Free-positioning multi-transmitter-coil wireless power transfer system with non-coherent power combining

Abstract

According to an aspect, there is provided a method for feeding a wireless power transfer, WPT, transmission coil arrangement comprising a plurality of transmission coils arranged as a 4 × 4 planar array. The method comprises feeding the plurality of transmission coils in the 4 × 4 planar array with a plurality of power signals corresponding, each, to a combination of a first power signal having a first frequency and a second power signal having a second frequency different from the first frequency. Phases of the first and second power signals for each transmission coil are selected such that full positional and rotational charging freedom is enabled for receiver devices.

Description

FREE-POSITIONING MULTI-TRANSMITTER-COIL WIRELESS POWERTRANSFER SYSTEM WITH NON-COHERENT POWER COMBINING TECHNICAL FIELD

[0001] Various example embodiments relate to wireless power transfer.BACKGROUND

[0002] In order to realize a large-area wireless power transfer (WPT) transmitter (Tx)device, Tx coils of the large-area WPT Tx device are typically spread over a suitably largetransmitting area. Ideally, regardless of the position and orientation of a WPT receiver (Rx)device, there should always be multiple Tx coils which are able to couple to the WPT Rxdevice. However, conventional ways of supplying and controlling such multi-Tx-coil WPTtransmitters have limited charging freedom or suffer from blind spots within the chargingarea. Blind spots are defined as positions where, although the WPT Rx device is still insidethe transmitting area of the WPT Tx device, no power transfer occurs between the twodevices. SUMMARY

[0003] According to an aspect, there is provided the subject matter of the independentclaims. Embodiments are defined in the dependent claims.

[0004] According to a first aspect, there is provided a method for feeding a wirelesspower transfer, WPT, transmission coil arrangement comprising a plurality of transmission coils arranged as a 4 × 4 planar array, the method comprising: feeding the plurality of transmission coils in the 4 × 4 planar array with a pluralityof power signals corresponding, each, to a combination of a first power signal having afirst frequency and a second power signal having a second frequency different from thefirst frequency, wherein phases of the first and second power signals for a transmission coil of an i-th row & a j-th column of the 4 × 4 planar array are defined as: -for i = 1 & j = 1, phases of the first and second power signals are 0° and 0°,- for i = 2 & j = 1, phases of the first and second power signals are 270° and 0°,- for i = 3 & j = 1, phases of the first and second power signals are 270° and 270°,- for i = 4 & j = 1, phases of the first and second power signals are 0° and 270°,- for i = 1 & j = 2, phases of the first and second power signals are 90° and 0°,- for i = 2 & j = 2, phases of the first and second power signals are 180° and 0°,- for i = 3 & j = 2, phases of the first and second power signals are 180° and 270°,- for i = 4 & j = 2, phases of the first and second power signals are 90° and 270°,- for i = 1 & j = 3, phases of the first and second power signals are 90° and 90°,- for i = 2 & j = 3, phases of the first and second power signals are 180° and 90°,- for i = 3 & j = 3, phases of the first and second power signals are 180° and 180°,- for i = 4 & j = 3, phases of the first and second power signals are 90° and 180°,- for i = 1 & j = 4, phases of the first and second power signals are 0° and 90°,- for i = 2 & j = 4, phases of the first and second power signals are 270° and 90°,- for i = 3 & j = 4, phases of the first and second power signals are 270° and 180°,and -for i = 4 & j = 4, phases of the first and second power signals are 0° and 180°.

[0005] According to a second aspect, there is provided method for feeding a wirelesspower transfer, WPT, transmission coil arrangement comprising a plurality of transmission coils arranged as a 4 × 4 planar array, the method comprising: feeding the plurality of transmission coils in the 4 × 4 planar array with a plurality of power signals corresponding, each, to a combination of a first power signal having a first frequency or a second frequency different from the first frequency and a secondpower signal having the first frequency or the second frequency, wherein frequencies andphases of the first and second power signals for a transmission coil of an i-th row & a j-th column of the 4 × 4 planar array are defined as: -for i = 1 & j = 1, the first and second power signals have the first frequency,and phases of the first and second power signals are 0° and 90°, -for i = 2 & j = 1, the first and second power signals have, respectively, thesecond and first frequencies, and phases of the first and second power signals are 180° and 90°, -for i = 3 & j = 1, the first and second power signals have the second frequency,and phases of the first and second power signals are 180° and 270°,- for i = 4 & j = 1, the first and second power signals have, respectively, thefirst and second frequencies, and phases of the first and second power signals are 0° and 270°, -for i = 1 & j = 2, the first and second power signals have, respectively, thesecond and first frequencies, and phases of the first and second power signals are 0° and 90°, -for i = 2 & j = 2, the first and second power signals have the first frequency,and phases of the first and second power signals are 180° and 90°, -for i = 3 & j = 2, the first and second power signals have, respectively, thefirst and second frequencies, and phases of the first and second power signals are 180° and 270°, -for i = 4 & j = 2, the first and second power signals have the second frequency,and phases of the first and second power signals are 90° and 270°, -for i = 1 & j = 3, the first and second power signals have the second frequency,and phases of the first and second power signals are 0° and 90°, -for i = 2 & j = 3, the first and second power signals have, respectively, thefirst and second frequencies, and phases of the first and second power signals are 180° and 90°, -for i = 3 & j = 3, the first and second power signals have the first frequency,and phases of the first and second power signals are 180° and 270°, -for i = 4 & j = 3, the first and second power signals have, respectively, thesecond and first frequencies, and phases of the first and second power signals are 90° and 270°, -for i = 1 & j = 4, the first and second power signals have, respectively, thefirst and second frequencies, and phases of the first and second power signals are 0° and 90°, -for i = 2 & j = 4, the first and second power signals have the second frequency,and phases of the first and second power signals are 180° and 90°, -for i = 3 & j = 4, the first and second power signals have, respectively, thesecond and first frequencies, and phases of the first and second power signals are 270° and 270°, and -for i = 4 & j =4, the first and second power signals have the first frequency,and phases of the first and second power signals are 0° and 270°.

[0006] According to a third aspect, there is provided a method for feeding a wirelesspower transfer, WPT, transmission coil arrangement comprising a plurality of transmission coils arranged as a 4 × 4 planar array, the method comprising: feeding the plurality of transmission coils in the 4 × 4 planar array with aplurality of power signals corresponding, each, to a combination of a first power signalhaving one of first, second, third and fourth frequencies and a second power signal havingone of first, second, third and fourth frequencies, wherein the first, second, third and fourth frequencies are different from each other, and frequencies and phases of the first and second power signals for a transmission coil of an i-th row & a j-th column of the 4 × 4 planar array are defined as: -for i = 1 & j = 1, the first and second power signals have, respectively, thefirst and second frequencies, and phases of the first and second power signals are 0° and 0°,- for i = 2 & j = 1, the first and second power signals have, respectively, thethird and second frequencies, and phases of the first and second power signals are 180° and0°, -for i = 3 & j = 1, the first and second power signals have, respectively, thethird and fourth frequencies, and phases of the first and second power signals are 180° and180°, -for i = 4 & j = 1, the first and second power signals have, respectively, thefirst and fourth frequencies, and phases of the first and second power signals are 0° and 180°,- for i = 1 & j = 2, the first and second power signals have, respectively, thethird and second frequencies, and phases of the first and second power signals are 0° and 0°,- for i = 2 & j = 2, the first and second power signals have, respectively, thefirst and second frequencies, and phases of the first and second power signals are 180° and0°, -for i = 3 & j = 2, the first and second power signals have, respectively, thefirst and fourth frequencies, and phases of the first and second power signals are 180° and180°, -for i = 4 & j = 2, the first and second power signals have, respectively, thethird and fourth frequencies, and phases of the first and second power signals are 0° and180°, -for i = 1 & j = 3, the first and second power signals have the third and fourthfrequencies, and phases of the first and second power signals are 0° and 0°,- for i = 2 & j = 3, the first and second power signals have, respectively, thefirst and fourth frequencies, and phases of the first and second power signals are 180° and0°, -for i = 3 & j = 3, the first and second power signals have, respectively, thefirst and second frequencies, and phases of the first and second power signals are 180° and180°, -for i = 4 & j = 3, the first and second power signals have, respectively, thethird and second frequencies, and phases of the first and second power signals are 0° and180°, -for i = 1 & j = 4, the first and second power signals have, respectively, thefirst and fourth frequencies, and phases of the first and second power signals are 0° and 0°,- for i = 2 & j = 4, the first and second power signals have, respectively, thethird and fourth frequencies, and phases of the first and second power signals are 180° and0°, -for i = 3 & j = 4, the first and second power signals have, respectively, thethird and second frequencies, and phases of the first and second power signals are 180° and180°, and -for i = 4 & j = 4, the first and second power signals have, respectively, thefirst and second frequencies, and phases of the first and second power signals are 0° and180°.

[0007] According to a fourth aspect, there is provided an N-legged converter for directcurrent to alternating current, AC-to-DC, conversion, wherein the N-legged converter is configured to implement the method according to any of the first, second or third aspect for feeding the WPT transmission coil arrangement comprising at least the plurality of transmission coils arranged as the 4 × 4 planar array.

[0008] According to a fifth aspect, there is provided a WPT transmitter comprising:a WPT transmission coil arrangement comprising a plurality of transmission coils arranged as a 4 × 4 planar array; a plurality of compensation networks, respectively, for the plurality of transmission coils; the N-legged converter according to the fourth aspect, wherein each leg of the N-legged converter is connected to a transmission coil of the WPT transmission coilarrangement via a compensation network of the plurality of compensation networks; anda direct current, DC, voltage source connected to the N-legged converter.

[0009] According to a sixth aspect, there is provided a WPT transmission–receptionsystem comprising: a WPT transmitter according to the fifth aspect; and one or more WPT receivers comprising, each, at least one reception coil for mutually coupling to the plurality of transmission coils.

