Omnidirectional Wireless Power Transfer System Based on Rotary Transmitting Coil for Household Appliances

An omnidirectional magnetically coupled resonant wireless power transfer (WPT) system based on rotary transmitting coil is presented. The proposed scheme can ease the variations of the transfer efficiency and output power caused by the deviation of transfer direction, and improve the unbalanced power distribution phenomenon between the receivers, which are still not fully achieved in current WPT systems. The modified coupled-mode model is built first to describe the non-rotary multi-receiver WPT system. The analysis indicates that the transfer efficiency and output power of the system can be expressed as functions of the deviation angle between the transmitting coil and receiving coil, which has a non-negligible influence on the system performances. Then, the modified high order coupled-mode model containing time-varying parameters about the deviation angle is derived for the proposed omnidirectional WPT system. Theoretical analysis and simulated results indicate that this system can transfer power to multiple receivers around the transmitter synchronously and evenly, which is very suitable for wireless charging for household appliances indoors. The scheme feasibility and theoretical analysis are verified by experimental results.


Introduction
These years WPT field has witnessed a great progress in many fields, especially in low power applications (such as medical implants [1,2] and mobile devices [3,4]).Wireless charging for medium and high power applications (such as mobile robots [5] and electric vehicles [6]) has also been developing.Specially, Kurs et al. [7] proposed a new kind of WPT technology based on magnetic-resonance in 2007, which extended the transfer distance of WPT system to a large extent.
As WPT technology is getting mature, many products equipped with the function of wireless charging have matched the related commercial and technical standards, and widely entered into human life.For example, both the latest iPhone 8 and iPhone X have installed chips of wireless charging, which enhances their ability to hold a charge.It can be imagined that in the near future, most of household appliances and portable devices can be charged by wireless power, which will realize a true efficient, clean and green wireless home environment.
However, current WPT systems are limited by the directionality of the coils, that is, only when the transmitting coil and receiving coil are coaxial can the system transmission capacity get its peak [8].Absolutely this feature quite blocks the valid area of the system.Besides, due to the limitation brought by the directionality, generally only two receivers can be charged by one transmitting coil simultaneously, which brings a great waste of resources.There is thereby an urgent need but it is still a significant challenge to build a system to enable the omnidirectional WPT that multiple receivers can be charged wirelessly at any direction.
Nevertheless, much work just focuses on point-to-point WPT systems to achieve high efficiency and long distance, only a few articles study the directional limitation of WPT.Hwang et al. [9] designed an autonomous coil alignment system for providing energy wirelessly to electric vehicles.Lin et al. [10][11][12] proposed 2-D and 3-D WPT systems to realize omnidirectional wireless charging with multiple transmitters.These schemes utilize load detecting technology, which needs complicated control method to achieve the aim, and only one receiver can pick up power with high efficiency.In [13], the authors designed a ball-joint system, which can also realize the function of omnidirectional WPT.However, this scheme only applies to the mechanical systems with single-receiver movable mechanical parts and is unsuitable for household environment.Chabalko et al. [14] used the natural electromagnetic modes of hollow-metallic structures to produce uniform magnetic fields which can simultaneously power multiple small receiver coils contained almost anywhere inside, where the charging area is seriously limited.
On the other hand, some work has been done to study the unbalanced power distribution phenomenon in multi-receiver WPT systems [15].Li et al. [16] designed a WPT system based on dual transmitters and dual receivers, but their aim is to upgrade the system power capacity.Several wireless charging platforms for multi-receiver applications were proposed [17][18][19], while their planar structures limit the receiver working flexibility when being charged.
Therefore, this paper proposes an omnidirectional magnetically-coupled resonant WPT system based on rotary transmitting coil, where the rotary coil is driven by an electric motor.This scheme can realize omnidirectionality simply and transfer power to multiple receivers simultaneously, evenly and efficiently, which can indeed be applied in household multi-application environment.Firstly, a high order coupled-mode model is built to describe the single-receiver and multi-receiver WPT systems based on non-rotary transmitting coil.The transfer efficiency and output power can be expressed as functions of the deviation angle related to the transmitter and receiver.The analysis indicates that the deviation angle has a non-negligible impact on the system performances.Secondly, a high order coupled-mode model containing time-varying parameters about the deviation angle is established to describe the proposed omnidirectional single-receiver and multi-receiver WPT systems.Theoretical analysis and simulations imply that the proposed system not only can transfer power to multiple receivers synchronously, but also can improve the problem of the unbalanced power distribution between each receiver.Furthermore, it is verified that utilizing two rotary transmitting coils can eliminate the dead zones of power supply.The scheme feasibility and theoretical analysis have been identified by the experimental results.

