Critical Analysis of Simulation of Misalignment in Wireless Charging of Electric Vehicles Batteries

Abstract

The transition from conventional to electric transportation has become inevitable in recent years owing to the significant impact of electric vehicles (EVs) on energy sustainability, reduction of global warming and carbon emission reduction. Despite the rapidly growing global adoption of EVs in today’s electrical and transportation networks, energy storage in EVs, particularly in regards to bulky size and charging process, still remains a major bottleneck. As a result, wireless charging of EVs via inductively coupled power transfer (ICPT) through coupled coils is becoming a promising solution. However, the efficiency of charging EV batteries via wireless charging is hugely affected by misalignment between the primary and secondary coils. This paper presents an in-depth analysis of various key factors affecting the efficiency of EV battery charging. Finite element analysis (FEA) using Ansys Maxwell^® is performed on commonly used coil designs such as circular and rectangular coils under various misalignment conditions. In addition, various reactive power compensation topologies applied in ICPT are investigated and the behavior of each topology is observed in simulation. It is revealed that circular structures with S–S compensation topology show more robustness in misalignment conditions and maintain the desired efficiency for a wider range of displacement. A critical analysis of coil designs, compensation techniques and the combination of both factors is accomplished and conclusions are presented.

1. Introduction

Transportation accounts for a large percentage of global energy consumption and greenhouse gas emissions [1,2]. EVs are becoming more commercialized due to the global transition from internal combustion engine vehicles (ICEVs) to EVs. Studies suggest that the number of EVs is growing significantly due to their environment-friendly merits and high efficiency [3]. In this regard, batteries are considered as the heart of electric transportation [4,5]. Given that EVs essentially work on the basis of electricity, one vital issue is to address the challenges of charging the electric reservoir of the vehicles, namely, the batteries. Conventional conductive charging methods are still widely used; however, their drawbacks such as wiring, trip hazards, contact wear and risk of tearing [6,7] are motivating researchers to pursue the idea of wireless power transfer (WPT). Compared to conductive charging, wireless charging offers safer, more convenient and more robust power transfer [8,9]. In addition, wireless charging benefits from the advantages of automated charging processes [10], i.e., the charging process becomes driver-independent. In the 1990s, the idea of plug-in inductive charging was proposed [11,12,13,14,15,16,17], but the issue of plugging in the charger cable remained unsolved until early 2000s, when the idea of contact-less charging was significantly redeveloped [16]. Therefore, the design and production of efficient wireless charging methods became more vital.

Power is essentially transferred between two coils through the air medium [18] via the ICPT system. The coupling between the two coils is evaluated by measuring the coupling coefficient (k). The system is termed as tightly coupled if k > 0.5, and loosely coupled if k < 0.5 [19]. The efficiency of the charging process is affected by the coupling coefficient, which itself depends on the linkage flux and alignment between the coils [18,20,21,22]. Once displacement is applied to the relative position of coils, the linkage flux reduces, resulting in lower coupling and lower efficiency, and causing disturbance to the output power stability [23]. Numerous solutions have been proposed by scholars to improve the misalignment tolerance, e.g., enlarging the transmitter coil size or using multicoil structures rather than single coil systems [23,24,25,26], albeit at an extra cost. The tolerance of WPT system against displacement possess more importance in Dynamic wireless charging (DWC) systems than static wireless charging (SWC) due to higher vulnerability of efficiency against misalignment [27]. SWC refers to the wireless charging of an EV while the vehicle is stationary, such as at home or in office parking, whereas DWC refers to charging an EV while it is moving on the road, e.g., on highways. The emergence of DWC may revolutionize the EV industry by alleviating the energy storage issue, which is a critical bottleneck of today’s costly EVs [28]. The driving range of EVs can be extended by increasing the size and capacity of the batteries, but this increases the price of the product for the customer [29]. Thus, the idea of DWC could tackle the issue. Having said this, despite SWC being commercially feasible, DWC has not been commercialized yet due to its significant challenges [10]. As implied in [16], the investment cost of DWC may be as high as 10% of a highway lane. To solve the misalignment issue, Ahmad et al. investigated the reduction of efficiency due to misalignment by simulating different displacements applied to coils, and proposed the concept of an “automatic alignment receiver system” to address the problem by employing Hall effect sensors and electromechanical motors to adjust the receiver coil to the best possible aligned position [6]. However, this approach could make the charging process slow and mechanically complex [30]. Therefore, in order to achieve an efficient fast-charging system, it is necessary to have a highly misalignment-tolerant coupling circuit. One factor that affects the coupling between the two coils is the use of shielding in the couplers. Kushwaha et al. investigated variations of mutual inductance and efficiency of a WPT system with and without shielding in various types of misalignment [18]. The effect of shielding on the performance of the system depends on the structure of couplers, which will be elaborated on later in this paper.