[0010] One or more examples of implementations are set forth in more detail in theaccompanying drawings and the description below. Other features will be apparent from the description and drawings, and from the claims. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] FIGs. 1A & 1B illustrate a system for wireless power transfer according to anembodiment from above and in a cross-sectional side view;

[0012] FIG. 2 illustrate a WPT feeding configuration for a WPT transmission coilarrangement comprising a plurality of transmission coils arranged as a 4 × 4 planar arrayaccording to an embodiment;

[0013] FIG. 3 illustrates a two prior WPT feeding configurations for a WPTtransmission coil arrangement comprising a plurality of transmission coils for reference;

[0014] FIG.4 illustrates one exemplary implementation a transmission coil along withits compensation circuit;

[0015] FIG. 5 illustrates two alternative reception coil structures usable inembodiments;

[0016] FIG.6 illustrates, in top part, receiver movements with regard to a transmissioncoil along with the defined reference flux direction for each coil and, in bottom part, mutualinductance Mij variations in terms of the value and sign (positive / negative);

[0017] FIG. 7 illustrates an N-legged converter according to an embodiment for directcurrent to alternating current (DC-to-AC) conversion;

[0018] FIG. 8 illustrates an equivalent circuit for a Tx building block according to anembodiment;

[0019] FIG. 9 illustrates a receiver-side simplified circuit with ideal AC voltagesources;

[0020] FIG. 10 illustrates receiver-side power combinations (induced voltage vectors)within the transmission area: examples of (a) non-coherent combination at multiple frequencies, (b) coherent, special Case 1: single frequency with the same phase, (c) coherent,special Case 2: single frequency with 90° phase difference; and

[0021] FIGs.11 & 12 illustrate two alternative WPT feeding configurations for a WPTtransmission coil arrangement comprising a plurality of transmission coils arranged as a 4 × 4 planar array according to two embodiments. DETAILED DESCRIPTION OF SOME EMBODIMENTS

[0022] In the following, the following mathematical notational conventions areemployed. Vectors are denoted using non-bold italic letters with an overlining (horizontal)arrow. Scalars are denoted using non-bold italic letters.

[0023] In the following, the term “power signal” may be defined as an electromagneticsignal or field generated by a wireless power transfer (WPT) transmitter to transfer energywirelessly to a WPT receiver. Unlike data signals, a wireless power signal is designed typically solely for the purpose of delivering energy to charge or power devices withoutphysical connections, using inductive, resonant, or radiative coupling methods. A powersignal may be equally called a wireless power signal (WPS), an energy signal or a wireless energy signal.

[0024] Efficient and uninterrupted wireless power transfer (WPT) in a large areafacilitates wireless charging for a wide range of applications encompassing consumer electronics [1], kitchen appliances [2], and automated robots [3]. For example, a WPT system employing multiple transmitters (Txs) can be integrated into a table or kitchen top toenable seamless charging of multiple consumer electronics devices and kitchen appliances.

[0025] Compared to the solutions using a single large Tx coil [3] or supply rails [4],applications of multiple small Tx coils [5] are more flexible, and provide possibilities of charging multiple receivers (Rxs) at the same time. In a multi-Tx system, it is easier to avoid standby losses and unwanted electromagnetic exposure by turning off the Tx coils in the uncoupled areas [6], [7].

[0026] By arranging spiral Tx coils in a transmitting array [8], [9], conventionalsolutions achieve one-dimensional (1D) charging freedom for linear Rx movements. To enhance the charging freedom in a 2-dimensional (2D) space, there have been numerous studies targeting higher transfer robustness and misalignment tolerance. Different coupler structures such as DD-type

[0010] , DDQ-type

[0011] , quadrature coils

[0012] , fluxpipe

[0013] , or crossed-flat solenoid coils

[0014] have been employed to optimize the transfer power and efficiency at misaligned Rx positions. However, the above solutions bring rapid increases to the complexity of coil structures as well as the design process. Besides, the designs in

[0010] ,

[0014] allow only linear Rx movements, while the solution

[0012] needs additional control algorithms and circuits to reach the rotational charging freedom.

[0027] On the other hand, to keep relatively simple spiral coils for the whole Tx-area,several crossed flat structures

[0015] ,

[0016] have been proposed for the Rx. These Rx designs have intrinsic rotational charging freedom, but blind spots (i.e., positions where the power transferred to Rx is zero) still exist in the transmitting area whenever the center of the Rx coil is located at the center of a Tx block. In

[0017] , a planar Rx with two subcoils is proposed to achieve omnidirectional wireless power transfer. However, the Rx coil structure is rather complicated in terms of design considerations. Moreover, similarly to

[0015] ,

[0016] , separaterectifier circuits are necessary for each sub-coil, which increases system complexity.

[0028] Seeking other possibilities to reach full charging freedom of multi-Tx WPT ina large area, a few studies suggested to apply dynamic control of Tx coils based on the Rxposition and orientation. For example,

[0018] proposed to adjust the duty cycle of the Tx supplyvoltage to enhance the power transfer at weak coupling positions, but the control algorithmstill could not help with power transfer at blind spots where the coupling is completely zero.To achieve full charging freedom including linear and rotational movements in any desireddirection, paper [3] proposed receiver detection and transmitter activation methods based onsensing of the input current through a periodical turn ON of the system. However, substantialsensing and control resources are imperative, particularly for accurately detecting the Rxorientation to activate the necessary Tx coils and correctly assign the phase. A separateinverter is mandatory for each Tx coil in such a WPT system due to the need for phasecontrol. This condition, in turn, necessitates a high switch count per Tx coil leading to aconsiderable escalation of cost. In addition, the dynamic current direction control does notoffer any capacity for simultaneous charging of multiple devices, as it merely relocates blindspots from the Rx’s current position to another location rather than completely eliminatingthem.

[0029] To overcome or at least alleviate these problems of complicated coil designsand control / detection algorithms, the embodiments provide a new coil-energizing pattern based on the non-coherent method that combines power at multiple frequencies. The proposed approach enables freedom of wireless charging without any blind spots and eliminates the need for complex control mechanisms. We introduce an expandable pre-fixedTx configuration with two slightly different operating frequencies and four phase angles,that grants complete positional and rotational charging freedom for multiple Rxs. Moreover, both DD and fluxpipe Rx structures are compatible with the proposed solution. The proposed configuration also works in line with simple detection and activation methods, e.g., anymethod of Rx detection together with ON / OFF control can be implemented to activate Txproperly.

[0030] FIG. 1A & 1B illustrate a system for wireless power transfer according to anembodiment from above and in a cross-sectional side view, respectively. The system ofFIGs.1A & 1B comprises a WPT transmission coil arrangement 101 and a WPT reception coil 104. The WPT transmission coil arrangement comprises a plurality of transmission coils102 arranged as an array. The array may be specifically a rectangular (or square) periodicplanar array (e.g., a 4 × 4 array or a multiple / subset thereof). All of the plurality oftransmission coils 102 may be identical. The plurality of transmission coils 102 are arrangedon a ferrite substrate 103. In the example of FIGs.1A & 1B, the WPT receiver coil 104 is aflux pipe based WPT reception coil 104 comprising a ferrite core 105 (i.e., the flux pipe) anda coil 106 wound around the ferrite core 105.

[0031] In the WPT system of FIGs. 1A & 1B, each of the plurality of transmissioncoils 102 may be fed independently. However, the question remains how should the plurality of transmission coils 102 be fed so that charging would be possible regardless of the positioning and orientation of the WPT reception coil 104. For example, one might considera 4 × 4 WPT transmission coil arrangement where every other row of the 4 × 4 array is fed with a first phase shift and every other with a second phase shift having a 180° difference tothe first phase shift. However, the WPT receiver coil 104 would have only 1D chargingfreedom in such a case: linearly moving along the middle line between two rows, with anorientation orthogonal to its movement direction. Similar problems may be observed with many other Tx supply current configurations.

[0032] FIG.2 shows a WPT feeding configuration (equally called a WPT transmissionconfiguration, a WPT supply current configuration or a Tx supply current configurations)for a WPT transmission coil arrangement comprising a plurality of transmission coils 201arranged as a 4 × 4 planar array 200. All of the plurality of transmission coils 201 in the 4×4array 200 may be identical. The 4 × 4 planar array 200 may be a rectangular or square array.The WPT transmission coil arrangement of FIG. 2 may correspond to the WPT transmissioncoil arrangement of FIG.1.

[0033] The terminals of the transmission coils 201 are supplied or fed by powersignals containing, each, two different frequency components, each of said frequencycomponents having a specific phase value selected from 0°, 90°, 180°, and 270°. Said powersignals may be provided, for example, by an N-legged converter, as will be discussed indetail in connection with FIG. 7. Each transmission coil is shown, in FIG. 2, as a squareblock containing two triangular sub-blocks. Each triangular sub-block is associated with oneof first and second frequencies (^^ & ^^) and one of the aforementioned phase values 0°, 90°,180°, and 270, as shown in FIG.2. It should be emphasized that this division of the blocksto triangular sub-blocks serves merely to highlight the two power signal componentssupplied to each transmission coil, that is, it does not imply any “split” in the transmissioncoil geometry itself.

[0034] In other words, the plurality of transmission coils 201 in the 4 × 4 planar array200 are fed with a plurality of power signals corresponding, each, to a combination of a firstpower signal having a first frequency and a second power signal having a second frequencydifferent from the first frequency. As shown in FIG.2, phases of the first and second powersignals for a transmission coil of an i-th row & an j-th column of the 4 × 4 planar array 200are defined as: -for i = 1 & j = 1, phases of the first and second power signals are 0° and 0°,- for i = 2 & j = 1, phases of the first and second power signals are 270° and0°, -for i = 3 & j = 1, phases of the first and second power signals are 270° and270°, -for i = 4 & j = 1, phases of the first and second power signals are 0° and 270°,- for i = 1 & j = 2, phases of the first and second power signals are 90° and 0°,- for i = 2 & j = 2, phases of the first and second power signals are 180° and0°, -for i = 3 & j = 2, phases of the first and second power signals are 180° and270°, -for i = 4 & j = 2, phases of the first and second power signals are 90° and270°, -for i = 1 & j = 3, phases of the first and second power signals are 90° and 90°,- for i = 2 & j = 3, phases of the first and second power signals are 180° and90°, -for i = 3 & j = 3, phases of the first and second power signals are 180° and180°, -for i = 4 & j = 3, phases of the first and second power signals are 90° and180°, -for i = 1 & j = 4, phases of the first and second power signals are 0° and 90°,- for i = 2 & j = 4, phases of the first and second power signals are 270° and90°, -for i = 3 & j = 4, phases of the first and second power signals are 270° and180°, and -for i = 4 & j = 4, phases of the first and second power signals are 0° and 180°.Here, 1st row (i = 1) corresponds to the top row of square blocks of FIG. 2, and 1st column(j = 1) corresponds to the leftmost column of square blocks of FIG.2.

