Analysis of resonant coupling coil configurations of EV wireless charging system: a simulation study

Abstract

Nowadays, internal combustion engine vehicles are considered as one of the major contributors to air pollution. To make transportation more environmentally friendly, plug-in electric vehicles (PEVs) have been proposed. However, with an increase in the number of PEVs, the drawbacks associated with the cost and size, as well as charging cables of batteries have arisen. To address these challenges, a novel technology named wireless charging system has been recently recommended. This technology rapidly evolves and becomes very attractive for charging operations of electric vehicles. Currently, wireless charging systems offer highly efficient power transfer over the distances ranging from several millimeters to several hundred millimeters. This paper is focused on analyzing electromagnetically coupled resonant wireless technique used for the charging of EVs. The resonant wireless charging system for EVs is modeled, simulated, and then examined by changing different key parameters to evaluate how transfer distance, load, and coil’s geometry, precisely number of coin’s turns, coin’s shape, and inter-turn distance, influence the efficiency of the charging process. The simulation results are analyzed and critical dimensions are discussed. It is revealed that a proper choice of the dimensions, inter-turn distance, and transfer distance between the coils can result in a significant improvement in charging efficiency. Furthermore, the influence of the transfer distance, frequency, load, as well as the number of the turns of the coil on the performance of wireless charging system is the main focus of this paper.

Keywords

electromagnetically coupled resonator / near-field power transfer / wireless power transfer (WPT)

Introduction

The transportation sector is considered as one of the largest consumers of fossil fuels worldwide; therefore, it can be considered as one of the most crucial players in mitigating fuel demand [¹]. To decrease depletion of the fuel reserves, researchers and engineering societies are intensively working on turning from internal combustion engine vehicles to hybrid electric vehicles (HEVs), electric vehicles (EVs), and hydrogen fuel cell vehicles (FCVs) [¹–³]. Wu et al. in Ref. [¹] state that EVs are relatively more effective and beneficial than FCVs in terms of efficiency, cost, and weight of battery. They require simpler charging stations than HEVs and produce zero emissions, while operation of HEVs is still associated with the trivial amount of pollution. However, despite this fact, there are still many drawbacks associated with EVs. The main one is the electricity storage technology [¹–³]. In fact, batteries commonly utilized in EVs have to meet the following requirements: high energy density, proper standard safety, low cost, and long lifetime.

References [¹–³] show that, lithium-ion batteries are considered as one of the most suitable options to be utilized and implemented in EVs since they have high energy efficiency, a wide range of operational temperatures, rapid charge capability, and relatively low self-discharge level. However, they require several hours for a single charge. Therefore, if a car is required to be charged immediately; complete battery charging might not be accomplished. On the other hand, frequent and incomplete recharging, i.e. the battery is partially charged, may decrease the life of the battery. Thus, in order to operate an EV without compromising its performance, it is required to plug the battery to the charging station for at least eight to ten hours, which in some cases is inconvenient or even impossible [²].

Another challenge posed by EVs is charging stations, or to be more specific, the charging cables. Research studies [¹,²] state that plug-in charging systems have disadvantages related to cables and connectors used. Precisely, they deliver higher power than typical household appliances, which, in turn, increases the risk of electric shock and human damage.

One of the solutions for the aforementioned assumed problem is the wireless power transmission (WPT) technology. A general diagram of a WPT charging system is shown in Fig. 1. The principle of wireless charging is based on inductive coupling, which has an interface created by the primary and the secondary windings of a two-port transformer [⁴]. The input power is converted into a high-frequency AC (HFAC) signal at the conversion stage, and transferred wirelessly to the side of the vehicle. The received HFAC is then converted into a DC signal by a rectifier and supplied to the battery [⁴].

For the past few years, there has been a great improvement in the field of the WPT technology. Mainly, WPT is utilized in applications such as radio frequency technology, near-field energy transfer, energy conversion, and management [⁵].

The following parameters are suggested to be of critical importance when a WPT system for the charging of the EV is designed [¹]:

(1) Power level: it will determine how long it will take to fully charge the battery;

(2) Maximum charging distance: the distance between the system and the vehicle has to be designed in accordance with the clearance of a typical EV to be charged;

(3) Efficiency: the efficiency of the WPT has to be comparable to that of the plug-in systems;

(4) Charging tolerance: the process of adjusting the vertical and horizontal position of a vehicle with respect to the charging equipment has to be relatively easy for a normal driver to park;

(5) Size and weight: the parts required for charging must be easily installable into a regular-sized vehicle.

With the implementation of wireless charging system, the drawbacks related to the wires, such as electric shocks in wet weather conditions and tripping hazards, are eliminated. However, this technology is currently inferior to the existing plug-in charging systems in terms of power transfer efficiency, energy transferring distance and charging time [⁵].

