On-Road Wireless EV Charging Systems as a Complementary to Fast Charging Stations in Smart Grids

Abstract

Electric vehicle (EV) users have the flexibility to fulfill their charging needs using either high-speed charging stations or innovative on-road wireless charging systems, ensuring uninterrupted travel to their destinations. These options present a spectrum of benefits, enhancing convenience and efficiency. The adoption of on-road wireless charging as a complementary method influences both the timing and extent of demand at fast-charging stations. This study introduces a comprehensive probabilistic framework to analyze EV arrival rates at fast-charging facilities, incorporating the impact of on-road wireless charging availability. The proposed model utilizes transportation data, including patterns from the US National Household Travel Survey (NHTS), to predict the specific times when EVs would need fast charging. To account for uncertainties in EV user decisions concerning charging preferences, a Monte Carlo simulation (MCS) approach is employed, ensuring a comprehensive analysis of charging behaviors and their potential impact on charging stations. A queuing model is developed to estimate the charging demand for numerous electric vehicles at a charging station, considering both scenarios: on-road EV wireless charging and relying exclusively on fast-charging stations. This study includes an analysis of a case and its simulation results based on a 32-bus distribution system and data from the US National Household Travel Survey (NHTS). The results indicate that integrating on-road EV wireless charging as complementary to fast charging significantly reduces the peak load at the charging station. Additionally, considering the on-road EV wireless charging system, the peak load of the station no longer aligns with the peak load of the power grid, resulting in improved power system capacity and deferred system upgrades.

1. Introduction

Electric vehicles (EVs) have emerged as critical components of sustainable transportation, driven by increasing environmental concerns and the transition away from fossil fuels. The effectiveness and accessibility of EV charging infrastructure are pivotal to facilitating the widespread adoption and acceptance of this technology. Among the charging options available, plug-in and wireless charging have gained prominence due to their complementary benefits. Plug-in charging, which involves a physical connection between the EV and a power source, is favored for its faster charging capabilities, particularly in the case of DC fast charging. In contrast, wireless charging offers enhanced convenience by eliminating the need for cables and utilizing electromagnetic induction to transfer energy from a ground-installed charging pad to an EV’s receiver.

The dynamic nature of EV charging demand, coupled with the need to optimize power grid operations, necessitates innovative approaches to infrastructure planning. This challenge is compounded by variability in EV usage patterns and user preferences. Traditional plug-in charging stations have been the cornerstone of EV infrastructure, yet they impose significant load demands on the power grid, especially during peak hours. The introduction of on-road wireless charging systems offers a potential solution, providing supplementary energy to EVs in transit and reducing reliance on stationary charging points. This dual-charging approach not only mitigates grid stress but also enhances the flexibility and usability of EVs.

The charging of electric vehicles (EVs) and its implications for the electrical grid have been extensively studied. Several studies have proposed stochastic models and planning approaches to address various aspects of EV charging and grid integration. Salman Habib et al. [1] presented a framework for evaluating the risks associated with integrating EVs into residential distribution networks (RDNs). They emphasized the importance of managing voltage behavior, imbalances, system losses, and thermal transformer limits for stable and reliable RDN operation. The design of large EV charging sites and their role in promoting EV adoption were discussed in [2], wherein a stochastic model was proposed to generate realistic EV arrival patterns and power demand profiles, which can aid in operational decisions, collaboration with grid operators, and investment choices. A two-stage stochastic programming model was introduced in [3] to design a public EV charging station network in a community, considering uncertainties related to various factors. The developed model showed that increasing the number of charging stations improves accessibility but reduces utilization, with implications for policy decisions. Tao Shun et al. [4] proposed a method for analyzing EV charging demands using the stochastic simulation of trip chains. The method provides valuable insights for planning charging demands and optimizing power system infrastructure. A stochastic approach using Monte Carlo simulation was proposed in [5] to estimate the load demand of a fleet of domestic plug-in electric vehicles (PEVs). The developed approach has utility for distribution system planning, load management, probabilistic load flow analysis, and infrastructure sizing. The authors of [6] presented a two-stage stochastic programming model to optimize charger allocation and EV flow distribution, which outperformed existing methods in simulations on Massachusetts highways. Lingwen Gan et al. [7] proposed a decentralized algorithm for optimal EV charging, utilizing elasticity and formulating it as an optimal control problem, ensuring convergence to optimal profiles irrespective of EV specifications. Partition-based random routing, as a flexible routing policy for EV charging systems with stochastic demand, was proposed in [8] to effectively reduce response time and adapt to different charging demand dynamics. The aggregated load profile of a fast-charging station (FCS) for EVs was modeled in [9], considering factors like traffic flow and EV efficiency using Monte Carlo simulation and real-world data from a Norwegian FCS. The authors of [10] investigated using parked EVs in parking lots as grid energy storage, proposing a stochastic model to assess various EV behaviors and their potential as energy resources for the grid. A stochastic planning model was developed in [11] for an EV charging station that integrates distributed energy sources to minimize the station’s total cost, considering uncertainties in EV charging demand and PV power generation. These studies have collectively contributed valuable insights into the challenges and opportunities related to EV charging and its integration into the power grid, providing a foundation for future research and policy decisions in the field. However, wireless charging of electric vehicles obviates the necessity for physical cables and connections. This system involves a charging pad set up within a parking area or other selected location and a receiving pad integrated within the electric vehicle. When an electric vehicle is placed above a charging pad, energy transfer occurs wirelessly through electromagnetic induction. At present, wireless charging is less efficient in terms of speed compared to traditional plug-in methods and is primarily utilized for supplementary charging in locations like homes, parking areas, or while the vehicle is in motion. Factors such as the availability of wireless charging infrastructure and the specific capabilities of the vehicle influence the choice between wireless and plug-in charging. While plug-in options, including DC fast charging, are optimal for quickly replenishing energy during long trips, wireless charging offers a practical and convenient solution for frequent, incremental energy replenishment at designated points.