[0035] As mentioned above, the first and second frequencies are not equal but theymay be close to each other. For example, in some embodiments, a difference between the first and second frequencies may be larger than or equal to 0.5 kHz and / or smaller than orequal to 6 kHz. For example, said difference may be 2 kHz. Here,+ ^^) / 2 = 200 kHzmay apply, for example.

[0036] With the combination of the two frequency components and the four phasevalues, the basic activation pattern in 4×4 transmission coil array 200 can be extended to anynumber of transmission coils arranged over a large area. In other words, the 4×4 WPTtransmission coil arrangement 200 of FIG. 2 may be repeated n times along the horizontaldirection of FIG. 2 and / or m times along vertical direction of FIG. 2. Here, n and m may beintegers larger than one or, more generally, rational numbers which are multiples of 0.25 andare larger than one. The feeding arrangement (comprising, e.g., a DC voltage source, an N-legged converter and a compensation network) associated with the 4×4 WPT transmissioncoil arrangement 200 may also be repeated in a similar manner or a joint feeding arrangementmay be implemented. In other embodiments, a subset (or subarray) of the WPT feedingconfiguration for the 4×4 transmission coil array 200 of FIG. 2 may be employed for feedinga K×L transmission coil array, where K and L are both integers smaller than or equal to 4,and at least one of K and L is smaller than 4. In some embodiments, K and L may be, e.g.,equal to 2 or 3. For example, the top three rows and top three columns of the WPT feedingconfiguration of FIG.2 (or any other subarray of the same size) may be employed for feedinga 3×3 transmission coil array, in some embodiments. In some embodiments, a 3×2transmission coil array and associated (subset) feeding configuration may be employed.

[0037] The feeding configuration of FIG. 2 is advantageous compared to conventionalsingle-frequency (DD-pattern) Tx-area configuration methods illustrated in FIG. 3:“Conventional x” (where each row has the same phase) and “Conventional y“ (where eachcolumn has the same phase). Expandable building blocks with the conventional DD patternsin FIG. 3 (marked using thick black borders) contain two transmission coils working 180°out-of-phase in the same frequency. A detailed comparison between conventional andproposed Tx-configurations is given in the below Table. For example, the flux generated byConventional x Tx blocks always flows in the y-direction. Therefore, Tx-flux can only becaptured by the Rx when it also has a y-oriented flux and moves along the x-direction,providing limited charging freedom with only one direction of linear movements. Fullcharging freedom, including linear and rotational movements, is not possible in theconventional patterns without an appropriate dynamic control of the Tx current phasesaccording to instantaneously varying Rx positions and orientations. In contrast, with the helpof combining two frequencies and four phases, the proposed WPT transmissionconfiguration can establish three types of power combining, including non-coherent and twospecial cases of coherent combining at Rx regardless of its position. All blind spots areeliminated in the proposed method rather than shifted to other positions by dynamic control,which provides possibilities for simultaneous multi-Rx charging (i.e., charging of multipleRx devices having any location and / or orientation simultaneously). Thus, the WPT systemaccording to embodiments facilitates complete free positioning at any position or orientationfor multiple Rxs within the transmitting area. Conventional x (y) ProposedTx coil structure spiral spiralRx coil structure DD or flux-pipe DD or flux-pipeExpandable block 2 Tx coils 16 Tx coilsWorking frequency f1 f1, f2Supply voltage phase 0°, 180° 0°, 90°, 180°, 270°Charging freedom have blind spotsno blind spots y(x) orient Rx360° Rx orientations + full x (y) linear movement 2D movement Control dynamic phase control ON / OFF controlMulti-Rx charging no yes

[0038] FIG. 4 shows in detail one exemplary implementation of one of thetransmission coils 401 of the 4×4 array 200 of FIG. 2 along with its compensation circuit402 (equally called a compensation network). The same implementation may be employedwith all of the plurality of transmission coils 201 of FIG. 2. The transmission coil 401 is, inthis example, a spiral-shaped coil. The compensation circuit 401 may be, for example, anLCC compensation circuit. With identical Tx blocks inside the charging area, we denote oneterminal 403 of the Tx block in the i-th row and j-th column, Tx^^a, linked to the upper righttriangle of a Tx block in FIG. 2, while the other terminal 404, denoted as Tx^^b, is linked tothe lower left triangle. In this way, we supply alternating current (AC) voltage and currentwith corresponding frequency and phase to the transmission coil as illustrated in FIG. 2. InFIG. 4, ^^^,^ corresponds to a phase of a first power signal (having frequencyfed to atransmission coil in the i-th row and j-th column of the 4×4 array 200 while ^^^,^ correspondsto a phase of a second power signal (having frequency ^^) fed to a transmission coil in the i-th row and j-th column of the 4×4 array 200.

[0039] In some embodiments, decoupling inductors (not shown in FIG. 4) may beemployed for eliminating crosscoupling between the plurality of transmission coils of the4×4 array 200. The decoupling inductors may be similar to ones proposed in [3].

[0040] FIG. 5 illustrates two alternative exemplary reception coil structures 510, 520usable in connection with the WPT transmission arrangement of FIG. 2. Namely, FIG. 5 shows a flux-pipe reception coil structure 510 (similar to FIGs. 1A & 1B) and a double-D(DD) reception coil structure 520. As described in connection with FIGs. 1A & 1B, the flux-pipe reception coil structure comprises a ferrite core 511 (i.e., the flux pipe itself) and a coil 512 wound around the ferrite core 511. The double-D (DD) reception coil structure 520comprises first and second (spiral-shaped) coils 521, 522 arranged adjacent to each other andconnected to each other (via their outermost windings). Terminals of the DD reception coilstructure 520 are connected to the centers of the first and second coils 521, 522. Current flowsin opposite directions in the adjacent sections of the first and second coils 521, 522. This creates a specific magnetic field distribution that improves coupling.

[0041] FIG. 6 illustrates, in top part, Rx movements with regard to the Txij coil, withthe defined reference flux direction for each coil and, in bottom part, mutual inductance Mijvariations in terms of the value and sign (positive / negative). Consider the reference fluxdirection inside the Rxs (defined as shown in FIG. 5) and in the identical Txs (defined ascoming out) as illustrated in FIG. 4, the Rx has a positive mutual inductance Mij with thecoil Txijwhen its flux flows through the Rx in the same direction as the Rx referencedirection, cf. FIG. 6 on the right side, while Mij is negative when the flux directions areopposite to each other, cf. FIG. 6 on the left side.

[0042] To realize the power signals having the specific frequencies and phasesdiscussed above in connection with FIG. 2, an N-legged converter topology may beemployed

[0019] . FIG. 7 shows an N-legged converter 702 according to an embodiment fordirect current to alternating current (DC-to-AC) conversion. The illustrated N-leggedconverter 702 is specifically an 8-legged converter (i.e., N = 8). The N-legged converter 702is configured to implement the WPT feeding configuration of FIG 2. Thus, the 8 legs 704 to711 of the converter 702 provide all the necessary combinations of supply frequencies (^^,^^) and phases (0°, 90°, 180°, 270°). Each leg 704 to 711 of the converter 702 comprisesfirst and second (transistor-based) switches 721, 722. The first and second switches arearranged in a half-bridge configuration. Moreover, each (half-bridge) leg 704 to 711comprises first and second diodes 723, 724 connected in parallel with first and secondswitches 721, 722, respectively. The midpoint of the leg 704 to 711 (where the switches 721,722 meet) is the output terminal for that leg 704 to 711. Said midpoint is called, in thefollowing, a middle switching node. In addition to the legs 704 to 711, the converter furthercomprises a (DC filtering) capacitor 703. The converter 702 is connected, via its inputterminals, to a DC voltage source 701.

[0043] Considering only the DC and fundamental components, the voltage ^^^,^^ atthe middle switching node (indicated in FIG. 7 with a dot) of one converter leg 704 to 711can be written aswhere ^ = 1,2 indicates the frequency ^^ or ^^ (angular frequencies ^^,^), and this notationis used also in the following. Moreover, ^^ ∈ [0°, 90°, 180°, 270°] is the phase value for thecorresponding frequency channel (i.e., for the corresponding power signal component).

[0044] FIG. 8 shows an equivalent circuit for a Tx building block comprising an LCCcompensation network 805 and a transmission coil 804 ^^^ of the plurality of transmissioncoils of the 4×4 array. FIG. 8 indicates the connections of the LCC compensation 805network and terminals Tx^^a (connected to thebranch) and Tx^^b (connected to the ^^branch). The equivalent circuit of FIG. 8 may correspond, for example, to FIG. 4 with theassumption that the compensation network 402 is an LCC compensation network. The LCCcompensation network 805 comprises a first inductor 801 ^^, a first capacitor 802 ^^ and asecond capacitor 803 ^^^ . A first terminal of the first inductor 801 corresponds to theterminal Tx^^a (i.e., it acts as an input for a first power signal obtained from the N-leggedconverter). A second terminal of the first inductor 801 is connected to a first terminal of the first capacitor 802 and to a first terminal of the second capacitor 803. A second terminal ofthe first capacitor 802 corresponds to the terminal Tx^^b (i.e., it acts as an input for a secondpower signal obtained from the N-legged converter). First and second terminals of thetransmission coil 804 are connected, respectively, to a second terminal of the second capacitor 803 and to the second terminal of the first capacitor 802 (and, thus, the secondterminal of the transmission coil corresponds also to the terminal Tx^^b).