Section 2 demonstrates a general classification of different misalignment types. Since the theoretical calculations of mutual inductance of coils under misaligned conditions are relatively complex [31], the behavior of a WPT system in misalignment is analyzed using finite element analysis (FEA) simulation with Ansys Maxwell^®, while the effect of coil shape on magnetic coupling is investigated in Section 3. Section 4 includes the analysis of power transfer efficiency under different compensation topologies during misalignment conditions using ANSYS Simplorer^® software. Based on the investigations on different types of coil designs for different misalignment conditions, a conclusion is presented in Section 5.

2. Classification of Different Types of Misalignments

Fundamentally the function of a WPT system relies on two separate coils forming mutual inductance. Any alterations in the shape and position of these two coils is known as misalignment and leads to a deforming airgap, which alters the mutual inductance and thus affects the transferred power [32]. This can put the stability of the system at risk, as well as producing oscillations in output voltage [33]. Moreover, misalignment creates challenging safety issues due to increased chances of electromagnetic exposure [34]. In [33], a classification of different misalignments is presented for different positions of two square coils. The two coils are perfectly aligned when the planes are close enough and both axes are parallel to each other, as shown in Figure 1. There are different classifications of misalignment in the literature. In this paper, displacements are categorized by the type of movement, which can be either translational or angular.

Various structures of coils have been introduced by scholars. The design of the coil impacts the magnetic flux distribution and the linked flux between the two coils [35,36]. Moreover, mutual inductance, self-inductance and the coupling coefficient are affected by the design of coils [35]. Mostak et al. [37] has shown the impact of the core on the coupling coefficient in horizontal misalignment. As reported, the core significantly increases the coupling coefficient. Misalignment in cases of circular- and rectangular-shaped coils have are further elaborated in this paper.

The misalignment phenomenon occurs when either translational or rotational displacement occurs in one or both of the coils; thus, there are two main types of misalignment:

(1)

Translational misalignment;

(2)

Angular and rotational misalignment.

Translational misalignment refers to either lateral or longitudinal displacement of planes with respect to each other, as shown in Figure 2a,b. Therefore, the linkage flux is reduced, resulting in reduction of MI, and the system enters loose coupling mode, with diminished efficiency [38,39]. In [16], longitudinal and lateral misalignments are referred to as X-axis and Y-axis misalignments, respectively.

In Figure 2c,d rotational misalignment is depicted where one plane rotates around its axis either in-plane or out of the parallel plane, classified as rotational and angular misalignment, respectively. In practice, there is a high possibility of a combination of different types of misalignments occurring. Although perfect alignment is desirable, placing the vehicle at the exact point of perfect alignment does not necessarily guarantee the best performance, since the load of the vehicle alters the height of the airgap; thus, changing the airgap between the two coils results in a different MI and different efficiency. This situation is not considered to be misalignment and is categorized as vertical variation [18].

In addition to rectangular structures, circular coils are also employed in practice. Although both systems are based on mutual inductance and magnetic interaction between the two coils, their tolerance to misalignment differs hugely. As shown in Figure 1b, in the circular design, as long as the two planes are parallel, any flat rotation in the position of the coils does not change the linked flux density. In addition, due to the intrinsic symmetrical geometry, there is no difference between lateral or longitudinal displacement in circular pads. Therefore, as depicted in Figure 3, the possible displacement scenarios for circular structures diminishes to two classes, i.e., translational and angular misalignment.

3. The Effect of Coupler Structure on the Efficiency of a WPT System

As described earlier, the performance of a WPT system is affected by the coupling coefficient [40]. The coupling coefficient is considerably affected by coupler design; thus, the structure of the magnetic couplers is one of the most substantial factors in a WPT system [41]. More precisely, the coupling coefficient determines what portion of the flux created by the primary coil is linked with the secondary coil [10]. The rest of the flux that is not linked with the secondary is termed as flux leakage. As a result, the voltage induced in the secondary coil depends on the coupling coefficient. The relation between the coupling coefficient and mutual inductance is shown in (1):

$$M=\mathrm{k}\sqrt{L_p{L}_s}$$

(1)

Equation (1) indicates the linear relationship between mutual inductance (M) and coupling coefficient (k). The results of the simulation can compute M, which then can be used to find the efficiency of the system [18]. Thus, in order to investigate the impact on the efficiency of a WPT system, the mutual inductance and the coupling coefficient can be analyzed; then, the efficiency can be derived from the results.