Analysis of Wireless Power Transfer System with Non-Rotary Transmitting Coil
Here, the WPT system of non-rotary transmitting coil refers to the WPT system whose transmitting coil remains still in working state.To compare with the system of rotary coil, in this part, theory and simulation analyses of transfer characters of the non-rotary single-receiver system and multi-receiver system are presented below, respectively.

Analysis of Single-Receiver System
A simplified diagram of the single-receiver system of non-rotary coil is shown in Figure 1, in which the red long rectangle represents the coil of transmitter T s , the black long rectangle represents the coil of receiver R X1 , d s1 is the distance between the centers of the two coils, and θ is the angle between central axises of the two coils (hereinafter referred to as "deviation angle").
Differently from the ideal cases in considerable articles where the deviation angle is assumed to be zero when the system is working, in most of actual situations, directional misregistration is very difficult to be avoided, which has an impact on system performances.Thus, to analyze the system more precisely and closely to the reality, influence of the deviation angle should be considered in the corresponding model.The modified equations based on coupled-mode theory to describe the system are deduced, as shown in (1).
Here, a s,1 are field amplitudes of the resonant cavities of T s and R X1 such that |a s,1 | 2 represent the energies stored in the cavities.ω s and ω 1 are intrinsic angular frequencies of the two cavities.Fu s (t) is power supply item [5].As shown in ( 2) and (3), γ s and γ 1 are intrinsic loss rates of T s and R X1 , where L s and L 1 are self-inductances of the transmitting coil and receiving coil, R s and R 1 are resistances of the transmitting coil and receiving coil, and R L is resistance of the load.In (3), γ 1 consists of loss rates made by R 1 and R L , which are defined as γ 10 and γ L , respectively.
The expression of the modified coupling rate κ(θ) is shown in (4), and it is a function of deviation angle θ.
M max is maximal mutual inductance between the two coils (when θ = 0) and can be calculated by (5) [20,21], in which µ is air permeability, N s and r s are the number of turns and radius of the transmitting coil, and N 1 and r 1 are the number of turns and radius of the receiving coil, respectively.
When both ω s and ω 1 are equal to the angular frequency of power supply ω, the whole system meets the condition of resonance [22].Solving the equations in (1), the analytic expressions of a s and a 1 can be obtained, as shown in (6).
The output power P out and transfer efficiency η are determined by the power dissipated in the system resistance and load.Substituting ( 2)-( 4) and ( 6) into the formulas of output power and transfer efficiency according to [5], ( 7) and ( 8) can be obtained.
(7) and ( 8) indicate that both output power and transfer efficiency can be expressed as functions of θ.The parameters used for analysis are: self-inductance values of the coils are L s = L 1 = 13 µH, compensation capacitance values are C s = C 1 = 1.9 nF, resistances of the coils are R s = R 1 = 0.5 Ω, the load resistance is R L = 10 Ω, the maximal mutual inductance is M max = 0.65 µH, the power supply item u s (t) is 20cosωt and F = j/ √ 2L s according to [22], the operating frequency f = 1 MHz (ω = 6.28 × 10 6 rad/s), and the step size is h = 1 × 10 −8 s.
The results of steady-state values in Figures 2 and 3 are listed in Table 1.It reveals that the output power is influenced by the deviation angle.In addition, when the deviation angle gets larger, the output power does not always increase or decrease monotonously.On the other hand, a concomitant decrease in the transfer efficiency can be observed with the value of |cos θ| getting smaller.All the analysis results imply that the deviation angle has a big impact on output power and transfer efficiency, that is, the system characters are quite influenced by different receiver positions.

Analysis of Multi-Receiver System
When there is more than one receiver, two assumptions are established to simplify the analysis: 1.
All the receivers are evenly placed around the transmitter.In other words, the linkages between centers of the receiving coils compose a regular polygon.