[0045] As mentioned above, in some embodiments, decoupling inductors (not shownin FIG. 8) may be employed for eliminating crosscoupling between the plurality oftransmission coils of the 4×4 array 200, similar to [3]. Namely, a first decoupling inductormay be connected between the second terminal of the second capacitor 803 and the firstterminal of the transmission coil 804, and a second decoupling inductor may be connectedbetween the second terminal of the first capacitor 802 and the second terminal of thetransmission coil 804. The first decoupling inductor of the present Tx building block may be coupled to a second decoupling inductor of a first adjacent Tx building block, and the second decoupling inductor of the present Tx building block may be coupled to a first decouplinginductor of a second adjacent Tx building block. The mutual inductance in either case maybe −^^.

[0046] As indicated in FIG. 8, by connecting the middle switching node of thecorresponding converter leg to the Tx-terminal a or b (Tx^^a or Tx^^b) according to the WPTfeeding configuration of FIG. 2, we can obtain AC voltage ^^^^,^ across the LCC-compensated input terminals Tx^^a, b, which contains voltage in both frequencieswhere the amplitude is represented by ^^ = 2^^^ / ^ . Here, ^^^,^ ∈[0°, 90°, 180°, 270°] represents the corresponding phase ^^ of the leg connected to the inputterminal a or b of Tx^^block.

[0047] Therefore, the supply voltage and current in each Tx coil contain componentsfrom both frequencies ^^and ^^. By applying Kirchhoff’s law, the current flowing through the LCC-compensated Tx coil is written as (3)where ^^⃗^^,^represents the vector form of the AC voltage. The corresponding input currentof the LCC circuit is represented by ^^^^ = ∑^^^,^ ^^^^,^ following FIG. 8.

[0048] Determined by the supply voltages ^^^^^,^, the Tx current ^⃗^^^^ also containsboth frequencies and is independent of load or mutual inductance variations. Therefore, theLCC compensation circuit provides load-independent current in the Tx coil, which ensuressafe operation of the WPT system for those Tx coils with no coupling to the Rx

[0020] .

[0049] In the proposed method, the transmitter configuration is fixed and does notrequire any (dynamic) phase or current control. However, to achieve even betterperformance in terms of higher system efficiency and minimized electromagnetic exposure,a dynamic activation method can also be applied to the Tx area based on any existing Rxdetection methods, e.g., the detection and activation method of [3].

[0050] In the following, it is discussed how the WPT channel is established with theproposed Tx configuration excited with two frequencies and four phase angles withreference to FIG. 9 (and later FIG. 10). FIG. 9 shows an Rx-side simplified circuit with idealAC voltage sources 901. In FIG. 9, the induced voltage (represented by the voltage sources901) from each Tx coil contains both frequencies ^^ and ^^, and all the effective Tx coils(i.e., Tx coils having non-zero mutual inductance with the Rx coil) will provide inducedvoltage at the Rx side. The Rx-side circuit further comprises a diode bridge rectifier 910,formed of four diodes 902, 903, 904, 905, for AC-to-DC conversion, a rectifier output DCfiltering capacitor 906 ^^ and a load 907.

[0051] In some embodiments, the rectifier output DC filtering capacitor 906 ^^ mayhave a capacitance value larger than or equal to 10 µF and smaller than or equal to 130 µF. For example, the capacitance of the rectifier output DC filtering capacitor 906 ^^may be equal to 90 µF.

[0052] In the following discussion of non-coherent and coherent power combining,reference is made to coordinates (^, ^, ^) which are defined as follows. The coordinates(^, ^) indicate the position of the Rx center, and their values equal to the actual distance in(cm) normalized to the Tx coil size in (cm). The coordinates (^, ^) are defined similar to asshown in FIG. 3. Considering the 4×4 array 200 of FIG. 2, the origin (i.e., the coordinate (0, 0)) is located at the center of the leftmost-top transmission coil (i.e., the centerof the leftmost-top square in FIG. 2) with y-axis pointing down and x-axis pointing to theright. The spacing between the centers of adjacent squares in FIG.2 is, thus, 1. Coordinate^ is defined as shown in FIG. 5, that is, as the clockwise-measured angle of the Rx referenceflux direction from the positive y-direction.

[0053] Considering one WPT power channel, i.e., from one Tx coil to an Rx device atone single frequency, the Tx-side circuit can be modeled as an induced voltage source 901, ^^^,^ in the Rx-side equivalent circuit. The phase and amplitude of the inducedsource 901 are determined by the mutual inductance as well as the source voltage

[0021] according to the time-domain equationwhere (^, ^, ^) describes the position and orientation of the Rx coil, ^^^(^, ^, ^) is themutual inductance between Rx and a particular transmitter Tx^^ . It is noted from FIG. 6 that^, ^) also contributes to the phase of the induced voltage, since the mutualcan be either positive or negative. Therefore, any effective Tx coil that has non-zero mutualinductance with the Rx (i.e., ^^^(^, ^, ^) ≠ 0) contributes to two induced voltage sources^^^,^ and ^^^,^ (representing two frequencies) at the Rx-side, as depicted in FIG. 9.

[0054] Following (4), since the induced voltage on the Rx-side is always load-independent, the power combining at the Rx-side is also represented by combining of theinduced voltage source components. The total induced voltage of the Rx circuit, ^^^,^^, is thesum of the induced voltage components from all the effective Tx coils at both frequencies, given as=^^^,^(^, ^, ^, ^) + ^^^,^(^, ^, ^, ^), (5)= 1 or 2) is the sum of all the induced voltage components at thefrequency ^^, represented by their amplitudes ^^^,^ , and phases ^^^,^ as

[0055] Power may be combined according to the power combining equation (5) non-coherently or coherently. In the following, non-coherent power combining is discussed first,followed by a discussion on two special cases of coherent power combining.

[0056] Applying the power combining equation (5) for a given Rx position (^, ^, ^),when non-zero voltage components at more than one frequency appear on the Rx-side, i.e.,the power is combined in a non-coherent manner. Based on the definition in (7), non-coherent power combining happens at most of the Rx positions within the Tx area. If wetake an Rx position (^, ^, ^) = (2.5, 1.5, 45°) as an example, given in FIG. 10(a), byconsidering ^^ and ^^ frequencies separately, the induced voltage at the same frequency canbe first added up following their vector relations. Thus, we obtain the total induced voltage^⃗^^,^for frequency ^^, and ^^⃗^,^for frequency ^^, cf. (5) for their time-domain forms.

[0057] Furthermore, ^^^,^ and ^^^,^ at two different frequencies are combined to ^^^,^^in a non-coherent way, where the rules of vector-combining are not applicable. As shown inFIG.10(a2), the relative phase difference between two voltage vectors ^⃗^^,^ and ^^⃗^,^ arealways varying with regard to time since their frequencies are not the same, resulting in atime-varying total induced voltage ^^⃗^,^^. To add up two voltage components at differentfrequencies, we consider the time-domain equationwhere the amplitude ^^^and phase ^^^of the Rx-side total induced voltage source ^^^,^^are calculated according to: ^^^(^, ^, ^, ^) =^^^^^^ (^, ^, ^) + ^ ^^^^ (^, ^, ^) + 2^^^^^^^^cos {Δ^^ + [^^^,^(^, ^, ^) − ^^^,^(^, ^, ^)]} (9)where Δ^ is defined as ^^ − ^^. From these equations, we notice that with non-coherentpower combining, the amplitude and phase of the total induced voltage ^^^,^^ are alsofunctions of time t instead of only affected by the Rx position. Such features are greatlyimportant in terms of eliminating blind spots that exist in conventional systems where onlycoherent power combining takes place.

[0058] For the non-coherent example position in FIG. 10(a), the time-domainwaveform ^^^,^^(2.5, 1.5, 45°, ^) was observed to have an amplitude varying with time withthe period ^^ = 1 / |^^ − ^^| . It was also observed that, when employing the Conventionaly configuration of FIG. 3 instead of the proposed Tx configuration of FIG. 2, there exists ablind spot waveform at Rx position (^, ^, ^) = (2, 1.5, 90°), while the power can still becombined incoherently when using the proposed Tx configuration of an embodiment. Atsaid blind spot position, the ^^^ waveform in non-coherent power combination was observedto show only instantaneous moments for zero power transfer, with a recurring period of ^^.Therefore, at the conventional blind spot positions (i.e., the positions where blind spotsappear when using Conventional y configuration), the time-averaged root-mean-square(RMS) amplitude of the combined induced voltage source is (|^^^^| + |^^^^|) / √2 for theproposed WPT system, in comparison to ^^^ = 0 in the conventional coherently-combinedcase.

[0059] When examining power combining across the entire Tx area, specific positionsexist where the induced voltage components at one frequency incidentally nullify each other. In two examples given in FIG.10(b) & (c), one of the voltage components ^^^,^or ^^^,^is nullified. Therefore, the total induced voltage ^^^,^^will contain only one frequency in such special cases. We will explain these two types of special coherent power combining cases individually in the following.

[0060] First, the case where coherent power combining with the same phase occurs isdiscussed. FIG.10(b) gives an example of power combining in the case. At position(^, ^, ^) = (1.5, 1.5, 45°), two effective Tx coils Tx11 and Tx22 have the same mutualinductances with the Rx, but of the opposite signs. From (4), we observe that the phase ofinduced voltage is decided by the phase of the Tx-side AC supply ^⃗^^^,^ together with thesign of mutual inductance ^^^ . Due to the 180° phase-shift between the supply voltages^⃗^^^,^and ^⃗^^^,^, the sources at frequency ^^induce voltage vectors from these two Txs,^^⃗^,^ and ^^⃗^,^, that have the same directions and are added up on the Rx side. In contrast,since the phases of Tx11 and Tx22 supply voltages are the same at frequency ^^ , thecorresponding induced voltage components ^^⃗^,^ = −^⃗^^,,^ cancel out with each other anddo not contribute to the power transfer. The corresponding vector relations at twofrequencies are also shown in FIG.10(b1). Therefore, the Rx side receives a coherent powercombination at one single frequency ^^, and the vectors are added up with the same phase.As indicated in FIG. 10(b2), the total induced voltage ^^^,^^ contains only one frequency, soits amplitude has a constant value with regard to time.

