Investigation of triple quadrature pad for wireless power transfer system of electric vehicles

Ali Mosallanejad, Department of Electrical Engineering, Shahid Beheshti University, Tehran, Iran. Email: a_mosallanejad@sbu.ac.ir Abstract Inductive Power Transfer (IPT) system is an appealing approach among researchers as well as industrial manufacturers of electric vehicle (EV) charging systems. IPT can be used to transfer power through the air gap by generating a high‐frequency current in the transmitter pad and inducing current magnetically in the receiver pad. A triple quadrature pad (TQP) has been proposed to enhance transferred power in larger misalignments and various air gaps. This pad excels in its previous three‐coil structures by implementing a fewer number of inverters and lower dimensions compared to other similar structures. All these features result in a higher coupling coefficient in low misalignments and higher tolerance to misalignment in horizontal displacements. A laboratory‐scale prototype has been designed and built for 26 kHz switching frequency and 150 mm air gap in order to deliver maximum power in different displacements. Simulations have been done by the finite element analysis (FEA) tool of ANSYS Maxwell. The prototype has been built to validate the simulation results.


| INTRODUCTION
Electric vehicles (EVs) have been in great demand to decrease fossil fuel consumption and their ensuing detrimental impacts on the environment. Inductive power transfer (IPT) systems or wireless power transfer (WPT) systems can transfer power through air gap without any contact and extra cables to charge the battery of EVs. Safety charging as well as being impervious to a dusty environment, humidity and storms are some of the main reasons that make IPT systems an attractive solution to charge batteries in static, dynamic or quasi-dynamic application modes [1][2][3][4][5][6][7]]. An IPT system contains two main transmitter and receiver sides, as depicted in Figure 1. Both transmitter and receiver sides consist of an AC to DC converter as well as a DC to AC converter to transfer the desired high-frequency power from the power supply to the transmitter coil(s) and DC to DC converter respectively. The DC to DC converter is utilised to adjust the output voltage and current to supply the battery. It is also possible to employ an AC to AC converter, as discussed in Ref. [8,9]. Reducing reactive power drawn from the supply and maximising resistances of the transmitter and receiver coils when the system operates at the resonant frequency maximises efficiency, which is the aim of designing transmitter and receiver compensation circuits [10,11]. Various compensation circuits have been utilised such as LC series, LC parallel, LCL, LCC and LCCL in Ref. [12][13][14][15][16][17][18][19][20][21][22].
The magnetic structure has a significant impact on the overall system efficiency. It includes transmitter and receiver coils or power pads. Previous topologies of inductive pads were double-sided pads with poor efficiency due to the aluminium shielding [21][22][23]. Single-sided pads are more conventional inductive pads that generated flux flows only to one side of the pad. These pads are categorised into two main non-polarised and polarised pads based on the type of generated flux and which circular pad (CP) and double-D pad (DDP) are the common structures for mentioned categories [23][24][25][26][27]. Although flux path height of DDP is two times higher than CP for the same size, both pads suffer from low tolerance to misalignment when the receiver pad is misaligned and also poor interoperability while operating with other types of pad [28,29]. In Reference [30], an extra coil has been added to DDP to increase tolerance to misalignment and interoperability significantly. This new pad is called double-D quadrature pad (DDQP). However, the amount of consumed copper is relatively higher than DDP and CP in similar size and turns, and also it is not fully interoperable with CP as the transmitter pad [28]. Bipolar pad (BPP) is another topology consisting of two quadrature coils having partial overlap and is mutually decoupled. BPP can generate polarised and non-polarised flux by phase control of each coil besides consuming less copper compared to DDQP [31,32]. Recently, a new transmitter pad with three mutually decoupled coils is introduced in References [ [33][34][35] called tripolar pad (TPP) with lower leakage magnetic field in misalignment by generating various magnetic field shapes. In these articles, an extensive controlling system with a specific algorithm has been proposed to alter the amplitude and phase of the transmitter currents to obtain the most efficacious current regarding higher transferred power. Moreover, these three transmitter coils are supplied from three different inverters because they are mutually decoupled to maintain transferred power in the highest amount. Even though the additional inverter and the control system enhance the performance of the IPT system, they would raise the cost of the total system and complicity of the control system.
