Dynamic Wireless Charging of Electric Vehicles Using PV Units in Highways

Abstract

Transitioning from petrol or gas vehicles to electric vehicles (EVs) poses significant challenges in reducing emissions, lowering operational costs, and improving energy storage. Wireless charging EVs offer promising solutions to wired charging limitations such as restricted travel range and lengthy charging times. This paper presents a comprehensive approach to address the challenges of wireless power transfer (WPT) for EVs by optimizing coupling frequency and coil design to enhance efficiency while minimizing electromagnetic interference (EMI) and heat generation. A novel coil design and adaptive hardware are proposed to improve power transfer efficiency (PTE) by defining the optimal magnetic resonant coupling WPT and mitigating coil misalignment, which is considered a significant barrier to the widespread adoption of WPT for EVs. A new methodology for designing and arranging roadside lanes and facilities for dynamic wireless charging (DWC) of EVs is introduced. This includes the optimization of transmitter coils (TCs), receiving coils (RCs), compensation circuits, and high-frequency inverters/converters using the partial differential equation toolbox (pdetool). The integration of wireless charging systems with smart grid technology is explored to enhance energy distribution and reduce peak load issues. The paper proposes a DWC system with multiple segmented transmitters integrated with adaptive renewable photovoltaic (PV) units and a battery system using the utility main grid as a backup. The design process includes the determination of the required PV array capacity, station battery sizing, and inverters/converters to ensure maximum power point tracking (MPPT). To validate the proposed system, it was tested in two scenarios: charging a single EV at different speeds and simultaneously charging two EVs over a 1 km stretch with a 50 kW system, achieving a total range of 500 km. Experimental validation was performed through real-time simulation and hardware tests using an OPAL-RT platform, demonstrating a power transfer efficiency of 90.7%, thus confirming the scalability and feasibility of the system for future EV infrastructure.

1. Introduction

Converting operating vehicles using petrol or gas to electricity has become a great challenge not only to reduce gas emanation and petrol costs but also to be a source of energy storage. Electric vehicles (EVs) can be found in four types: EVs operated by rechargeable batteries (EVBs) based on propulsion with no need for an internal combustion engine (ICE); EVs operated by ICE utilizing the regenerative braking for charging batteries called hybrid EVs (EVHs); plug-in EVs (EVPs) which operate as EVBs but use wires connected to power stations for charging; and finally wireless charged electric vehicles (WCEVs), which operate as EVBs but are wireless [1,2].

1.1. Motivation

The“plug-in” EVs using wires for charging face many problems such as limited travel range, bulky heavyweight batteries, and a long charging duration. WCEVs are introduced to reduce the realized shortcomings of wire technology, leading to reduced costs and hazards [3,4]. The WCEV system can be categorized as quasi-dynamic wireless charging (QWC), dynamic wireless charging (DWC), and static wireless charging (SWC) [5]. Many WCEV challenges were studied by researchers, such as battery capacity [6], wireless charging substation locations [7], and the required power electronic design [8,9], which can affect the cost and utilization of EVs.

1.2. Literature Review

The WC technology can be implemented using near-field or far-field methods. The magnetic field is capable of transmitting power over larger distances compared to the electric field, as it can penetrate objects [10]. The WC near-field technology is commonly implemented through methods like inductive power transfer (IPT-WC), coupled magnetic resonance (CMR-WC), or permanent magnet coupling (PMC-WC) [10]. The integration of electric and magnetic fields, first described by Maxwell in 1864, has been enhanced over time by adjusting parameters such as air gap, frequency, and power transfer levels [11]. CMR-WC focuses on optimizing magnetic resonance coupling for maximum power transfer, improving the system power factor for applications like online EVs and dynamic wireless charging (DWC) setups. PMC-WC relies on utilizing permanent magnets as couplings or gears to achieve efficient power transfer, with about 81% efficiency at 150 kHz for a 15.0 cm gap [12]. However, this design may pose mechanical challenges such as increased vibration, noise, and alignment issues, especially in the context of EV charging. Overall, wireless charging technologies present both opportunities and challenges due to power transfer and EV charging. In QWC, battery electric buses (BEBs) can charge momentarily when they promptly stop due to traffic blocks. ABB company could employ bus gained 400 kW charging after 15 s. QWC system has been introduced for vehicle-to-grid and grid-to-vehicle systems [13]. A comparative economic study was conducted between QWC, SWC, and DWC [14]. It concluded that DWC capital and operating costs can be reduced by using QWC.

One major concern in EV adoption is the time taken for charging and the limited availability of charging services, which can lead to doubts about sufficient energy to reach destinations [15]. Efforts have been made to address this issue by focusing on reducing energy requirements for EVs; improving charging efficiency; enhancing battery capacity; and exploring alternative charging methods like battery swapping, static wireless charging (SWC), and DWC. SWC relies on the electromagnetic coupling between coils but still encounters challenges in charging time and service distribution [5]. DWC encounters challenges related to transportation schedules, arrangements, and operations. The state of charge (SOC) of EVs can significantly impact their activities and performance when using DWC [16]. An innovative approach that combines SWC and DWC has been proposed. Other studies have explored the application of DWC with wireless power transfer (WPT) technology to reduce the size of EV batteries [17]. The implementation of DWC has led to cost minimization and the integration of electric and transportation networks, reducing the total travel costs. The original design of DWC involved creating a magnetic linkage with a 3 mm air clearance at a high frequency of up to 100 kHz, generating 8.3 kW power with 87% efficiency [18]. Recent advancements have allowed for an increase in the air gap to automate the charging process, with efforts focused on extending this distance up to meters using modern electronic devices to enhance power production and address the challenge of distant charging [19]. WPT technologies are typically classified into three groups: inductive-based WPT (IWPT), magnetic resonant coupling (MRC)-based WPT, and electromagnetic radiation-based WPT. MRC-WPT offers advantages in terms of high safety levels and long transmission distances [2].