2.
All the receivers can be placed around the transmitter with their planes facing the center of transmitting coil.
Then a simplified diagram of multi-receiver system can be shown in Figure 4 (a five-receiver system is shown here to explain), in which d si is the distance between centers of the transmitting coil and the ith receiving coil, d im is the distance between centers of the the ith and the mth receiving coils, θ si is the deviation angle between the transmitting coil and the ith receiving coil, and θ im is the deviation angle between the ith and the mth receiving coils (i, m = 1, 2, . . ., n, I = m, and n is the number of receivers).As the number of receivers n has increased, (1) should be derived to (n + 1) orders.In a similar way, defining a i as field amplitude of resonant cavity of the ith receiver, γ i as the ith receiver intrinsic loss rate, ω i as the ith receiver intrinsic angular frequency, κ n.si (θ si ) as modified coupling rate between the transmitter and the ith receiver, and κ n.im (θ im ) as modified coupling rate between the ith and the mth receivers, the system can be described by (9).
The related expressions and parameters in ( 9) are explained below.Since the sum of the interior angles of an n-sided polygon is π(n − 2), the expressions of κ n.si (θ si ) and κ n.im (θ im ) can be derived and the results are shown in (10) and (11), where L i and L m are self-inductances of the ith and the mth receiving coils, M nsi.max is maximal mutual inductance between the transmitting coil and the ith receiving coil, and M nim.max is maximal mutual inductance between the ith and the mth receiving coils.
The values of M nsi.max and M nim.max can be calculated by ( 12) and ( 13), where r i and N i are the radius and number of turns of the ith receiving coil, and r m and N m are the radius and number of turns of the mth receiving coil, respectively.
According to cosine law, there is a relation between d im and d si , that is: It indicates that the value of M nim.max can be determined based on ( 12)-( 14) once the values of M nsi.max and d si are set.
At last, the value of γ i can be obtained by (15).
Here, γ i consists of γ Li and γ i0 , which are loss rates made by R Li and R i .R Li is resistance of the i th load and R i is resistance of the ith receiving coil.
Let the values of L i , C i , R i , R Li , M nsi.max and ω i equal to those of L 1 , C 1 , R 1 , R L , M max and ω in Section 2.1, respectively.Besides, set d si = 0.3 m and other values of parameters the same as those in Section 2.1.Then the results of steady state solutions for three-receiver, four-receiver and five-receiver systems are listed in Table 2.
The output power P i and transfer efficiency η i of the ith receiver is calculated by ( 16) and (17).16) The data in Table 2 demonstrates that when more than one receiver is around the non-rotary transmitter, even though there is no difference between the receivers, the energy, output power and transfer efficiency of the system are all distributed unevenly to each receiver as a consequence of directionality problem.In particular, when the receiving coil and transmitting coil are perpendicular, the receiver cannot pick up any power.

Analysis of Wireless Power Transfer System with Rotary Transmitting Coil
According to Section 2, there are many directional limitations in traditional WPT systems.Therefore, an omnidirectional WPT system based on rotary transmitting coil is proposed, which is especially suitable for charging wirelessly for household appliances indoors.

System Structure
A structure schematic of the system mentioned above is shown in Figure 5, and a working sketch is shown in Figure 6.In Figure 5, the transmitting coil is fixed on a rotor of the electric motor, connecting to the power supply by an electric slip ring.Thus the transmitting coil can rotate with the rotor in the same speed and all the appliances around it can be charged wirelessly.Besides, the rotating speed of the rotor is adjustable.The mathematical model and analysis are presented in the following parts of this section.

Analysis of Single-Receiver System
As the transmitting coil is rotating, time-varying items should be added to the coupling rate, and it can be expressed by (18), in which ω n is the rotating angular frequency of the motor rotor.
Then the modified system model can be obtained, as presented in (19).
Setting ω n equal to 314 rad/s (f n = 50 Hz) and other parameters used for analysis the same as those in Section 2.1, the waveforms of |a s,1 |, output power and transfer efficiency are presented in Figure 7 with solid lines.
From the figures it seems that energy, output power and transfer efficiency of the rotary system all vary periodically with time.Here the distortion of output power waveform is because of the non-monotonous relation between the output power and coupling rate.Similarly, the distortion of |a 1 | waveform is because of the non-monotonous relation between |a 1 | and coupling rate.Letting θ = 0 and taking the derivative of M max in (8), it is found that P out will get its maximal value when M max ≈ 0.365 µH.Setting M max equal to this value, a new set of waveforms are obtained, as presented in Figure 7 with imaginary lines.On this occasion, the distortions discussed above are eliminated.It means that both output power and energy will get their maximal values when θ = 0.
In order to measure the validity of the proposed system, average output power P out and average efficiency η are defined and can be calculated as follows.
Through numerical integration based on trapezoid formula, P out and η can be calculated numerically.When the rotating frequency is 50 Hz, P out = 70.19W. Compared with the results in Table 1, it is lower than the value under the condition where the deviation angle is 3π/10 but higher than the values under some adverse conditions, e.g., where the deviation angle is 2π/5.
Figure 8 shows the curves of average output power and average efficiency under the conditions of different rotating frequencies from 20 Hz to 80 Hz.The average efficiency keeps constant at 48.62%, while the average output power keeps nearly constant with the value change no more than 0.07 W. The results reveal that the rotating frequency has little impact on transfer characteristics.Since rotating the transmitting coil is a kind of periodic behavior and the total energy pick up by the receiver per circle is fixed, the above results are reasonable.

