of the manuscript.

Configuration of EVCS using DAB converter and HRE

Figure 1 shows the layout of EVCS with HRES based on a DAB converter. PV, FC and BES system are connected together with a shared DC bus, which acts as the central power coupling point where the energy enters and exits the system. The PV system is the main source of RE, which delivers power based on the sun availability and the FC includes a backup and dispatchable generation to supplement renewable intermittency. The battery acts as an energy buffer, which stores the extra RE when demand is low and provides the power when there are the highest EV charging requirements. The DAB converter plays a central role in the system by enabling bidirectional and galvanically isolated power transfer between the DC bus and the EV load. It consists of active H-bridge converters on the primary (P1-P4) side tied to DC bus and secondary (P5-P8) side tied to the EV battery and to the EV load via DC/DC interface and AC/DC interface. High-frequency transformer, series inductor makes it easy to match voltages, provide electrical isolation and controlled power transfer, as well as provides safe voltage control and smooth current profiles. The phase-shift control of the DAB converter is a method of power flow regulation, in which the amplitude and direction of transmitted power depend on the phase difference between primary and secondary bridge switching signals. The inductor smooths current variations and minimizes ripple, enabling stable and efficient power conversion. Control signals generated by the proposed framework dynamically adjust the DAB operating conditions based on EV charging demand and the availability of RES, thereby maintaining DC bus voltage stability and reliable energy delivery. The coordinated use of the PV, FC, and battery resources leads to the economic optimization, and the focus on the low-cost RE should be considered first. The battery charging and discharging time is defined to minimize the use of more costly generation and reduce energy losses and DAB converter working is controlled to improve the conversion efficiency. This combined power management approach has a direct effect of reducing the LCOE and guarantees efficient, uninterrupted, and cost-efficient EV charging operation.

Fig. 1.

Structure of EVC using DAB converter and HRE.

EVCS size, capacity, and simulation parameters

The EVCS considered in this study represents a low-to-medium power DC charging configuration suitable for HRE integration. The rated charging power of the EVCS is 4.1 kW and the energy is provided by PV generation, a FC, and BES using a DAB-converter-based architecture. The detailed size, capacity, component ratings, and simulation settings of the EVCS-HRES system are summarized in Table 2.

Table 2.

Key model parameters of the EVCS-HRES system.

Component	Parameter	Value
EV	Battery capacity	5 kWh
	Nominal voltage	230 V
	Rated charging power	4.1 kW
	SoC limits	0.2–0.9 p.u
PV System	PV array area	12 m2
	PV efficiency	18%
	Rated irradiance	1.0 kW/m2
FC	Rated voltage	290 V
	Rated power	4.0 kW
BESS	Energy capacity	5 kWh
	Nominal voltage	270 V
	Max charge/discharge power	2.5/2.5 kW
	Charging/discharging efficiency	0.95/0.90
DAB converter	Transformer turns ratio	1:1
	Leakage inductance	200 µH
	Switching frequency	20 kHz
	DC bus voltage	410 V
	Phase-shift range	0-π/2 rad
Simulation	Simulation time	5 s

Modelling of EV

The EV measure considers a set of EVs, denoted by N, that are accessible within the MG system. The primary objective of each EV is to fulfill the mobility requirements of its user. Owing to variations in individual driving behaviors, each EV is characterized by a distinct set of operating conditions²⁶. Accordingly, the key parameters associated with an EV are defined as follows.

1

where indicates the time of arriving, represents battery capacity of the EV . denotes charge’s original state, indicates charging and discharging power at time slot .

2

EV operability is represented by the binary variable in this equation.

3

where indicates how long an EV has been connected to the grid.

4

5

where denotes discharging behaviour, denotes charging state, and denotes an optimization variable with continuously changeable properties.

Modelling of PV

In essence, solar radiation determines how much power the PV system produces²⁷. A bi-exponential distribution, which can be thought of as a mixture of two distinct exponential distribution functions, is frequently used to describe the hourly radiation distribution at a certain site.

6

7

where w represents weighting factor, provides shape factor, and are scale factors, and denotes solar radiation expressed in kW/m². The following provides definition of radiation to power conversion function.