Couplers are the most substantial part of a WPT system and should have high coupling coefficient and good misalignment tolerance [10]. Research on square coil design [42,43,44] and circular design [45,46] has been presented in the literature. Utilizing different coil geometries can change the magnetic coupling considerably [47]. Various structures have been proposed by scholars to achieve the desired characteristics. Conventionally, couplers used in EV charging have either a flat spiral circular shape or a cylindrical spiral solenoid [16]. Compared to solenoidal types, the flat spiral coils offer various advantages including compactness, robustness and light weight [31]. Coil geometries vary from basic structures such as circular and square-shaped pads to more complex designs such as double D (DD) and DD-quadrature (DDQ) [48]. Covic and Boys [16] presented a review of different coupler structures and analyzed the performance of interoperation of different coupler designs, showing the tolerance of each design to displacements in the x- and y-axes. In a comparison between circular pads and polarized solenoidal pads, circular pads were found to have poorer coupling ability. However, polarized pads are restricted in terms of the direction in which the vehicle approaches the pad, while circular pads can be approached in any direction [16], proving that circular pads are strongly robust against rotational misalignment. Li et al. argued that for similar size, DD coils provide a better coupling, with a charging area almost two times larger than that of a circular pad, making them a possible solution for DWC [41].

Although using DD coils can improve the lateral misalignment tolerance, in the EV industry, circular-shaped and square-shaped coils are mostly used for static wireless charging [47]. Both circular and square-shaped (including rectangular) geometries offer a single-sided field that goes through the coil from its front [10,49]. The higher coupling coefficient of circular geometries compared to square-shaped or rectangular coils has been pointed out by scholars [50]. However, there still remains a lack of analysis of their performance in misalignment. The proposed assessment is based on the comparison of coupling coefficients computed by the simulator. Apart from the coil structure and displacement, there are other factors such as shielding that could affect the result. Patil et al. compared the coupling coefficient and misalignment tolerance of various structures such as circular, combined circular and square, circular with ferrite bar, bipolar and three-circular coils [10]. It was concluded that the bipolar structure demonstrated the best performance without shielding, whereas with aluminum shielding, the coupling coefficient of circular coils was less affected and thus achieved better performance than bipolar pads. As a general conclusion, the effect of shielding on couplers with a single-sided flux path is low, while it has a considerable impact on couplers with a double-sided flux path. This is because the double-sided coils have half of their flux on the front side and half on the rear side, while single-sided pads offer the advantage of having most of their flux on one side, with only a small portion making its way through the back [41]. Nevertheless, given that the computations without considering the effects of shielding are still valid [51], it is not included in this paper. Moreover, different coil shapes can be used interchangeably, e.g., a circular coil can be placed as a secondary coupled with a square-shaped primary. However, the following simulations are executed on identical coupled coils.

3.1. Circular Coils

Circular pads are the most reported structure and the most widely used couplers for SWC charging in EVs [10,50,52,53]. Due to the nature of circles, there is no difference between lateral and longitudinal displacement in this design, i.e., it is non-directional [52]. In addition, due to the symmetrical shape, rotational displacement is not applicable for this type of coils. In this section, the behavior of a coil set during lateral and angular misalignment is examined. Moreover, the effect of height alteration between the two coils is also investigated. To evaluate the behavior of the couplers in misalignment, various parameters such as magnetic field density, coupling coefficient and mutual inductance were computed by simulation using ANSYS Maxwell ^®. The simulation was executed in a boundary area with relative permeability of 1 and conductivity of 0; this boundary emulates ambient conditions identical to air.

In order to calculate the coupling coefficient, this simulation was performed in magnetostatic mode and a parametric sweep was executed to analyze the alterations experienced by the coupling system during misalignment conditions. The values of the parameters used for the simulation are presented in

Table 1. Simulation parameters for circular coupler set.

Parameters	Values
Current in Rx	10 A
Coil inner radius (Tx and Rx)	50 mm
Coil outer radius (Tx and Rx)	70 mm
Vertical distance between coils	30 mm
Tx turns	20
Rx turns	20

. The airgap between the coils was set to one quarter of the coils’ average diameter [54].