[0061] Now, let us consider the case where coherent power combining occurs with90° phase shift. FIG.10(c) gives an example of power combining in the case for a position(^, ^, ^) = (2.5, 2, 90°). This coherent case 2 corresponds to a similar coupling situation ascoherent case 1 of FIG. 10(b) where ^^^ = −^^^. The ^^ supply voltage for coils Tx22 andTx23 are in-phase, i.e., ^^^,^ = ^^^,^ = 180°, resulting in full cancellation of the Rx-sideinduced voltages: ^^^,^ + ^^^,^ = 0. However, the ^^ supply voltages have a 90° phase-difference in this special case instead of the 180° in coherent case 1, and the induced voltagevectors are orthogonal to each other, as shown in FIG. 10(c1). Compared to the powercombination in coherent case 1, the total induced voltage has a lower amplitude due to thephase-shifted add-up, however, the two induced voltage vectors still do not cancel eachother. This is also the main reason for selecting the phase-difference as 90°, since the inducedvoltage vector in either 0° or 180° will never cancel even partially with the vector at 90° or270°.

[0062] Exemplary specifications and coil parameters of the proposed WPT system aregiven in the below Table. Operating frequencies around 200 kHz are selected as an examplefollowing the Qi standards for middle-range wireless power transfer

[0022] . Considering the trade-off between the WPT link efficiency and the rectifier output DC filtering capacitance, CL, in FIG.9, too small frequency gap betweenand ^^creates difficulties for filtering theoutput voltage ripple, while a large frequency gap will degrade the WPT link efficiency

[0021] .parameter value parameter value parameter valuef1, f2 199, 201 kHz VDC 30 V RL 100 ΩDistance 35 mm Lf 11.4 µH Cf 55.2 nFTx size 157 × 157 mm2 LTx 21 µH CTx 67.2 nFRx size 255 × 115 mm2 LRx 360 µH CRx 1.75 nF

[0063] Simulations were conducted to select the appropriate combination of thefrequency gap and the DC output capacitance ^^ (element 906 of FIG. 9). The simulationswere made based on the system parameters at Rx position (2.5, 1.5, 45°), where the non-coherent effect is fully revealed. Based on the simulations, in order to get rid of the high DCvoltage ripple while still maintaining a high RMS value, a 2 kHz frequency gap and a 90 μFDC filtering capacitor may, for example, be used for the proposed WPT system. In general,any frequency difference values within the range |^^ − ^^| ∈ [0.5, 6] kHz (preferably|^^ − ^^| ∈ [1, 6] kHz, more preferably |^^ − ^^| ∈ [1.5, 6] kHz) may be used. The voltagedifference |^^ − ^^| may be one of 0.5 kHz, 1 kHz, 1.5 kHz, 2 kHz, 3 kHz, 4kHz, 5 kHz or6 kHz. Additionally or alternatively, the capacitance of the DC filtering capacitor may havea value within the range ^^ ∈ [10, 130] μF (or preferably ^^ ∈ [50, 130] μF ). The DCoutput capacitance ^^ may be one of 10 μF, 50 μF, 90 μF, 110 μF or 130 μF. Here, it maybe assumed that (^^ + ^^) / 2 = 200 Hz applies.

[0064] Following the Tx power supply configurations shown in FIG. 2, a laboratoryprototype of a WPT system with spiral Tx coils and a flux-pipe Rx coil was built. Asdiscussed above, an LCC compensation circuit is applied to each Tx coil, and seriescompensation is used for Rx tuning, for implementation simplicity. In addition,crosscoupling between the Tx coils is eliminated using decoupling inductors, as proposed in[3]. Therefore, the Tx coils act as independent and decoupled multiple Tx coils. In summary,the compensation topology or the cross-coupling cancellation methods are not affected bythe types of power combining. Due to the symmetry of power combining in the proposed4×4 Tx-configuration map, cf. FIG. 2, a charging area filled by 3×2 coils was set up. Sucha charging area is capable of showing all the special Rx positions for different types of powercombining.

[0065] In the experimental WPT system, the Tx coils were driven by six half-bridgelegs (model LMG5200) containing combinations of two frequencies and four phases, and a digital signal processor (DSP) TMS320F28379 is used to generate corresponding control signals. A FSV10120V-based diode bridge rectifier is used at the Rx-side, together with a passive resistor bank as the load. The waveforms were observed using an oscilloscope, DCvoltages and currents are measured using industrial-grade true-RMS meters (FLUKE 28-II).

[0066] First, charging freedom against Rx linear movements in x, y-directions wasstudied. The Rx coil was moved linearly in the x-direction while keeping the orientation ofthe Rx aligned with either x or y axes. We define the Rx orientation angle ^ as the Rxreference flux direction clockwise rotation angle from the positive y direction, as shown inFIG. 5. It was observed that when the Rx coil moves along the x direction while the Rxreference flux direction is kept along the x-axis (i.e., ^ = 90°), the proposed Tx configurationensures an almost constant transfer power and efficiency by combining the powerincoherently. In comparison, the Conventional y supplying pattern has a blind spot with nullpower transfer and efficiency when the center of the Rx coil is aligned with the center of oneof the Tx coils, since the adjacent two columns have the same flux directions and theirinduced voltage components cancel out at the Rx-side. This cancellation never happens withthe proposed supplying pattern as the Rx side will always receive a non-coherently combinedpowers with a 90° phase shift. Moreover, with Conventional x configuration, the Rx doesnot receive any power due to zero coupling, as discussed above.

[0067] Second, charging freedom against Rx rotational movements was studied.Namely, load voltage and efficiency within 0° to 180° rotation angles of the Rx device wasstudied. The performance is the same for ^ ∈ [180∘, 360∘] due to the symmetry of the Rxstructure. It was observed that the proposed approach exhibits continuous power receptionat all rotation angles, whereas both Conventional x, y solutions suffer from blind spots withalmost zero power at the Rx. Similar observation was made both when the center (that is,both the physical and rotational center) of the Rx device was arranged over a corner of a Txbuilding block and when and the center (that is, both the physical and rotational center) ofthe Rx device was arranged over a center of a Tx building block. Regardless of the powercombining method, the proposed Tx-configuration can transfer power with full Rx rotationalfreedom with a constant DC-DC efficiency around 85%, in comparison with twoconventional patterns that have blind spots at the quadrant orientations.

[0068] Finally, the experimental voltage and current waveforms of the transmitter andreceiver in the non-coherent and coherent power combining cases were measured atrespective Rx positions (2.5, 1.5, 45°) and (1.5, 1.5, 45°) . According to the previousanalysis, the non-coherent power transfer is time-varying, and due to the existence of a large DC filtering capacitance at the system output, the instantaneous power transfer is brought down to zero when it is not enough to supply the output. Therefore, the period having powerwith constant zero power is defined here as the “ zero power transfer ” period. Themeasurements showed that, during the active power transfer period, the inverter outputcurrent ^^,^^ (supplied to the WPT stage through the compensation inductor ^^, cf. FIG. 9)follows the shape of the Rx coil current ^^^which includes a combination of two frequencies^^and ^^. The two supply voltage components atand ^^are almost in the same phase, soit contributes to high instantaneous power transfer to the Rx. However, according to themeasurements, at the zero power transfer period, the inverter output (^^,^^) and the Rx coil(^^^) currents are zero. The instantaneous power is low because the AC voltage components are nearly out-of-phase. This attribute of the Rx current and inverter current establishes the foundation for efficiency on par with conventional methods, while simultaneouslyeliminating blind spots. Coherent power combining waveforms were measured for the Rxposition (^, ^, ^) = (1.5, 1.5, 45°) where the Rx device obtains power from Tx11 and Tx22.Based on the measurement, the waveforms do not have any low-frequency envelope sincethere is only one frequency ^^. The transmitter current ^^^^^ was also measured in this case.In accordance with (3), it was observed to be dependent only on the supply voltage (not onthe receiver side operations) and to contain both frequencies.

[0069] Finally, it is noted that the experimental results demonstrate that the Rxconsistently achieves charging efficiency between 82% and 93%, irrespective of its positionor orientation when employing the WPT feeding configuration of FIG. 2.

[0070] While the above discussion of embodiments assumed use of the particularWPT feeding configuration shown in FIG. 2, other WPT feeding configurations possessingsimilar favorable properties may also be envisioned. Two alternative WPT feeding configuration are discussed in the following in connection with FIGs.11 & 12.

[0071] FIG. 11 shows an alternative WPT feeding configuration for a WPTtransmission coil arrangement comprising a plurality of transmission coils 1101 arranged as a 4 × 4 planar array 1100. All of the plurality of transmission coils 1101 in the 4×4 array1100 may be identical. The 4 × 4 planar array 1100 may be a rectangular or square array. Ingeneral, the 4×4 array of transmission coils 1100 itself may be defined as described inprevious embodiments (that is, the difference lies in the frequencies and phases of the powersignals supplied to the transmission coils 1201). The terminals of the transmission coils 1101are supplied by power signals containing, each, two different frequency components, eachof said frequency components having a specific phase value selected from 0°, 90°, 180°, and270°. In contrast to FIG. 2 where these two frequency components for all transmission coilsalways had the same two frequencies, the two frequency components for a giventransmission coil may be, here, the same or different in terms of frequency (though, in theformer case, the two frequency components still differ in terms of phase). Said power signalsmay be provided, for example, by an N-legged converter (e.g., the one shown in FIG.7).

[0072] Similar to FIG.2, each transmission coil is shown, in FIG.11, as a square blockcontaining two triangular sub-blocks representing the two frequency components fed to thattransmission coil. Each triangular sub-block is associated with one of first and secondfrequencies (^^ & ^^) and one of the aforementioned phase values 0°, 90°, 180°, and 270°,as shown in FIG.11.