Wireless charging of electric vehicles is a relatively new technology, and its history can be traced back to the early 21st century. In 2006, the Massachusetts Institute of Technology unveiled a prototype of a wireless charging system for electric vehicles that used magnetic resonance coupling to transfer power without the need for physical contact. In 2010, the company Evatran, now known as Plug-less Power, launched a wireless charging system for electric vehicles called the Plug-less L2 System. The system used inductive charging technology to wirelessly transfer power to an electric vehicle’s battery, and it was available for the Nissan Leaf and Chevrolet Volt. Since then, several other companies have entered the market with their own wireless charging systems for electric vehicles, including WiTricity, HEVO Power, Momentum Dynamics, and Qualcomm. Wireless charging technology for electric vehicles has also been tested in several pilot projects and demonstration programs around the world, including in Germany, the United States, and South Korea. These projects have focused on testing the technology’s efficiency, safety, and reliability, as well as its impact on the grid and the environment. While wireless charging technology for electric vehicles is still in its early stages of development, it has the potential to greatly simplify the charging process for electric vehicle owners and improve the overall convenience and accessibility of electric vehicle charging. Within the context of studying wireless charging for electric vehicles and its role in reducing the pressure on the electrical grid, many researchers have directed their focus toward understanding this role. Several studies have addressed these challenges and proposed models and frameworks to optimize EV charging. Researchers studying wireless charging cover various aspects of dynamic wireless power transfer (DWPT) systems for electric vehicles (EVs) and their potential impact on EV charging infrastructure and efficiency. In [12], the design parameters of grid-tied and PV-integrated DWPT systems for EVs were presented and discussed. Aqueel Ahmad et al. [13] presented a comprehensive review of wireless charging technologies for EVs, including conductive and wireless charging. They addressed technical aspects, challenges, and opportunities, as well as sustainability and safety implications. They identified research gaps and future directions, including vehicle-to-grid applications. A review of dynamic wireless charging methods for EVs was presented in [14], highlighting the potential to overcome range anxiety and reduce battery size. The authors of [15] addressed the challenges and developments in designing wireless charging pads for DWPT systems in EVs. They focused on CO2 emission reduction, battery capacity, and safe charging infrastructure. Different magnetic resonance coupling topologies and in-motion testing have also been explored. Emrullah Aydin et al. [16] compared the coupling coefficients of different coil structures for WPT system design and analysis. They highlighted the advantages of using hexagonal coil shapes for improved power transfer efficiency, reduced misalignment effects, and potential for EV applications. A dynamic wireless power transfer system was presented in [17] for light-duty EVs, using multiple power transmission sectors in parallel with a single inverter circuit to reduce power loss and cost. The efficiency of power transfer and gap variations have also been investigated. The implementation and experimental characterization of a prototype WPT charging infrastructure within the FABRIC project were presented in [18], covering extensive tests and system characterization, technical and economic challenges, and potential applications in urban areas. A scheme was proposed in [19] to adjust coil alignment by moving the receiver coil in response to the magnetic field of the transmitter coil, ensuring optimal power transfer efficiency for wireless charging systems. The potential of wireless charging systems was reviewed in [20], based on magnetic inductance and resonance principles to address EV charging infrastructure challenges and provide convenience and flexibility. The authors of [21] provided an overview of wireless power transfer technology, particularly resonant inductive wireless charging, for driverless EVs. They discussed various types of inductive pads, compensation technologies, and challenges for efficient deployment. The impact of coil misalignment on the efficiency of EV wireless charging was investigated in [22], highlighting the need for an automated vehicle alignment system to eliminate misalignment issues during charging. Ehsan Jafari et al. [23] addressed the problem of online charging and routing for EVs in a network with stochastic and time-varying travel times. The authors proposed algorithms to minimize expected costs, considering travel time and charging costs. These research works provide insights into the progress, challenges, and potential solutions related to dynamic wireless power transfer systems for electric vehicles and highlight the importance of advancing wireless charging technology for the widespread adoption of electric mobility. As the deployment of EVs increases to address environmental concerns, it puts additional pressure on the electric grid. Controlling the EV charging process becomes necessary to alleviate grid pressure, lower energy costs, and reduce waiting times at charging stations. Additionally, given the different charging methods available, including plug-in charging and wireless charging, there is a need to study and predict charging loads, as well as their distribution in space and time, and to consider factors such as battery state of charge and economic aspects. A comprehensive understanding of these factors aids in designing an optimal charging process based on the predicted data.

