Improved Resonant Converter for Dynamic Wireless Power Transfer Employing a Floating-Frequency Switching Algorithm and an Optimized Coil Shape

This paper offers a new EF-class converter for dynamic wireless power transfer application. The proposed high-frequency converter employs a floating-frequency switching algorithm to control the converter in a continuous frequency range, eliminate the requirement to any additional operational data from the secondary (receiver) side, accelerate the load impedance match while moving, maximize the transferred power rate, reduce charging interval and compensate power transfer tolerances. Moreover, an optimized super elliptical shape coil is designed to cope with lateral misalignment, enhance coil coupling, and increase efficiency. In the proposed converter, (i) soft switching is implemented to increase switching frequency, decrease passive components size, and improve power density, (ii) undesired voltage harmonics are attenuated to reduce peak voltage stress of the power switch in a wide frequency range, (iii) the receiver side is enabled for higher mobility with stable power transfer, and (iv) the resonant frequency is updated to compensate non-accurate values of passive components in experimental prototyping. In this study, the operational analytics, compensation method, control algorithm, coil design and converter optimization are followed with some comparisons to present the converter capabilities. In addition, simulation and experimental results are provided under different degrees of misalignment to verify the accuracy of theoretical analytics.


I. INTRODUCTION
With wide applications in electrical vehicles [1], medical devices [2], robotics [3], and mobile phones [4], wireless power transfer (WPT) is becoming an emphatic, growingly-dominant and controversial issue in industry. This challenging power transfer method provides isolation between source and load ports, prevents connector fatigue, diminishes over-dependence on the charging battery, presents more flexibility, and improves the reliability rate in undesirable environmental conditions [5]. Meanwhile, coil coupling, operation in misalignment, parasitic components, topology and coil shape design, power transfer rate, charge duration, and receiver-side data transfer have been the main issues to be researched and improved in recent years [6]. In [7], the effect of misalignment tolerance has been analyzed on the transferred power and output voltage of an inductive WPT resonant converter where different compensation methods have been tested. Other recent studies have investigated the efficiency improvement of the WPT technique by co-implementing of inductive and capacitive methods [8], cascading a buck-boost converter [9], optimizing driver operation [10], utilizing a series-parallel resonant coupling [11], and adding an intermediate coil [12]. Moreover, a multi-phase parallel inverter and a parallel LCL topology have been used in [13,14], respectively, to enhance the transferred power.
Dynamic wireless power transfer (DWPT) is one of the emerging subject matters in industrial and research fields, which presents some additional features, such as charging interval, installed battery size, weight and cost reduction. Moreover, it can improve battery life [15]. In [16], a converter has been introduced for DWPT with mutual inductance (MI) estimation in misalignment. However, low switching frequency has increased its coil size. In [17], a resonant converter utilizing a φ2 class inverter has been presented to reduce input current ripple where the obtained efficiency is low. The suggested converter in [18] has concentrated the control algorithm improvement by utilizing an active rectifier for simultaneous implementation of a phase-locked loop and a chained trigger mode, which has led to a complicated control system. In [19], a multiphase WPT converter has been presented. Although it has been aimed to improve transferred power rate, employing a high number of semiconductors has restricted industrial applications of [19]. The presented converter in [20] has tried to accomplish a higher power transfer rate in DWPT by integrating a two-layer receiver-side coil; meanwhile, using four resonant tanks with series compensation has increased the system weight. In [21], different compensation approaches have been evaluated in a DWPT converter to decrease load voltage sensitivity in misaligned conditions. In addition, detailed analytics of a resonant WPT converter with series-series compensation and using a dq synchronous reference frame model have been provided in [22]. The literature [23] has aimed to compensate coupling factor changes in a DWPT converter by employing an active variable reactance rectifier. The main drawbacks of [23] are the requirement for a secondary control system and operation under a fixed frequency. In [24][25][26], the effects of a series/series-parallel compensation tank, ferrite core geometry and resonant frequency mismatch have been evaluated on the efficiency and output voltage of the DWPT system. The suggested converter in [27] has concentrated on solving the current imbalance problem of a WPT system with a high order resonant tank. Nevertheless, the accessibility requirement of sender and receiver ports for control implementation has restricted its applicability. In [28], a new topology for WPT has been introduced to widen loading conditions where high number of passive and active components has reduced its efficiency. The main aim of [29] is to suggest a soft switching inverter with WPT application; however, load and MI changes, misalignment, and frequency modulation have not been considered. The literature [30] has proposed a new multi-phase structure for WPT. Although using a multi-phase rectifier has improved the power transfer rate, poor coil coupling has limited the application of [30] in low power implementation. In [31], a maximum efficiency point tracking algorithm has been suggested for a DWPT converter where the wireless communication between the sender and receiver has increased cost and restricted its application in noisy enlivenments.
In this paper, a new resonant converter is proposed for the DWPT application where its main contribution can be categorized in: (i) a new topology to reduce switch voltage stress and attenuate undesired voltage harmonics, (ii) an optimized coil shape to improve dynamic coil coupling, cope with misalignment and enhance power density, and (iii) a floating-frequency switching algorithm with receiverside data estimation to accelerate the load impedance match while moving, maximize the transferred power rate, reduce charging interval, and compensate power transfer tolerances. The main application of the proposed converter is in the wireless charging system of low power robotic carriers. The rest of this paper is organized as follows: In Section II, the proposed DWPT topology is introduced. Section III is devoted to the converter operation features and optimized design. Section IV presents the implemented floating-frequency switching algorithm. Comprehensive optimized-coil design and operation are provided in Section V which are followed by the experimental results of a 0.8kW prototype in Section VI, and the conclusion in Section VII.

