Three‐phase bi‐directional wireless EV charging system with high tolerance to pad misalignment
2019; Institution of Engineering and Technology; Volume: 12; Issue: 10 Linguagem: Inglês
10.1049/iet-pel.2018.6279
ISSN1755-4543
AutoresYuan Song, Udaya K. Madawala, Duleepa J. Thrimawithana, D. Mahinda Vilathgamuwa,
Tópico(s)Advanced Battery Technologies Research
ResumoIET Power ElectronicsVolume 12, Issue 10 p. 2697-2705 Special Issue: Advanced Technologies Utilised in Wireless Power Transfer SystemsFree Access Three-phase bi-directional wireless EV charging system with high tolerance to pad misalignment Yuan Song, Corresponding Author Yuan Song yson551@aucklanduni.ac.nz Department of Electrical and Computer Engineering, The University of Auckland, 314-390 Khyber Pass Road, Newmarket, Auckland, New ZealandSearch for more papers by this authorUdaya K. Madawala, Udaya K. Madawala Department of Electrical and Computer Engineering, The University of Auckland, 314-390 Khyber Pass Road, Newmarket, Auckland, New ZealandSearch for more papers by this authorDuleepa J. Thrimawithana, Duleepa J. Thrimawithana Department of Electrical and Computer Engineering, The University of Auckland, 314-390 Khyber Pass Road, Newmarket, Auckland, New ZealandSearch for more papers by this authorMahinda Vilathgamuwa, Mahinda Vilathgamuwa School of Electrical Engineering and Computer Science, Queensland University of Technology, Gardens Point Campus, Brisbane, AustraliaSearch for more papers by this author Yuan Song, Corresponding Author Yuan Song yson551@aucklanduni.ac.nz Department of Electrical and Computer Engineering, The University of Auckland, 314-390 Khyber Pass Road, Newmarket, Auckland, New ZealandSearch for more papers by this authorUdaya K. Madawala, Udaya K. Madawala Department of Electrical and Computer Engineering, The University of Auckland, 314-390 Khyber Pass Road, Newmarket, Auckland, New ZealandSearch for more papers by this authorDuleepa J. Thrimawithana, Duleepa J. Thrimawithana Department of Electrical and Computer Engineering, The University of Auckland, 314-390 Khyber Pass Road, Newmarket, Auckland, New ZealandSearch for more papers by this authorMahinda Vilathgamuwa, Mahinda Vilathgamuwa School of Electrical Engineering and Computer Science, Queensland University of Technology, Gardens Point Campus, Brisbane, AustraliaSearch for more papers by this author First published: 26 July 2019 https://doi.org/10.1049/iet-pel.2018.6279Citations: 5AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract Electric vehicles (EVs), which are becoming increasingly popular, can be charged by either wired or wireless means. The latter, based on wireless power transfer (WPT) technology, is convenient and safe, but pad misalignment is one of the major concerns as it causes a reduction in charging power level, prolonging the charging process. Therefore, wireless charging systems with high tolerance to pad misalignment are necessary. This study proposes a three-phase bi-directional wireless power transfer (BD-WPT) system with a control scheme that offers high tolerance to pad misalignment in EV charging applications. The system uses simple coil designs for pads and utilises the magnetic coupling among pads to compensate for the power variation. A comprehensive mathematical model, incorporating all magnetic cross-coupling effects, is presented to investigate the charging performance of the system under pad misalignment and different pad spacings. To demonstrate the validity of the proposed system, theoretical and simulated results are presented, benchmarking against a single phase WPT system, and in comparison to a prototype 1.3 kW three-phase BD-WPT system. Results are convincing and indicate that the proposed three-phase BD-WPT system with small pad spacing is more tolerant to wide pad misalignment in EV charging applications. 