To better represent the issue, relevant figures are provided where needed. Given that mutual inductance is not a function of current, there is no load applied to the secondary coil, i.e., the secondary coil is an open circuit. The effects of induced voltage and current (in order to assess the efficiency rate) in the secondary coil are analyzed in detail in further sections.

Figure 4 depicts the distribution of magnetic flux density around the transmitter. To analyze the effect of misalignment on the coupling coefficient and mutual inductance, the receiver coil was first moved both vertically and horizontally and the output parameters were computed at certain distances; the same approach was implemented for the angular (tilted) displacement. In the final stage, the values were plotted against different variables to assess tolerance against each type of misalignment. Figure 5a shows that the coupling coefficient decreases hyperbolically when the height of the secondary coil increases from 5 to 200 mm; in this case, the coupling coefficient drops from around 0.6 to close to zero. In Figure 5b, lateral displacement in applied to the secondary coil. As can be seen, the curve plunges to zero at a point regarded as the “null coupling position” or “flux cancellation” area, and rises again as the displacement increases [40,52]. The reason for this local zero coupling area is that at this particular distance, the amount of flux intersected by the secondary pad is equal to the intersected flux in the reverse direction, resulting in a net flux equal to zero. Ke and Chen et al. developed a method to correct this phenomenon [40]. In this case, the flux cancellation occurs at around 80 mm lateral offset, confirming the results of the empirical formula derived by [40] and implying that the flux cancellation zone of circular pads occurs at a displacement of approximately 50% of the coil outer diameter. However, this can vary based on the airgap between the two coils. Figure 5c represents the alterations of the coupling factor with angular misalignment from 0 to 20 degrees.

3.2. Rectangular Coils

Another basic shape for couplers is rectangular. To obtain fair comparison results, the surface area of the rectangular coil in the x-y plane (7520 mm²) is kept close to that of circular coil (7540 mm²). This means that the quantity of copper used for manufacturing both structures is the same. The simulation parameters are shown in the

Table 2. Simulation parameters for rectangular coupler set.

Parameter	Value
Current in Rx	10 A
Coil length (Tx and Rx)	140 mm
Coil width (Tx and Rx)	88 mm
Vertical distance between coils	30 mm
Tx turns	20
Rx turns	20

. The magnetic flux distribution around the rectangular coil is shown in Figure 6.

Rectangular and square-shaped geometries have been widely investigated by scholars [18,31,33,55,56]. The rectangular design creates a polarized magnetic flux spread. Thus, the flux linkage is better than circular design coils [57] and is suitable for mid-range ICPT systems [56]. Wang et al. investigated a rectangular coupler set at a fixed distance of 5 cm to analyze lateral and angular misalignment effects [56]. However, rotational misalignment was not covered. Kushwaha et al. examined the misalignment tolerance of rectangular coils and confirmed that the results of analytical and experimental methods are in close agreement with simulation results [18]. In [33], a detailed analysis was conducted on square-shaped coils with all types of misalignment. However, the null coupling zone was not analyzed. The layout of the magnetic flux density of rectangular coil geometry is depicted in Figure 6. As can be seen, under vertical and angular misalignment, the rectangular coil experiences a similar pattern to that of a circular structure. Figure 7b shows sensitive this structure is to lateral displacement, while longitudinal offset has less of an impact on the linked flux. The null coupling zone occurs at approximately 60 and 105 mm for lateral and longitudinal displacements, respectively. In addition, such coils are vulnerable to rotation of the secondary coil, i.e., when the vehicle approaches the ground pad at an angle. Figure 7d shows that rotational misalignment leads to a significant reduction in coupling coefficient from around 0.45 to below 0.15. However, this alteration varies based on the airgap between the windings. For an airgap of 30 mm, the alteration range is significantly reduced.

3.3. Comparative Analysis

In order to visualize the differences between the two coil shapes, in this section, the results of both structures are superimposed. As depicted in Figure 8a, a circular pad offers better tolerance to vertical displacement, as the rectangular coil experiences a steeper slope. At 50 mm height, the circular pad considerably outperforms the rectangular coil with a 50% higher coupling coefficient. Figure 8b indicates that the coupling coefficient of the rectangular coil plunges more drastically when lateral displacement is applied. However, due to the lengthened geometry of the rectangular coil, it achieves better performance than the circular coil in terms of longitudinal misalignment. This could make such coils a suitable choice for DWC, where high tolerance to longitudinal misalignment is more desired. The behavior of the system against angular misalignment is shown in Figure 8c, where the circular coil outperforms the rectangular pad slightly. Given that both structures require the same amount of copper for production, circular coils achieve greater tolerance to against misalignment overall. Moreover, such couplers offer better performance under rotational displacement due to their intrinsic neutrality to flat rotation.