II. PROPOSED RESONANT CONVERTER
The proposed resonant DWPT converter for the robotic carrier's application is shown in Fig. 1(a), which consists of an input DC supply, a Chebyshev filter, a single switch (S) inverter, primary-and secondary-side compensated resonant tanks, a WPT coil, a receiver-side rectifier, output filter (Lo) and output load (Ro). The WPT coil is modeled through a sender (LS) and a receiver (LR) self-inductance, and a mutual inductance (M). Moreover, RS, RR, CS and CR are the internal coil resistances and compensation capacitors, respectively. In this topology, a series-series compensation is employed in the sender-receiver sides, which provides higher efficiency, simpler analytics, and easier control than other compensation approaches [18,22]. The T-model of the simplified topology for first harmonic with components reflection to the AC side is depicted in Fig. 1(b) which leads to (1) 2017 9 In (1) (3)

A. Optimized Topology Design
The coupling factor between the sender and receiver coils is defined as follows: (4) Unlike transformers with constant k values close to the unit, k equals much lower values in DWPT systems. Moreover, due to the permanent misalignment of coils while moving, M and consequently k are variable. The main aim of the proposed DWPT converter is to improve k, which is equivalent to transferring higher portion of energy from the sender to the receiver coil, and preventing energy storage in the coils leakage inductances. Considering X = XS = XR and ignoring Ri, RS and RR in Fig. 1(b), output power of the proposed converter is given by (1 ) In order to maximize Po with regards to the tank design, /0 = o dP dX should be satisfied, which results in 0 = X or 2 − M  . In other words, XS and XR should be simultaneously equal to zero to improve k values to the unit which can be summarized as ( With variable values of M, (6) leads to = S R L L and = S R CC . Therefore, the primary-and secondary-side tanks parameters should be designed the same to obtain optimized power transfer. Based on Fig. 1(b), equation of the converter efficiency is concluded as follows: By ignoring RS and RR, and full compensation of XS and XR, (7) can be simplified as  (9) and (10), respectively. As evaluated in this section, optimization of Po and  , or reduction of Po and  sensitivities with respect to (AC) o R contribute to different design and operation conditions. In other words, simultaneous optimization of these factors is unfeasible. In this paper, optimization of Po under acceptable  is focused, which is suitable for battery size and charging time reduction.