A general comparison of mentioned pads is summarised in Table 1. In this table, different pads have been compared qualitatively according to their type of generated flux, tolerance to misalignment, interoperability and relative cost of the material. Therefore, in the following article, a recently proposed pad called triple quadrature pad (TQP) consisting of three coils as a transmitter pad has been investigated not only to provide additional magnetic features but also to overcome the previously mentioned drawbacks [36]. Its advantages over TPP and other IPT pads in papers can be stratified as (1) application of two independent inverters instead of three to control transmitter coils according to two main excitation modes (2) total dimension of pad and coils being 27.6% smaller than TPP, while magnetic performance of the IPT system such as coupling coefficient and tolerance to misalignment are improved and (3) higher coupling coefficient in lower displacements in X and Y-axis compared to TPP. These features result in the lower total cost of the designed pad while maintaining the performance of TQP in high level.
The operation of TQP as the transmitter pad and DDP as the receiver pad are analysed in this article. In Section 2, the structure of TQP consists of three similar coils placed side by side with partial overlap between adjacent coils. Two lateral coils are supplied from an inverter, and the central coil is supplied from another inverter to generate various magnetic fluxes according to the receiver pad displacement. In Section 2, TQP is analysed from two perspectives: magnetic analysis and mathematical analysis. The magnetic analysis involves studying two main excitation modes having the most significant impact on generated flux and investigation of the exposure limit of leaked magnetic flux to ensure meeting all requirements of the ICNIRP guidelines. Mathematical model of the total IPT system with proposed TQP-DDP is presented afterwards in order to theoretically analyse the total system, as well as principal parameters of the IPT system such as uncompensated transferred power (S u ) and coupling coefficient (k) and also output parameters involving output power and the system efficiency. In Section 3, simulation results are presented for a system of 26 kHz operating frequency, 150 mm air gap and 8 A excitation current. In this section, the variation of uncompensated power and coupling coefficient as a function of horizontal displacement for two main excitation modes are presented, and the parameter values are listed in Table 2. Experimental analysis is conducted in Section 4 to confirm the simulation results. The proposed system is built in the laboratory with respect to the associated parameters, and the variation of uncompensated power and coupling coefficient as a function of horizontal displacement are compared with the simulation results in three different air gaps in order to show the ability of pad in transferring power to the higher air gaps. Furthermore, the experimental waveforms of the prototype are included for maximum output power and maximum efficiency of 800 W and 94.7%, respectively, for low misalignments. It shows great compatibility with simulation results. In addition, the efficiency of the system in a 150 mm air gap and various displacements is proposed at the end of this section. Finally, the conclusion is provided in Section 5.

| Magnetic analysis
Proposed TQP, as shown in Figure 2, involves three equal coils supplied from two individual inverters with series capacitors as F I G U R E 1 Structure of an inductive power transfer (IPT) system ESMAEILI JAMAKANI ET AL.
-59 a compensation circuit. Ferrite bars and aluminium sheets are located under coils to decrease the resistance of the flux path and leakage flux on the other side of the pad where the receiver pad is not located. The overlap between central and lateral coils is adjusted to be magnetically decoupled. By phase control of transmitter coils, various excitation modes can be determined according to whether the phase of the current in second and third coils is in-phase or out of phase concerning the phase of the first coil in Figure 2. Additionally, other modes can be considered when at least one coil is excited. The investigations show that only two main excitation modes have the most contribution to generating longitudinal flux along the length of the pad to enhance tolerance to misalignment, as illustrated in Figure 3. The best excitation mode can be chosen regarding the lateral displacement of the receiver pad in order to maximise flux linking of the receiver pad. Consequently, this pad will be able to transfer power to a larger horizontal displacement along the length of the pad in �Y-axis.