It can be concluded that for low or medium required WPT amounts, MRC is more suitable than the others. IWPT is the optimal choice for high-voltage WPT as it eliminates resonance [20]. A design for IWPT was proposed by positioning the primary winding of the power transformer in the ground on the same axis as the secondary winding in EVs, achieving efficiency levels ranging from 85% to 96% [21]. Increasing the air gap diminishes power transfer efficiency [22]. Conversely, when extreme power transfer capabilities are needed in WPT, the design of the air gap width should prevent overheating [23]. The degree of fine linkage primarily relies on the magnetic linkage coefficient, with a higher coefficient necessary for high power transfer [24]. A power of 60 kW with efficiency reaching 80% could be transferred using 85 kHz through a 20 cm air gap and lateral tolerance of 24 cm [25,26]. A power of 82 kW could be achieved for the very high-speed train with 83% efficiency with a 5 cm gap [27].

A wireless synchronization controller for vehicle parts was introduced to wireless charging EVs under stationary and semi-dynamic conditions, increasing the output power and efficiency [28]. A new dynamic two-way strategy to improve charging for dynamic EVs and fulfill their requirements using an improved mixed-integer linear program and numerical tests was proposed [29]. An integrated control strategy was proposed to overcome the mutual inductance instability that arises with dynamic EVs using an internal model-based regulator, and the results were confirmed by introducing a prototype model. The method exhibited less disruption and higher accuracy [30]. A superimposed dislocation coil (SDC) was suggested for dynamic and static WPT to guarantee a fixed coupling coefficient between the transmitting and receiving coils [31]. A new method was presented to evaluate the continuity of dynamic power transfer and its actual effects on the electric network [32]. An optimization technique was introduced to determine the optimal dynamic charging of EVs using a nonlinear integer programming model to minimize DWC requirements and cost considering stable charging resources in highways, the EV battery’ nonlinear charging performance, and traffic capacity limits [33]. Another study proposed an optimized design of a DWC charging system integrated with distributed generator resources, which was incorporated with main networks and tested in a large road network in Sharjah, UAE [34]. A traffic assignment model was suggested using the DWC system considering user equilibrium and the probability of EV batteries running out. The suggested system used DWC system planning [17]. The cover-like coupling structure and the return-like coupling structure were designed to improve the DWC by reducing its cost and electromagnetic radiation in addition to increasing its efficiency using Ansoft software 2021 for simulation and analysis [35]. A comparative study was conducted between static and dynamic charging systems for EVs to analyze their operation, practicality, and applications [36]. Fixed output voltage for DWC was obtained by using a successful optimal control method considering the time-varying flux caused by mutual inductance as a result of EV motion [37]. A new methodology was suggested to control the switching of transmission lane segments depending on the location of the EV, which could be accurately detected [38]. A new optimization technique was proposed, and a plan was prepared to locate the quasi-dynamic wireless charging (QWC) plants in the road lane to study and define the charging requirements of battery electric buses. The optimization’s main objectives are minimizing energy loss and fixed and variable costs, in addition to defining the optimal position of QWC, battery sizing, and length of power transmitters [39]. A new method was developed to evaluate the number and distance of wireless charging segments required to permit the maximum number of EVs to pass and charge in a specific highway while they are running [40].

1.3. Gaps

In summary, the wireless charging of EVs has garnered significant attention as a promising technology to enhance the convenience and efficiency of EV charging. Several challenges impede the widespread adoption of wireless charging. High coupling frequencies can affect nearby electronic devices and require stringent shielding measures. In addition, the large size of transmitting coils (TCs) and receiving coils (RCs) can add considerable weight to the vehicle, affecting its efficiency and performance. High-frequency operations also generate heat, necessitating special cooling systems that increase the complexity and cost of the charging setup. Although the efficiency of TCs and RCs typically hovers around 80%, this figure often neglects the losses in the inverters and other associated components.

1.4. Contribution

This paper aims to address the challenges in WPT for EVs by focusing on optimal coupling frequency and coil design to balance efficiency while minimizing EMI and heat generation. The authors propose a novel coil design and adaptive hardware to improve power transfer efficiency (PTE) in magnetic resonant coupling WPT and mitigate coil misalignment, a crucial roadblock in the acceptance of WPT for EVs.

A methodology was introduced to arrange and design lanes and roadside facilities to operate EVs. The TC RC compensation circuit and high-frequency inverters/converters were optimized using the partial differential equation toolbox (pdetool) to achieve the highest WPT efficiency. In addition, the integration of wireless charging systems with smart grid technology was explored to optimize energy distribution and reduce peak load issues.

This paper proposes multi-segmented transmitters for the DWC of EVs integrated with adaptive renewable photovoltaic (PV) units along the EV road and a battery system with the utility main grid as backup. The required PV array capacity station battery size and inverters/converters were designed, ensuring maximum power point tracking (MPPT). A control methodology for the operation of PV units, station batteries, and the main grid was established. To validate the proposed system, it was applied to two scenarios: charging one running EV battery (EVB) at three different speeds and simultaneously charging two EVBs at the same speed over a 1 km stretch for 50 kW, achieving a total distance of 500 km. The results confirm the effectiveness of the proposed system demonstrating significant advancements in WPT for EVs. The contribution of the paper can be concluded as follows:

• The development of a novel coil design and adaptive hardware for improved PTE and coil misalignment mitigation in WPT;
• The design of multi-segmented transmitters for DWC integrated with adaptive renewable PV units and a battery system;
• The introduction of a methodology for arranging and designing roadside lanes and running EV facilities;
• The optimization of the TC RC compensation circuits and high-frequency inverters/converters using pdetool;
• The establishment of a control methodology for PV units station batteries and the main grid;
• The validation of the proposed system through practical application and analysis demonstrating its effectiveness in real-world scenarios.
• To validate the results, a wireless EV charging prototype using OPAL-RT 4510, OPAL-RT, Montreal, QC, Canada was created and integrated with the simulation MATLAB Simulink Software 2022 with WPT technology. The results confirmed the effectiveness of the proposed DWC system and could reliably transfer power to the moving EVs with high efficiency.

2. Proposed System Methodology (Description)

The proposed methodology involved preparing a side road of a specific length with two distinct arrangements, as illustrated in Figure 1. In the first arrangement, a transmitter coil (TC) was buried underground along the side road’s path. This coil was connected to its power source through a normally open switch and was positioned adjacent to the side road. This setup was replicated intermittently along the lane’s length, with each pair of adjacent arrangements spaced apart by the length of a car. The TC mechanism embedded in the ground was designed to move slightly downward when a car passed over it. This movement triggered the switch to close, establishing a connection to the power supply. The second component was the receiving coil (RC), which was mounted underneath the EV to receive power from the TC via an AC/DC converter. This arrangement enabled the EV to be supplied with power as it traveled along the specially prepared side road. Through this system of transmitter and receiver coils, the EV could effectively receive power wirelessly as it moved along the designated path, ensuring a seamless charging experience.