Despite advancements in EV charging technologies, existing research has not comprehensively addressed the interplay between on-road wireless charging systems and conventional fast-charging stations. This glaring gap propels the introduction of a probabilistic framework aimed at estimating the rate of EV arrivals at an EV fast-charging station while factoring in the potential inclusion of on-road EV wireless charging as an alternative charging method within the distribution system. This paper makes the following significant contributions to the advancement of EV charging infrastructure and wireless charging systems:

• We introduce a probabilistic framework to estimate the arrival rates of EVs at fast-charging stations, considering the inclusion of on-road wireless charging systems. This framework leverages real-world transportation data to predict temporal charging patterns, which enhances the accuracy of planning charging infrastructure.
• We employ Monte Carlo simulation to address uncertainties in EV user behaviors and charging preferences. This approach enables a detailed exploration of various charging scenarios, providing insights into the dynamic interaction between on-road wireless charging and traditional plug-in stations.
• We develop a queuing model to estimate charging loads at stations under different conditions, both with and without on-road wireless charging. This model aids in understanding how wireless charging can alleviate peak loads, ensuring stability and efficiency in EV charging station operations.
• We propose the integration of solar photovoltaic (PV) power to support wireless charging systems, creating a sustainable and eco-friendly charging infrastructure. By demonstrating how wireless charging reduces peak demands and distributes loads more evenly, this study highlights its potential to enhance grid stability and delay costly system upgrades.

The structure of this study is outlined as follows. Section 2 presents the integration of on-road wireless charging as a supplementary option to conventional fast-charging stations. Section 3 explains the foundational concepts of wireless charging, deriving formulas to evaluate power transfer efficiency based on system characteristics. It also introduces an Electric Vehicle Decision Tree (EVDT) to estimate the timing and probability of EVs requiring fast charging using real-world transportation data. A Monte Carlo simulation (MCS) is applied to account for uncertainties in EV user charging preferences, offering a comprehensive analysis of charging scenarios. Furthermore, a queuing model is developed to assess charging demand at stations, considering scenarios both with and without on-road wireless charging. Section 4 investigates the influence of on-road wireless charging systems on the load distribution of rapid EV charging stations. Finally, Section 5 concludes with a detailed summary of the findings and implications derived from the research.

2. On-Road Wireless Charging as a Complement to Fast-Charging Stations

Figure 1 illustrates a dual-strategy charging approach for electric vehicles that integrates wireless charging as a supplementary method alongside fast charging. Employing Monte Carlo simulations, this study models the hourly charging requirements of EVs and proposes a synergistic system that merges conventional fast-charging techniques with a novel solar-powered wireless charging alternative. This strategy is designed to offer a versatile and eco-friendly charging solution that caters to the diverse needs of EV users throughout the day.

3. EV Wireless Charging Systems

EV wireless charging methods have emerged as a promising solution to streamline the charging process and increase comfort for EV owners. There are essentially three types of wireless charging techniques: inductive charging, resonant inductive coupling, and capacitive coupling.

3.1. Inductive Charging

Inductive charging is one of the earliest wireless charging techniques, dating back to the late 19th century when Nikola Tesla experimented with wireless power transfer. But it became popular in modern electric vehicles in the early 2010s. Inductive charging depends on electromagnetic fields to convey power from a transmitting charging pad on the ground to a receiving coil mounted on the vehicle’s undercarriage. Inductive wireless charging offers an effective way to charge EVs without the need for physical connectors. The charging pads can be installed in parking spaces or inserted in roadways, allowing for wireless charging while stationary or driving. Inductive charging can suffer from lower efficiency due to energy losses in the transfer process. Proper alignment between the charging pad and receiver is crucial for optimal performance, which may not always be achieved in real-world scenarios.

3.2. Resonant Inductive Coupling

Resonant inductive coupling was developed as an improvement over traditional inductive charging and gained attention in the mid-2010s. This technique uses resonance to enhance power transfer between the charging pad and the vehicle’s receiver coil. Resonance allows for the minimization of energy losses and the increase in charging efficiency by matching the frequencies of the two systems. Moreover, resonant inductive coupling offers increased misalignment tolerance between the charging pad and the EV’s receiver. Resonant inductive coupling is more suitable for commercial applications and high-power EVs since it offers faster charging rates. However, it also increases system complexity, leading to higher implementation and maintenance costs.