[0073] In other words, the plurality of transmission coils 1101 in the 4 × 4 planar array1100 are fed with a plurality of power signals corresponding, each, to a combination of afirst power signal having a first frequencyor a second frequency ^^ different from the firstfrequency ^^ (i.e., ^^ ≠ ^^) and a second power signal having the first frequency ^^ or thesecond frequency ^^. As shown in FIG.11, phases of the first and second power signals for a transmission coil of an i-th row & a j-th column of the 4 × 4 planar array 1100 are defined as: -for i = 1 & j = 1, the first and second power signals have the first frequency,and phases of the first and second power signals are 0° and 90°, -for i = 2 & j = 1, the first and second power signals have, respectively, thesecond and first frequencies, and phases of the first and second power signals are 180° and 90°, -for i = 3 & j = 1, the first and second power signals have the second frequency,and phases of the first and second power signals are 180° and 270°, -for i = 4 & j = 1, the first and second power signals have, respectively, thefirst and second frequencies, and phases of the first and second power signals are 0° and 270°, -for i = 1 & j = 2, the first and second power signals have, respectively, thesecond and first frequencies, and phases of the first and second power signals are 0° and 90°,- for i = 2 & j = 2, the first and second power signals have the first frequency,and phases of the first and second power signals are 180° and 90°, -for i = 3 & j = 2, the first and second power signals have, respectively, thefirst and second frequencies, and phases of the first and second power signals are 180° and 270°, -for i = 4 & j = 2, the first and second power signals have the second frequency,and phases of the first and second power signals are 90° and 270°,- for i = 1 & j = 3, the first and second power signals have the second frequency,and phases of the first and second power signals are 0° and 90°, -for i = 2 & j = 3, the first and second power signals have, respectively, thefirst and second frequencies, and phases of the first and second power signals are 180° and 90°, -for i = 3 & j = 3, the first and second power signals have the first frequency,and phases of the first and second power signals are 180° and 270°, -for i = 4 & j = 3, the first and second power signals have, respectively, thesecond and first frequencies, and phases of the first and second power signals are 90° and 270°, -for i = 1 & j = 4, the first and second power signals have, respectively, thefirst and second frequencies, and phases of the first and second power signals are 0° and 90°, -for i = 2 & j = 4, the first and second power signals have the second frequency,and phases of the first and second power signals are 180° and 90°, -for i = 3 & j = 4, the first and second power signals have, respectively, thesecond and first frequencies, and phases of the first and second power signals are 270° and 270°, and -for i = 4 & j =4, the first and second power signals have the first frequency,and phases of the first and second power signals are 0° and 270°.Here, 1st row (i = 1) corresponds to the top row square blocks of FIG. 11, and 1st column (j= 1) corresponds to the leftmost column of square blocks of FIG. 11.

[0074] As mentioned above, the first and second frequencies are not equal but theymay be close to each other. The first and second frequencies may be defined here as inprevious embodiments. For example, in some embodiments, a difference between the firstand second frequencies may be larger than or equal to 0.5 kHz and / or smaller than or equalto 6 kHz. For example, said difference may be 2 kHz. Here,+ ^^) / 2 = 200 kHz mayapply.

[0075] With the combination of the two frequency components and the four phasevalues, the basic activation pattern of the 4×4 transmission coil array 1100 can be extendedto any number of transmission coils arranged over a large area. In other words, the 4×4 WPTtransmission coil arrangement 1100 of FIG. 11 may be repeated n times along the horizontaldirection of FIG. 11 and / or m times along vertical direction of FIG. 11. Here, n and m maybe integers larger than one or, more generally, rational numbers which are multiples of 0.25and are larger than one. The feeding arrangement (comprising, e.g., a DC voltage source, anN-legged converter and a compensation network) associated with the 4×4 WPT transmissioncoil arrangement 1100 may also be repeated in a similar manner or a joint feedingarrangement may be implemented. In other embodiments, a subset of the WPT feedingconfiguration for the 4×4 transmission coil array 1100 of FIG. 11 may be employed forfeeding a K×L transmission coil array, where K and L are both integers smaller than or equalto 4, and at least one of K and L is smaller than 4. K and L may be, e.g., equal to 2 or 3. Forexample, the top three rows and top three columns of the WPT feeding configuration of FIG.2 (or any other subarray of the same size) may be employed for feeding a 3×3 transmissioncoil array, in some embodiments. In some embodiments, a 3×2 transmission coil array andassociated (subset) feeding configuration may be employed

[0076] Any of the features and definitions discussed in connection with FIGs. 4 to 8may apply, mutatis mutandis, for the alternative WPT feeding configuration of FIG. 11. Forexample, the transmission coil 401 and the compensation network 402 of FIG.4, either of the reception coil structures 510, 520 of FIG.5, the N-legged converter 702 of FIG 7 and / or the compensation network 805 of FIG.8 may be employed in connection with the alternative solution of FIG.11. Notably, in FIG.4 when combined with FIG.11, element 403 may be associated with ^^or ^^(i.e., not always with ^^) while the element 404 may also beassociated with ^^ or ^^ (i.e., not always with ^^). Similar consideration applies also for FIG.8 (i.e., Tx^^a is not always associated with the first frequency ^^ and Tx^^b is not alwaysassociated with the second frequency ^^). It should also be noted that while the analysis,simulations and measurements discussed following the discussion of FIG. 8 is not directly applicable to the alternative solution of FIG. 2, the alternative WPT feeding configuration of FIG. 11 exhibits similar beneficial properties as discussed for the WPT feeding configuration of FIG.2, as will be discussed below.

[0077] FIG. 12 shows another alternative WPT feeding configuration for a WPTtransmission coil arrangement comprising a plurality of transmission coils 1201 arranged asa 4 × 4 planar array 1200. All of the plurality of transmission coils 1201 in the 4×4 array1200 may be identical. The 4 × 4 planar array 1200 may be a rectangular or square array. Ingeneral, the 4×4 array of transmission coils 1200 itself may be defined as described in previous embodiments (that is, the difference lies in the frequencies and phases of the powersignals supplied to the transmission coils 1201). The terminals of the transmission coils 1201are supplied by power signals containing, each, two different frequency components. While,in previously discussed embodiments, it was assumed that each of said two frequencycomponents for all of the plurality of transmission coils 1201 contains one of two possiblefrequencies (^^ & ^^), in this embodiment, the two frequencies of respective two powersignal signals (or frequency components) supplied to a given transmission coil 1201 areselected from a set comprising a first frequency ^^, a second frequency ^^, a third frequency^^ and a fourth frequency ^^. Moreover, each of said frequency components has a specificphase value selected from 0° and 180° (as opposed to from 0°, 90°, 180° and 270° like inprevious embodiments). In other words, instead of employing two different frequencies andfour different phases, four different frequencies and two different phases are employed inthis embodiment. Nevertheless, said power signals fed to the plurality of transmission coils1201 may be provided also here, for example, by an N-legged converter (e.g., like the oneshown in FIG. 7) with the appropriate configuration.

[0078] Similar to FIGs. 2 & 11, each transmission coil is shown, in FIG. 12, as asquare block containing two triangular sub-blocks representing the two frequencycomponents fed to that transmission coil. Each triangular sub-block is associated with oneof first, second, third and fourth frequencies (^^, ^^, ^^ & ^^) and one of the aforementionedphase values 0° and 180°, as shown in FIG. 12.

[0079] In summary, the plurality of transmission coils 1201 in the 4 × 4 planar array1200 are fed with a plurality of power signals corresponding, each, to a combination of afirst power signal having one of first, second, third and fourth frequencies (^^, ^^, ^^ & ^^)and a second power signal having one (or, specifically, other one) of the first, second, thirdand fourth frequenciesThe first, second, third and fourth frequencies aredifferent from each other. Also, the two frequencies of each of the plurality of (combined)power signals are different from each other. As shown in FIG. 12, phases of the first and second power signals for a transmission coil of an i-th row & a j-th column of the 4 × 4 planar array 1200 are defined as: -for i = 1 & j = 1, the first and second power signals have, respectively, thefirst and second frequencies, and phases of the first and second power signals are 0° and 0°,- for i = 2 & j = 1, the first and second power signals have, respectively, thethird and second frequencies, and phases of the first and second power signals are 180° and0°,- for i = 3 & j = 1, the first and second power signals have, respectively, thethird and fourth frequencies, and phases of the first and second power signals are 180° and180°, -for i = 4 & j = 1, the first and second power signals have, respectively, thefirst and fourth frequencies, and phases of the first and second power signals are 0° and 180°,- for i = 1 & j = 2, the first and second power signals have, respectively, thethird and second frequencies, and phases of the first and second power signals are 0° and 0°,- for i = 2 & j = 2, the first and second power signals have, respectively, thefirst and second frequencies, and phases of the first and second power signals are 180° and0°, -for i = 3 & j = 2, the first and second power signals have, respectively, thefirst and fourth frequencies, and phases of the first and second power signals are 180° and180°, -for i = 4 & j = 2, the first and second power signals have, respectively, thethird and fourth frequencies, and phases of the first and second power signals are 0° and180°, -for i = 1 & j = 3, the first and second power signals have the third and fourthfrequencies, and phases of the first and second power signals are 0° and 0°,- for i = 2 & j = 3, the first and second power signals have, respectively, thefirst and fourth frequencies, and phases of the first and second power signals are 180° and0°, -for i = 3 & j = 3, the first and second power signals have, respectively, thefirst and second frequencies, and phases of the first and second power signals are 180° and180°, -for i = 4 & j = 3, the first and second power signals have, respectively, thethird and second frequencies, and phases of the first and second power signals are 0° and180°, -for i = 1 & j = 4, the first and second power signals have, respectively, thefirst and fourth frequencies, and phases of the first and second power signals are 0° and 0°,- for i = 2 & j = 4, the first and second power signals have, respectively, thethird and fourth frequencies, and phases of the first and second power signals are 180° and0°,- for i = 3 & j = 4, the first and second power signals have, respectively, thethird and second frequencies, and phases of the first and second power signals are 180° and180°, and -for i = 4 & j = 4, the first and second power signals have, respectively, thefirst and second frequencies, and phases of the first and second power signals are 0° and180°.Here, 1st row (i = 1) corresponds to the top row of square blocks of FIG. 12, and 1st column(j = 1) corresponds to the leftmost column of square blocks of FIG. 12.