The objective of this paper is to simulate one of the existing wireless power transfer techniques, which can be employed for charging EVs and identifying measures to improve the efficiency and the performance of the system. The analysis is conducted in the ANSYS and MATLAB environments. The system under consideration is electromagnetically coupled resonator, which is widely used in wireless charging of EVs [⁶]. The following parameters have been studied and simulated in order to analyze their effect on the efficiency of the system: the distance between the transmitting and the receiving coils, the number of turns, the spacing between the turns, and the shape of the receiving coil. The novelty of this paper lies in using the values of the variable mutual inductance retrieved from ANSYS simulation in order to identify the efficiency of the general system via MATLAB.

Current state of the art

History

Over the last decade, WPT systems have become an integral part of the international technological agenda. They are widely used in medicine, space, and automotive engineering etc. According to the research studies [⁷,⁸], wireless power transfer system is defined as a foundation for energy transportation over long distances without using any transmission lines. Brown [⁸], divided the history of wireless power transmission systems into three main periods. The first period was associated with Maxwell and his equation, published in 1873 [⁸]. It proposed energy transmission in free space using electromagnetic waves. In 1888, Hertz experimentally proved Maxwell’s theory and the existence of electromagnetic radiation [⁸]. The second period was linked to the founder of alternating current electricity, Nikola Tesla, who proposed to use our planet as a conductor and transmit energy to any point on Earth wirelessly [⁸–¹²]. In 1896, he transferred microwave signals over 48 km, and during the period from 1891 to 1904, conducted several experiments using both inductive and capacitive coupling for energy transmission [¹³,¹⁴]. The last period of the WPT’s history started during the Second World War, when scientists tried to use parabolic reflectors to focus energy into a narrow beam [⁸]. In his study, Brown concentrated on that type of energy, which is harvested utilizing solar cells installed on satellites, and then “beamed” to Earth, where it is converted into DC power [⁸,¹¹]. The history of WPT, described in Refs. [⁸–¹³], showed that despite having one aim to transfer power wirelessly; researchers designed various experiments using a range of methodologies. This, in turn, yielded different results in terms of efficiency, transfer distance, and frequency. Nowadays, the WPT techniques are divided into two main groups according to the range of operation: far-field and near-field [⁸–¹³]. History shows that far-field ssystems are still poor in performance; they have low efficiency and low safety level, while near-field counterparts become more popular [¹²].

Far-field power transfer

Rankhamb and Mane [¹³], in their research study, stated that far-field WPT technique, commonly known as radiative, used beams of electromagnetic radiation to transfer energy from a source to a receiver. Using the far-field WPT approach, power could be transmitted over long distances, up to several kilometers. The transfer range, in this case, was much larger than the diameter of sending or receiving devices [¹⁵]. Generally, far-field transmission was performed using either micro-scale waves (purpose-designed antennas) or lasers (visible light) [¹³–¹⁷]. In Ref. [¹⁵], the authors declared that the dimensions of the system could be determined according to the distance between the receiver and the transmitter, the wavelength and the Rayleigh criterion. Rayleigh criterion, in turn, stated that any laser beam, radio- or microwave became weaker over the distance [¹⁵]. Therefore, the authors proposed to employ a larger transmitting antenna or a laser aperture, in order to make radiation more focused and avoid total diffusion of the beam [¹⁴].

Microwave power transmission

Microwave technique utilized focused microwave energy beam to transfer power [¹⁵–¹⁷]. The general process of transmission was divided into four main stages: conversion, transmission, reception and reversed conversion [¹⁵].

During the conversion stage, conventional energy was transformed into a microwave by a converter. After that, at the transmission stage, it was transferred using a transmitting antenna. The reception and reversed conversion stages were responsible for receiving and transforming the microwave back into conventional energy using rectifying antenna, most commonly known as rectenna. The realized conversion efficiency was equal to some 95% [¹⁶].

The authors of Ref. [¹⁵], highlighted that microwave systems were much more advanced than laser ones. Therefore, they were preferable in energy transfer applications. However, for the long-range power transfer, microwave systems required the use of large transmitting antennas, which were harmful to health due to high-intensity radiation [¹⁵].

Laser beam transfer

The transfer of energy via a laser beam was performed with the help of solar panels. The laser light was focused on a photovoltaic element, which converted the laser emission into electricity. The main advantage of the laser technology was the fact that it provided a non-divergent beam with high energy density. This, in turn, made it possible to use receiving antenna with a smaller diameter compared to the microwave rectennas of the same power rating [¹⁵]. However, this type of WPT was characterized by low efficiency, which peaked at 40%–50% [¹⁵,¹⁶]. This, in turn, meant that roughly half of the energy was dissipated during the transmission [¹⁵,¹⁶]. To achieve better performance, solar cells with higher efficiencies could be employed [¹⁵]. In addition, when utilizing laser beaming technique there was a possibility of damaging living beings, in case they accidentally stood on the way of the power transfer [¹⁵].