4. Impact of Compensation Topology on System Performance

Inductive power transfer can be efficient when the two coils are at close relative distance of a few centimeters, but its efficiency plunges drastically as a result of increased leakage inductance when the distance is increased [58,59]. The inductive nature of the circuit and high leakage flux leads to a high reactive current and, thus, a high VA rating of the power source. In addition, the excessive current results in higher losses and subsequently lower efficiency. Therefore, the presence of a compensatory capacitor is vital [10]. The simultaneous use of capacitive and inductive elements results in a resonance state, which realizes the concept of resonant coupling. The value of the resonant capacitors depends on the desired frequency of resonance. There is a trade-off between choosing the desired frequency and reactive components X_L, X_C, in that higher frequencies lead to a higher quality factor, but may cause higher losses in the switching stage [60]. By operating at the resonance frequency, the capacitor cancels out the effect of the inductive component, i.e., cancelling out the leakage inductance effect; thus, the volt–amp capacity of the inverter on the primary side is optimized. When reducing the phase angle between the primary voltage and current to zero, known as the zero phase angle (ZPA), the power factor (PF) hovers around 1, which is desirable. ZPA maintains the necessary conditions for soft switching of electronic components [41]. Depending on the application, the tuned frequency at which the circuit is designed to operate is determined. Therefore, a precise control system is needed to keep the circuit operating at the resonance frequency even when the coupling is changed due to the misalignment. This frequency control is significantly dependent on the compensation topology [30]. In compliance with the SAE J2954/1 standard, the nominal frequency should be 85 kHz [10]. Nevertheless, the frequency can range between 81.38–90 kHz, which is the agreed frequency spectrum internationally, as it has the least interference with other facilities [10]. One widely used method of compensation comprises only two capacitors; this is also the most economical approach [36]. Therefore, there are four principal compensation networks classified based on the position of compensatory capacitors in the circuit. The capacitors are placed either in series or parallel on both the primary and secondary sides; hence, there are four basic designs of compensation network—series–series (S–S), series–parallel (S–P), parallel–series (P–S) and parallel–parallel (P–P). Each of these topologies has its own merits and drawbacks, which results in a trade-off based on the desired application. Sohn et al. investigated all four schemes in terms of maximum efficiency, maximum transferred power, load-independency, k-independency and no magnetic coupling performance, concluding that current-sourced S–S and S–P topologies have better performance [61]. However, the author mentions that there remains uncertainty regarding which compensation is the most suitable choice depending on the application. In another study, Shevchenko et al. conducted a comprehensive review of basic compensation topologies, as well as a comparison of more complex hybrid compensation approaches [47]. It was concluded that using series primary compensation leads to higher efficiency amongst the four abovementioned topologies [47]. Apart from these four basic compensation strategies, many scholars have proposed more complex compensation topologies. For instance, Villa et al. investigated the performance of four basic topologies under misalignment conditions to find a high-misalignment tolerant design, and presented the use of SPS topology in an ICPT system [30]. In [47], it is concluded that amongst complex topologies, LCL and LCC are more advantageous, with an efficiency of more than 95%. In this paper, however, the four basic topologies are investigated and other more complex designs are excluded. Although in some designs the circuit is driven by a current source, in this paper, a voltage-sourced circuit is evaluated.

The impact of different compensation topologies on the efficiency of a WPT system under misalignment conditions is essentially based on how the circuit reacts to changes applied to the circuit. Different parameters such as mutual inductance (equivalent to the coupling coefficient) [62], operating frequency and load variations eventually result in changes in system efficiency. Here, the aim of the analysis is to determine the impact of mutual inductance alterations on the efficiency of power transfer. It has been determined that each compensation topology has a certain behavior to mutual inductance alterations, which will be analyzed in this section.