1 Introduction Hybrid vehicles and pure electrical vehicles (EVs) are becoming increasingly attractive on a global scale as a result of the general public's awareness of environmental pollution due to excessive use of fossil fuels. However, there are several problems that need to be addressed before a wider acceptance of EVs is feasible. Compared to the ease of fuelling traditional vehicles, EVs need sufficient on-board battery storage and long charging times to recharge to maintain their driving range, which can make the driving experience somewhat inconvenient for users. To shorten the charging time, the power rate of the charger needs to be high. A plug-in connection is the most accepted way of charging an EV's battery, which requires users to insert a plug into a power outlet. However, it increases the risk of electrocution, especially in wet and hostile environments. Also, long charging wires/cables pose trip hazards, and in harsh climates, where there are snow and ice, the plug may become frozen onto the vehicle [1]. As an alternative, wireless power transfer (WPT) technology has been gaining recognition as a convenient way to deliver power across an air gap through weak magnetic coupling with no physical connection [2, 3]. WPT is flexible, safe, and convenient and hence becoming popular in EV charging applications. A typical EV charging system, based on WPT technology, is shown in Fig. 1. The grid/primary side of the system consists of a low-frequency AC–DC converter and a high-frequency DC–AC converter, which energises the coils on the primary charging pad through a resonant tuning circuit. The low-frequency converter on the grid/primary side can be a single- or three-phase rectifier when the power flow is unidirectional from the primary to the pick-up side [4, 5]. In vehicle-to-grid (V2G) systems, it is an active rectifier to realise bidirectional power flow and both energy storage and retrieval [6-9]. An 85 kHz current is generated by the high-frequency converter in the coils on the primary charging pad. The pick-up pad, mounted underneath the EV and magnetically coupled to the coils on the primary pad, is connected to a high-frequency AC–DC converter through a resonant tuning circuit. AC power transferred from the primary pad through inductive coupling and across the air gap is converted to DC and to feed the battery pack of the EV. Tuning circuits are usually in the form of inductor–capacitor–inductor (LCL) parallel or capacitor–inductor (CL) series topologies and are used on both sides to minimise the VA rating of power converters and to improve efficient power transfer capability. Fig. 1Open in figure viewerPowerPoint Typical EV charging system based on WPT EVs can be wirelessly charged/discharged through inductive coupling when the vehicle is parked on top of the primary charging pad in V2G systems. The performance of WPT-based EV charging systems is largely governed by the accuracy of the alignment between the charging pads. However, pad misalignment is unavoidable, and causes variations in magnetic reluctance, self-inductance and mutual inductance, resulting in instability, variation in power transfer, and increasing power losses due to detuned conditions [10, 11]. Therefore, several strategies, based on new control methods, compensation strategies and pad designs, have been proposed to overcome the drawbacks caused by pad misalignment. In [12-19] various pad (coil) designs and optimisation techniques have been proposed to improve the magnetic coupling. Pad design is a direct way to improve the coupling tolerance to pad misalignment. However, in general, a trial-and-error approach is used to explore the magnetic flux, coil winding and structural design to create optimised pads for WPT systems. Also, more ferrite is usually needed to regulate flux paths, which also increases the cost. Previous studies [20-22] proposed control schemes to maintain stable power transfer under detuned operation. However, these control methods compromised both efficiency and reliability. The approach in [23] proposed a system using uniform-gain frequency tracking control to improve alignment flexibility. By changing the system operating frequency, within the narrow allowable range, the output voltage can be kept at a stable level when the two coils are misaligned. However, due to high circulating currents, liquid cooling must be used to mitigate overheating, thus increasing whole system costs. Impedance adjustment is another way to improve tolerance for pad misalignment. A hybrid WPT system [24] has been proposed using