The primary circuit comprised a utility supply high-frequency inverter and transmitter resonant circuit, as depicted in Figure 1. In this study, it was suggested that the utility supply would primarily include photovoltaic (PV) panels, and a battery bank for energy storage was also proposed. These energy sources were supplemented by the main grid as a backup connected through an AC/DC converter to the DC bus. The magnetic field generated by the TC would interact with the RC as an EV drove over the transmitter setup. The AC magnetic field produced by the RC was converted to DC using a converter to charge the EV’s batteries. Multiple charging points across the side road lane were strategically positioned to ensure that the EV batteries were fully charged with sufficient energy to propel the vehicle over a specific distance. The placement of these arrangements was predetermined based on the design outlined in [41]. This innovative system enables the efficient wireless charging of EVs as they travel along the side road, providing a seamless and convenient charging solution.

When a car passes by the first arrangement and due to the car’s weight, the ground mechanism vertically moves a little bit down, and the normally open power switch latches to supply the TC circuit for the best utilization of power. Also, the RC moves down, which decreases the distance between TC and RC to maximize the amount of flux linkage and start charging the EVB while it is moving. This operation is repeated along the lane until it is fully charged. Multiple EVs can be charged at the same time. The best coil arrangement, coil design, suitable resonant frequency, number of arrangements per lane, and supply system supported by PV units were then modeled and designed, as described in the next sections.

3. Proposed System Modeling

3.1. Station Supply

This section explains how to size the PV array battery and inverter and the maximum power point tracking (MPPT) in addition to selecting the suitable voltage control. To estimate the electrical parameters for a particular PV module, the IV and PV characteristics, short-circuit current, and open-circuit current at different operating conditions, such as solar radiation and module temperature, should be defined. A PV array comprises solar panels that have numerous series–parallel solar cells, DC-DC voltage converters (in some cases, DC-AC voltage inverters), controllers, and batteries. Figure 2 demonstrates the equivalent circuit of a solar panel.

The voltage of the open circuit is determined by the cell operating temperature, which differs from the ambient temperature. Equations (1) and (2) are used to calculate the cell operating temperature as a function of both the ambient temperature $T_a$ and solar radiation $H_T$. The PV voltage current and power can be estimated using Equations (3)–(5), respectively [42].

$$T_c=T_a+0.03·H_T$$

(1)

$$H_T=H_b{R}_b+H_d{R}_d+(H_b+H_d)R_r$$

(2)

$$V_{oc}=V_{oc0}+(-2.3\mathrm{mV}/°\mathrm{C})(T_c-{T_a}^r)$$

(3)

$$I=I_{PV}-I_0[e^{{\displaystyle \frac{V+R_{s}I}{\alpha V_t}}}-1]-{\displaystyle \frac{V+R_{s}I}{R_p}}$$

(4)

$$P_{PV}=k_1{H}_{T}A[1+k_2(T_a-{T_a}^r]$$

(5)

In this context, various parameters are defined as follows: $I_{PV}$ denotes PV current; $I_0$ signifies saturated reverse current; $\alpha$ represents the diode ideality; $V_t$ stands for thermal voltage; $R_p$ is the parallel equivalent resistance; $R_s$ is the series equivalent resistance; $\epsilon$ symbolizes the PV conversion efficiency; A denotes the PV surface area; $H_T$ indicates the hourly PV power output in “${\mathrm{kWh}/\mathrm{m}}^2$”; Hb and Hd refer to beam and diffuse radiation, respectively; and $R_b$, $R_d$, and $R_r$ are the tilt factors for beam diffuse and reflected solar radiation. The panel’s characteristic dispersion ($k_1$) varies between 0.095 and 0.105, with ($k_2$) set at −0.47%/°C. Increasing the output voltage can be achieved by connecting PV cells in series, while the parallel electrical connection is recommended for handling high current outputs. The proper sizing of the PV array battery and inverter is essential to meet electricity demand, ensuring adequate voltage and current ratings. Equations relating to PV power and voltage (Equations (3) and (5)) are influenced by system temperature, highlighting the importance of accurately estimating electrical power generation through cell temperature estimation.

3.2. PV Array Sizing

To ensure that the solar PV system can independently supply the EV without relying on the electrical grid, it is necessary to calculate the total energy required by the PV array. The required energy $E_r$ should satisfy the required energy to charge the EV in addition to any potential losses. To avoid under-sizing and to have an accurate design, it can be estimated by dividing the total power demand throughout the day by the efficiency of all components in the system, as per Equation (6).

$$E_r={\displaystyle \frac{E_{demand}}{{\eta }_{sys}}}$$

(6)

where $E_{demand}$ represents the amount of energy demanded in watt-hours “Wh”, while ${\eta }_{sys}$ denotes the efficiency of the entire system. To calculate the peak power generated by the PV system ($P_{peak}$) designed for a building, the daily energy requirement is divided by the average sun hours per day of its geographic location, as in Equation (7). This yields the value of $P_{peak}$ in watts “W”, with $T_{min}$ representing the minimum peak sun hour (in “hours”).

$$P_{peak}={\displaystyle \frac{E_r}{T_{min}}}$$

(7)

The total number of PV arrays ($n_{PV}$) can be determined using Equation (8), where $P_{unit}$ represents the power of each PV unit. The number of series and string units comprising the total number of PV arrays can then be deduced by Equations (9) and (10), where $n_{PV}\left(s\right)$ represents the number of series units, $n_{PV}\left(p\right)$ represents the number of string units in series, and $V_{DC}$ denotes the DC-link voltage.

$$\begin{array}{cc}\hfill n_{PV}& ={\displaystyle \frac{P_{peak}}{P_{unit}}}\hfill \end{array}$$

(8)

$$\begin{array}{cc}\hfill n_{PV}\left(s\right)& ={\displaystyle \frac{V_{DC}}{V_{mpp}}}\hfill \end{array}$$