Near-field power transfer

Near-field power transfer utilized magnetic fields, created by the inductive coupling between coils [¹³]. Three methods were used in near-field applications, namely electromagnetic (EM) radiation, inductive coupling, and magnetic resonance coupling. One of the main advantages of these techniques compared to the far-field ones was the fact that near-field WPT emitted tolerable (for human body) amount of radiation and could be utilized without being harmful to people’s health [¹⁴–¹⁷]. That was the reason why near-field techniques were sometimes called “non-radiative” [¹⁷].

Electromagnetic radiation

A study by Shidujaman et al. [¹⁷] showed that EM waves formed during the process of emission by electromagnetic radiation could be used to transmit energy from a power source to a receiving antenna. This type of energy transfer could operate using both omnidirectional (more than one receiver) and unidirectional (one receiver) radiation modes [¹⁴,¹⁷]. Due to the small size of the receiver and small amount of power lost during the transmission, omnidirectional energy transfer was easier and more suitable for energy transfer than unidirectional [¹⁷]. However, due to the quick decay of the EM waves, the efficiency of the omnidirectional system fell with the increase in transferring distance. It was revealed that for distances close to 30 cm energy transfer’s efficiency becomes only 1.5% [¹⁵].

Inductive coupling

The working principle of inductive coupling or inductive power transfer (IPT) was based on a circuit assembled of two coils, which created magnetic fields to transmit energy between them [¹⁴,¹⁵,¹⁷]. The first energy transfer via inductive coupling was conducted in 1960, when the power was transmitted over animals’ chest walls [¹⁸]. The studies, described in Refs. [¹⁴] and [¹⁷], explained IPT as a generation of the varying magnetic field of the first coil over the second one. The efficiency of such system was quite poor and declined as the distance between the coils increased. Therefore, in order to enhance its performance, the secondary coil was commonly tuned at the operating frequency of the primary coil [¹⁴].

Magnetic resonance coupling

One of the greatest challenges of utilizing inductive coupling is that it has low efficiency at increased transfer distances. An alternative approach commonly known as magnetic resonance coupling aimed to overcome the drawback mentioned above [¹⁴,¹⁵]. This type of near-field energy transfer used an evanescent-wave coupling, which generated energy and transmitted it between two coils through the variation and oscillation of the magnetic field [¹⁴,¹⁵,¹⁷]. Due to the same resonant frequency, coils were strongly coupled with one another, which made them very efficient. Devices employing this technique demonstrated energy transmission efficiency peaking at 92.6% [¹⁴]. Moreover, this coupling could maintain a higher efficiency at longer distances compared to IPT [¹⁴]. In addition, magnetic resonance transfer could be applied to one transmitter and many receivers, which allowed charging several devices simultaneously [¹⁵].

Advantages and disadvantages of using WPT

Since WPT systems are considered as a replacement for wired ones, it is important to evaluate them, and determine what advantages and disadvantages they possess. According to Ref. [¹⁰], WPT systems presented more benefits than drawbacks, which made them very attractive for different applications such as solar power satellites, charging of EVs and robots, etc. Table 1 summarizes the advantages and disadvantages of WPT systems for EV charging applications.

Electric vehicle wireless charging

Figure 2 provides a general layout of a wireless charging system for EVs. It demonstrates that the system mainly consists of the receiving and transmitting coils, which are utilized to charge a car. The charging process commences with a power supply producing HFAC at the transmitting pad embedded into a parking lot. The pad, in turn, inductively transfers power to the receiving coil installed on an EV. The received power is then converted to DC by the electronics onboard the vehicle and supplied to the battery [¹¹].

According to Ref. [³], the main difference between a wireless charger and a wired one is the fact that a set of loosely coupled coils is used instead of transformers. The simplified coil and compensation network used for power exchange calculation are shown in Fig. 3.

Considering Fig. 3, a simplified form of power exchange between the coils can be obtained as per Ref. [³]:

(1)S_{\mathrm{12}}=-U_{\mathrm{12}}{I}_2^{*}=\omega M{I}_1{I}_2\sin {\phi }_{\mathrm{12}}-j\omega M{I}_1{I}_2\cos {\phi }_{\mathrm{12}},

(2)S_{\mathrm{21}}=-U_{\mathrm{21}}{I}_1^{*}=-\omega M{I}_1{I}_2\sin {\phi }_{\mathrm{12}}-j\omega M{I}_1{I}_2\cos {\phi }_{\mathrm{12}},

where I*₁ and I*₂ are the currents in the transmitting and the receiving coils, respectively; I₁ and I₂ are the root-mean square values of the currents flowing through the coils; U₁₂ and U₂₁ are the voltages induced by the transmitting coil into the receiving one and vice versa; S₁₂ and S₂₁ are the apparent power values transferred from the transmitting circuit to the receiving one and vice versa; j₁₂ is the phase difference between I₁ and I₂; M denotes the mutual inductance between the coils; and w represents the angular frequency.