3.3. Capacitive Coupling

Capacitive coupling is the most recent addition to wireless EV charging techniques. It advanced significantly in the early 2020s. In this approach, the transfer of power occurs through electric fields. Charging occurs when the vehicle is parked over a charging plate, creating an electric field that transfers energy to the EV’s capacitive plates. A capacitive coupling charging system is lighter and more compact since it eliminates the need for physical coils. It is also highly efficient when properly designed, as it reduces electromagnetic interference. One of the main challenges of capacitive coupling is the relatively short range of power transfer compared to other wireless methods. Moreover, it requires precise alignment, which may pose difficulties during public charging scenarios.

Each type of wireless EV charging technique has unique limitations. Inductive charging offers simplicity but suffers from alignment-related inefficiencies. Resonant inductive coupling provides better efficiency and alignment tolerance but at the cost of increased complexity. Capacitive coupling, which is the most recent option, offers lightweight and efficient charging but with a limited range and alignment requirements. As technology continues to evolve, further advancements in wireless charging may address these limitations, making wireless charging an even more attractive option for the future of electric vehicles. In this paper, we adopt resonant inductive coupling as a wireless EV charging technique to complement existing fast-charging stations. The goal is to provide EV owners with a convenient and accessible charging option, especially when fast-charging stations are not readily available. By combining fast-charging stations with inductive coupling technology, we aim to create a comprehensive charging solution that caters to different needs and scenarios. Using wireless charging while parked helps manage electricity grid loads more efficiently, reducing peak demands. However, successful implementation requires careful planning and higher deployment costs, which may affect the feasibility and adoption of this approach. It is crucial to note that while resonant inductive coupling offers numerous benefits, it also poses certain challenges. The successful implementation of this technology necessitates meticulous planning and coordination to ensure the ideal positioning of charging pads and coverage areas. Moreover, the cost of deploying wireless charging infrastructure may be higher compared to traditional fast-charging stations, which could potentially impact the overall feasibility and adoption of this approach.

Design Equations for Resonant Inductive Wireless Charging Approach

Resonant inductive wireless charging is a method through which electric vehicles are wirelessly charged via electromagnetic induction and resonant coupling. It utilizes two main components: a charging pad or coil installed on the ground (transmitter), and a receiver coil mounted on the bottom of the EV (receiver). The basic principle of resonant inductive wireless charging involves the transmission of energy from the transmitter coil to the receiver coil through a process called electromagnetic induction. The resonance between the transmitter and receiver coils plays a crucial role in making resonant inductive wireless charging more efficient. By matching the frequencies, energy transfer is optimized, allowing for higher charging efficiency and longer charging distances compared to non-resonant inductive charging. Figure 2 shows the main components of resonant inductive wireless energy transfer, consisting of the transmitting and receiving coils, $L_p$ and $L_s$, and the two capacitors, $C_p$ and $C_s$, which are added to resonate with $L_p$ and $L_s$, respectively. $R_p$ and $R_s$ represent the ohmic resistances of the transmitting and receiving coils, respectively. $R_L$ represents the input resistance of the remaining charging circuit, comprising the rectifier circuit followed by the battery to be charged. $U_{in}$ and $I_p$ are the input voltage and current, respectively, while $I_s$ is the output current.

$$\left[\begin{array}{cc}{R}_p+j{X}_p& j\omega M\\ j\omega M& R_s+R_L+j{X}_s\end{array}\right]\left[\begin{array}{c}{I}_p\\ I_s\end{array}\right]=\left[\begin{array}{c}{U}_{\mathrm{in}}\\ 0\end{array}\right]$$

$$\left\{\begin{array}{c}{X}_p=\omega L_p-{\displaystyle \frac{1}{\omega C_p}}\hfill \\ X_s=\omega L_s-{\displaystyle \frac{1}{\omega C_s}}\hfill \end{array}\right.$$

$$\eta ={\displaystyle \frac{{\left(\omega M\right)}^2{R}_L}{(R_S+R_L)\left[R_P(R_S+R_L)+{\left(\omega M\right)}^2\right]}}\times 100\%$$

(1)

Table 1. Simulation data [25].

Description	Value
Self-Inductance (transmitting coil)/μH	238
Self-Inductance (receiving coil)/μH	77.5
Resonant Capacitor (transmitting side)/nF	14.7
Resonant Capacitor (receiving side)/nF	45.2
Frequency/kHz	85

gives the values of these parameters [25]. This circuit is treated as a two-port circuit, relating the input voltage and current to the load voltage and current, as shown in the figure below.