(9)

$$\begin{array}{cc}\hfill n_{PV}\left(p\right)& ={\displaystyle \frac{n_{PV}}{n_{PV}\left(s\right)}}\hfill \end{array}$$

(10)

3.3. MPPT

MPPT is vital for optimizing power generation in PV systems [43]. This study focuses on a temperature-based MPPT technique ensuring fast convergence, low complexity, and high efficiency. By calculating cell temperature and utilizing the open-circuit voltage, optimal power output is achieved through the precise adjustment of the PV panel resistance. Equation (11) describes the correlation between the maximum output voltage and cell temperature. It includes parameters such as $T_{ref}$ for the reference temperature (25 °C) and ${\beta }_{ref}$ for cell efficiency.

$$V_{MPPT}=V_{MPPTref}+{\beta }_{ref}(T-T_{ref})$$

(11)

3.4. Station Battery Sizing

This section describes how to calculate the necessary electrical storage energy “$E_{storage}$” required during the daytime until sunset to meet the EV demand. $E_{storage}$ can be determined by considering the charging capacity of the EV station. To prevent over-discharging, the storage energy must be designed within the safety threshold, determined using Equation (12), where $E_{safe}$ represents safe storage energy in Wh, and $M_d$ is the maximum depth of discharge percentage.

$$E_{safe}={\displaystyle \frac{E_{storage}}{M_d}}$$

(12)

The topology of the battery system can be defined by identifying the combination number of series/parallel batteries that satisfy EV loading based on the total current required by battery bank I, battery current $I_b$, battery voltage $V_{battery}$, and the required system output voltage $V_{DC}$. The required current by bank I, the total number of bank batteries $N_{battery}$, the number of series batteries $N_s$, and the number of parallel paths $N_p$ is estimated using Equations (13)–(16).

$$\begin{array}{cc}\hfill I& ={\displaystyle \frac{E_{safe}}{V_{battery}}}\hfill \end{array}$$

(13)

$$\begin{array}{cc}\hfill N_{battery}& ={\displaystyle \frac{I}{I_b}}\hfill \end{array}$$

(14)

$$\begin{array}{cc}\hfill N_s& ={\displaystyle \frac{V_{DC}}{V_{battery}}}\hfill \end{array}$$

(15)

$$\begin{array}{cc}\hfill N_p& ={\displaystyle \frac{N_{battery}}{N_s}}\hfill \end{array}$$

(16)

The voltage regulator required for the station battery is essential for managing the current flow. To ensure optimal performance, a voltage regulator must withstand both the maximum current generated by the array and the maximum load current. The appropriate sizing of the voltage regulator is determined using Equations (17) and (18), where $I_{vc}$ represents the rated current of the voltage controller in A, $I_{sc}$ denotes the short-circuit current of the battery, F refers to the safety factor “set at 1.25”, $N_{cont}$ represents the number of controller units, and $I_{cont}$ denotes controller current.

$$\begin{array}{cc}\hfill I_{vc}& =I_{sc}\ast n_{PV}\left(p\right)\ast F\hfill \end{array}$$

(17)

$$\begin{array}{cc}\hfill N_{cont}& ={\displaystyle \frac{I}{I_{cont}}}\hfill \end{array}$$

(18)

3.5. Station Operation Control Methodology

The focus of the charging control system in this research is to power an EVB using either a PV–battery system or the electrical grid. The control loop illustrated in Figure 3 facilitates selling excess energy to the grid to generate profit.

• The EVB is charged from the PV units supported by station batteries without relying on the network;
• In case of sunset conditions, and if station batteries are fully discharged, the EVB can be charged from the main network as backup;
• If there is surplus energy after charging the EVB from the PV, the station batteries are used;
• If there is surplus energy after charging the EVB from the PV, and the batteries are fully charged, the surplus energy is sold to the grid.

3.6. Wireless Charging Circuit Design

The wireless charging system design can be categorized as coil design, compensation circuit, and high-frequency inverter/converter design. The coil design requires defining sufficient inductance to produce the required magnetic field to be transferred to charge the EVB. The coil arrangement is mandatory to complete the design.

3.6.1. Coil Arrangements

Magnetic field coupling is one of the most important methods to transfer energy from one circuit to another without direct connections. The coupling can mainly be achieved using two coils: TCs and RCs. The design and arrangement of the two coils are vital to obtain the maximum benefits of the input energy transferred from the source to the load and to avoid magnetic field leakage and interference with the adjacent atmosphere. There are two categories of coils: air-core coils and magnetic-core coils. The magnetic core is preferred for strong coupling applications [41]. In WPT, the amount of power to be transferred and the transferring efficiency are highly affected by coil arrangement, coil sizing, and design. The application of WCEV involves the use of the WPT technology. In EVs, the transferring distance coil sizing and coil arrangement are the necessary parameters that should be identified. Coil sizes are always larger than the transferring distance, which ranges between 100 and 300 mm. The two-coil arrangement suits short-range applications, and the systems with one or two coils are better for medium-range applications. Low- and medium-rating applications can be implemented using coils with magnetic shields where high-power ratings require active core shields [44,45]. The coils required for WPT can be categorized based on the polarity of its flux spreading into unipolar polarized and double polarized [46]. Most of the coil structures used for EVs are circular, square, rectangular double coils, bipolar coil, and tripolar, as shown in Figure 4. Circular coils are unipolar polarized, producing a uniform field distribution, which reduces stress on power electronic components at the receiving side. In addition,  leakage can be easily minimized by proper design. Both square and rectangular coils have nearly the same assembly representing polarized flux spreading, but their behavior is dissimilar. They have the largest coupling but with the highest leakage flux compared to other coil types [10]. Double coils are magnetically linked and have the advantage of both a mutual flux pipe and a circular pad design with polarization flux combination assembly at one side. The double coil system can be used for static and semi-dynamic operation in addition to its capability to deliver a higher rate of power transfer even if there is misalignment. It has some drawbacks, such as longer coil length and large flux leakage [3]. Bipolar coils are composed of two rectangular coils internally connected with a higher coupling coefficient and lesser misalignment compared to the rectangular coil system, in addition to saving copper, thus achieving better efficacy [47]. Tripolar coils are non-polarized systems containing three coils that can produce sufficient transmitted current and coupling factor. These systems suit the high-power requirements under static operation [48]. In this paper, the commonly used circular coil system shown in Figure 4a was chosen for the proposed strategy.