So, the active power transfer between two coils (from Eqs. (1) and (2)) can be obtained as

(3)P_{\mathrm{12}}=\omega M{I}_1{I}_2\sin {\phi }_{\mathrm{12}},

while the total complex power will be given as [³]

(4)\begin{array}{l}S=S_1+S_2\\ =\mathrm{j(}\omega L_1{I}_1+\omega M{I}_2)I_1^{*}+\mathrm{j(}\omega L_2{I}_2+\omega M{I}_1)I_2^{*}\\ =j\omega (L_1{I}_1^2+L_2{I}_2^2+2M{I}_1{I}_2\cos {\phi }_{\mathrm{12}}\mathrm{),}\end{array}

where L₁ and L₂ stand for the self-inductances of primary and secondary coils, respectively; and S₁ and S₂ represent the apparent power flowing into L₁ and L₂.

By defining quality factors, Q₁ and Q₂, for the transmitting and receiving coils as Q₁= wL₁/R₁ and Q₂= wL₂/R₂, respectively, where R₁ and R₂ represent resistances associated with the corresponding coils, the transfer efficiency can be calculated using Eq. (5) retrieved from [¹⁹].

(5)\eta ={\displaystyle \frac{k^2{Q}_1{Q}_2}{{(1+\sqrt{1+k^2{Q}_1{Q}_2})}^2}}.

The term k is known as a coupling coefficient between L₁ and L₂. Equations (1)–(5) are the general equations, which are used to describe and quantify WPT systems. Currently, there are three types of wireless power transfer techniques used in EV charging, namely inductive, capacitive and microwave. They are classified according to the physical mechanisms they employ [²¹–²⁵]. A comparison between these wireless charging systems is provided in Table 2.

This study concentrates on analyzing the applicability of magnetically coupled resonators for the charging of the EV and testing of the influence of various parameters on the performance of the proposed WPT system.

Mathematical modeling

The electromagnetic resonant technique commonly employs two circuit topologies, namely two-coil and four-coil structures [⁶,²⁶]. The four-coil system consists of two resonant coils and two induction coils. This is performed to ensure that the power supply is isolated from the transmitting coil and the load is isolated from the receiving coil. The two-coil system, in turn, has only receiving and transmitting resonant coils. This makes the power transfer more efficient by eliminating intermediate inductive links. Thus, the two-coil system is simpler and more efficient in implementation considering wireless power transfer for the charging applications of the EV [²⁶]. Therefore, in this study, the research efforts are concentrated on the two-coil electromagnetic resonant circuit.

Compensation topology

To improve the efficiency of the power transfer in a resonant circuit, a pair of capacitors can be connected to the primary and secondary sides of the transformer [²⁷]. Considering the relative position of the capacitors with respect to the windings, four basic compensation topologies are typically distinguished in electromagnetic resonant WPT systems [⁶,²⁷–³¹]:

(1) Series – Series (S-S): both capacitors are connected in series with the transmitting and receiving coils;

(2) Series – Parallel (S-P): one of the capacitors is placed in series with the transmitting coil, while the other is connected in parallel with the receiving coil;

(3) Parallel – Series (P-S): one of the capacitors is connected in parallel with the transmitting coil, while the other is placed in series with the receiving coil;

(4) Parallel – Parallel (P-P): both capacitors are placed in parallel with transmitting and receiving coils.

Since the majority of the modern EVs use Li-ion batteries, characterized by the two stages of charging, namely constant current charging and constant voltage charging, respectively, it is extremely beneficial to use the S-S topology for the resonant circuit due to the fact that it acts as a constant voltage source [²⁸,²⁹].

Circuit theory analysis

Figure 4 exhibits a two-coil circuit for the proposed electromagnetic resonant WPT system.

To develop the mathematical model of the given system, a circuit theory is employed. Having considered the schematic in Fig. 4, V_S stands for the voltage source, which generates signals at an angular frequency equal to w = 2pf and R_S denotes its internal resistance. Capacitors C₁ and C₂ are the resonant capacitors. They are connected in such a way that the S-S topology presented in Ssection 4.1 is formed. The remaining elements are L₁and L₂, which stand for the self-inductances of the coils, R₁ and R₂ denoting the parasitic resistances of the coils, and R_L representing the active load [²⁰,³²].

Considering the proposed circuit and by applying Kirchhoff’s voltage law, the system of equations, that is, Eq. (6) can be derived [³³].

(6)\{\begin{array}{l}{V}_S=\left(R_1+j\omega L_1+{\displaystyle \frac{\mathrm{1}}{j\omega C_1}}\right)I_1+j\omega M{I}_2,\\ 0=j\omega M{I}_{\mathrm{1}}+\left(R_L+R_2+j\omega L_2+{\displaystyle \frac{\mathrm{1}}{j\omega C_2}}\right)I_2.\end{array}

In the resonant state, reactive terms jwL₁+ 1/(jwC₁) and jwL₂+ 1/(jwC₂) are equal to zero. Hence, Eqs. (7) and (8) can be obtained.