Analysis of Multi-Receiver System
Similarly, add the time-varying items to the coupling rate κ n.si , and its expression is shown in (22).
Then the coupled-mode equations for multi-receiver WPT system based on rotary transmitting coil can be deduced: The analyses on output power and transfer efficiency of three-receiver, four-receiver and fivereceiver systems are also implemented with f n = 50 Hz and values of other parameters the same as those in Section 2.2.The results are shown in Figures 9-11.The value of M nsi.max has been selected properly, thus there is no distortion in the output power waveforms.
The average output power values pick up by every receiver in three systems are 20.07W, 12.50 W and 8.51 W. It illustrates that the proposed system ensures all the receivers around the rotary transmitter can pick up power averagely, which quite improves the unbalanced power distribution phenomenon between receivers in the non-rotary system mentioned in Section 2.2.

Analysis of Dual-Supply System
According to the analysis in part 2 and part 3 of this section, both the output power and transfer efficiency have dead zones when there is only one rotary transmitting coil.This problem can be solved by increasing the number of transmitting coils appropriately.Here a dual-supply system is proposed.The only difference is that in this kind of system, there are two orthometric rotary transmitting coils working together so that when one of the transmitting coils is perpendicular to the receiving coil, the other one can supply power to the receiver.The system model is presented in (24).
Here, a s1 and a s2 are field amplitudes of the two transmitter resonant cavities.κ s1 (t) and κ s2 (t) are coupling rates between the receiver and two transmitting coils, respectively.Besides, let the expression of κ s1 (t) the same as (18) and then the expression of κ s2 (t) is: Note that because of the orthogonality of two transmitters, the coupling rate between a s1 and a s2 is zero, it does not appear in (24).
Figure 12 presents the output power waveform.The values of parameters for analysis are the same as those in Section 3.2.The results reveal this kind of systems can eliminate the aforementioned dead zones, and the average output power is 112.89W. Furthermore, although increasing the number of transmitters will to some extent increase the setup cost, it can decrease the needed rotating speed of the motor.

Experimental Verifications
The omnidirectional WPT system based on rotary transmitting coil shown in Figure 5 has been fabricated and the setup photograph is shown in Figure 13.Here, A is a signal generator used to generate signal of high frequency.B is a broadband power amplifier.C is an impedance matcher used to adjust the resonant frequency of the coils.D is a DC power supply for the electric rotating motor E. F is the transmitting coil connected to a 12-access 2A electric slip ring.G are the receiving coils with loads.H is a motor speed meter.I is a motor speed regulator.
The operating frequency is 1 MHz, the transmitting coil and receiving coil both have six turns, the diameters of the two coils are 32 cm, and the diameter of the copper wire is 2 mm.Self inductance and capacitance of the receiving coil are measured by the impedance analyzer and the values are 25.76 µH and 893.28 pF, which determines the coil intrinsic frequency of 1.04 MHz.The transmitting coil intrinsic frequency is also adjusted to 1 MHz by the impedance matcher.

Single-Receiver Rotating Experiment
In this part, there is only one receiver.The receiver consists of one receiving coil and one set of loads, which include three series of 3 × 3 W LEDs.The distance between the centers of two coils is 30 cm.

System with One Rotary Transmitting Coil
By adjusting the motor speed, it can be observed that the flicker frequency of LEDs varies accordingly.The more quickly the motor rotor rotates, the shorter LEDs' off time is.When the speed reaches a certain value, human eye can no longer tell whether the LEDs are flickering or not, and at this time it can be thought that the brightness of the LEDs remains stable.The experimental results indicate that when the speed reaches 589 rpm, LEDs can supply stable light.

System with Two Rotary Transmitting Coils
In order to verify the function of two orthometric rotary transmitting coils analyzed in Section 3.4, a dual-supply experiment setup has been built, which is shown in Figure 14.Experimentally, all the LEDs keep luminous during the system operating time, certifying that the aforementioned dead zones have been eliminated successfully.Besides, the experimental results indicate that when the speed reaches 286 rpm, LEDs can supply stable light.