8

where represents total solar surface area in denotes efficiency given as a percentage, and is the PV output power in kW.

Modelling of FC

The FC is a kind of galvanic cell that transforms chemical energy into electrical energy through an electrochemical reaction²⁸. The reaction is started by oxygen alone and doesn’t require any heat or mechanical operations. Equation (9) can be used to express the FC voltage.

9

where, FC voltage, which is total of the four voltage components including denotes reversible voltage, denotes activation losses voltage, denotes concentration losses voltage, and denotes losses voltage.

Modelling of battery

The following is an expression for BESS stored energy²⁹;

10

where represents time slot duration, , denotes BESS charging and discharging efficiency, , denotes BESS charging and discharging power at time , and indicates energy stored in the BESS at time .

To prevent overcharging, stored energy is kept under maximum charging limit.

11

12

13

where and represents minimum and maximum stored energy in BESS, and represents maximum BESS charging and discharging power.

Modelling of DAB converter

According to the waveform of the inductor current and the phase difference between the voltages of the primary and secondary transformer³⁰.

14

Current flows through switches and on the primary and switches and on the secondary during interval two. As a result, transformer’s secondary voltage is , and its primary voltage, also known as secondary, is positive and equal to . The design states that . As a result, throughout this time, the inductor current stays constant.

15

Current flows through switches and on the secondary and on the primary during interval three, hence, is the secondary voltage and is the primary voltage, also known as the secondary, which is negative. Equation 3 determines the inductor current’s slope in this interval. The inductor current drops at this time because of the negative slope.

16

Current flows via switches and on the transformer’s primary side and switches and on the secondary side during interval four. As a result, the transformer’s secondary voltage is , while the primary voltage is . Equation (17) is used to determine the inductor current’s slope. , hence the inductor current stays constant throughout this time.

17

During transition from interval two to three, primary switches and turn off, and turn on, while secondary switches and continue conducting. During dead time, inductor energy discharges capacitance across and , ensuring zero-voltage turn-on, reducing losses. The DAB power transfer is governed by Eq. 5, where φ represents the phase shift between the bridges.

18

where denotes required power transfer, denotes leakage inductor for a particular phase shift.

Proposed POA-AMOGCN approach for EVCS

The proposed POA-AMOGCN technique for reducing the LCOE combines the POA and the AMOGCN to enhance the economic performance of an EVCS integrated with a DAB converter and HRES. The POA is able to optimize power management by adjusting the power that is generated by the RES and battery storage to meet the demand of EVCS and produce control signals to the DAB converter. At the same time, the AMOGCN effectively estimates optimal control variables of the DAB converter, which guarantees the optimal allocation of resources and an uninterrupted integration of EVs and RES. This mixed approach is aimed at increasing the cost-efficiency and dependability of EVCS.

Interaction of renewable variability, storage, and load demand in EVCS

In the EVCS with hybrid sources of renewable power, power demand and power availability is extremely time-varying. The PV source is inherently intermittent due to changing solar irradiance, while the FC provides controllable but cost-sensitive supplementary generation. At the same time, the requirement of EV charging depends on the battery SoC and user charging requirements, creating dynamic load behaviour at the DC bus. The ESS of battery-based energy storage has a vital compensatory role that absorbs the surplus of the RE during the low demand periods and provides the power during peak charging periods or during the lack of RE. Nevertheless, unsynchronized battery functioning can be more harmful to reduce losses and speed up degradation and decrease economic functioning. Thus, to ensure the stability of the system and cost-efficiency, coherent scheduling charging and discharging is necessary. A hybrid optimization-prediction framework is used to ensure that these coupled dynamics can be properly managed. The POA is an algorithm that is used to make optimal power management decisions by reducing the LCOE, taking system constraints into consideration based on variable renewable and load conditions. In parallel, the AMOGCN predicts optimal control signals for the DAB converter by capturing higher-order dependencies among renewable sources, storage behavior, and EV load demand. This integrated way of operation guarantees the consistent interaction between generation, storage, and consumption, the stable operation and the economically optimized EV charging.