combined LCL and LC series tuning topology to balance the total input impedance on the primary side automatically while the pick-up side moves. It can improve spatial tolerance within a certain displacement range. However, the reflected impedance of the LC series part will drop sharply when the pick-up side moves further, which leads to large currents in the circuit and the possibility of short-circuits with no control protection. Another study [25] proposed the use of different optimised tuning capacitors to change the system impedance and maintain power output within a displacement range. However, due to the characteristics of the LC series tuning topology, additional control strategies are needed to limit the current on the primary side. In contrast to the attempts above, this paper proposes a three-phase bi-directional wireless power transfer (BD-WPT) system that uses a simple control method, based on cross-couplings between the coils, to compensate for power variations due to pad misalignment. This approach is suitable for wireless EV charging applications without additional cameras and park assistant systems. The proposed three-phase structure raises the power level with the use of low voltage semiconductors. The converters in each phase can be individually controlled to change both the magnitude and phase angle of coil currents. Hence the flux linked between coils can be adjusted and reformed, and the power flow direction can also be changed. It provides a flexible control platform to compensate for power variations. The coils (pads) used in the proposed system are simply wound in circular form without complicated 2D/3D magnetic design and optimisation. All the coupling coefficients are calculated in ANSYS and measured from the system prototype when the pads are at different positions. A comprehensive mathematical model is derived to describe the behaviour of the proposed three-phase BD-WPT system with cross-coupling. A compensation method is then proposed and verified experimentally with the use of a 1.3 kW three-phase BD-WPT prototype in the presence of pad misalignment. Results are presented, benchmarking against a typical single-phase WPT system, to demonstrate the viability of the proposed three-phase EV charging system. 2 Proposed three-phase BD-WPT system The proposed three-phase BD-WPT system is schematically shown in Fig. 2. It can be used for V2G systems and other applications that need forward and backward power transfer between the primary (the grid) and pick-up (EVs) sides. Vin is derived from the grid using a low-frequency converter, which is not shown for simplicity. EV battery is represented by Vout. LCL parallel resonant circuits, driven by full-bridge converters, consist of inductors Lpt1, Lpt2 and Lpt3 on the primary side and Lst1, Lst2 and Lst3 on the pick-up side, respectively. Wireless power transfer takes place across the air-gap between inductors Lpt,m and Lst,n, which are magnetically coupled to each other through the mutual inductance , where ki,j is the coupling coefficient between two coupled coils. Fig. 2Open in figure viewerPowerPoint Three-phase BD-WPT system For typical WPT systems, the coupling coefficient normally varies from 0.01 to 0.35 with the separation between the two coils. The converters on the primary and pick-up sides are controlled individually to produce voltages Vpi,n and Vsi,n at the resonant frequency f. All LCL networks are tuned to the fundamental frequency of Vpi,n, as given by (1)As discussed in [6], under tuned conditions, the relative phase angle between and the magnitudes of output voltages Vpi,m and Vsi,n of the converters can be controlled to regulate both the magnitude and the direction of power flow between the primary and pick-up sides. If cross-coupling is not considered, the expression for the output power of the pick-up in any given phase operating under steady-state conditions is given by (2)where ωT = 2πf is the fundamental angular frequency. Vpi,n and Vsi,n are the output voltages of converters on both sides. θn,n is the phase angle between Vpi,n and Vsi,n. Mi,j is the mutual inductance between Lpt,n (coil i) and Lst,n (coil j) in the same phase. The configuration of the magnetically