3.4. Mutual Inductance Between Two Air-Core Circular Coils with Lateral Misalignment and Axial Separation

Experimental outcomes pertaining to the mutual inductance between two air-core circular coils [26,27] serve as the foundation for developing a design formula that can be used to calculate or predict mutual inductance in similar setups. The formula for cases of lateral misalignment and axial separation is as follows:

$$\begin{array}{c}\hfill M\left(\mu H\right)=N_p^2{N}_s^2{a}^4\{-2.88\times {10}^{-2}{\left({\displaystyle \frac{d}{a}}\right)}^4+0.27{\left({\displaystyle \frac{d}{a}}\right)}^3-0.75{\left({\displaystyle \frac{d}{a}}\right)}^2+7.3200\times {10}^{-2}\left({\displaystyle \frac{d}{a}}\right)\\ \hfill +1.39\}\times \left\{0.27{\left({\displaystyle \frac{s}{a}}\right)}^4-3.18{\left({\displaystyle \frac{s}{a}}\right)}^3+14.28{\left({\displaystyle \frac{s}{a}}\right)}^2-29.10\left({\displaystyle \frac{s}{a}}\right)+23.73\right\}\end{array}$$

(2)

where $N_p$ is the number of turns of the transmitting coil, $N_s$ is the number of turns of the receiving coil, s is the axial separation between the transmitting and receiving coils (m), a represents the radius of the transmitting/receiving coils (m), and d is the lateral displacement between the two coils (m).

By employing these empirical findings, researchers and engineers can establish a comprehensive and practical approach to designing air-core circular coils with desired mutual inductance characteristics.

3.5. Formula to Calculate the Amount of Charge Received by an EV Battery While Driving over a Charging Area at a Constant Speed

This section introduces a formula to estimate the amount of charge transferred to an EV battery while traversing a charging area at a constant speed:

$$\mathrm{amount}\mathrm{of}\mathrm{energy}\left(\mathrm{kWh}\right)={\mathrm{coupling}\_\mathrm{factor}}_{\mathrm{lateral}}\times {\displaystyle \frac{P_t\times \eta \times Z\times n_s}{{10}^3\times u\times N_{\mathrm{EVs}}}}$$

(3)

where $P_t$ is the available power from a PV source at that time of the day (kW); Z is the length of one segment of a charging zone (m); u is the EV speed (km/h); $\eta$ is the coupling efficiency between the transmitting pads and EV receiving coils, ranging from 0.8 to 0.95, according to their axial separation, as described by Equation (1); $n_s$ is the number of charging segments energized by the same PV source; and $N_{EVs}$ is the number of EVs sharing the same charging zone simultaneously. ${\mathrm{coupling}\_\mathrm{factor}}_{\mathrm{lateral}}$ is a coupling factor representing the loss of received power due to lateral misalignment between the transmitting and receiving coils. It is equal to 0.5, which is the average value between fully aligned and fully misaligned coils.

3.6. Formula to Calculate the Amount of Charge Received by an EV Battery While Stopped at Traffic Lights

When an electric vehicle (EV) stops at traffic lights equipped with wireless charging infrastructure, it can receive a partial charge during the stationary period. This section presents a formula to estimate the amount of charge transferred to an EV battery while waiting at traffic lights:

$$\mathrm{Amount}\mathrm{of}\mathrm{Energy}\left(\mathrm{kWh}\right)=\left({\displaystyle \frac{P_t·\eta ·t_{\mathrm{stop}}}{60·N_{\mathrm{EVs}}}}\right)$$

(4)

where $t_{stop}$ is the stop time at the traffic light (in minutes).

3.7. Formula to Calculate the Amount of Charge Received by an EV Battery While Accelerating

For an EV accelerating from rest or decelerating until stopping, the amount of energy acquired by the EV’s battery is

$$\mathrm{Amount}\mathrm{of}\mathrm{Energy}\left(\mathrm{kWh}\right)={\mathrm{coupling}\_\mathrm{factor}}_{\mathrm{lateral}}\left({\displaystyle \frac{P_t·\eta ·t_{\mathrm{acc}}}{60·N_{\mathrm{EVs}}}}\right)$$

(5)

where $t_{acc}$ is the time taken by an EV during the period of acceleration, which is given by

$$t_{\mathrm{acc}}=\sqrt{\left({\displaystyle \frac{2Z{n}_s}{\mathrm{acc}}}\right)}$$

4. Load Modeling of EV Plug-In Charging Stations

The queuing model is used to describe the charging process of multiple plug-in electric vehicles (PEVs) at a fast-charging facility on a campus. By applying virtual depots and queuing theory using an M/M/c model, we can estimate the anticipated demand for charging electric vehicles [24,28,29]. At the charging facility, PEVs are treated as customers waiting in a queue, potentially experiencing wait times to charge their batteries. Based on previous research, the assumptions listed below are made regarding the operation of the facility. These assumptions allow us to model the charging process at the facility using the M/M/c queuing model. Moreover, to ensure a thorough analysis, the estimation of input and simulation data for this study incorporates the following factors and assumptions:

• The inter-arrival times of PEVs (time between arrivals) are independent and follow an exponential distribution, resembling a Poisson process, where the arrival of one PEV does not affect the arrival of another.
• The charging rates of PEVs per hour at the facility are independent and exponentially distributed, also resembling a Poisson process.
• Each Electric Vehicle Charging Facility (EVCF) can handle a maximum of 20% of the total projected number of plug-in electric vehicles (PEVs) on an average day. Four EVCFs collectively serve 80% of the estimated PEV population, with each EVCF accommodating a maximum of 20% of forecasted PEVs. The remaining 20% of PEVs are assumed to charge at alternative locations using Level-2 charging infrastructure.
• The typical hourly residential power consumption is estimated at 1500 kWh, translating to a calculated reference of 2.08 kW for overall electricity demand estimation.
• PEV population estimation, utilizing data from the National Household Travel Survey (NHTS), estimates the average number of vehicles per household at 1.9. Considering PEV penetration, the total number of households, and the average number of vehicles per household, this study calculates the number of PEVs for each year of the planning period.
• PEVs are designed to operate within an SOC range of 20% to 90%, resulting in a functional window of 70%. This range is chosen to balance optimal battery utilization with maintaining sufficient capacity for charging needs.
• The analysis assumes that PEVs are fully charged at home before commencing a journey, eliminating the need for additional charging during the trip, except for overnight recharging. Under this assumption, fast charging is treated as a supplemental option to regular home charging.
• This study leverages data from the National Household Travel Survey (NHTS), covering approximately 1,000,000 trips and 300,000 vehicles. To improve analytical precision, this study focuses on specific vehicle categories, including automobiles, sports utility vehicles, vans, and pickup trucks, while excluding incomplete data. Consequently, the refined dataset comprises 850,000 trips and 150,000 vehicles.
• For computational efficiency and relevance, vehicles traveling less than 20 miles in total daily distance (across all trips) are excluded from the analysis. These vehicles are considered to have a negligible impact on charging demand.

The stability of the queuing system [30] is ensured by maintaining the occupancy rate of fast chargers below one. The probability of a fast charger being in use is calculated by dividing the expected arrival rate of PEVs at the facility by the product of the number of available identical fast chargers and their charging rates. This relationship can be expressed mathematically as follows:

$${\psi }_k={\displaystyle \frac{{\lambda }_k}{c{\mu }_k}}\le 1$$

Using the above equation and the stability condition for a queuing model, the minimum number of fast chargers required to ensure a stable queue at the facility must satisfy the following inequality [31]:

$$c>{\displaystyle \frac{{\lambda }_k}{{\mu }_k}}$$

To estimate the expected number of occupied fast chargers, we use the probability of having a specific number, “n”, of discharged PEVs at the facility, as described by

$$P_{n,k}=\left\{\begin{array}{cc}{\displaystyle \frac{1}{n!}}{\left({\displaystyle \frac{{\lambda }_k}{{\mu }_k}}\right)}^n{P}_o\hfill & \mathrm{if}0\le n\le c-1,\hfill \\ {\displaystyle \frac{1}{c!c^{n-c}}}{\left({\displaystyle \frac{{\lambda }_k}{{\mu }_k}}\right)}^n{P}_o\hfill & \mathrm{if}n\ge c\hfill \end{array}\right.$$

where $P_o$ is defined by the following equation:

$$P_o={\left[\sum _{n=0}^{c-1}{\displaystyle \frac{1}{n!}}{\left({\displaystyle \frac{{\lambda }_k}{{\mu }_k}}\right)}^n+{\displaystyle \frac{1}{c!}}{\left({\displaystyle \frac{{\lambda }_k}{{\mu }_k}}\right)}^c{\displaystyle \frac{c{\mu }_k}{c{\mu }_k-{\lambda }_k}}\right]}^{-1}$$

To calculate the number of fast chargers in use when there are n discharged plug-in EVs, the smaller value between n and c, where c is the total number of chargers, is used. The expected number of active chargers, denoted as E[Z], is determined using the following formula:

$$E\left(Z_k\right)=\sum _{n=0}^{\infty }{P}_{n,k}min(n,c)={\displaystyle \frac{{\lambda }_k}{{\mu }_k}}$$

To estimate the charging station’s power demand, the average power output of each fast charger is multiplied by the expected number of occupied fast chargers:

$${\mathrm{PD}}_k^{\mathrm{EV}}=E\left(Z_k\right)·P^{\mathrm{AVG}}$$

By integrating these assumptions and factors into the research, a thorough examination of charging demand and Electric Vehicle Charging Facility (EVCF) design can be carried out. This approach considers a range of real-world variables and potential scenarios, enabling a comprehensive analysis. The proposed framework is implemented using the General Algebraic Modeling System (GAMS) [32].