Pelican optimization algorithm

POA is a nature-inspired optimization method that models hunting and cooperative foraging of pelicans³¹. Pelicans catch prey efficiently by utilizing dynamic soaring, coordinated diving, and adaptive movement, demonstrating a near-optimal balance between exploration and exploitation in their search strategies. Inspired by these behaviours, POA employs adaptive position updates and intelligent movement patterns to navigate complex optimization landscapes, ensuring efficient convergence toward optimal solutions. When charging EVs sustainably with the help of a DAB converter and HRES, POA is utilized to optimize power management through balancing between RE generation, battery storage, and EV charging needs and delivering the required control signals to the DAB converter. Using its cooperative search mechanism makes POA more stable in a grid, conversion of power more efficient, energy cost decreased, and economic performance of EVCS better. The specific steps are given below:

Step 1: Initialization

Configure the input parameters such as the current and voltage of PV, FC, and DC bus and the current and voltage of EV battery.

Step 2: Random generation

The input parameter is created at random after startup.

Equation (19) is first used to randomly initialize population members based on the top and bottom borders of the problem.

19

where represents number of population members, indicates number of issue variables, provides random number in interval, denotes lower bound, denotes upper limit of problem variables, and indicates value of the variable indicated by candidate solution.

Here is the population matrix in Eq. (20).

20

If is the pelican and is the pelican population matrix.

Step 3: Fitness Function Estimation

21

Step 4: Exploration phase

This improves POA’s capacity for accurate problem-solving space exploration. Equation (22) presents a mathematical simulation of the pelican’s approach to the prey site.

22

where represents random number, represents location of prey in dimension, represents objective function (OF) value, and represents new status of the pelican in dimension based on phase 1. The number represents parameter, and it can randomly equal either 1 or 2.

If the value of OF is increased in new pelican position, it is accepted in proposed POA. Equation (23) is utilized to model this process.

23

where indicates OF value and represents  pelican’s new status.

Step 5: Exploitation phase

This procedure improves POA’s exploitation capability and local search power. Equation (24) provides a mathematical simulation of this pelican hunting behavior.

24

where indicates iteration counter, represents maximum number of iterations, represents neighbour-hood radius of , and denotes updated status of pelican in dimension based on phase 2. The radius of the population members neighbour-hood represented by coefficient ; it is used to search locally close to each member to converge to a better solution.

At this stage, new pelican position, which is represented by Eq. (25), has also been.

accepted or rejected via efficient updating.

25

where represents OF value based on phase 2 and indicates pelican’s new status. Flowchart of POA is given in Fig. 2.

Fig. 2.

Flowchart of POA.

Step 6: Termination

Examine the termination criteria. In case optimal solution is reached, end the process. Otherwise, move on to step 3.

Attributed multi-order graph convolutional network

The AMOGCN is a superior deep learning architecture that optimizes the processing and analysis of graph-structured data through the use of multi-order feature propagation and feature representation as attributes on nodes³². Unlike traditional Graph Convolutional Networks (GCNs), AMOGCN captures higher-order dependencies within the network, allowing for a more comprehensive understanding of complex relationships in dynamic systems. AMOGCN employs the benefits of multi-hop connection and attribute-enhanced learning to guarantee higher feature extraction and effective information propagation over the graph. AMOGCN is applied in the scenario of sustainable EV charging with a DAB converter and HRES to predict optimal control signals to be applied to the DAB converter to make the energy distribution effective and manage the loads. Its ability to analyse multi-source energy interactions enhances the stability of power flow, ensuring seamless integration of RESs with EVCS. The multi-order AMOGCN capability allows it to capture nonlinearities in the energy demand patterns so that they can increase the adaptability of the system and the accuracy of the decision-making process. In this form of the architecture, power forecasting can be done efficiently together with real-time control signal generation and classically optimized resource allocation that can significantly increase optimization capabilities in SG EV charging infrastructure.

Formulate an l-length meta-path as a collection of different first-order adjacency matrices. The sequential adjacency matrix multiplication, for instance, can be used to describe a straightforward l-length meta-path.