coupled coils (charging pad) design is shown in Fig. 3. The aluminium bases of both pads, which are used to mount the three-phase coils and to shield the leakage magnetic flux, are not shown for clarity. Coils 1, 3 and 5 are the inductors Lpt1, Lpt2 and Lpt3 of the primary pad. Coils 2, 4 and 6 are the inductors Lst1, Lst2 and Lst3 of the pick-up pad. All six coils are simply wound in the same circular configuration. Fig. 3Open in figure viewerPowerPoint Charging pads arrangement in the proposed three-phase BD-WPT system 3 Mathematical model with cross-coupling To gain an understanding of the characteristics of the proposed three-phase BD-WPT system, the following mathematical model with cross-coupling effects is developed. The voltage vpi,n is produced by the converter on the primary side. The switches in the left-hand-leg (LHL) are operated at the resonant frequency f, and at 50% duty cycle to generate the voltage vpa,n. The right-hand-leg (RHL) switches are also operated at f and 50% duty cycle to produce voltage vpb,n, with a phase shift of φpi,n concerning vpa,n. The phase shift φpi,n between the LHL and RHL switches controls the magnitude of the converter voltage vpi,n on the primary side. Similarly, φsi,n is the phase shift between the LHL and RHL switches on the pick-up side. Controlling φpi,n and φsi,n to regulate the voltages vpi,n and vsi,n produced by converters on both sides will be referred to as the phase shift modulation (PSM) in this paper. The Fourier series of vpi,n, which is shifted in time by θpi,n concerning reference 0, can be expressed by (3)Similarly, the voltage produced by the pick-up side converter, vsi,n, which is shifted in time by θsi,n concerning 0, can be expressed by (4)where Vin and Vout are the DC input voltages, m is the harmonic order number, and θpi,n and θsi,n are the phase angles of input voltages on both sides, which are shifted in time by θpi,n and θsi,n concerning 0, respectively. In the proposed system, θpi1 is set at 0 as the reference, and other voltages are shifted in time by different phase angles concerning vpi1. The series capacitors Cp,n and Cs,n are primarily used for DC voltage blocking on both sides [26]. In order to simplify the analysis, the impedance of the series capacitor–inductor–resistor combination (Cp,n–Lpi,n–Rpi,n and Cs,n–Lsi,n–Rsi,n) of the primary and pick-up sides can be expressed as equivalent impedances Zpi,n and Zsi,n, respectively in (5) at an angular frequency ω (5)Similarly, the equivalent impedances of the series inductor–resistor combination (Lpt,n–Rpt,n and Lst,n–Rst,n) on primary and pick-up sides can be given by (6)where ω = mωT and m is the order of the harmonics. The currents Ipt,n and Ist,n flow through the coils Lpt,n and Lst,n and induce voltages Vsr,n and Vpr,n on the pick-up and primary windings, respectively. These induced voltages are functions of coil currents and mutual inductances Mij, which are expressed as (7)where Mij is the mutual inductance between any two coupled coils. According to Fig. 2, the input currents Ipi,n and Isi,n, coil currents Ipt,n and Ist,n, and the voltages across the capacitor Cpt,n and Cst,n can be expressed by KVL and KCL as (8) (9) (10)By combining (5)–(10), the induced voltages Vpr,n and Vsr,n in terms of input voltages Vpi,n and Vsi,n can be expressed and simplified as follows: (11)where induced voltages Vpr,n and Vsr,n, mutual inductance M, Z, C and input voltages V are given by (14)–(23) (see the Appendix). The mathematical model developed previously can be used to gain an insight into the steady-state behaviour of the three-phase BD-WPT system under any given operating conditions and thus, is useful for the design and optimisation of the system. It can be used to analyse cross-coupling effects on power and investigate sensitivity to system tolerance to pad misalignment. By substituting the derived expression (11) to (8)–(10), the current Isi,n on the pick-up side can be obtained as follows: (12)The power flow direction between the primary and pick-up sides can be controlled in the proposed BD-WPT system. The power consumed/sourced by the pick-up converters of the three phases, depending on charging/discharging demands, can be calculated