B. Chebyshev Filter Design
According to the misalignment, variable M, and the requirement of load impedance matching to maximize the transferred power rate, the proposed DWPT converter should operate with floating frequency. Therefore, main features of the converter should be achievable in a wide frequency spectrum. In this paper, a Chebyshev filter is implemented in the primary side of the proposed converter which presents (i) higher attenuation rate than Butterworth and Bessel filters, and (ii) less sensitivity to the passive components values than Elliptical filters. This band rejection filter should be designed to attenuate the 2 nd -order harmonic of f which satisfies lower switch voltage stress and soft switching in S. In this case, the DWPT converter becomes capable to operate with higher input voltage and power transfer rate. In addition, various families of power switches with low drain-to-source resistances and higher switching frequencies can be utilized as S which facilitates the manufacturing procedure. Based on the filter design rules in [32] and the attenuation profile of a band rejection filter in Fig. 2, the filter bandwidth proportion is defined as 4 1 where, C BW and BW are the corresponding 3dB and desired attenuation bandwidth, respectively. In this paper, /2 C BW BW = is selected where the desired attenuation of 20dB and considering the bandwidth ripple of 1dB result in a 3 rd -order Chebyshev filter in Fig. 1(a). The filter components are designed based on (12) for parallel and (13) for series resonant tanks [32].
where, Cn, Ln and f0 = 2 f are the normalized capacitor and inductor, and the cutoff frequency of the Chebyshev filter. They are equal to 2.216 n C = and 1.088 n L = for the initial design assumption of this paper [32]. Furthermore, the input inductor of the proposed converter is calculated as 1 22 4   1  9 L fC  = (14)

C. Switch Voltage Stress
In some previous literature, switch voltage stress decrease is concentrated where the presented φ2 class converter in [33] is one of the most successful candidates. That converter comes up with the switch voltage stress of which provides higher input voltage, power density, and switching frequency capabilities. Meanwhile, narrow band rejection spectrum restricts the applicability of [33] in DWPT systems with high misalignment tolerance. This drawback is expressed in Fig.  3 where all features-i.e., low switch voltage stress and soft switching-are lost in a little frequency variation of 7.5% − f . In order to cope with misalignment and floating frequency, the proposed converter presents a wider band rejection spectrum, which is demonstrated with the seen impedance magnitude evaluation of switch (   As depicted in Fig. 1(a), capacitor C4 is placed in parallel with S which can be either the parasitic capacitance of S, or a separate external capacitor. Attenuation of ds Z in the 3 rd -order harmonic is the main role of C4, and it should be designed large enough to present acceptable attenuation. The effect of C4 on the switch voltage stress is shown in Fig. 6.

D. Zero Voltage Switching
High switching frequency, high power density and low resonant tank size are the capabilities satisfied through soft switching condition. As compared in Fig. 7, zero voltage switching (ZVS) is achieved in a wider switching frequency band for the proposed converter than the φ2 class converter. Note that the lagging phase of  ds Z provides ZVS condition for S ( 0  ds Z ). In order to finalize the proposed converter capabilities verification, normalized

IV. VARIABLE FREQUENCY CONTROL STRATEGY
Inaccessibility of receiver-side control signals in the primary side, due to the lack of feedback control loop, is the main challenge in the control procedure of a WPT system. In some previous literature, wireless signal communication is introduced to develop a closed loop feedback from the receiver to the sender side [27, 34 and 35]. Meanwhile, FIGURE 10. Control diagram of the DWPT system based on receiver-side data estimation.
complicated control system, various environmental conditions and noise of the environment or the WPT converter restrict wireless signal communication applicability. These obstacles are highlighted in DWPT systems due to permanent misalignment of coils. In this paper, a simple control algorithm based on the receiver-side data estimation is presented to overcome the aforementioned obstacles (see Fig. 10). Considering the operation conditions of DWPT, some initial requirements should be satisfied. For instance, a coil-embedded road is necessary for electrical vehicles DWPT where the data of the load and receiver-side coil/compensator (based on vehicles standard design) are detected in the beginning of the road to pay the charges. With this sensible assumption and without any additional measured data from the receiver side, the proposed method estimates the receiver-side load current ( (k) This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
In the preceding equations, is obtained from (6), and based on the estimated output power value, f is increased or decreased which reflects the increment or reduction of M, respectively. Eventually, by reducing M (f), the alignment of sender and receiver coils decreases to zero and the control loop ends. Using this control algorithm helps to (i) faster dynamic response and load impedance match due to less measurements and data transfer, (ii) shorter charging interval, (iii) better resonant tank compensation, (iv) effective operation in noisy environments and (iv) higher power transfer rate while moving.