3.6.2. Coil Design

Consider the circuit in Figure 5, showing two ideal inductor coils with a resistance in series.

Consider a single-circular wire loop of diameter $D_{OUT\left(s\right)}$ and wire diameter of $w_s$. The self-inductance in a medium of permeability $\mu$ can be calculated analytically [49] considering the skin effect using Equation (19) as follows:

$$L_1={\displaystyle \frac{\mu D_{OUT\left(s\right)}^2}{2}}ln\left({\displaystyle \frac{8D_{OUT\left(s\right)}}{w_s}}\right)-2$$

(19)

where $\mu ={\mu }_0{\mu }_r$, ${\mu }_0$ is the permeability of free space (vacuum), and ${\mu }_r$ is the relative permeability. If ${\mu }_r=1$, then $\mu ={\mu }_0$, and $L_1$ can then be expressed using Equation (20) as follows:

$$L_1={\displaystyle \frac{{\mu }_0{D}_{OUT\left(s\right)}^2}{2}}ln\left({\displaystyle \frac{8D_{OUT\left(s\right)}}{w_s}}\right)-2$$

(20)

For a coil of $N_1$ turns, as shown in Figure 4a, the self-inductance of the sending end loop $L_1$ can be calculated using Equation (21) as follows:

$$L_1={\displaystyle \frac{{\mu }_0{N}_1^2{D}_{OUT\left(s\right)}^2}{2}}ln\left({\displaystyle \frac{8D_{OUT\left(s\right)}}{w_s}}\right)-2$$

(21)

Similarly, the self-inductance of the receiving end coil $L_2$ with a diameter $D_{OUT\left(r\right)}$ wire diameter $w_r$ and $N_2$ turns can be calculated using Equation (22) as follows:

$$L_2={\displaystyle \frac{{\mu }_0{N}_2^2{D}_{OUT\left(r\right)}^2}{2}}ln\left({\displaystyle \frac{8D_{OUT\left(r\right)}}{w_r}}\right)-2$$

(22)

The mutual inductance M between the sending and receiving coaxially placed coils is given in Equation (23) as follows:

$$M={\displaystyle \frac{N_1{N}_2{\mu }_0{D}_{OUT\left(s\right)}^2{D}_{OUT\left(r\right)}^2}{m^{3/2}C\left(m\right)}}$$

(23)

where $C\left(m\right)$ is a function representing the complete elliptic integral and can be calculated using Equation (24) as follows:

$$m={\displaystyle \frac{D_{OUT\left(s\right)}{D}_{OUT\left(r\right)}}{D_{OUT\left(s\right)}^2+D_{OUT\left(r\right)}^2+h^2}}$$

(24)

where h is the distance between the centers of the coils. The transmitter and receiver coil voltages can be calculated from Figure 5. The current $I_1$ in the transmitter coil (TC) induces a changing magnetic field, which generates an emf $V_1$. This is due to the self-inductance of TC. The same changing magnetic field in the TC also links the receiver coil (RC) and induces an emf $V_2$ due to the mutual inductance between the two coils. As a result, a current $I_2$ flows through the RC, inducing another emf due to the self-inductance of the RC. The equations in the frequency domain can be expressed using Equations (25) and (26) as follows:

$$\begin{array}{cc}\hfill V_1& =(r_1+jw{L}_1)I_1+jwM{I}_2\hfill \end{array}$$

(25)

$$\begin{array}{cc}\hfill V_2& =(r_2+jw{L}_2)I_2+jwM{I}_1\hfill \end{array}$$

(26)

The output power ($P_{out}$) of the DWC system can be obtained using the open-circuit voltage ($V_{oc}$) and short-circuit current ($I_{sc}$) of the receiver coil and the quality factor ($Q_2$), as formulated in Equations (27)–(30) [50].

$$V_{oc}=jwM{I}_1$$

(27)

Ignoring the resistive component, the short-circuit current is determined as follows:

$$I_{sc}={\displaystyle \frac{M{I}_1}{L_2}}$$

(28)

The $P_{out}$ is then determined using Equations (29) and (30) as follows:

$$P_{out}={\displaystyle \frac{V_{oc}{I}_{sc}{Q}_2}{L_2}}={\displaystyle \frac{jwM{I}_1·M{I}_1}{L_2}}·Q_2={\displaystyle \frac{jw{M}^2{I}_1^2}{L_2}}·Q_2$$

(29)

Since $Q_2={\displaystyle \frac{w{L}_2}{R_{EV}}}$ then

$$P_{out}={\displaystyle \frac{j{w}^2{M}^2{I}_1^2}{R_{EV}}}$$

(30)

where $R_{EV}$ is the electric vehicle (EV) load resistance. The power output ($P_{out}$) can also be given in terms of the voltage $V_1$ across $L_1$, the current $I_1$, coupling coefficient (k), and the quality factor using Equation (31).

$$P_{out}=V_1{I}_1{k}^2{Q}_2$$

(31)

The coupling coefficient (k) is the measure of the extent to which the primary coil links the secondary coil and is given by Equation (32) as follows:

$$k={\displaystyle \frac{M}{\sqrt{L_1{L}_2}}}$$

(32)

Also, the inductance can be increased by increasing the number of turns, the diameter of the turns, and/or the number of layers.

In this paper, the commonly used circular coil system shown in Figure 4a was chosen for the proposed strategy. The design of the coil was based on the calculated inductance $L_1$, $L_2$ and M, as per Equations (21)–(23), respectively. A software program was used to determine the coil design. The inductance of a single-layer inductor can be calculated using Equations (33)–(35) as follows:

$$\begin{array}{cc}\hfill L& ={\mu }_o·N^2·{\displaystyle \frac{D_{avg}}{2}}·\left[ln\left({\displaystyle \frac{C_2}{\rho }}\right)+C_3·\rho +C_4·{\rho }^2\right]\hfill \end{array}$$

(33)

$$\begin{array}{cc}\hfill \rho & ={\displaystyle \frac{D_{out}-D_{in}}{D_{out}+D_{in}}}\hfill \end{array}$$

(34)

$$\begin{array}{cc}\hfill D_{avg}& ={\displaystyle \frac{D_{out}+D_{in}}{2}}\hfill \end{array}$$

(35)

where N is the number of turns; ${\mu }_o$ is the vacuum permeability and equal $4\pi \times {10}^{-7}$; $\rho$ is the fill ratio; $D_{in}$ is the coil turns’ inner diameter; $D_{out}$ is the coil turns’ outer diameter; and $C_1$, $C_2$, $C_3$, and $C_4$ are layout coefficient shown in

Table 1. Layout dependent coefficient (reprinted from Ref. [51]).