In order to investigate the circuit behavior, an equivalent model of the system is required (see Figure 9). The load impedance can be modeled as reflected impedance to the primary side, as shown in Figure 9c.

$$Z_r=-\frac{j\omega M{I}_2}{I_1}$$

(2)

$$I_2=\frac{j\omega M{I}_1}{Z_{eq}^{ 2}}$$

(3)

Substituting (2) in (3) returns the reflected impedance relation:

$$Z_r=\frac{{\omega }^2{M}^2}{Z_{eq}^{ 2}}$$

(4)

The reflected secondary impedance to the primary side is derived in (4), where ω is the resonance frequency, Z_eq² is the equivalent impedance of the secondary side and Zr is the reflected Z_eq² to the primary side. The formation of capacitor and load determines the value of Z_eq² and, consequently, Zr. Thus, it is vital to calculate the equivalent impedance based on the compensation topologies used in primary and secondary sides (Figure 10). The equivalent impedance of the secondary side (neglecting the parasitic winding resistance) can be found using (5) and (6):

$$\mathrm{Series} \mathrm{secondary} \mathrm{compensation}: {Z_{eq}}^2=j\omega L_S+\frac{1}{j\omega C_S}+Z_L;$$

(5)

$$\mathrm{Parallel} \mathrm{secondary} \mathrm{compensation}: {Z_{eq}}^2=j\omega L_S+\frac{1}{j\omega C_S+\frac{1}{Z_L}}.$$

(6)

Using (4) to transfer Z_eq² to the primary side, the input impedance seen by the source is determined (

Table 3. Total impedance seen by the source [10].

Compensation Topology	Reflected Impedance
S–S	$\left(R_1+j\left(\omega L_1-\frac{1}{\omega C_1}\right)\right)+\frac{{\omega }^2{M}^2}{R_2+R_L+j\left(L_2\omega -\frac{1}{C_2\omega }\right)}$
S–P	$\left(R_1+j\left(\omega L_1-\frac{1}{\omega C_1}\right)\right)+\frac{{\omega }^2{M}^2}{R_2+\frac{ R_L}{1+j{R}_L{C}_2\omega }+j{L}_2\omega }$
P–P	$\frac{1}{j\omega C_1+\frac{1}{R_1+j{L}_1\omega +\frac{{\omega }^2{M}^2 \left(1+j{R}_L{C}_2\omega \right)}{R_L+\left(R_2+j{L}_2\omega \right)\left(1+j{R}_L{C}_2\omega \right)} }}$
P–S	$\frac{1}{R_1+j{L}_1\omega +\frac{{\omega }^2{M}^2}{R_2+R_L+j\left(L_2\omega -\frac{1}{C_2\omega }\right)}+j{C}_1\omega }$

). The circuit can be fed by either a voltage source or current source. In Figure 11, the circuit is driven by voltage source Vs, where the load is represented by Z_L, which is considered as a purely resistive load. The parasitic resistances of the primary and secondary windings are modeled by R1 and R2, while L1 and L2 represent the self-inductances of the respective windings. The secondary capacitor is selected such that the imaginary part of the secondary impedance becomes zero to achieve the maximum transfer capability [63]. To achieve the maximum efficiency, the secondary capacitor is determined by (7) [28].

$$\mathrm{Secondary} \mathrm{side} \mathrm{capacitor}: C_2=\frac{1}{{\omega }^2 L_2}$$

(7)

The resultant impedance is reflected to the primary side, which is seen by the source. The primary capacitor compensates for the reactive power and, thus, the imaginary part of the equivalent impedance seen by the source (including the reflected impedance) is eliminated to ensure that the circuit is operating in ZPA mode; this achieves the minimum VA rating of the power source [63]. Depending on what topology is used, the capacitance of the primary capacitor is determined [29,61,63,64]. The values of the primary and secondary compensating capacitors are determined such that the system resonates at the desired frequency of 85 kHz. The value of the primary capacitor, depending on the corresponding compensation topology, is given by

Table 4. Primary capacitance for different topologies [64].

Compensation Topology	Primary Capacitance
S–S	$\frac{1}{{\omega }_{0 }^2{L}_1}$
S–P	$\frac{1}{{\omega }_{0 }^2\left(L_1-\frac{M^2}{L_2}\right)}$
P–P	$\frac{L_1-\frac{M^2}{L_2}}{{\left(\frac{M^{2}R}{L_2^2}\right)}^2+{\omega }_{0 }^2{\left(L_1-\frac{M^2}{L_2}\right)}^2}$
P–S	$\frac{L_1}{{\left({\omega }_{0 }^2\frac{M^2}{R}\right)}^2+{\omega }_{0 }^2{L}_1^2}$

.