26

where denotes the undirected meta-path, and is obtained through arbitrary permutations of first-order adjacency matrix multiplications, resulting in a high-order adjacency matrix of meta-paths with varying .

To create semantic adjacency matrix, choose each node’s top k comparable neighbours. Create semantic adjacency matrix formulaically using

27

where essential connections predicted by node homophily are included in multi-order adjacency matrix fusion using pre computed . This is because distant but comparable nodes should tend to be connected by a high-order neighbour-hood relation. Consequently, the loss function can be used to quantify the supervision of semantic information.

28

where the number of non-zero elements in is denoted by . As the semantic node homophily information merely suggests possible relationships between comparable ascribed nodes. Therefore, simply take into account the supervision from already-existing semantic links.

The loss function of AMOGCN for semi-supervision classification, which combines label and semantic information supervision, is

29

where denotes cross-entropy loss function and denotes trade-off hyper parameter.

30

where the label information from the training set is contained in the matrix .

Result and discussion

To illustrate the efficacy of the suggested method, the simulation’s outcomes are presented here. The POA-AMOGCN approach is presented in the EVCS integrated with a DAB converter and HRES. The suggested POA-AMOGCN strategy is developed on the MATLAB platform and assessed against a number of current techniques, such as GTO, HCSA-PSO, NN-IPSO, FBIAOA, and PSO.

Figure 3 shows analysis of output current for PV, FC, battery and load. At 0 s, the FC provides 15 A, while the DC load stabilizes at 10 A. The PV source contributes 7 A initially, followed by a stepped reduction to 6 A at 1 s, 5.5 A at 2 s, and 5 A at 5 s. The current in the battery begins with negative current of − 4 A, which means that it is charging, and after 1 s, it reaches the value of 0 A. The FC shows a fluctuating response, decreasing to 10 A at 1 s, followed by stepped increments, reaching 16 A at 5 s, compensating for variations in PV and battery contribution. The DC load is maintained at 10 A during the time. The battery initially absorbs current, reducing charging at 0.5 s and maintaining minimal contribution afterward. The hybrid renewable system dynamically adjusts between PV, battery, and FC to ensure a steady supply. The integrated response demonstrates the optimization of energy allocation, as the FC includes a significant portion of offsetting the power; PV progressively decreases the output, which guarantees a consistent power supply to the EVCS. Figure 4 compares the PV, FC, battery and load output voltage. The DC load voltage rapidly rises to 400 V within the first second and remains stable. The PV system starts at 50 V, increases to 230 V, and stabilizes, with minor drops below 220 V at 2 s and 4 s due to transient adjustments. The FC maintains around 290 V with slight fluctuations, while the battery remains steady at 270 V, supporting a balanced power supply. This coordinated voltage regulation ensures uninterrupted EV charging and mitigates fluctuations in RE contributions. Figure 5 analyses the output power of PV, FC, battery, and load. The DC load power quickly rises to 4500 W within the first second and remains stable. The FC begins with the 2500 W and rises gradually up to 4000 W and stabilizes the power fluctuations. The PV system initially provides 2000 W but gradually decreases to 1000 W. The battery takes a short time to absorb the surplus energy and then dips to − 1500 W, and then reaches an almost zero point. This is because this distribution of power allows continuous charging of EVs, which underscores the efficiency of integrating hybrid RE. Figure 6, shows analysis of EV Battery voltage. The voltage increases between 0 V and approximately 230 V within the first second and almost 90% of the overall charging voltage has been recovered. After duration of approximately 0.5 s, the battery is approaching the value of 207 V, which is approximately 90% of the final voltage value. Following this sharp rise the voltage then approaches a peak of approximately 240 V, and levels off thereafter at a constant value until the final instant of the 5-s interval. This behavior reflects standard EV charging patterns, where the battery first charges rapidly before transitioning to a slower, more controlled phase. Using HRESs ensures consistent energy delivery, allowing the battery to charge efficiently while protecting it from overvoltage and ensuring system stability. Figure 7 shows analysis of EV Battery current. The current decreases to − 30 A at the beginning of charging, which means that the initial energy absorption is high, and the current increases gradually to − 20 A in several seconds, which stabilizes by 5 s. It is this increase that leads to the constant voltage phase where the current reduces and the voltage remains constant. In hybrid RE systems, this ensures stable energy flow, efficient charging, and battery health by preventing overcurrent and minimizing system stress.