The best excitation mode can be chosen regarding the lateral displacement of the receiver pad in order to maximise flux linking of the receiver pad. Consequently, this pad will be able to transfer power to a larger horizontal displacement along the length of the pad in �Y-axis. As represented in Figure 3 by setting current of two adjacent coils in phase and third coil out of phase, total generated flux around the centre of the pad can be maintained high even with larger displacements. Based on these analysis and excitation modes, the only phase of the central coil should be changed due to the position of the receiver pad. Hence, two lateral coils can be supplied from the same inverter, as shown in Figure 5. In this case, redundant switches, which have no participation in changing current phases, can be removed.
According to the ICNIRP guidelines [37], for the 3 kHz-10 MHz range, the limitation of leakage magnetic flux and occupational exposure should be less than 27 and 100 µT respectively. The flux density of the TQP is shown in Figure 4. Simulations thoroughly demonstrate the low value of magnetic leakage flux based on ICNIRP requirement.

| Mathematical analysis
Circuit diagram of the utilised IPT system with proposed TQP is shown in Figure 5. In this system, an LC series compensation circuit has been implemented. This topology precedes other topologies in this study in several aspects, including inherent protection against short circuit, safe operation when operating frequency and resonant frequency are different and also, utilising less inductance, which leads to lower cost and weight [38]. However, the main reason for choosing this system over other compensation topologies is that the compensation capacitors only depend on the selfinductance. In this way, the circuit can be designed regardless of the variation of load and available misalignment. Hence, the variation of the mutual inductance in different horizontal displacements does not affect the calculated compensation capacitor. It results in the accurate tuning of the compensation system [38,39].
Equivalent circuit of the system is shown in Figure 6. Since coil one and coil three have the same supplier, they are shown  Figures 5 and 6. Thus, it is easier to illustrate the relation of the mutual inductance between two lateral coils (M t1t3 ). According to Figure 6, even though the amplitude of the input voltage in coil one and coil three are equal, the phase of the voltage in coil three is 180°out of phase. By considering the red loop and a KVL in this path, the following equation can be obtained: Z t1 :I t1 À jωM t1r :I r À jωM t1t3 :I t3 À Z t3 :I t3 þ jωM t3r :I r þ jωM t1t3 :I t1 ¼ 0 ð1Þ -61 ðZ t1 þ jωM t1t3 Þ:I t1 À ðZ t3 þ jωM t1t3 Þ:I t3 þ ðjωM t3r À jωM t1r Þ: Where subscripts t and r denote transmitter and receiver pad respectively. I t1 , I t2 and I t3 indicate currents flowing L t1 , L t2 and L t3 respectively. ω is the operating frequency, M t1r , M t2r and M t3r are mutual inductances between lateral coils and receiver pad. Z t1 , Z t2 and Z t3 are impedances of transmitter coils with compensation capacitors which can be determined as: where n denotes the number of transmitter coils. R tn , L tn and C tn are resistance, self-inductance and compensation capacitor of each transmitter coil respectively.
According to Equations (1) and (2), I t3 can be determined as a function of I t1 and I r as: where a and b can be defined as follow: Based on the previous equations and the relationship of the I t3 with I t1 and I r , the system operation can be expressed with a 3 * 3 matrix as Equation (7): where V t1 and V t2 indicate voltage across the lateral and central coils, and Z 11 , Z 13 , Z 31 and Z 33 can be defined as: Also in Equation (7), Z 22 ¼ Z t2 . In the same way, the impedance of the receiver coil is: The operating frequency of the system is described as follows: ω ¼ 1 ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffiffi L tn :C tn p ¼ 1 ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi L r :C r p ð13Þ Consequently, Open circuit voltage can be inferred from Equation (7) when I r becomes zero as: Short circuit current can also be determined by setting receiver voltage zero as: Uncompensated power can be deduced from Equations (14) and (15) as: In simple IPT systems with only one coil in the transmitter and one coil in the receiver side, the coupling coefficient is the relation of mutual inductance between the transmitter and the receiver pad and self-inductance of transmitter and receiver pads as k ¼ ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi M=L t :L r p . However, for more complicated systems involving two or more coils in the transmitter, receiver or both sides, the coupling coefficient is composed of the contribution of all transmitter or receiver coils and their mutual inductances [28]. In this case, k can be expressed as the relation of the total uncompensated transferred power and total input volt ammeter when the receiver is open circuit as: k ¼ ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi where V A in OC can be defined as: Output power is shown in (19) as: where Q s is the loaded receiver tuning factor and its value is between 2 and 10 in literature. Higher and lower values result in difficult adjustment and harmonic in voltage and current waveforms, respectively [28,40]. R o is the equivalent resistance of load and can be calculated from [38]: By neglecting the resistance of the compensation capacitors (C tn and C r ), core losses and parasitic couplings, the efficiency and the power losses of LC series compensation topology can be calculated as Equations (21) and (22), as a result of the joule losses in the resistances of the primary and secondary coils, as mentioned in Reference [38]: Efficiency of the total system is calculated and shown as a function of lateral misalignment along the Y-axis in section 4 for proposed TQP.