(7)I_1={\displaystyle \frac{(R_2+R_L)V_S}{R_1(R_2+R_L)+{\omega }^{\mathrm{2}}{M}^{\mathrm{2}}}},

(8)I_2={\displaystyle \frac{j\omega M{V}_S}{R_1(R_2+R_L)+{\omega }^2{M}^2}}.

Consequently, applying Eqs. (7) and (8), the equations for power and efficiency can be derived as per Ref. [³⁴].

(9)P={\displaystyle \frac{{(\omega M)}^2{R}_L}{{[R_{\mathrm{1}}{R}_L+R_{\mathrm{1}}{R}_{\mathrm{2}}+{(\omega M)}^2]}^2}},

(10)\eta ={\displaystyle \frac{{(\omega M)}^2{R}_L}{R_1{(R_2+R_L)}^2+{(\omega M)}^2(R_2+R_L)}}.

Mutual inductance term, which defines the strength of the coupling between the two coils, is represented by M, and can be obtained, as expressed in Eq. (11) [²⁴,³⁴].

(11)M=k\sqrt{L_1{L}_2},

(12)k={\displaystyle \frac{1}{{[{\mathrm{1+2}}^{\mathrm{2/3}}{(D/\sqrt{r_{\mathrm{1}}{r}_{\mathrm{2}}})}^2]}^{\mathrm{3/2}}}},

where D is the distance between the coils, while r₁ and r₂ are the radii of the transmitting and receiving coils, respectively [³³]. From Eq. (10) it can be stated that the efficiency of the system directly depends on the mutual inductance between the receiving and transmitting coils. Moreover, Eq. (11) states that M depends on the coupling coefficient, k, which in turn, according to Eq. (12) is directly proportional to the radii of the coils and inversely proportional to the distance between them.

Simulation study

ANSYS model

To estimate the mutual inductances and the coupling coefficients between the coils, the ANSYS software was employed. A 3D model, depicted in Fig. 5, of the two identical air-core planar coils situated at a variable distance apart, was created. The following geometry was applied to both receiving and transmitting coils:

(1) rectangular height: 8 mm;

(2) rectangular width: 6.4 mm;

(3) inner radius:225 mm;

(4) number of turns: 12;

(5) spacing between turns: 3 mm.

Considering Fig. 5, it should also be highlighted that the coils are situated one on top of the other and they are perfectly centered with respect to each other in the horizontal (XY) plain.

The simulation conducted includes four independent parametric studies with the following criteria:

(1) The distance between the coils was alternated in a range from 0 to 300mm with a step of 100mm;

(2) The number of the turns of coils was increased for both coils simultaneously from 5 to 15 in steps of 2;

(3) The spacing between the turns varied for both coils simultaneously in a range from 3 to 10 mm in steps of 2 mm;

(4) The receiving coil was changed to a D-shape.

Each case yielded a set of four parameters, namely the self-inductances L₁ and L₂ of the coils, the mutual inductance M, and the coupling coefficient, k. The results are presented in the Tables 3–6 in Section 6. In addition, some of the received parameters, e.g. M, k, etc., were used in the simulation study, which ultimately aimed to estimate the efficiency of power transfer.

Simulated model

To quantify and analyze the output current and voltage of the proposed WPT model demonstrated in Fig. 6 and consequently estimate its efficiency, the system was modeled and simulated in the simulator environment.

As it can be seen from Fig. 6, DC voltage is used as the input source. Then, the H-bridge inverter, presented in Fig. 7, is utilized to invert DC voltage into AC. R₁₁, L₁₁ and C₁₁ are the compensation resistance, self-inductance and capacitance, respectively, used to remove noises and condition the signal coming into the WPT system. Terms C₁ and C₂ are the series compensation capacitances of the transmitting and receiving coils, while R₁ and R₂ are the resistances of coils. In addition, L₁ and L₂ stand for self-inductances, and S₁, S₂, S₃, and S₄ are the switches of the H-bridge inverter. The following initial input parameters received from ANSYS and shown in Table 3, were used as the input for the proposed model: V_DC = 100 V, C₁ and C₂ = 155 nF, R_L = 10 Ω, self-inductances L₁ = 118.69 mH and L₂ = 118.76 mH, M = 47.991 mH, and k = 0.404. During the simulation, all parameters in the model were considered as constants, while the mutual inductance was alternated to see the corresponding reaction of the output current and voltage.

According to Eqs. (11) and (12), and taking into account the fact that the shape of the coils has been assumed constant, i.e. the radii does not change, only the distance between the coils has the influence on the mutual inductance in this study. Therefore, only one parametric study in the simulator environment, aiming to identify the response of the system to the change in the mutual inductance has been conducted.

Simulation results

ANSYS simulation results

ANSYS was employed in order to demonstrate how the mutual inductance and the coupling coefficient between the coils vary due to the change in distance between the coils, the number of turns of the coil, and the spacing between the turns. Tables 3–5 show the results of the parametric studies mentioned in Subsection 5.1.