[0080] Similar to other embodiments, the first, second, third and fourth frequenciesare not equal but they may be close to each other. A difference between each pair offrequencies selected from the first, second, third and fourth frequencies may be defined hereas discussed for the first and second frequencies in previous embodiments. For example, insome embodiments, a difference between each pair of frequencies selected from the first,second, third and fourth frequencies may be larger than or equal to 0.5 kHz and / or smallerthan or equal to 6 kHz. For example, said difference may be, on average, 2 kHz.

[0081] With the combination of the four frequency components and the two phasevalues, the basic activation pattern of the 4×4 transmission coil array 1200 can be extendedto any number of transmission coils arranged over a large area. In other words, the 4×4 WPTtransmission coil arrangement 1200 of FIG. 12 may be repeated n times along the horizontaldirection of FIG. 12 and / or m times along vertical direction of FIG. 12. Here, n and m maybe integers larger than one or, more generally, rational numbers which are multiples of 0.25and are larger than one. The feeding arrangement (comprising, e.g., a DC voltage source, anN-legged converter and a compensation network) associated with the 4×4 WPT transmissioncoil arrangement 1200 may also be repeated in a similar manner or a joint feedingarrangement may be implemented. In other embodiments, a subset of the WPT feedingconfiguration for the 4×4 transmission coil array 1200 of FIG. 12 may be employed forfeeding a K×L transmission coil array, where K and L are both integers smaller than or equalto 4, and at least one of K and L is smaller than 4. K and L may be, e.g., equal to 2 or 3. Forexample, the top three rows and top three columns of the WPT feeding configuration of FIG.2 (or any other subarray of the same size) may be employed for feeding a 3×3 transmissioncoil array, in some embodiments. In some embodiments, a 3×2 transmission coil array andassociated (subset) feeding configuration may be employed.

[0082] Any of the features and definitions discussed in connection with FIGs. 4 to 8may apply, mutatis mutandis, for the alternative WPT feeding configuration of FIG. 12. Forexample, the transmission coil 401 and the compensation network 402 of FIG.4, either ofthe reception coil structures 510, 520 of FIG. 5, the N-legged converter 702 of FIG. 7 (withappropriate changes matching FIG. 12 to the frequencies and phases realized in the differentlegs) and / or the compensation network 805 of FIG.8 may be employed in connection withthe alternative solution of FIG. 12. Notably, in FIG. 4 when combined with FIG. 12, element403 may be associated with one of ^^, ^^, ^^ or(i.e., not always withwhile the element404 may also be associated with one of ^^, ^^, ^^(i.e., not always with ^^). Similarconsideration applies also for FIG. 8 (i.e., Tx^^a is not always associated with the firstfrequency ^^ and Tx^^b is not always associated with the second frequency ^^). Moreover,when employing the N-legged converter 702 of FIG. 7 in combination with the FIG. 12,appropriate changes matching FIG.12 need to be carried out to the frequencies and phasesrealized in the different legs of the N-legged converter. Namely, the 8 legs of the 8-leggedconverter are, in this case, configured to implement the following phase–frequencycombinations: 0° & ^^, 0° & ^^, 0° & ^^, 0° & ^^, 180° & ^^, 180° & ^^, 180° & ^^ and 180°& ^^It should also be noted that while the analysis, simulations and measurements discussed following the discussion of FIG. 8 is not directly applicable to the alternative solution of FIG. 2, the alternative WPT feeding configuration of FIG. 12 exhibits similar beneficial properties as discussed for the WPT feeding configuration of FIG. 2, as will be discussed below.

[0083] The WPT feeding configuration for a WPT transmission coil arrangementaccording to any of the embodiments discussed above (e.g., as discussed in connection with any of FIG.2, 11 or 12) provide at least the following benefits: ^A full positional and rotational charging freedom with appropriately pre-defined andfixed Tx configurations of frequency and phase values is provided for Rx devices. The Rx devices can be charged with high efficiency whenever they appear on top of the transmitting area (comprising one or more 4 × 4 arrays of transmission coils of any of FIGs. 2, 11 or 12). No blind spots for power transfer exist when using the WPT feeding configuration according to any of the embodiments. The three proposed frequency–phase configurations shown in FIGs. 2, 11 and 12 provideeffective solutions for eliminating Rx-side cancellation which happens inconventional multi-Tx WPT systems. ^Simple ON / OFF switching is enabled with no need for dynamic control (i.e., no needfor a control unit for dynamically adjusting the phases and / or frequencies). With the pre-defined Tx current frequencies and directions, no control algorithms on amplitudes or current directions are required anymore. Basic ON / OFF switching byturning on the required Tx coils (coupled with the Rx device) and turning off the idlecoils (with no coupling with the Rx) can be easily applied for efficiency improvementin case of a large-area charging system. ^The WPT feeding configurations according to embodiments are applicable to allcommon types of receiver coil structures. The WPT feeding configurations according to embodiments consistently provide high performance of full charging freedom andhigh efficiency for various commonly used receiver coil structures, including DDtype and flux pipe Rx structures.^ The WPT feeding configurations according to embodiments enable simultaneouslycharging of multiple Rx devices when said Rx devices are placed at any positionsover the transmitting area, without any requirement of dynamic control.

[0084] All of the embodiments rely on the same principle for enabling full Rxpositional and rotational freedom above the Tx area. The equivalent circuit on the Rx side considering all the effective induced voltages from the Tx side as series-connected equivalentvoltage sources is shown as FIG. 9. The sum of induced voltage sources from effective Txs,^^^^^^, will contain at least one of the same-phase coherent power combining, 90° phase-shifted coherent power combining or (frequency difference) non-coherent power combining.Therefore, the total induced voltage is always non-zero at any spatial positions and rotationangles, providing full charging freedom. Considering the non-coherent power combining,the instantaneous phase between two voltage vectors with different frequencies is alwayschanging with time. Therefore, the maximum ^^^^^^ would happen when the induced voltagecomponents are in-phase, while the minimum appears when the induced voltage componentsare out-of-phase, with 180° phase difference. But the time-averaged power seen from Rxside is not completely zero in any case.

[0085] Reference throughout this specification to one embodiment or an embodimentmeans that a particular feature, structure, or characteristic described in connection with theembodiment is included in at least one embodiment of the present solution. Thus, appearances of the phrases “in one embodiment” or “in an embodiment” in various places throughout this specification are not necessarily all referring to the same embodiment.

[0086] As used herein, a plurality of items, structural elements, compositionalelements, and / or materials may be presented in a common list for convenience. However, these lists should be construed as though each member of the list is individually identified as a separate and unique member. Thus, no individual member of such list should be construed as a de facto equivalent of any other member of the same list solely based on their presentation in a common group without indications to the contrary. In addition, variousembodiments and example of the present solution may be referred to herein along withalternatives for the various components thereof. It is understood that such embodiments, examples, and alternatives are not to be construed as de facto equivalents of one another, butare to be considered as separate and autonomous representations of the present solution.

[0087] Even though embodiments have been described above with reference toexamples according to the accompanying drawings, it is clear that the embodiments are notrestricted thereto but can be modified in several ways within the scope of the appendedclaims. Therefore, all words and expressions should be interpreted broadly and they are intended to illustrate, not to restrict, the embodiment. It will be obvious to a person skilled in the art that, as technology advances, the inventive concept can be implemented in various ways. Further, it is clear to a person skilled in the art that the described embodiments may, but are not required to, be combined with other embodiments in various ways. INDUSTRIAL APPLICABILITY

[0088] At least some embodiments find industrial application in wireless powertransfer. REFERENCES[1] J. Yin, D. Lin, C. K. Lee, T. Parisini, and S. Y. Hui, “Front-end monitoring of multipleloads in wireless power transfer systems without wireless communication systems,” IEEETransactions on Power Electronics, vol. 31, no. 3, pp. 2510–2517, 2016.[2] J. I. Agbinya, “20 Induction Cooking and Heating,” in Wireless Power Transfer 2ndEdition. River Publishers, 2016, pp.681–702. [3] S. Al Mahmud, I. A. Panhwar, and P. K. S. Jayathurathnage, “Large-Area Free-Positioning Wireless Power Transfer to Movable Receivers,” IEEE Transactions onIndustrial Electronics, pp.1–1, 2022.[4] S. Y. Choi, B. W. Gu, S. Y. Jeong, and C. T. Rim, “Advances in Wireless PowerTransfer Systems for Roadway-Powered Electric Vehicles,” IEEE Journal of Emergingand Selected Topics in Power Electronics, vol. 3, no. 1, pp. 18–36, 2015.[5] J. Shin, S. Shin, Y. Kim, S. Ahn, S. Lee, G. Jung, S.-J. Jeon, and D.-H. Cho, “Design and Implementation of Shaped Magnetic-Resonance-Based Wireless Power TransferSystem for Roadway-Powered Moving Electric Vehicles,” IEEE Transactions onIndustrial Electronics, vol. 61, no. 3, pp. 1179–1192, 2014.[6] Q. Xu, H. Wang, Z. Gao, Z. Mao, J. He, and M. Sun, “A Novel Mat-Based System forPosition-Varying Wireless Power Transfer to Biomedical Implants,” IEEE Transactions onMagnetics, vol. 49, no. 8, pp. 4774–4779, 2013.[7] Z. Zhang and K. T. Chau, “Homogeneous Wireless Power Transfer for Move-and-Charge,” IEEE Transactions on Power Electronics, vol. 30, no. 11, pp. 6213–6220, 2015.[8] F. Lu, H. Zhang, H. Hofmann, and C. C. Mi, “A Dynamic Charging System WithReduced Output Power Pulsation for Electric Vehicles,” IEEE Transactions on IndustrialElectronics, vol.63, no.10, pp.6580–6590, 2016.[9] J. M. Miller, O. C. Onar, C. White, S. Campbell, C. Coomer, L. Seiber, R. Sepe, and A.Steyerl, “Demonstrating Dynamic Wireless Charging of an Electric Vehicle: The Benefitof Electrochemical Capacitor Smoothing,” IEEE Power Electronics Magazine, vol. 1, no.1, pp.12–24, 2014.