| SIMULATION OF TRIPLE QUADRATURE PAD
TQP as the transmitter pad and DDP as the receiver pad have been simulated to evaluate critical parameters of an IPT system such as S u and k. As mentioned in the previous sections, TQP coils can be excited independently in order to generate intensive and centralised magnetic flux according to the receiver pad position. Thus, power can be transferred uninterruptedly regardless of displacements up to �200 mm without a null point. Simulations are done based on the 8 A (RMS) transmitter excitation current and the 26 kHz switching frequency. All parameter values and dimensions are summarised in Table 2. The variation of uncompensated transferred power and coupling coefficient in the Y direction for two main excitation modes have been simulated and shown in Figures 7 and 8, respectively, to confirm the proper operation of the pad. It shows that by changing only the phase of the current of the central coil, higher power can be transferred when the receiver pad is displaced in the positive or negative direction from the ideally aligned position. A simple control system can be designed to automatically select the best excitation mode regarding the position of the receiver pad, which has not been addressed in this article, and it is considered for further researches.

| EXPERIMENTAL RESULTS
The prototype model has been built using parameter values given in Table 2. The Inverter used in this setup has been built using I sc MOSFET switches (IRFP250MP) selected based on maximum power transferred and maximum current. Coils have been built using 295 � AWG 38 litz wire with a total diameter of 2.4 mm.
-63 Also, each coil of DDP consists of 15 turns. The coil structures are shown in Figure 9. All measurements are based on dotted observation of voltage and current at horizontal intervals of 40 mm at three different air gaps of 150, 175 and 200 mm. Inferred results from experimental measurements are compared with simulation results to show validation and correlation of results.
As shown in Equation (16), in order to calculate the uncompensated transferred power as well as the coupling coefficient of the prototype, open circuit voltage and short circuit current across the receiver pad are measured for the maximum power transmission modes (<|I 1 À I 3 | ¼ 0, <|I 1 À I 2 | ¼ 0 and <|I 1 À I 3 | ¼ 0, <|I 1 À I 2 | ¼ 180). For each horizontal interval of 40 mm along X and Y axes, the values of V oc and I sc have been measured, respectively, and then by multiplying the V oc and I sc , S u can be obtained. At first, transmitter and receiver pads were located without misalignment, as shown in Figure 10. The values of V oc and I sc were measured, and then, the receiver pad was moved to 40 mm along the Y and X axes respectively. Variations of S u in the direction of Y and X axes are shown in Figure 11a,b respectively.
It is highly important to note that the objective of this study is to transfer maximum power to the receiver pad. Accordingly, the excitation mode along the þY axis is different from the excitation mode along the -Y axis by changing the phase current of coil two, as discussed in Section 3 and Figure 7. Therefore, the waveform of S u along the �Y axis is symmetrical. In this case, maximum power transferred to the receiver pad occurs when there is �60 mm misalignment in the Y direction. On the other hand, S u along the X-axis declines as the misalignment increases.
The coupling coefficient is calculated from Equation (17) for each displacement interval along with �Y and �X axes, and the results are shown in Figure 11c,d. These figures clearly explain the theoretical concepts and simulations done in the previous sections.
The measurement of V oc and I sc has been done in three various air gaps from 150 to 200 mm in order to show the ability of TQP in transferring power in higher air gaps.