Multi-Receiver Rotating Experiment
Another set of LEDs and a receiving coil has been added.In this experiment, the distance between the centers of transmitting coil and each receiving coil is 20 cm.Regard the deviation angle of the first receiver as reference angle and record it as θ.Two receiving coils are placed perpendicularly such that the deviation angle of the second receiver is always π/2 larger than θ.According to the theoretical analysis, two sets of LEDs would glow alternately with the value of θ varying in cycles.The experimental phenomena with different values of θ are presented in Figure 15, which show a dynamic process of the working system.At first, when θ = 0, the first set of LEDs (hereinafter referred to as "LEDs1") get their greatest brightness while the second set of LEDs (hereinafter referred to as "LEDs2") are totally extinct.It implies all the power from the transmitter has been transferred to LEDs1.When θ = π/6, all the bulbs are on with LEDs1 a litter brighter than LEDs2.At this moment, LEDs1 pick up more power than LEDs2.Then we can see LEDs1 continue to become darker and LEDs2 become brighter.When θ gets π/4, the transmitter distributes equal power to each receiver due to symmetry of the positions so that LEDs1 and LEDs2 have the same brightness.Then with the increasing of θ, the power transferred to LEDs1 becomes less and more power is pick up by LEDs2.Until θ = π/2, LEDs2 get their greatest brightness while LEDs2 are totally extinct.At this time, all the power is picked up by LEDs2 and no power is transferred to LEDs1.And so on, LEDs1 and LEDs2 glow alternately.Furthermore, two sets of LEDs supply stable light of the same brightness when the motor speed gets fast enough, which reveals the balanced power distribution between the two receivers.
The above behavior is in great agreement with our analysis results presented in Section 3.3.

Discussion and Conclusions
This paper presents a theoretical study of a wireless power transfer system based on rotary transmitting coil.This system can be utilized to achieve omnidirectional wireless power transfer.In particular, it applies to multi-receiver system and ensures each receiver can pick up power synchronously and evenly.Besides, utilizing two rotary transmitting coils can eliminate the dead zones of power supply.Simulations and experimental results support the theoretical analysis.Through this scheme, household appliances equipped with receiving coils can be charged wirelessly regardless of their positions, which can realize a clean, efficient and convenient indoor environment.

Figure 1 .
Figure 1.A simplified diagram of the single-receiver system.

Figures 2
Figures 2 and 3 present the curves of output power and transfer efficiency against time with different deviation angle values for single-receiver WPT system of non-rotary coil.The parameters used for analysis are: self-inductance values of the coils are L s = L 1 = 13 µH, compensation capacitance values are C s = C 1 = 1.9 nF, resistances of the coils are R s = R 1 = 0.5 Ω, the load resistance is R L = 10 Ω, the maximal mutual inductance is M max = 0.65 µH, the power supply item u s (t) is 20cosωt and F = j/ √ 2L s according to[22], the operating frequency f = 1 MHz (ω = 6.28 × 10 6 rad/s), and the step size is h = 1 × 10 −8 s.The results of steady-state values in Figures2 and 3are listed in Table1.It reveals that the output power is influenced by the deviation angle.In addition, when the deviation angle gets larger, the output power does not always increase or decrease monotonously.On the other hand, a concomitant decrease in the transfer efficiency can be observed with the value of |cos θ| getting smaller.All the analysis results imply that the deviation angle has a big impact on output power and transfer efficiency, that is, the system characters are quite influenced by different receiver positions.

Figure 2 .
Figure 2. Output power against time with different deviation angle.

Figure 3 .
Figure 3. Transfer efficiency against time with different deviation angle.

Figure 4 .
Figure 4.A simplified diagram of the multi-receiver system.

Figure 6 .
Figure 6.A working sketch of the omnidirectional WPT system based on rotary transmitting coil for household appliances.(Four computers are being charged wirelessly and simultaneously by the rotating transmitter.)

Figure 7 .
Figure 7. Waveforms of the abs(a s,1 ), output power and transfer efficiency against time in the single-receiver system: (a) abs(a s,1 ); (b) output power; (c) transfer efficiency.

Figure 8 .
Figure 8.Average output power and average efficiency against rotating frequency in the single-receiver system.

Figure 9 .
Figure 9. Waveforms of the output power and transfer efficiency against time in the three-receiver system: (a) output power; (b) transfer efficiency.

Figure 10 .
Figure 10.Waveforms of the output power and transfer efficiency against time in the four-receiver system: (a) output power; (b) transfer efficiency.

Figure 11 .
Figure 11.Waveforms of the output power and transfer efficiency against time in the five-receiver system: (a) output power; (b) transfer efficiency.

Figure 12 .
Figure 12.Waveform of the output power against time in the dual-supply system.

Figure 14 .
Figure 14.Experiment setup of two rotary transmitting coils.

Table 1 .
Steady state solutions for single-receiver system.

Table 2 .
Steady state solutions for multi-receiver system.