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Claims

CLAIMS 1. A method for feeding a wireless power transfer, WPT, transmission coil arrangement comprising a plurality of transmission coils arranged as a 4 × 4 planar array, the method comprising: feeding the plurality of transmission coils in the 4 × 4 planar array with a pluralityof power signals corresponding, each, to a combination of a first power signal having afirst frequency and a second power signal having a second frequency different from thefirst frequency, wherein phases of the first and second power signals for a transmission coil of an i-th row & a j-th column of the 4 × 4 planar array are defined as: -for i = 1 & j = 1, phases of the first and second power signals are 0° and 0°,- for i = 2 & j = 1, phases of the first and second power signals are 270° and 0°,- for i = 3 & j = 1, phases of the first and second power signals are 270° and 270°,- for i = 4 & j = 1, phases of the first and second power signals are 0° and 270°,- for i = 1 & j = 2, phases of the first and second power signals are 90° and 0°,- for i = 2 & j = 2, phases of the first and second power signals are 180° and 0°,- for i = 3 & j = 2, phases of the first and second power signals are 180° and 270°,- for i = 4 & j = 2, phases of the first and second power signals are 90° and 270°,- for i = 1 & j = 3, phases of the first and second power signals are 90° and 90°,- for i = 2 & j = 3, phases of the first and second power signals are 180° and 90°,- for i = 3 & j = 3, phases of the first and second power signals are 180° and 180°,- for i = 4 & j = 3, phases of the first and second power signals are 90° and 180°,- for i = 1 & j = 4, phases of the first and second power signals are 0° and 90°,- for i = 2 & j = 4, phases of the first and second power signals are 270° and 90°,- for i = 3 & j = 4, phases of the first and second power signals are 270° and 180°,and -for i = 4 & j = 4, phases of the first and second power signals are 0° and 180°.

2. A method for feeding a wireless power transfer, WPT, transmission coilarrangement comprising a plurality of transmission coils arranged as a 4 × 4 planar array,the method comprising: feeding the plurality of transmission coils in the 4 × 4 planar array with a pluralityof power signals corresponding, each, to a combination of a first power signal having afirst frequency or a second frequency different from the first frequency and a second powersignal having the first frequency or the second frequency, wherein frequencies and phasesof the first and second power signals for a transmission coil of an i-th row & a j-th column of the 4 × 4 planar array are defined as: -for i = 1 & j = 1, the first and second power signals have the first frequency, andphases of the first and second power signals are 0° and 90°, -for i = 2 & j = 1, the first and second power signals have, respectively, the secondand first frequencies, and phases of the first and second power signals are 180° and 90°, -for i = 3 & j = 1, the first and second power signals have the second frequency,and phases of the first and second power signals are 180° and 270°, -for i = 4 & j = 1, the first and second power signals have, respectively, the firstand second frequencies, and phases of the first and second power signals are 0° and 270°, -for i = 1 & j = 2, the first and second power signals have, respectively, the secondand first frequencies, and phases of the first and second power signals are 0° and 90°,- for i = 2 & j = 2, the first and second power signals have the first frequency, andphases of the first and second power signals are 180° and 90°, -for i = 3 & j = 2, the first and second power signals have, respectively, the firstand second frequencies, and phases of the first and second power signals are 180° and 270°, -for i = 4 & j = 2, the first and second power signals have the second frequency,and phases of the first and second power signals are 90° and 270°, -for i = 1 & j = 3, the first and second power signals have the second frequency,and phases of the first and second power signals are 0° and 90°, -for i = 2 & j = 3, the first and second power signals have, respectively, the firstand second frequencies, and phases of the first and second power signals are 180° and 90°, -for i = 3 & j = 3, the first and second power signals have the first frequency, andphases of the first and second power signals are 180° and 270°, -for i = 4 & j = 3, the first and second power signals have, respectively, the secondand first frequencies, and phases of the first and second power signals are 90° and 270°, -for i = 1 & j = 4, the first and second power signals have, respectively, the firstand second frequencies, and phases of the first and second power signals are 0° and 90°, -for i = 2 & j = 4, the first and second power signals have the second frequency,and phases of the first and second power signals are 180° and 90°,- for i = 3 & j = 4, the first and second power signals have, respectively, the secondand first frequencies, and phases of the first and second power signals are 270° and 270°, and -for i = 4 & j =4, the first and second power signals have the first frequency, andphases of the first and second power signals are 0° and 270°.

3. The method of claim 1 or 2, wherein a difference between the first and secondfrequencies is larger than or equal to 0.5 kHz and smaller than or equal to 6 kHz.

4. A method for feeding a wireless power transfer, WPT, transmission coilarrangement comprising a plurality of transmission coils arranged as a 4 × 4 planar array,the method comprising: feeding the plurality of transmission coils in the 4 × 4 planar array with a pluralityof power signals corresponding, each, to a combination of a first power signal having oneof first, second, third and fourth frequencies and a second power signal having one of first,second, third and fourth frequencies, wherein the first, second, third and fourth frequencies are different from each other, and frequencies and phases of the first and second power signals for a transmission coil of an i-th row & a j-th column of the 4 × 4 planar array are defined as: -for i = 1 & j = 1, the first and second power signals have, respectively, the firstand second frequencies, and phases of the first and second power signals are 0° and 0°,- for i = 2 & j = 1, the first and second power signals have, respectively, the thirdand second frequencies, and phases of the first and second power signals are 180° and 0°,- for i = 3 & j = 1, the first and second power signals have, respectively, the thirdand fourth frequencies, and phases of the first and second power signals are 180° and 180°,- for i = 4 & j = 1, the first and second power signals have, respectively, the firstand fourth frequencies, and phases of the first and second power signals are 0° and 180°,- for i = 1 & j = 2, the first and second power signals have, respectively, the thirdand second frequencies, and phases of the first and second power signals are 0° and 0°,- for i = 2 & j = 2, the first and second power signals have, respectively, the firstand second frequencies, and phases of the first and second power signals are 180° and 0°,- for i = 3 & j = 2, the first and second power signals have, respectively, the firstand fourth frequencies, and phases of the first and second power signals are 180° and 180°,- for i = 4 & j = 2, the first and second power signals have, respectively, the thirdand fourth frequencies, and phases of the first and second power signals are 0° and 180°,- for i = 1 & j = 3, the first and second power signals have the third and fourthfrequencies, and phases of the first and second power signals are 0° and 0°,- for i = 2 & j = 3, the first and second power signals have, respectively, the firstand fourth frequencies, and phases of the first and second power signals are 180° and 0°,- for i = 3 & j = 3, the first and second power signals have, respectively, the firstand second frequencies, and phases of the first and second power signals are 180° and180°, -for i = 4 & j = 3, the first and second power signals have, respectively, the thirdand second frequencies, and phases of the first and second power signals are 0° and 180°,- for i = 1 & j = 4, the first and second power signals have, respectively, the firstand fourth frequencies, and phases of the first and second power signals are 0° and 0°,- for i = 2 & j = 4, the first and second power signals have, respectively, the thirdand fourth frequencies, and phases of the first and second power signals are 180° and 0°,- for i = 3 & j = 4, the first and second power signals have, respectively, the thirdand second frequencies, and phases of the first and second power signals are 180° and180°, and -for i = 4 & j = 4, the first and second power signals have, respectively, the firstand second frequencies, and phases of the first and second power signals are 0° and 180°.

5. The method according to any preceding claim, wherein the WPT transmissioncoil arrangement comprises a plurality of 4 × 4 planar arrays of transmission coils,comprising the 4 × 4 planar array and one or more further 4 × 4 planar arrays of transmission coils, arranged adjacent to each other, the method further comprising: feeding the one or more further 4 × 4 planar arrays of transmission coils using thesame frequencies and phases as used for the 4 × 4 planar array.

6. An N-legged converter for direct current to alternating current, DC-to-AC,conversion, wherein the N-legged converter is configured to implement the methodaccording to any preceding claim for feeding the WPT transmission coil arrangement comprising at least the plurality of transmission coils arranged as the 4 × 4 planar array.

7. The N-legged converter of claim 6, wherein each leg of the N-legged converter comprises two switches in a half-bridge configuration.

8. The N-legged converter of claim 6 or 7, wherein N is equal to 8, each leg of theN-legged converter being associated with a different phase–frequency combination needed for feeding the plurality of transmission coils.

9. A WPT transmitter comprising: a WPT transmission coil arrangement comprising a plurality of transmission coils arranged as a 4 × 4 planar array; a plurality of compensation networks, respectively, for the plurality of transmission coils; the N-legged converter of any of claims 6 to 8, wherein each leg of the N-leggedconverter is connected to a transmission coil of the WPT transmission coil arrangement via a compensation network of the plurality of compensation networks; and aDC voltage source connected to the N-legged converter.

10. The WPT transmitter of claim 8, wherein the plurality of transmission coils arespiral transmission coils.

11. The WPT transmitter of claim 8 or 9, wherein each leg of the N-leggedconverter comprises two switches in a half-bridge configuration, and an input of each ofthe plurality of compensation networks is connected to a middle point of a corresponding half-bridge leg of the N-legged converter.

12. The WPT transmitter of claim 8 to 10, wherein each of the plurality ofcompensation networks is an LCC compensation network comprising: an inductor having a first terminal acting as an input terminal for a first powersignal obtained from the N-legged converter and a second terminal,a first capacitor having a first terminal connected to the second terminal of the inductor and a second terminal acting as an input terminal for a second power signal obtained from the N-legged converter and being connected to a second terminal of a transmission coil of the plurality of transmission coils, anda second capacitor having a first terminal connected to the second terminal of the first capacitor and a second terminal connected to a first terminal of the transmission coil of the plurality of transmission coils.

13. The WPT transmitter of claim 8 to 12, further comprising:a capacitor connected between first and second terminals of the DC voltage source; and / or a plurality of decoupling inductors for eliminating crosscoupling between theplurality of transmission coils.

14. A WPT transmission–reception system comprising: aWPT transmitter according to any of claims 8 to 13; andone or more WPT receivers comprising, each, at least one reception coil for mutually coupling to the plurality of transmission coils.

15. The WPT transmission–reception system of claim 14, wherein, for each of theone or more WPT receivers, the at least one reception coil comprises at least one flux pipereception coil and / or at least one double D, DD, type reception coil.

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