Layout	${\mathit{C}}_1$	${\mathit{C}}_2$	${\mathit{C}}_3$	${\mathit{C}}_4$
Square	1.27	2.07	0.18	0.13
Hexagonal	1.09	2.23	0	0.17
Octagonal	1.07	2.29	0	0.19
Circle	1	2.46	0.2

.

Also, the inductance of the multilayer inductor shown in Figure 4a can be calculated using Equations (36)–(38) as follows:

$$\begin{array}{cc}\hfill L_{total}& =L_1+L_2\pm 2M\hfill \end{array}$$

(36)

$$\begin{array}{cc}\hfill M& =2K_c·\sqrt{L_1+L_2}\hfill \end{array}$$

(37)

$$\begin{array}{cc}\hfill K_c& ={\displaystyle \frac{N^2}{A·X^3+B·X^2+C·X+D·(1.67·N^2-5.84N+65.0.64)}}\hfill \end{array}$$

(38)

where $K_c$ is the coupling value; M is the mutual inductance; X is the distance between the inductors on the two layers; N is the number of inductor turns; and A, B, C, and D are constants shown in

Table 2. Inductor turn constants.

Category	A	B	C	D
Value	0.184	−0.525	1.038	1.001

.

The dimensions of the circular coil shown in Figure 4a can be calculated using Equation (39) as follows:

$$D_{out}=D_{in}+2W+W+S(2N-1)$$

(39)

where W is the width trace; S is the trace spacing, which can be changed from $\left(S_{min}\right)$ to $\left(S_{max}\right)$ with increment distance (e) taking into consideration that $\left(D_{out}\right)$ and $\left(D_{in}\right)$ are limited by the space specified to the TC and RC.

3.6.3. Compensation Network (Resonant Circuit)

The WPT efficiency can be increased by installing compensation elements to the TC and RC. On the primary side, a compensation network is used to eliminate the phase shift between the current and voltage and reduce the reactive power requirement in the source, while on the secondary side, a compensator capacitor is required to maximize power transfer and efficiency. The compensation leads to resonance between the two sides, reduces the required apparent power from the main source, and smoothly regulates the source loop current and the receiving loop with higher efficacy for higher gap distance than normal coupling [45]. The reactance of the TC and RC can be changed by installing additional specified capacitors on both sides simultaneously as per the load requirements. When the resonant frequency on both sides is equal, the maximum WPT is achieved. Figure 6 shows the most popular compensation circuit types required for resonance called: (a) series–series “SS”; (b) parallel–parallel “PP”; (c) series–parallel “SP”; and (d) parallel–series “PS”. Hybrid systems can be achieved by adding inductance and capacitance on both TCs and RCs. In this paper, series–series resonance type was selected because it can fix the power factor regardless of load and coupling coefficient changes, which suits WC.

The resonant frequency $f_r$ can be given by Equation (40) as follows:

$$f_r={\displaystyle \frac{1}{2\pi \sqrt{LC}}}$$

(40)

3.6.4. Design Procedure for DWC for EVB

In EVs and based on Equations (36), (37) and (40), the resonant frequency depends on L C and M values, which change by varying the distance between the TC installed in the ground and the RC installed in the bottom of the EV. The height of the EV to ground is known to be approximately between 14 and 16 cm. The detailed design procedure to calculate the optimum WPT for EVB is shown in Figure 7.

3.7. High-Frequency Inverter and Rectifier

Unlike in the transformer, where the primary and the secondary windings are installed around the same magnetic core, in a dynamic wireless charging system, the TC and RC are separated by an air gap. The RC mounted underneath the moving EV converts the pulsating magnetic flux into a high-frequency AC. A rectifier is then used to convert the high-frequency AC to stable DC to charge the batteries installed in the moving EV. This arrangement is associated with high leakage inductance. To reduce flux leakage and enhance power transfer efficiency, the supply voltage is converted into a high-frequency AC that powers the TC. This is achieved with the use of a high-frequency inverter, which can be specified using previously selected frequency and sending/receiving voltage. One common problem with high-frequency inverters is electromagnetic interference (EMI). This interference can affect other electronic devices or communication systems nearby. To reduce EMI, shielding techniques, filtering circuits, and proper grounding are often employed in the design of high-frequency inverters. Another challenge is the generation of higher amounts of heat due to increased switching frequency, which requires efficient cooling mechanisms to maintain optimal performance and reliability [52]. If heat dissipation increases, additional features may be required for cooling. The optimal frequency of operation for an inverter without affecting its performance can vary depending on the specific application and design considerations. In general, high-frequency inverters typically operate at frequencies ranging from several kHz to several hundred kHz. The choice of the optimal operating frequency is a balance between several factors, such as switching losses, efficiency, EMI considerations, component size, and cost.

4. EV Battery Charging Methodology

Wireless EV battery charging via inductive power transfer leverages magnetic fields to charge EV batteries wirelessly, minimizing the need for physical contact with charging stations. Using power electronics control, the process optimizes energy transfer efficiency, manages charging to prevent battery overload, and ensures safety. Charging methods such as constant voltage (CV), constant current (CC), and CVCC are employed, with CVCC combining these techniques to efficiently charge batteries. These methods are particularly suitable for Li-ion batteries while preventing overcharging. Smart charging utilizing microcontrollers adjusts charge parameters based on battery specifications and environmental conditions, thus effectively extending battery lifespan, and it is often applied in conjunction with Li-ion batteries by incorporating battery management units for enhanced control.

If multiple vehicles pass through the TC, the mechanism moves downward with the weight of a car, closing the switch and activating the power supply connection. The control mechanism determines the charging methodology, as shown in Algorithm 1.