Table 6 provides the results of a parametric study aiming to estimate the variations in mutual inductance and coupling coefficient with respect to the distance between the coils. However, it should be noted that for this experiment a D-shaped receiver was utilized instead of a circular one. The purpose of the experiment was to identify the influence of the shape of the receiver on the performance of the WPT system.

Simulation results

Using Eq. (11) and values of the mutual inductance and the coupling coefficient retrieved from Tables 3–5, the efficiency plots for different cases were produced using simulator, i.e., the output of the simulated parameters were utilized in a new simulator. In addition, the following typical realistic parameters were presumed: w = 2p× 85 kHz, R₁ = R₂ = 1.1 Ω, and R_L = 10 Ω. As a result, a set of plots depicted in Figs. 8–10 were obtained. Figure 8 shows the plot of efficiency alterations as a response to the change in distance between the receiving and the transmitting coils. The effect of increasing the number of the turns of the coil in the transmitting and receiving coils on the efficiency of the power transfer is displayed in Fig. 9, while Fig. 10 provides a correlation between the efficiency and various spacing values between the turns of the coil.

Discussion

It has to be noted that all the numerical conclusions and observations created in the simulation and discussed in the following section are valid only for the coil parameters indicated in Section 5.1. However, the trends presented are applicable for a general case of two-coil resonant WPT systems.

Having analyzed Tables 3–6, the following observations were made. According to Table 3, as the air gap between the transmitting and the receiving coils increases, both the coupling coefficient and the mutual inductance between the coils decrease.

That was technically expected by Eq. (11). Moreover, it is considered that the coils are “tightly coupled” only when k is greater than 0.5 [³⁵]. According to Table 3, the WPT system will be in the “tightly coupled” state when the distance between the coils does not exceed 10 cm. Therefore, to ensure reasonable coupling and, subsequently, high efficiency between the transmitting and the receiving coils, it is required to maintain a certain distance between them. Thus, a charging pad design should account for the adjustable air gap, in order to meet the requirements of the clearances of different EVs and at the same time maintain reasonable coupling between the coils.

The data obtained for the second case, when the distance between the coils is maintained at 10 cm, which corresponds to the tightly coupled regime in the previous simulation, while the number of turns for each coil is alternated, are presented in Table 4. It is demonstrated in Table 4 that with the increase in the number of turns, the coupling coefficient as well as the mutual inductance between the transmitting and the receiving coils increase. This behavior can be explained using Eq. (12), which states that with the increase in the radii of coils, the coupling coefficient and the mutual inductance also increase. Hence, it can be concluded that in order to get a strong coupling between the coils, it is advantageous to design wireless charging systems with the maximum possible number of coil turns. However, the economic feasibility of this approach is yet to be investigated. Moreover, incorporating coils with a larger number of turns into a vehicle will result in the increase in weight and alter the driving characteristics. Hence, these issues associated with the EVs with such systems onboard have to be further studied.

The correlation of the coupling coefficient and the mutual inductance values with respect to the change in spacing between the turns is shown in Table 5. Considering the increase in the gap between the turns of the coil, it is expected, that with the additional turn, the diameter of the circular planar coils expands. Hence, according to Eq. (12), the coupling coefficient between the coils is directly proportional to the radii of the coils. Therefore, when the gap between the turns widens, the radii of the coils increase, consequently the coupling coefficient, as well as the mutual inductance between the coils also rises. However, even though the radii of the coils expand, the changes in the coupling coefficient and the mutual inductance are minor. Table 7 provides the sensitivity analysis of Eq. (12) with respect to r₁ and r₂. It shows that even if the radii of both the transmitting and the receiving coils are increased by 9.3%, the coupling coefficient increases only by 2.41%. Therefore, it can be concluded that the variation of this parameter will play a minor role in the efficiency improvement.

Moreover, it can be observed that Tables 3–5 provide different values of the self-inductances of the coils, i.e. terms L₁ and L₂. For Tables 4 and 5, it has the theoretical explanation provided by Ref. [³⁵] that “when the number of turns and/or area of coils are increased or decreased, the self-inductance of coils will also increase or decrease” [³⁵]. The change in the distance, shown in Tables 3–6, should have no effect on self-inductances, since they are the intrinsic properties of the coil [³⁶]. However, small variations in the self-inductances can still be observed in Tables 3 and 6. This can be explained by a specific approach ANSYS environment employed in order to approximate and evaluate geometric models. The software used provides the results with a particular percentage of accuracy applied to them since the geometry modeled is not exact, but is assumed and approximated. Even though there is an uncertainty with regards to the values, they are still very accurate and are valid for the given study.

Finally, in order to analyze the influence of the shapes of coils on the performance of the WPT system, a D-shaped receiving coil was modeled and simulated next to a circular one. From the conclusions mentioned earlier, it is known that with the increase in distance between the coils, the mutual inductance, and the coupling coefficient of the system decrease. However, comparing Table 3, containing the data obtained using the circular receiver to the values in Table 6 produced by the D-shaped coil simulation, it can be noted that for the same distance between coils, two receivers having the same shape yields higher mutual inductance and coupling coefficient values than those having different shapes. Table 8 represents a comparative summary of these two cases. Thus, it can be concluded that it is important for a transmitter to be of an identical shape as the receiver to enable better coverage of the field and consequently better performance.