V. COIL FORMULATION, DESIGN AND OPERATION
Misalignment is inevitable in DWPT; hence, designing suitable resonant tank coils to satisfy the desired features alongside with misalignment is a challenging issue. Transferring high power in the fully aligned condition is the main characteristic of circular coils. However, MI decreases sharply in the misalignment. On the other hand, rectangular coils present lower MI with less sensitivity to the misalignment. This paper aims to propose the aforementioned features simultaneously. Therefore, the receiver coil is considered to be a super ellipse and the formulations are presented for the generalized shape conditions. Fig. 11 illustrates the location and shape of the sender (circle) and receiver (super ellipse) coils considering misalignment where the circle and super ellipse are centered at x are the longitudinal and lateral misalignments, respectively.
As discussed in Section III Part A, the higher M , the more transferred power rate. In this case, coil shape does not have any effect on the  values; meanwhile, it plays a determinative role in coils coupling. Therefore, MI can be considered as a metric to evaluate the capability of the coils in power transferring. Equations of magnetic potential (A) and MI of the depicted coils system in Fig. 11 are equal to [36] A dr (19) where, J1, 0  , e  and C are Bessel function of the first kind of order one, vacuum permeability coefficient, unit vector and integral closed loop path of the receiver coil, respectively. For a general super elliptical coil centered at where, n is the order (curve coefficient) of a super ellipse in the cylindrical coordinate system, and In order to take the impact of misalignment into account, the below-curve area of M in the whole range where two coils face each other is defined as Mdy q (24) In (24), q is the perimeter of receiver coil which is utilized to normalize the MI with regards to the coil size.
To evaluate effect of the parameters in Fig. 11 and achieve the optimized receiver coil shape, (21) is plotted under different conditions and M is calculated for each plot in Fig. 12. In Fig. 12(a), "b" is considered constant and  the effect of "a" variation is tested in different "n". The outcome verifies that a = b presents the highest M in all "n"; therefore, it is selected as the best solution for the super ellipse semi-axes. Moreover, it is clear that the super ellipse ( 2  n ) owes higher M than the corresponding circle ( 2 = n ) with the same diameter, which is reflected in the M improvement of 6% and 5% in 3 = n and 4 = n , respectively. This is the result of better coil coupling in the super ellipse than the circle during misalignment.
The next step is to select "n" which is assessed in Figs. 12(b)-(f) and Table 1 present the best feature. In this paper, 3 = n is selected for the receiver coil because: (i) it leads to lower coil copper (weight) than 3.5 = n , and (ii) it provides better coil coupling around laterally-aligned condition with higher power transfer. The geometrical shape of a super ellipse with 3 = n is shown in Fig. 13(a).  This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
It is clear that the accuracy of the model depends on the number of considered Taylor series terms where four terms are selected in this paper, and the result is satisfactory in Fig. 13(b). As a result of these simulations, the simulated MI plot in Fig. 14(a) verifies the theoretical plot of Fig.  12(a) for n = 3 which is tested without ferrite magnetics. In Fig. 14(b), k is depicted with respect to y2 and as declared, the obtained coupling coefficient is low without ferrite magnetics. Therefore, in order to enhance k and also satisfy the safety issues of industrial chargers, some ferrite magnetics are placed behind each coil, and the result shows considerable improvement of k in Fig. 14(c).