5. Results and Discussions

5.1. EV Wireless Charging Systems as Complements to EV Plug-In Fast-Charging Stations

Figure 3 shows the number of electric vehicles (EVs) requiring plug-in charging stations over time, with and without complementary wireless charging systems. Without wireless charging, the demand for plug-in stations increases over time, with distinct peaks during certain hours, reflecting typical EV usage patterns. In contrast, the inclusion of wireless charging systems significantly reduces and stabilizes the demand for plug-in charging, effectively smoothing peak periods. This indicates that wireless systems can balance charging needs and alleviate pressure on plug-in infrastructure. The reduced reliance on plug-in stations highlights the potential for wireless charging to optimize energy distribution, lower operational costs, and minimize energy losses, contributing to greater overall efficiency. These findings suggest that adopting wireless charging systems can enhance the sustainability and scalability of EV infrastructure; however, further details on the technology, energy consumption, and system performance would provide a more comprehensive understanding.

The hourly load of EV plug-in charging stations over a 24-h period, with and without complementary wireless charging systems, is presented in Figure 4. Without wireless charging, the load on plug-in stations is significantly higher, especially during peak periods such as late afternoon and evening, reflecting concentrated demand. In contrast, the inclusion of wireless charging systems reduces the overall load and distributes it more evenly throughout the day, smoothing peak demand and alleviating strain on the plug-in infrastructure. This suggests that wireless charging systems play a critical role in balancing energy demand, enhancing grid stability, and improving infrastructure efficiency. The reduced peak loads highlight potential cost savings in infrastructure development and energy management, contributing to a more sustainable and scalable EV ecosystem. These results emphasize the importance of integrating complementary wireless charging solutions to optimize load distribution and support the growing adoption of EVs, while further research is needed to explore technology-specific impacts and user behavior.

Figure 5 shows the hourly EV wireless charging loads, considering three different EV sizes: EV20, EV40, and EV60, representing battery capacities of 6.51 kWh, 10.4 kWh, and 15.6 kWh, respectively. The load increases proportionally with fleet size, as higher adoption levels result in greater demand for wireless charging. Across all scenarios, the load displays a diurnal pattern, with peaks during active usage hours, likely reflecting typical driving and charging behaviors. EV20 exhibits the lowest load, indicating minimal strain on the wireless infrastructure, while EV60 shows significantly higher demand, suggesting that, as EV adoption grows, wireless charging systems will face increased pressure. These results emphasize the scalability of wireless charging systems and their potential to meet varying levels of EV adoption, while also highlighting the need for strategic planning to accommodate higher loads, particularly during peak hours, to ensure efficiency and grid stability.

It can be observed that the peak EV wireless charging load occurs at 5:00 PM, reaching a total of 408 kW, as illustrated in Figure 5. This peak highlights the critical demand period requiring efficient load management strategies to ensure system stability and performance. Two scenarios for EV wireless charging have been designed to effectively accommodate this peak load during the critical hour, as presented and discussed below.

5.2. EV Wireless Charging Systems at Traffic Lights

This section presents a wireless charging scenario in urban areas that takes advantage of the waiting times at traffic lights. Traffic flow at these intersections typically experiences stoppages lasting about 2 min. Additionally, vehicles undergo acceleration and deceleration of approximately 10 km/h/s as they approach and leave the lights. To enable wireless charging, transmitting coils are embedded in the ground, covering a horizontal distance of 150 m before and after the traffic lights. These coils create a wireless power transfer system, allowing electric vehicles (EVs) passing over them to charge their batteries seamlessly. The system design assumes a maximum 50 kW power output from a solar photovoltaic (PV) source, as referenced in [25,33]. The available power from a PV source at a traffic light throughout the day is shown in Figure 6. From this curve, we find that the PV source at 5:00 PM produces 16.25 kW due to solar irradiance conditions.

Based on this configuration, a single EV can receive up to 0.54 kWh of energy while passing through one set of traffic lights (Figure 7). Notably, the majority of the energy (0.51 kWh) is transferred while the vehicle is stationary. This total transferred energy represents approximately 8% of a battery with the lowest capacity considered in this study (6.51 kWh), 5.2% of a battery with a medium capacity (10.4 kWh), and 3.5 % of a battery with the largest capacity (15.6 kWh). The total energy transferred during a trip depends on the number of traffic lights encountered. This example demonstrates the potential for partial on-the-go charging, which can complement plug-in charging at dedicated stations. The ability to wirelessly deliver 0.54 kWh per traffic light provides a convenient and practical solution to extend vehicle range while reducing reliance on plug-in charging. The details of this scenario are summarized in

Table 2. First wireless charging scenario: At traffic lights.