Fig. 3.

Analysis of output current for PV, FC, battery and load.

Fig. 4.

Analysis of output voltage for PV, FC, battery and load.

Fig. 5.

Analysis of output power for PV, FC, battery and load.

Fig. 6.

Analysis of EV battery voltage.

Fig. 7.

Analysis of EV battery current.

Figure 8 reveals the analysis of DC Bus voltage. Initially, voltage rises rapidly from 0 V to approximately 400 V within the first 0.5 s, indicating the activation of the power conversion stage and energy flow from the renewable sources. The rapid increase in the voltage implies an efficient energy transfer process, ensuring that the system is very quick to reach a predetermined value. After this, the voltage continues to maintain its constant level at around 410 V. This is the most important to maintain constant and reliable EV charging processes. At the second couple, there is a minor dip that momentarily falls below 400 V. This could be due to load transients or sudden fluctuations in RE inputs. But this gets balanced, showing smooth voltage regulation and control operation mechanisms. The voltage stabilizes slowly and continues to hold tight at around to 410 V throughout the observation period till 5 s. The DC load current initially rises from 0 A to 10.5 A within 0.5 s, demonstrating strong power transfer in EV charging. Thereafter, it stabilizes at about 10 A with minute oscillations for optimized battery lifetime and charging efficiency. An occasional pull going below 10 A shows up at the second mark due to some load or RE variations; however, there is quick equilibrium with just a dip below 10 A at the 5th s. This shows how efficiently the EM strategy secures reliability and stability in EV battery charging. Figure 9 illustrates analysis of DC Load Current. The DC load current initially rises from 0 A to 10.5 A within 0.5 s, indicating strong power transfer for EV charging. It then stabilizes around 10 A with minimal fluctuations, optimizing battery lifespan and charging efficiency. A brief dip below 10 A occurs at 2 s due to load or RE variations but quickly recovers, settling just below 10 A by 5 s. This proves that the EM strategy is effective in providing stable and reliable EV battery charging. Figure 10 shows analysis of DC Load Power. Initially, power output rapidly increases from 0 W to approximately 4000 W within the first 0.5 s, indicating a strong and immediate energy supply to the EV battery. This surge in the past corresponds to the stabilization of voltage and current for smooth electricity delivery. Following this cresting point, the power evened and does not vary, but wanders around the 4100-Watt mark, which reveals the signs of stable conditions, which contribute to a better charging performance and reduced energy losses. At about 2 s, there is a very brief dip below 4000 W. This minor variation is actually attributed to transitory changes in load demand or a small transient change of RE input. However, the system takes care of this excursion almost instantly and regulates the power back to nearly 4100 W for the rest of the 5 s. This performance clearly demonstrates the good response of the hybrid EM strategy to apply charging stations for EV power flow under reliable and continuous conditions. Figure 11 shows the analysis of EV battery current. The initial current is 0 A and decreases rapidly to − 30 A at 0 s, which suggests the activation of the charging process and depends on the initial SoC and power supply of the battery. The high negative current shows significant power absorption, typical for low SoC or fast charging. After this drop, the current gradually increases toward 0 A over 5 s, reflecting a controlled charging strategy managed by a smart EM system. It is a steady increase that leads to efficiency in energy transfer, eliminating overcharging, and changing with fluctuations of the RE, maximizing EV battery performance. Figure 12 shows analysis of EV Battery voltage. It rapidly increases from approximately 0 V to nearly 250 V within the first 0.5 s. This sharp rise indicates the immediate response of the battery to the applied charging voltage, which is likely regulated by a power converter to match the required charging profile. The sudden increase is characteristic of a controlled charging process where the system quickly stabilizes the voltage to an optimal level, ensuring efficient energy transfer from hybrid RESs such as solar and wind. After reaching around 250 V, the voltage remains nearly constant for the remaining 4.5 s. This stabilization suggests that the battery has entered a steady-state charging phase, where current regulation plays a dominant role in maintaining a safe and efficient charging process. The stability of the voltage indicates that the RE integration system is effectively managing power delivery, compensating for fluctuations in renewable sources while ensuring a consistent voltage supply to the EV battery. This behavior reflects an optimized charging strategy designed to enhance battery life and performance.