Algorithm 1 EV Charging Methodology

1: If Vehicle present: SW1 closed. Detect the state of charge (SoC) or EVB voltage ($V_b$). 2: Then select the charging type, constant current (CC) or constant voltage (CV). 3: If $V_b<V_{b\left(rated\right)}$ (CC Mode): Charge with constant optimal charging current, $I_b$. Supply the corresponding voltage $V_s$ from the source. Compute Duty cycle. 4: Else if $V_b=V_{b\left(rated\right)}$ (CV Mode): Charge with constant optimal charging voltage. Supply the corresponding current $I_b$ from the source. Compute Duty cycle.

5. Wireless System Design

To assess the proposed DWC methodology, it was used to charge moving EVBs using a multi-supply station system mainly containing PV units and batteries supported by a utility network in emergency situations. The resonant coupling required for WPT was introduced on the basis of the resonant-mode coupling effect and magnetic-field coupling using a two-element system of spiral resonators. The station components were designed to be installed along a roadside with a 1 km length to charge EVs simultaneously for a specific 50 kW to satisfy a 500 km cutting distance at optimum EV operation. Two hundred TC coils were distributed considering a 5 m distance between any two adjacent coils along the charging lane. The application was implemented in three phases. The first phase was to design the TC and RC in addition to selecting the best operation resonant frequency to minimize switching losses, EMI component size, and cost while maximizing efficiency. The second phase involved designing the station elements’ capacity. The third phase involved the analysis of the operation of the proposed system under different scenarios; when EV speed changed, the number of cars simultaneously increased, and charging EVBs and station loads occurred either by clean energy “PV–batteries” or by utility grid, and the energy management between the PV–battery system and the utility grid was also investigated.

Identifying TC RC and Resonant Frequency

In this application, the spiral coil was used with a 0.05 mm inner radius and 0.15 mm outer radius and then applied to the pdetool by its boundary points. The generated mesh from pdetool described by points and triangles was exported, as shown in Figure 8. The resulting number of turns of TC and RC was 6.25 turns. For each step, when increasing one more turn and starting with one turn, the spiral TC and RC impedance rates were estimated, and the corresponding resonant frequency was evaluated. Since the spiral coil is a magnetic resonator, a Lorentz-shaped reactance is expected and observed. The best resonant frequency for each step was identified by studying the effect of changing frequency around the pivotal frequency, which is normally taken as 30 kHz, as in Figure 9. The frequency range in this study was from 27 up to 32 kHz. The best resonant frequency was obtained with a value of 29.5 kHz, as indicated in Figure 9. Also, it can be observed that the reactance is highly affected by changing frequency. The reactance at which resonant frequency occurred was 2200 Ω.

The custom antenna mesh was utilized to import the mesh. The feed was created at the inner circle of the spiral mesh. The dominant magnetic field component of this resonance was strongly localized and observed, as shown in Figure 10. To maximize the WPT efficiency, two identical resonators were selected for the transmitter and receiver coils and modeled as a linear array at a specific distance, as shown in Figure 11.

This study investigated system efficiency by varying operating frequency and the coupling strength between the transmitter and receiver resonators through the analysis of the $S_{21}$ parameter depicted in Figure 12 and Figure 13. Increasing proximity between the two resonators led to higher coupling adjusted by modifying the element spacing within a range from half to one and a half times the spiral dimension (twice the outer radius). Consequently, system efficiency improved with reduced transfer distance until reaching the critical coupling threshold. Peak efficiency was achieved when the system operated at its resonant frequency with strong coupling between the resonators, even when they were over-coupled above the critical threshold.

6. Experimental Validation

In order to validate the results of the proposed system and confirm its capability to adapt the hardware, experimental validation was conducted. The experimental setup utilized in the Egypt–Japan University of Science and Technology (E-JUST) laboratory to validate the proposed solutions in this study is illustrated in Figure 14. The real-time operation of the microgrid model under investigation was achieved using the OPAL RT-4510 unit. Designing a wireless EV charging prototype using OPAL-RT 4510 involved integrating simulation hardware with WPT technology to develop an efficient and scalable EV charging system. The OPAL-RT 4510 is a real-time simulation and testing platform widely used for power systems, power electronics, and control system applications, making it an ideal choice for testing and optimizing wireless EV charging systems.

Figure 15 depicts a wireless electric vehicle charging system using a combination of MATLAB/Simulink simulation and hardware components integrated via the OPAL-RT platform. This setup provides a hardware-in-the-loop (HIL) environment to simulate and test various components, including power generation, power conversion, and wireless power transfer.

The detailed flow of the system is as follows:

• Power Generation (MATLAB/Simulink):

  –

  Power is generated either from a simulated PV model or from the electrical grid, depending on the scenario illustrated in Figure 3.

  –

  This power is managed by a DC-DC converter that controls the voltage and current supplied to the battery system.

• Station Battery (MATLAB/Simulink):

  –

  A simulated battery in the station stores energy and supplies it to the vehicle for charging.

  –

  This battery either charges from the grid/PV source or directly provides energy to the vehicle’s system as needed.

• OPAL-RT (HIL Interface):

  –

  The energy from the PV/grid simulation and station battery is transferred via Line 1 to the OPAL-RT platform for real-time processing.

  –

  OPAL-RT sends this power through Line 2 to the station’s high-frequency inverter (hardware) with a frequency of 29.5 kHz (computed from the design in Section 5) to convert DC to AC at a high frequency. This inverter is an actual hardware component responsible for generating the required AC power for wireless power transfer.

• Transmitting Coil and Receiving Coil (MATLAB/Simulink + Hardware)

  –

  The high-frequency AC power is transmitted back to the OPAL-RT platform via Line 3, which processes and sends the signal to the transmitter coil (simulated in MATLAB/Simulink) through Line 4.

  –

  The transmitting coil generates an alternating magnetic field used to transfer power wirelessly to the vehicle’s receiving coil.

  –

  The receiver coil on the EV side captures the magnetic field generated by the transmitting coil and converts it back into AC power.

  –

  This power is sent to OPAL-RT through Line 5, where it is processed and routed to the EV rectifier (hardware) through Line 6.

  –

  The sending and receiving coil designs are described in Section 5.