In lower air gaps, the ability of this pad to transfer more power in larger misalignments is significantly higher than larger air gaps. If S u of 125 VA and k of 0.14 are considered as base power and coupling coefficient according to Equations (17) and (19) by consideration of Q s of 4, TQP is able to transfer the desired power up to �185 mm, �170 mm and �150 mm in the Y direction and up to �165 mm, �150 mm and �85 mm in the X direction for 150, 175 and 200 mm air gaps respectively.
Although TQP is able to transfer power in large misalignments, tolerance to misalignment in the Y direction or along its length is relatively higher than the X direction due to the magnetic flux distribution pattern. Different values of compensation components from the calculated amount and non-idealities of switches are the result of the slight difference between experimental and simulation results. Amount of S u and k for various displacements from À 200 mm up to þ200 mm for horizontal displacement in two directions is shown in Figure 12 to illustrate the elaborate operation of TQP-DDP in the whole range.
The entire setup is designed to deliver a minimum power of 400 W. Thus, the amount of equivalent load can be determined from Equation (19) as follows: Waveforms of input voltages and currents of each transmitter coil are shown in Figure 13a,b for one excitation mode in an ideally aligned TQP and DDP position. Input voltage across the transmitter coils has the same amplitude, but the phase of the third coil is 180°out of phase to generate flux pattern, as shown in Figure 3. In this case, transmitter currents flowing through the transmitter coils are different in amplitude and phase due to the mutual inductance between lateral transmitter coils and applied voltages respectively. The induced current in lateral transmitter coils leads to higher current compared to the central coil, which can be controlled independently by adjusting the input voltage by a controller which is considered for further investigations.
Transmitter currents for lateral and central coils are 9.19 A (RMS) and 7.78 A (RMS) respectively. Voltage and current across DDP shown in Figure 13c are 7.8 A (RMS) and 56.56 V (RMS) respectively. Finally, output voltage and current across load R L are 64 V and 6.4 A from Figure 13d. Therefore, output power when the receiver pad is aligned with the transmitter pad with zero misalignment is 409 W.
However, the maximum power can be delivered in 60 mm misalignment along the Y-axis. In this case, as shown in Figure  14, in the term of constant input parameters, the amount of receiver voltage and current are 70 V (RMS) and 10.25 A (RMS), and likewise output voltage and current are 91 V and 9.4 A respectively. Thus, the maximum output power that can be obtained is about 855 W. Efficiency as a function of displacement in Y-axis is calculated from Equation (21) and shown in Figure 15. The amount of resistance of the transmitter and receiver coils used in Equation (22) is listed in Table 2. As transmitter current is kept constant at 8A, the -65 values of receiver current and the current flowing R o are measured for each misalignment. Correspondingly, the variation of efficiency as a function of misalignment along �Y axis is obtained as shown in Figure 15. As the current flowing receiver pad varies, the amount of efficiency changes between 88.3% and 94.7%. Maximum efficiency can be obtained in �60 mm misalignment along Y-axis.

| CONCLUSION
We propose a novel recently presented triple quadrature pad (TQP) as the transmitter pad consisting of three equal quadrature coils with overlap between every two adjacent coils. Various excitation modes for transmitter coils have been discussed, and variation of uncompensated transferred power (S u ) and coupling coefficient (k) based on horizontal displacement in the X and Y axes for two main excitation modes have been investigated in this article when DDP is the receiver pad. Moreover, the variation of S u and k in three different air gaps were studied to show the capability of TQP in transferring power in larger air gaps up to 20 cm with tolerance to horizontal misalignments. A prototype of TQP and DDP has been constructed to corroborate the simulation results. The experimental results showed that this inductive system is able to transfer a maximum power of 855 W in low misalignment and 409 W in an ideally aligned position with maximum efficiency of 94.7% in small displacement and 88.3% up to 160 mm displacement. These results completely correlate with the purpose of the paper. Furthermore, this designed pad is 27.6% smaller than the TPP pad, and it is able to transfer the power with a coupling coefficient between 0.1 and 0.4 up to �200 mm along the X and Y axes as TPP. However, the coupling coefficient for lower misalignment is considerably higher compared to TPP. All these features, as well as the reduced number of inverters and a simpler control system, make TQP a cost-effective solution, which provides the desired performance.