Fig. 8.

Analysis of DC bus voltage.

Fig. 9.

Analysis of DC load current.

Fig. 10.

Analysis of DC load power.

Fig. 11.

Analysis of EV battery current.

Fig. 12.

Analysis of EV battery voltage.

Table 3 shows a comparative analysis of the LCOE calculated with the various optimization-based EM strategies whereby, a lower value is considered to be more cost-effective. Among the benchmark methods, the GTO approach records the highest LCOE of 0.2489 $/kWh, followed by HCSA-PSO at 0.1917 $/kWh and NN-IPSO at 0.1438 $/kWh. Further cost reductions are achieved using FBIAOA and PSO, with LCOE values of 0.1127 $/kWh and 0.0981 $/kWh, respectively. Conversely, the proposed POA-AMOGCN-based EVCS-HRES has a significantly lower LCOE of 0.0549 $/kWh, which means that it has better economics.

Table 3.

LCOE comparison with suggested and existing approaches.

Techniques	LCOE ($/kWh)
GTO	0.2489
HCSA-PSO	0.1917
NN-IPSO	0.1438
FBIAOA	0.1127
PSO	0.0981
POA- AMOGCN (proposed)	0.0549

To precisely measure this enhancement, the suggested approach is compared to known benchmark and standard EVCS-HRES configurations that are reported in literature which are PSO, GTO, HCSA-PSO, NN-IPSO, and FBIAOA, which are popular baseline EM strategies with the same system sizing, load demand, and cost assumptions. As seen in Table 3, traditional EVCS-HRES designs have a range of LCOE values between 0.0981 and 0.2489 $/kWh, whilst the proposed POA-AMOGCN has an LCOE value of 0.0549 -0.0549 $/kWh. This corresponds to an LCOE reduction of approximately 44% compared to PSO-based systems and more than 70% relative to heuristic benchmark approaches such as GTO and HCSA-PSO. The achieved reduction is primarily attributed to improved coordination between RES, ESS, and EV charging demand, along with enhanced DAB converter control enabled by the hybrid POA-AMOGCN framework. These findings validate that the suggested method provides significant economic benefit when compared to more traditional EVCS-HRES designs rather than some incremental enhancement of algorithms.

Justification of comparative methods

More recent developments in deep reinforcement learning (DRL) such as Deep Deterministic Policy Gradient (DDPG), Proximal Policy Optimization (PPO) and Soft Actor-Critic (SAC) have demonstrated high adaptive and sequential control performance. Nevertheless, these techniques are based on reward-guided policy learning and demand clear Markov decision process, widespread interaction with the environment, and long training horizons. These needs greatly raise the complexity and training cost of computation. The main aim of the work is the economic optimization of an EVCS combined with a DAB converter and HRES and in particular the minimization of the LCOE and the prediction of optimal converter control signals. The proposed POA-AMOGCN framework directly addresses this objective by combining a constraint-aware optimization algorithm with an AMOGCN that captures higher-order energy flow dependencies, without relying on trial-and-error policy learning. The chosen methods of comparison are two popular optimization-based and learning-assisted approaches to the issues of EV charging and EM in the literature, which guarantees the methodological consistency of the methods and the objective assessment of their performance. Those more complex DRA-based controllers and other graph-based models are considered as complementary models especially in long-horizon adaptive control and are not represented within the current economic evaluation framework. Table 4 is a qualitative comparison of the proposed POA-AMOGCN framework with representative DRL models and graph-based models, indicating variations in the objective formulation, training, and using both in LCOE-driven EVCS.

Table 4.

Qualitative comparison of POA-AMOGCN with advanced methods.