• EV Rectifier (Hardware):

  –

  The EV rectifier (hardware) is responsible for converting the high-frequency AC power received from the OPAL-RT system back into DC power, suitable for charging the vehicle’s battery.

• EV Battery (Hardware):

  –

  The rectified DC power is then supplied to the EV battery via Line 7, completing the charging process.

7. Operation of the Proposed System

7.1. Design of Station Elements Capacity

The system was initially configured with a 50 kW load, and for this specific design, a crystalline PV module from the CHSM6612p series, Astronergy Co., Edmonton, AB, Canada was chosen. By utilizing mathematical expressions from Equations (7)–(10) and assuming $V_{DC}=300$ V, it was calculated that a total of 56 cells were needed. These cells were configured in seven units in series and eight units in parallel. For the specific battery chosen (DC260-12 8D 12V 260Ah AGM sealed lead acid battery, Full River Group Co., Camarillo, CA, USA) with a discharge coefficient ($M_d$) of 0.75, and in line with Equations (12)–(16) and (20), batteries were connected in series. The designated charge controller (Xantrex C60 charge controller 60A 12/24V C60, XANTREX, Elkhart, IN, USA) was selected. Following Equations (17) and (18) and with a safety factor (F) of 1.25, four controllers were linked in parallel for operation. Figure 16 provides a visual representation of the PV energy produced.

7.2. Dynamic Charging Performance

The operation of the proposed system was tested by applying two cases. In the first case, one car was charged while running at different speeds: 45, 60, and 75 km/h. The second case involved two cars that were charged simultaneously while running at the same speed, 45 km/h. The behavior of the system parameters was determined in terms of the sending and receiving power battery voltage; current DC link voltage; current roadside winding voltage; current vehicle side winding voltage and current; consumed active and reactive power source voltage and current; and finally, car battery state of charging. The station performance results are presented in Figure 17, Figure 18, Figure 19, Figure 20, Figure 21, Figure 22, Figure 23 and Figure 24 for a car speed of 45 km/h. Finally, the station analysis results for a single car with speeds of 60 and 75 km/h in addition to two cars are provided in

Table 3. Station statistic.

Parameters	Single Car (60 km/h)	Single Car (75 km/h)	Two Cars (45 km/h)
Source
Voltage (V)	370	370	370
Current (A)	50	50	95
Active power (W)	5400	5400	10,000
Reactive power (Var)	2200	2200	4000
Dc link
Voltage (V)	275	275	275
Current (A)	19	19	38
Road converter
Voltage (V)	400	400	550
Current (A)	32	32	32
Vehicle converter
Voltage (V)	380	380	400
Current (A)	30	30	42
SOC charging %	2.5	1.8	3.6
Vehicle Battery
Voltage (V)	380	380	380
Current (A)	13	13	13
Receiving Power (W)	4900	4900	4800

.

7.3. Results and Observations

The experimental results confirmed the findings from Section 5, demonstrating that the proposed DWC system could reliably transfer power to moving EVs with high efficiency. The key results from the experimental validation are summarized as follows:

• Power Transfer Efficiency (PTE): The PTE achieved during testing exceeded 90.7%, which was consistent with the theoretical predictions. This was maintained even with slight misalignments in the receiver coil, thanks to the optimized coil design and frequency tuning.
• State of Charge (SOC): In the single-EV tests, the SOC increased by approximately 3.6% over a 1 km stretch at a speed of 45 km/h. At higher speeds, the SOC increase was slightly lower, reflecting the reduced time spent in the charging zone. However, the charging efficiency remained above 90%.
• Coil Misalignment and Compensation: The novel coil design proved effective in mitigating the impact of misalignment between the transmitting and receiving coils. The adaptive compensation circuit maintained resonance, ensuring minimal power loss during misalignment.
• Multiple EV Charging: In the simultaneous charging test, the system successfully charged two EVs with minimal interference between the transmitting coils. The SOC of both vehicles increased by approximately 3.6% over the 1 km stretch, validating the system’s scalability.
• Validation of Model Predictions: The experimental tests validated the model predictions made in Section 5. The real-time testing demonstrated that the coil design and operating frequency (29.5 kHz) were optimal for the intended application, achieving high efficiency even under varying operational conditions. Additionally, the integration of renewable PV power and battery storage was shown to be effective in supporting dynamic wireless charging without reliance on the main grid, except in backup scenarios. Overall, the experimental validation confirmed that the proposed system is not only theoretically sound but also practically feasible, offering a scalable solution for the future of dynamic wireless charging of electric vehicles.

8. Conclusions

This manuscript presented a new technique for dynamically charging EVs running along a lane supplied mainly by adaptive renewable PV units supported by batteries and backed up by the main electric network. TCs and RCs were designed via multiple segments of magnetic resonant coupling distributed along the lane to obtain the best power transfer efficiency. The required PV array unit sizing, station battery sizing, EVB sizing, and the resonant frequency were designed. To verify the proposed strategy, it was applied to simultaneously charge EVs for 50 kW for a lane with 1 km as a sample and to satisfy a 500 km cutting distance at optimum EV operation. The best number of turns of TC and RC were 6.25 turns generated by pdetool with a 0.05 mm inner radius and 0.15 mm outer radius. The obtained best resonant frequency was 29.5 kHz with a reactance of 2200 ohms. The maximum WPT efficiency was achieved at the resonant frequency. The required PV unit was calculated as 56 cells; seven units were connected in series as one string, and eight strings were connected in parallel to produce 300 VDC. The station batteries were calculated as 12v 260AH each. The operation of the proposed system was tested using two cases: one with the EV running at three different speeds (45, 60, and 75 km/h) and the second by charging two EVs simultaneously running at 45 km/h. The behavior of roadside parameters was analyzed, which ensured the effectiveness of the proposed system. The EVB was charged with about 3.6% along a lane of 1 km with a car speed of 45 km/h. It should be noted that this can be increased by increasing lane distance and/or by increasing the TC and RC, which will be our future research challenge. Finally, experimental validation was employed and the integration of renewable energy sources ensured that the system operated sustainably, offering a scalable and cost-effective solution for future EV infrastructure. Future work will focus on extending the charging lane distance, improving coil arrangements, and enhancing system efficiency while reducing operational costs.