As per the main goal of the given study, it is also important to analyze the efficiency trends depicted in Figs. 8–10. As it was expected by Eq. (10), the efficiency directly depends on the mutual inductance of the coils. Considering Fig. 8, the maximum possible efficiency value obtained is approximately equal to 88%, when there is no air gap between the coils. Moreover, it shows that with the increase in the air gap between the coils, the efficiency of the system demonstrates a falling trend. As a result, it can be stated that the ideal operating distance between the coils varies from 10 to 15 cm, where the efficiency ranges from 83% to 85%. Therefore, since the largest transmitting distance, which results in an efficiency higher than 80 percent is equal to 15 cm, it is considered as a reference distance for further calculations.

Figure 9 provides the relation between the numbers of the turns of the coil and the efficiency of the WPT system. It shows that when the number of the turns of the coil increases, the efficiency line gradually rises until the point when the number of turns equals 12. Having reached that peak point, the efficiency of the WPT system stabilizes at that level. In practical terms, this means that there is a threshold, when adding one more turn to the coils will not significantly improve the efficiency of the system. Moreover, as it was discussed above, the additional coils will increase the cost of the WPT system, and the vehicle will become heavier, which will alternate its driving characteristics.

As it was mentioned previously, changing the space between the turns does not significantly affect the coupling coefficient and the mutual inductance. From Fig. 10, it can be observed that with the expansion of the distance between the turns, efficiency line gradually rises. Using Eq. (13), the surface area of the circular coil can be calculated, where R_out and R_in are the outer and inner radii of the coils, respectively.

(13)A\mathrm{=\pi (}{R}_{\mathrm{out}}^2-R_{\mathrm{inner}}^2).

Table 9 provides the results of area calculation, and it shows that even if the surface area of the coils increases by 29.6% due to the increase in spacing between the turns of the coils, the efficiency of the system increases only by 1.4%. Thus, the increase in spacing between the coils does not affect the efficiency significantly and can be used for fine-tuning the parameters of the system.

Figure 11 obtained using Eq. (10), shows the influence of the load connected to the system on its efficiency. As it can be observed, the efficiency rises with the increase in the load. It then reaches a peak point, which is followed by a gradual decline. Thus, the choice of the load is of extremely importance in determining the efficiency of the system.

Having conducted the experiments presented above, it is possible to identify the parameters of the WPT system corresponding to the highest efficiencies for each case. These parameters are presented in Table 10. Moreover, it is reasonable to insert them into a new ANSYS simulation in order to find whether the combination of the optimal parameters for separate cases will yield the highest efficiency. The experiment was conducted using the model in the simulator described in Section 5.2.

Using the combination of parameters obtained in Table 10, a new 3D model of air-core coils in ANSYS was created and a new mutual inductance was obtained to be equal to 68.785 mH. Hence, using Eq. (10), a new efficiency is obtained, as expressed in Eq. (14).

(14)\eta ={\displaystyle \frac{{(\omega M)}^2{R}_L}{R_1{(R_2+R_L)}^2+{(\omega M)}^2(R_2+R_L)}}={\displaystyle \frac{{\mathrm{(2\pi \times 85000\times 68}{\mathrm{.785\times 10}}^{\mathrm{-6}})}^2\mathrm{\times 25}}{1\mathrm{.1\times (1}{\mathrm{.1+25)}}^2+{\mathrm{(2\pi \times 85000\times 68}{\mathrm{.785\times 10}}^{\mathrm{-6}})}^2\mathrm{(1}\mathrm{.1+25)}}}\mathrm{=0}\mathrm{.903}

.

As it can be noticed from Eq. (14) the efficiency of the system slightly exceeds 90%, which is greater than any other efficiency output of the experiments conducted in this study. Thus, it can be concluded that the WPT system, which utilizes the optimal parameters of the geometry and transfer distance of the coils is the most efficient. In practical terms, this means that that both the EVs and their wireless charging stations need to be as flexible as possible in order to be able to adjust their parameters to a particular vehicle/charging unit.

In addition, it is possible to develop an algorithm to optimize all the parameters for WPT of EV in an automated mode; however, there are still some parameters, which need to be inserted by the operator. These parameters come from the manufacturer’s production limitations and constraints, and therefore the participation of the engineers in the optimization process at this point cannot be eliminated.