using (4) and (12) and given below: (13)Due to the complexity of the expression Vsr,n, the output power Pout,n cannot be explicitly expressed using (13). However, it can be seen from (12), (13) and (23) that the induced voltage Vsr,n on the pick-up side is determined by the mutual inductance Mi,j and input voltages Vpi,n and Vsi,n. Pad misalignment causes variations in the mutual inductance Mi,j, resulting in power variations under any given input voltages Vpi,m and Vsi,n. For example, Vsr1 on the pick-up coil of phase one for any given power level is determined by the mutual inductances M12, M23, M24, M25 and M26, the input voltages Vpi1, Vpi2, Vsi2, Vpi3 and Vsi3 and the load. The output power Pout,n in (13), therefore, can be regulated by controlling the input voltages Vpi,n and Vsi,n from converters through adjusting both phases (θpi,n and θsi,n) and phase shifts (φpi,n and φsi,n) under different pad misalignment conditions. With proper voltage control strategies, therefore, the power variation caused by pad misalignment can be effectively compensated. 4 Compensation for power variations due to pad misalignment 4.1 Charging pads used in three-phase and single-phase systems The power transfer in WPT systems is highly dependent on magnetic coupling between the charging pads on the primary and pick-up sides. The coupling changes when the pick-up pad is misaligned concerning the primary pad causing variations in power transfer. Coil spacings of the charging pad affect coupling coefficients impacting on the amount of power transfer. Two types of charging pads used in three-phase BD-WPT systems, with large coil spacing (480 mm) and small coil spacing (360 mm), were built for comparison, as shown in Figs. 4a and b, to investigate the distance between charging pads. They are referred to as Type 1 and Type 2 in this paper. As the coil configuration of the pad is symmetric, the variation in output power when the pick-up pad moves along the x-axis is the same as when the pick-up pad moves along a line at a 60° angle to the x-axis, as shown by the dashed arrows in Fig. 5. This paper analyses the coupling coefficient changes and power variations due to pad misalignment along the x-axis in detail, and all pad misalignment scenarios in Fig. 5 of the proposed system are considered. Fig. 4Open in figure viewerPowerPoint Charging pads used in the three-phase BD-WPT system and single-phase WPT system (primary side) (a) Coil spacing 480 mm (Type 1), (b) Coil spacing 360 mm (Type 2), (c) Charging pad used in the single-phase WPT system Fig. 5Open in figure viewerPowerPoint Pad misalignment when the pick-up pad moves along the x-axis concerning the primary pad The charging pad used in the proposed three-phase BD-WPT system consists of six simply wound coils on the primary and pick-up sides. The radius of each coil is 185 mm. Six coils are magnetically coupled to each other. The coupling coefficients are shown in Fig. 2. In the following analysis, the coupling coefficient ki,j is used to represent the mutual inductance Mi,j. In Fig. 2, k12, k34 and k56 are defined as main coupling coefficients (in red). The coupling coefficients between any two coils on the same side, k13, k15, k35, k24, k26 and k46, are referred to as side coupling coefficients (in blue). The remaining coupling coefficients k14, k16, k32, k36, k52 and k54 are defined as cross-coupling coefficients (in green). A typical single-phase WPT EV charging system, using one circular pad, shown in Fig. 4c, is modelled in MATLAB and simulated in SIMULINK/PLECS to benchmark against the proposed three-phase BD-WPT system. The coil's radius is 370 mm, and the dimension comparison between the charging pads used in the three-phase BD-WPT system and single-phase WPT system is shown in Fig. 4. 