The performance of the compensation network is assessed by computing the efficiency of the power transmitted by the transmitter and acquired by the load. Although in practice, the load is often a rectifier, filter and switched controller, it is possible to model the load with an equivalent resistor [31]. To evaluate the efficiency, simulations were executed in ANSYS Simplorer^®. The results previously achieved using ANSYS Maxwell^® (in Section 3) were used to determine the mutual inductance for simulation in this section. The Maxwell results indicate that the primary and secondary inductances remain constant at 59 uH, whereas the mutual inductance changes as a result of changing the relative coil positions. A constant resistance is placed at the secondary terminals as a load. The simulation was executed in AC-analysis mode in Simplorer to investigate the system efficiency across a wide range of frequencies, including the resonant frequency. The efficiency was then found by computing the ratio of the real power received on the secondary side to the transmitted real power on primary side [65]. The efficiency was plotted in the frequency domain to compare the consistency of the resonance frequency.

$$\eta =\frac{P_{Received}}{P_{transmitted}}$$

(8)

To investigate the overall behavior of various combinations of different compensation methods with different coil designs, simulations were executed for all four basic compensation topologies with both circular and rectangular coils. A lateral displacement of 0–200 mm was then applied to the secondary coil and the efficiency of the system was measured during misalignment. It is desirable that the system maintain its maximum efficiency for a wide range of misalignment.

4.1. S–S (Series–Series)

S–S compensation is widely used in WPT charging for EVs [23]. In terms of copper mass, S–S is the best choice among all four options [47,51]. Another merit of this topology is that the required capacitor for compensation is independent from the coupling coefficient and load variations [10,28,58,59,63]. Therefore, the frequency of resonance remains constant when misalignment occurs (see Figure 12a) [28]. This stability of resonant frequency during misalignment makes WPT suitable for applications with high misalignment requirements. Furthermore, the current drawn on the secondary side depends upon the AC source regardless of the voltage induced at the secondary coil, which is beneficial for battery charging purposes [66]. Another merit of this design is that since the imaginary part of the reflected impedance remains zero (see Table 3), the unity power factor is maintained during misalignment [28,67]. As a result, S–S-compensated systems are the most appropriate for EV charging applications [28,68,69]. Moreover, in terms of charging requirements, this topology can provide constant voltage and current for battery charging applications [28,70,71]. Nevertheless, one major drawback of S–S topology is its performance at light-load conditions and when no receiver is on the secondary side [28]. This is because the equivalent impedance seen by the primary side is reduced when the coupling is weakened, which results in a tremendous current on the primary side and an extreme voltage at the secondary terminal when the circuit is supplied by a voltage source [10,41]. Therefore, working in zero-coupling mode must be avoided [47].

4.2. S–P (Series–Parallel)

Due to the series primary connection, both S–S and S–P designs have the advantage of transferring higher power than rated [59]. S-P topology, however, lacks the benefit of independence from mutual inductance, in contrast to S-S topology. In addition, it requires a larger capacitor on the primary side. S–P compensation is usually employed to maintain a constant voltage output [63]. Nevertheless, it has the hazard of excessive current when the secondary side is not in proximity due to the negligible impedance seen by the source [10]; therefore, a current limit mechanism is needed. As depicted in Table 4, the primary capacitance changes with mutual inductance alterations, and given that the capacitor is fixed in practice, a change in the mutual inductance leads to significant resonance frequency mutation (see Figure 12b).

4.3. P–P (Parallel–Parallel)

The relationships of primary capacitance and impedance in this topology are relatively complex. Using a parallel capacitor in the primary side is safe in case of the absence of a secondary coil [59]. However, this also leads to large input impedance, which requires high voltage to transfer power sufficiently [47]. A merit of this technique is that if an appropriate alignment is guaranteed by the coupling unit, it offers a high efficiency with suitable robustness against frequency mutations (see Figure 12c). However, since the value of the primary capacitor depends on both mutual inductance and load impedance (see Table 4), this method has a low misalignment tolerance, as shown in Figure 12c [28]. Another disadvantage of this technique is its low power factor [10]. This topology is not widely investigated due to its numerous disadvantages [10,65,72].