Conclusions

The main aim of this study was to identify what are the most efficient wireless techniques available today, what are the parameters influencing the efficiency of the wireless power transfer, and how can one combine them in order to achieve a better performance. This study revealed that out of the far-field techniques, represented by the microwave and the laser beam power transfer, and near-field techniques, represented by the electromagnetic radiation, inductive and resonance inductive coupling, the latter is the most promising technique in terms of power transfer efficiency. Thus, taking resonant inductive technique into consideration, a mathematical model of power transfer under this approach was created in order to identify the most important parameters influencing the power transfer efficiency of the system. These parameters include, but not limit themselves to the choice of compensation topology, which tune the circuit to a specific resonant frequency, the number of turns in the transmitting and receiving coils, the spacing between the turns as well as the transmission distance.

A simulation study was conducted in order to explore the geometry of the coils as well as subsequent change in the coupling coefficients and the mutual inductances between transmitter and receiver coils. In addition, a model aiming to estimate the change in the efficiency of the system related to the geometric change was employed. A set of four parametric studies was conducted. The first one aimed to analyze the influence of the transmitting distance on the efficiency of the WPT system. It was revealed that the efficiency reduces exponentially as the distance between the coils grows to infinity. The largest recorded efficiency, i.e. roughly 90%, was recorded at the distance of 0 cm between the coils, which is practically unrealistic for the case of EVs charging. For the distances, ranging from 10 to 15 cm, which correspond to the typical clearances of the modern EVs, the efficiency was estimated to be in a range of 80% to 85%.

The second parametric study explored the influence of the number of the turns of the coils, i.e. both that of the transmitter and that of the receiver, on the efficiency of the system. As predicted by the mathematical model, the increase in the number of the turns of the coils’ consequently leads to the increase in efficiency. However, it was revealed that there is a limit on the efficiency gain under this approach. In other words, it was found that after a certain number of turns, in the case of the given study it is 12, the efficiency of the system stabilizes and does not change significantly. In practice, this means that on the one hand, the greater number of the turns of the coils for the wireless charger of the EV is beneficial in terms of high efficiency, while on the other hand, there is a certain number of the turns of the coils that will potentially deliver the maximum efficiency of the system. In addition, this result is very insightful in terms of the economy of the system. In fact, it is possible to save the material while manufacturing the coils and make the system lighter without compromising its efficiency, if the optimal number of turns is identified.

Under the third parametric study aiming to examine the influence of the space between the turns of the coils on the efficiency of the WPT, it was concluded that the inter-turn distance in the transmitter and the receiver has a minor effect on it. Mathematically it was confirmed that expanding the spacing between the turns of the coils will increase their radii, which will positively affect the efficiency. Although, the simulation confirmed the prediction, the gain was not substantial. Precisely, it was calculated that by increasing the spacing between the turns of the coils by approximately 10%, the overall area of the planar transmitter would grow by at least 30%. Furthermore, the efficiency under these changes to the system will marginally increase by a factor of 1.4%. From the standpoint of practical implementation, there is no limitation in terms of scaling up the transmitting coils of the EVs chargers since they are typically embedded into a parking lot. However, there is a strict constrain to the receiving coil posed by the space available under a typical EV. This, in turn, means that although there is a possible gain in the efficiency offered by the given approach, it is relatively limited by the dimensions of the EV.

The present study also analyzed the case when the shapes of the transmitter and the receiver are not identical. This case was tested in the simulator by means of replacing a circular receiver by a D-shaped one. It was found that the wireless charging system employing a D-shaped receiver is characterized by a poorer coupling with the circular transmitter as compared to the system employing circular coils only. This, in turn, means that some of the energy as well as efficiency will be lost due to the mismatch in the shapes of the coils.

Having considered the abovementioned parametric studies, the wireless power transfer efficiency of the system under investigation did not exceed 85% for any of the cases. Thus, a combination of the parameters of the coils, resulting in the highest efficiency values under the previous studies, was utilized to create a new pair of transmitting and receiving coils. The new geometry was simulated and resulted in the efficiency of the WPT equal to approximately 90%. This, in turn, means that in order to improve the efficiency of the wireless charging system of the EVs, it is not enough to change one parameter at a time to achieve optimal performance. On the contrary, a set of parameters such as the shape of the coil, the number of turns, the desired transfer distance etc. should be delicately considered. All of the parameters mentioned above directly affect the efficiency of the system and its performance.

The future work includes, but not limits itself to conducting further study into the influence of coil parameters, such as shape (circular, wheel, D-shape), cross-section type (square, rectangular, circular), material type of the coils (aluminum, copper), and number of coils (3, 4, and etc.) on the efficiency of the WPT system. It should also be pointed out that the limitation of this research is in the optimization algorithm employed to calculate the efficiency of the system. In the given case, each isolated parameter was first considered and then selected manually, which in some case may be extremely laborious and subjective. However, a more detailed optimization study employing multiple variables simultaneously will be beneficial. Thus, it would be possible to apply more sophisticated optimization techniques such as genetic algorithms or ant colony optimization for the optimal efficiency improvement.

In addition, this research has not considered the impact of wireless charging system on human health, which can be a part of the future work on this topic. Finally, it is important to investigate the influence of other electromagnetic emitters on the performance of the given system as well as the means and measures to shield it from the undesirable interferences.

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