4.2 Variations of coupling coefficients due to pad misalignment The variations in all coupling coefficients of the pads are analysed and plotted in Fig. 6, when the pick-up pad moves along the x-axis from the perfect alignment position (x = 0 mm). Figs. 6a–c show coupling coefficients variations of the three-phase BD-WPT system with Type 1 charging pad (coil spacing 480 mm). Figs. 6d–f show coupling coefficients variations of the three-phase BD-WPT system with Type 2 charging pad (coil spacing 360 mm). Fig. 6Open in figure viewerPowerPoint Variations in the coupling coefficients of the pads used in the three-phase BD-WPT system and single-phase WPT system with pad misalignment along the x-axis (a) Main coupling coefficients of Type 1 pads; (b) Side coupling coefficients of Type 1 pads; (c) Cross-coupling coefficients of Type 1 pad; (d) Main coupling coefficients of Type 2 pad; (e) Side coupling coefficients of Type 2 pad; (f) Cross-coupling coefficients of Type 2 pad; (g) Coupling coefficients of the charging pad used in the single-phase WPT system Although coupling coefficients are always positive by convention, the polarity of induced voltages in this particular case changes with the position of the pick-up pad concerning the primary pad or misalignment as flux linkage changes from positive to negative. This effect is therefore represented using either a positive or a negative coupling coefficient. The output power Pout calculated from (13) is sum of the individual output power of three phases on the pick-up side, and it relates to three induced voltages Vsr,n, and the sign of Pout indicates whether a pick-up is delivering or receiving power. It should be noted that the polarity of Vsr,n is hard to observe directly from (11) and (23). According to Figs. 6a and d, the main coupling coefficients k12, k34 and k56 show identical trends; these coefficients drop steeply from 0.28 and 0.38 at x = 0 mm to −0.05 and −0.08 at x = 240 mm and rise slightly to −0.02 at x = 360 mm. When the pick-up pad aligns at around x = 180 mm, the main coupling coefficients drop to 0 and then become to negative values when the pick-up pad moves from x = 200 to 360 mm. The side coupling coefficients between any of two coils on the same side, shown in Figs. 6b and e, are smaller compared to the main coupling coefficients, and they are almost kept constant because the relative position of the coils on the same side does not change. Figs. 6c and f describe the variations in cross-coupling coefficients. The absolute value of k54 between coils 4 and 5 increases from −0.002 (Type 1) and −0.05 (Type 2) at x = 0 mm to 0.11 and 0.47 at x = 360 mm due to the closer proximity of coils 4 and 5. The cross-coupling coefficient k14 between coils 1 and 4 increases from −0.002 (Type 1) and −0.03 (Type 2) at x = 0 mm to around −0.05 and −0.09 in the range from x = 120 to 240 mm, and then decreases to around 0 at x = 360 mm. Other cross-coupling coefficients change to almost 0 when the pick-up pad is most misaligned and are negligible when the pick-up pad moves along the x-axis. Both Type 1 and Type 2 pads showed increases in cross-coupling coefficients with pad misalignment, which can potentially be used to compensate for power variation. In particular, Type 2 pad arrangement, which offers higher coupling coefficients, is more suitable for the proposed three-phase BD-WPT charging system as verified mathematically as well as with simulations and experimental results in Section 4.3. For a fair comparison, the variation in the coupling coefficient of the single-phase WPT system due to pad misalignment is also simulated and shown in Fig. 6g. The pad has a larger main coupling coefficient around 0.56 at x = 0 mm, compared with that of the pad of the three-phase BD-WPT system, which has the main coupling coefficients of around 0.28 (Type 1) and 0.38 (Type 2). The coupling coefficient drops slowly to 0 at around x = 340 mm, compared to the results of the three-phase BD-WPT system in Figs. 6a and d, where the main coupling coefficients k12, k34 and k56 drop to 0 at around x = 170 mm because the two-fold increase in diameter of the pad in single-phase WPT system allows an almost two-fold increase in the misalignment range. 