4.4. P–S (Parallel–Series)

Due to the parallel connection on the primary side, the relationship of the primary capacitor in this topology is also relatively complex. The primary capacitor is strongly affected by mutual inductance and load. Compared to P–P, the primary capacitor for P–S has a steeper relation with mutual inductance, as it decreases with the fourth power of M. Another drawback of this design is that it requires more copper than the other three topologies (30% more than S–S) [47]. Unlike other topologies, the reflected impedance in P–S is inversely correlated with the mutual inductance, meaning that the impedance increases when misalignment occurs; thus, the current is limited during misalignment (Table 3). A major advantage of using P–S topology is that it provides soft-switching for semiconductors [47]. However, it is not capable of transferring sufficient power when misalignment happens [28,70]. It also has a low tolerance to frequency mutations [28], especially in misalignment conditions (see Figure 12d).

4.5. Comparative Analysis

Figure 12a–d reveals that there is a trade-off between misalignment tolerance and robustness to frequency mutations. Using series compensation on the secondary side results in higher efficiency during misalignment, but lower tolerance to frequency alterations. This can increase costs, since it requires a high frequency control system to maintain the exact optimal frequency with high precision. On the contrary, using a parallel compensation on the secondary side leads to higher frequency tolerance, but misalignment tolerance is compromised. Each compensation technique has been simulated under the same parametric conditions (see Figure 12a–d). In [10], a comparison indicates that S–S and P–S topologies demonstrate higher efficiency at low mutual inductances than S–P and P–P, meaning that having series compensation on the secondary side offers better tolerance under misalignment [73]. A reconfigurable resonant and hybrid circuit for the ICPT system has been proposed to sustain the changes in load and misalignment variation [74]. However, in terms of economic analysis, using a series capacitor on the primary side, namely, S–S or S–P, is more suitable for high-power applications [51]. Sohn et al. [61] concluded that in terms of maximum efficiency, S–S and P–S schemes offer complete k-independency, meaning that S–S and P–S offer better performance in misalignment conditions.

To compare the performance of all four schemes, the efficiency of each topology was measured at the frequency of 85 kHz while lateral misalignment was applied to the secondary position at certain steps.

Due to the changes in coupling, the resonant frequency was shifted when the misalignment was applied to the system. Figure 12a,d indicates that using a series capacitor on the secondary side (S–S and P–S) mitigates the frequency shift caused by misalignment; hence, better performance is achieved during misalignment. It should be noted that although the efficiency of P–S drops more sharply than S–S, the frequency shift is not considerable and the efficiency can be maintained around the desired area by using a frequency control circuit. However, this can increase the production costs. Figure 13 implies that S–S has the most robust curve under misalignment, whereas P–P and S–P experience more deterioration in efficiency as the mutual inductance decreases. S–P demonstrates the weakest misalignment tolerance of all the topologies.

5. Limitations and Future Trends

Various limitations still persist in EV wireless charging systems. Conventional control methods of WPT charging systems use communication devices; however, there can be delays data transmission causing unnecessary energy loss. In addition, despite extensive research in achieving high-misalignment-tolerant designs; a high risk of electromagnetic field exposure remains during misalignment. Moreover, the interoperability of different charging coil designs and circuit configurations lacks careful consideration of misalignment.

The future prospects of this technology demand further investigation of the following topics:

• A reconfigurable arrangement of coil design that can switch different arrangements of coils to offer high coupling coefficients between EVs and chargers for each misalignment condition;
• Instead of using communication between the EV and the charging circuit, a new control using system parameters whose changes reflect misalignment between the charging coils, e.g., mutual inductance deviations, should be a candidate for future research;
• Current studies on the thermal failure of the ferrite core employed in coil construction are inadequate, making it difficult to draw any firm conclusions;
• Although dynamic wireless charging is a promising solution to the challenges of EVs, there are limited studies considering misalignment with this type of EV charging.

6. Conclusions

A comparison of non-polarized coupler structures and basic compensation topologies used in EV battery charging is presented in this paper. It was found that with regards to misalignment tolerance, circular pads outperform rectangular structures due to their maintaining a higher coupling coefficient, as well as offering freedom of approach direction. In terms of compensation topology, it was concluded that using series compensation on the secondary side leads to higher misalignment tolerance, while system robustness against frequency alterations is compromised. The S–S topology demonstrates the best performance considering its independency from load and coupling mutations and its ability to provide suitable charging conditions for EV battery charging applications. Given that there are various trade-offs between different designs, selection of the most optimal mixture of coil structure and compensation topology must be determined based on the EV specifications, e.g., chassis height, size, dimensions and battery capacity.