Parameter	Value
Maximum power available from solar panels at each traffic light (kW)	50
Number of electric vehicles at each traffic light	1
Time at traffic light (minutes)	2
Acceleration before reaching and after leaving the traffic light (±10 km/h/s)	±10
Horizontal distance of wireless charging at each traffic light (meters)	2 × 150
Amount of energy transferred @ one traffic light per 1 EV @ noon (kWh)	0.54

.

5.3. EV Wireless Charging Systems on Highways with Heavy Traffic

The second proposed scenario targets highways prone to traffic congestion. In this setup, wireless charging infrastructure is installed in areas where vehicles are forced to slow down due to heavy traffic. For instance, with an average vehicle speed of 15 km/h over a 300-m-long charging zone, a single EV can receive 0.15 kWh of energy under these conditions (Figure 8), as detailed in

Table 3. Second wireless charging scenario: On highways with high traffic.

Parameter	Value
Maximum power available from solar panels at each section of high-traffic location (kW)	50
Number of electric vehicles passing and sharing this section	1
Horizontal distance of wireless charging at each high-traffic location (meters)	300
Average speed during high traffic (km/h)	15
Amount of energy transferred (kWh)	0.15

. This amount represents 2.3%, 1.4%, and 0.96% of 6.51 kWh, 10.4 kWh, and 15.6 kWh batteries, respectively. To enhance the energy transfer at such traffic locations, the system could increase the available power from the PV source or extend the charging zone length.

5.4. Comparison of Different Wireless Charging Scenarios

Both scenarios use solar-powered wireless charging technology to address the growing demand for efficient EV charging solutions. However, when infrastructure costs and PV power capacities are held constant, the energy transferred at traffic stops significantly exceeds that transferred in highway congestion zones. This is primarily due to longer interaction times at traffic lights, where vehicles remain stationary, allowing for more effective energy transfer. Wireless charging is a promising alternative to meet the charging needs of EVs, enabling significant portions of the charging to occur while the vehicle is in motion. Conversely, relying on high-traffic zones for wireless charging infrastructure is less economically efficient due to the lower energy transfer per vehicle. Therefore, urban traffic light scenarios provide a more viable and impactful solution for integrating wireless charging into EV infrastructure.

5.5. Wireless Charging Infrastructure Required

To assess the feasibility of installing wireless charging infrastructure near traffic lights, knowing that the maximum energy demand and capacity required to support electric vehicles (EVs) at peak hour (5:00 PM) is 407.8 kWh, we start by formulating the problem as follows:

• Each EV stopping at a traffic light for 2 min can receive approximately $0.54\mathrm{kWh}$ of energy via wireless charging.
• The traffic light cycle repeats every 2.67 min, meaning a vehicle can stop a maximum of

  $${\displaystyle \frac{60\min }{2.67\min }}\approx 22.5\mathrm{times}\mathrm{per}\mathrm{hour}\mathrm{at}\mathrm{the}\mathrm{same}\mathrm{traffic}\mathrm{light}.$$
• There is a 50% probability that an EV encounters a red light, enabling charging.

Taking this probability into account, the effective number of charging events per hour at one traffic light is reduced to

$$22.5\times 0.5=11.25\mathrm{charging}\mathrm{events}\mathrm{per}\mathrm{hour}.$$

The total energy transferred (assuming a single EV at one traffic light) in one hour is, therefore,

$$0.54\mathrm{kWh}/\mathrm{event}\times 11.25\mathrm{events}=6.1\mathrm{kWh}.$$

To meet the total peak energy demand of $407.8\mathrm{kWh}$, the number of charging locations required at traffic lights is

$${\displaystyle \frac{407.8\mathrm{kWh}}{6.1\mathrm{kWh}}}\approx 67.$$

Thus, approximately 67 traffic lights equipped with wireless charging infrastructure would be required to meet the maximum energy during peak hour.

6. Conclusions

This research provides a comprehensive evaluation of on-road wireless charging systems as a complementary solution to traditional plug-in fast-charging stations for EVs. By introducing a probabilistic framework, this study models the dynamic charging behaviors of EV users, leveraging real-world transportation data and Monte Carlo simulations to address uncertainties in user preferences. The developed queuing model effectively estimates the impact of wireless charging on load distribution at EV charging stations, emphasizing its potential to alleviate peak loads and enhance grid stability. The findings demonstrate that integrating wireless charging systems significantly reduces the strain on plug-in infrastructure by distributing charging demand more evenly throughout the day. This synergy enhances the scalability and sustainability of EV ecosystems, mitigating the need for costly grid upgrades. Wireless charging scenarios at urban traffic lights and on highways showcase the practicality and adaptability of this technology, substantiating its role in fostering efficient and convenient EV charging solutions. This study contributes to the field of sustainable transportation and enhances our understanding of EV charging dynamics.