4.3 Power variations due to pad misalignment and proposed compensation control strategy Pad misalignment invariably leads to changes in coupling coefficients, causing power variations. A 1.3 kW three-phase BD-WPT system using two types of charging pads shown in Figs. 4a and b, was modelled in MATLAB and simulated in SIMULINK/PLECS, to investigate this effect as well as to validate the developed theoretical model and to propose a control method to compensate for the power variation. A single-phase WPT system, using the charging pad shown in Fig. 4c, was modelled and simulated to compare with the proposed three-phase BD-WPT system. When the Type 1 charging pad was used in the three-phase BD-WPT system, the primary converters of three phases were powered by a 200 V DC power supply, and the pick-up converters were connected to a 200 V DC active load. Each converter was designed to source or consume up to 420 W of power. The primary and the pick-up of the system were operated at a tuned frequency of 85 kHz with a 120° phase difference between three phases so that Vpi2 lagged Vpi1 by 120° and Vpi3 led Vpi1 by 120°. The relative phase angle θ between Vpi,n and Vsi,n of three phases was set at 90°, and phase shifts φpi,n and φsi,n between the legs of each converter on both sides were set at 90°, to deliver rated 650 W of power from the primary side to the pick-up side. The parameters of the proposed three-phase BD-WPT system are given in Table 1. When the Type 2 charging pad was used in the three-phase BD-WPT system, the input voltage was set at 158 V DC to transfer rated 650 W of power because of higher main coupling coefficients. The single-phase WPT system was operated at the same condition except the 232 V DC input voltage to deliver 650 W of power. Table 1. Parameters of the three-phase BD-WPT system prototype Parameter Measured value Vin = Vout 200/158 Vdc (using Type 1/2 pad) Lpi1, Lpi2, Lpi3 39.24 μH, 39.42 μH, 39.53 μH Rpi1, Rpi2, Rpi3 33.2 mΩ, 33.4 mΩ, 33.5 mΩ Lpt1, Lpt2, Lpt3 (x = 0 mm) 35.77 μH, 35.98 μH, 36.15 μH Rpt1, Rpt2, Rpt3 78.5 mΩ, 66.1 mΩ, 55.4 mΩ Lsi1, Lsi2, Lsi3 38.57 μH, 39.29 μH, 39.52 μH Rsi1, Rsi2, Rsi3 32.9 mΩ, 33.2 mΩ, 33.5 mΩ Lst1, Lst2, Lst3 (x = 0 mm) 35.89 μH, 36.16 μH, 35.62 μH Rst1, Rst2, Rst3 63.8 mΩ, 69.4 mΩ, 72.1 mΩ Cpt1, Cpt2, Cpt3 97.31 pF, 97.74 pF, 94. 25 pF Cst1, Cst2, Cst3 97.42 pF, 96.15 pF, 97. 46 pF Cp1, Cp2, Cp3 2.47 μF, 2.32 μF, 2.36 μF Cs1, Cs2, Cs3 2.31 μF, 2.29 μF, 2.43 μF frequency 85 kHz air gap 106 mm (Type 1), 84 mm (Type 2) switches C3M0065090D power rating 1.3 kW Figs. 7 and 8 show the output power of the single-phase WPT system and the three-phase BD-WPT system using Type 1 charging pad (coil spacing 480 mm) and Type 2 charging pads (coil spacing 360 mm), respectively. The three red lines represent the theoretical results and the three blue lines show the simulation results when the pick-up pad was misaligned at different positions from 0 to 360 mm along the x-axis concerning the primary pad. Fig. 7Open in figure viewerPowerPoint Output power with pad misalignment along the x-axis of the three-phase BD-WPT system with Type 1 charging pad (coil spacing 480 mm) and the single-phase WPT system Fig. 8Open in figure viewerPowerPoint Output power with pad misalignment along the x-axis of the three-phase BD-WPT system with Type 2 charging pad (coil spacing 360 mm) and the single-phase WPT system The uncompensated output power of the three-phase BD-WPT system is plotted in dashed lines. The proposed system was operated to supply a power of 650 W forward at x = 0 mm. When the pick-up pad misaligned along the x-axis from 0 to 200 mm, shown in Figs. 7 and 8, the power consumed by the pick-up side dropped significantly from 650 to 0 W, because the main coupling coefficients k12, k34 and k56 decreased from 0.28 (Type 1 charging pad) and 0.38 (Type 2 charging pad) to 0 as shown in Figs. 6a and d. The pick-up side began to supply power back instead of consuming it when the pick-up pad was placed in the range of x = 200–360 mm since the polarities of induced voltages across the pick-up coils changed. The proposed system facilitates the control of six converters individually to regulate power flow in terms of both magnitude and direction in each phase. By changing the relative voltage phase angle between Vpi,n and Vsi,n and modulating the phase shifts φpi,n and φsi,n of the voltages from converters to control the currents in the coupled coils, the flux generated by coil currents can be enhanced to deliver more power when the coupling increases. The solid lines in Figs. 7 and 8 present the compe
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