VI. EXPERIMENTAL VERIFICATION
The experimental setup and its components are illustrated in details in Fig. 15. Moreover, the designed values of converter and coils are tabulated in Table 2 where the Chebyshev filter components are designed to attenuate the 2 nd order harmonic of switch voltage stress for 20dB. As a practical design consideration, CS and CR are implemented by a series-parallel combination of film capacitors to: (i) reduce their equivalent series resistance (ESR), and (ii) tolerate high voltage and current stresses. Instead of utilizing Litz wiring for the coils, they are built with a thicker single-string wire since it presents better forming features in circle and super ellipse shapes. In addition, due to the existence of sufficient air gap in the ferrite-magnetimplemented coils, saturation of ferrite cores is ignored in the design procedure. Fig. 16 shows the examples of experimental results under different misalignment conditions where Vi (DC) = 70V.
In Figs. 16(a)-(c), the floating f is equal to 513.9 kHz, 496.8 kHz and 475.1 kHz to cope with the coupling coefficients of k = 0.1, k = 0.05 and k = 0.01, respectively, which verifies the capability of the proposed topology in maximizing the transferred power, accelerating loadimpedance match, correct receiver-side load current and MI estimation, low switch voltage stress and coping with misalignment. Fig. 16(a) reflects the converter operation in its maximum MI of 2 μH where the 2 nd -order harmonic of switch voltage stress is attenuated considerably. Moreover, the 3 rd -order harmonic of Vds is low by selecting an adequate value for C4 and ZVS is satisfied. As the main feature expressed in Figs. 16(b) and (c), the proposed converter provides maximum possible power transfer, acceptable power efficiency and ZVS simultaneously, even in the very low coupling coefficient of k = 0.01. In Fig.  16(d), the Fast Fourier Transform (FFT) spectrum of Vds is presented, which highlights the 2 nd -order harmonic attenuation and low value of the 3 rd -order harmonic. As discussed in Section II, achieving the maximum power transfer and the highest efficiency is not feasible simultaneously. Hence, a strategy is considered in the experimental tests to obtain maximum power transfer with acceptable efficiency. However, higher misalignment values lead to MI, and then efficiency, drop sharply. In this case, in order to prevent low efficiency values, f is adapted with small changes to improve efficiency, which results in little output power decrease. The two-and three-VOLUME XX, 2017 9 dimensional plots of output power and efficiency with respect to misalignment are shown in Fig. 17 and Fig. 18, respectively. As concluded from Fig. 18, the maximum power transfer is achieved in a ring centered at 22 ( , ) (0,0) = xy by implementing the proposed switching algorithm.

VII. CONCLUSION
In this paper, a new DWPT converter was proposed for the wireless charging system of the robotic carriers, which focused on improving topology operation characteristics, control strategy and coil shape design. The proposed topology employed a 3 rd -order Chebyshev filter in the sender side to attenuate the switch voltage 2 nd -order harmonic in a wider switching frequency spectrum with low attenuation ripple. Moreover, the switch parallel capacitor was designed to attenuate the switch voltage 3 rdorder harmonic while providing ZVS condition for the main switch. This condition enabled the proposed converter to operate under high switching frequency, low switching power loss, low passive components size, and high power density. From the control strategy point of view, a floatingfrequency switching algorithm was implemented on the proposed converter with no requirement to any load-side data measurement. This simple switching algorithm, which utilized the estimated mutual inductance to regulate the switching frequency, leaded to faster dynamic response in misalignment, higher mobility of receiver side, better resonant tank compensation, higher power transfer rate while moving, faster charging, and wider industrial applicability of the proposed converter in noisy environments. As one of the significant contributions of this paper, the optimized coils with circle and super ellipse ( 3 = n ) shapes in the sender and receiver sides were analyzed, evaluated and designed to achieve maximum power transfer and low sensitivity to the misalignment. The results verified the enhancement of more than 5% in the transferred power of the designed coil than the circular one for various misalignment conditions. In this paper, the design specifications, operation features and comparison outcome were validated through finite element simulation and experimental results.