Method	Learning principle	Objective handling	Training complexity	Computational burden	Suitability for LCOE minimization
DDPG	Actor-critic DRL	Reward-based	High	High	Moderate
PPO	Policy-gradient DRL	Reward shaping required	High	High	Moderate
SAC	Entropy-regularized DRL	Stochastic reward optimization	Very High	Very High	Moderate
Advanced Graph Models	Attention-based message passing	Indirect optimization	High	High	High
POA-AMOGCN (Proposed)	Optimization + multi-order GCN	Direct constraint-based	Moderate	Moderate	High

Converter efficiency and loss characteristics

The efficiency profile of the DAB converter depends on operating conditions such as transferred power level, phase-shift angle, and switching frequency. The leakage inductance and the current flowing through the power semiconductor devices during high-power transfer raise the conduction losses. However, the DAB topology enables effective current shaping through phase-shift modulation, which limits excessive current stress and reduces conduction-related losses compared to hard-switched converter structures. The soft-switching nature of the DAB converter is crucial in reducing switching losses which appear when turning the power devices on or off. With suitable phase-shift conditions zero-voltage switching can occur with both the primary and secondary bridge switches which leads to minimized switching energy losses and minimized electromagnetic stress during high-frequency operation. This is particularly advantageous during medium-to-high power transfer, where switching losses typically dominate in conventional converters. In the proposed framework, the POA-AMOGCN strategy dynamically regulates the DAB phase-shift angle according to RE availability and EV charging demand. This coordinated control avoids unnecessary power circulation and extreme operating points, maintaining the converter within an efficient operating region. Thus, decreased switching transitions, minimal current stress, and loss components are all aspects that lead to increased power conversion efficiency, allowing the efficient and economical functioning of the EVCS.

Discussion

This performance analysis of DAB converter in HRES shows that it is capable of stabilizing EV charging processes. The dynamic nature of the power transfer processes is confirmed through the output current and voltage waveforms, which balance energy through the PV, FC, and Battery. The POA-AMOGCN method gives an optimal result in maintaining a stable DC Bus voltage of 410 V and a DC load power of 4100 W, leading to an uninterrupted energy supply. The EV battery charging profile demonstrates a very rapid voltage increase to 230 V within a second, it thereafter remains stable, whilst current transitions from − 30 to − 20 A, and suggesting controlled charging effort. The proposed POA-AMOGCN method achieves the minimum LCOE of $0.0549/kWh, indicating a very high degree of improvement in cost-effectiveness and energy efficiency. These results validate robustness and reliability of methodology towards the optimization of RE integration and the power conversion efficiency of sustainable EV charging.

Conclusion

The paper introduces a hybrid POA-AMOGCN model to ensure the economic feasibility of an EVCS together with a DAB converter and a HRE supply. The suggested strategy yields a lower levelized energy cost of 0.0549 $/kWh and overcomes the problems of power conversion efficiency, system stability, and the cost optimization. The smooth power management and energy delivery plan increases the reliability and sustainability of renewable-powered EV charging infrastructure. The comparative analysis with the traditional optimization strategies shows that the proposed framework can be effective to enhance cost efficiency, which proves its possible relevance to the practical EVCS. Future developments will be aimed at improving predicting power in conditions of highly variable renewables and supporting the suggested framework with real-life case studies.

Limitations of the proposed POA-AMOGCN framework

Despite the fact that the suggested POA-AMOGCN framework shows better economic and operational performance, some limitations can be acknowledged. The assessment is based on a fixed EVCS configuration, and component ratings, and system performance can be different when it comes to various charging capacities or renewable penetration rates. In addition, the prediction module may require retraining when applied to operating environments with significantly different renewable availability or EV charging demand patterns. The combined optimization and prediction structure also introduces higher computational complexity compared to conventional approaches, which may affect scalability when applied to large-scale EV charging networks.

Author contributions

Priya Narayanan and Prabakaran Kandasamy; Conceptualization, methodology, software, writing—original draft, writing—review & editing, visualization, supervision. Project administration, Nehru Kandasamy; Supervision, Jaisiva Selvaraj; Resources, supervision, all authors reviewed the manuscript.

Funding

The author received no funding for this work.

Data availability

No datasets were generated or analyzed during the current study.

Declarations

Competing interests

The authors declare no competing interests.