Omnidirectional Magnetic Resonant Extender Design for Underwater Wireless Charging System

Long-range underwater wireless power transfer (WPT) systems have great application prospects in many industrial fields. However, conventional WPT systems may suffer different kinds of technical issues in this highly unstable operation environment, such as large output decay when the transmission distance increases, and output fluctuation caused by instability of the water flows. To solve these problems, this article proposes a novel solution to achieve an enlarged resonance range, higher efficiency, and more stable output. The LCC-S-S compensation circuit is adopted in the system with a highly stable primary current, which improves its fault tolerance ability to adapt to the unstable underwater environment. A portable omnidirectional magnetic resonant extender is designed as an intermediate device to extend the underwater transmission distance and raise the system’s efficiency. The specially designed structure enables it with two separate but complementary three-coil WPT systems which solves the conventional angular dead zones issue. Theoretical analysis proves that under the idealized conditions, both the magnitude and phase of the load current can be effectively maintained as absolute constant, with arbitrary water flow direction or velocity. Both circuit simulation and finite element analysis (FEA) results are presented to validate that the system is possessed with high fault tolerance. For further assessment, an experimental prototype is established, and the practical test results confirm that the system can maintain a relatively high transmission efficiency under large lateral and angular misalignments ranging from −90° to +90°.


I. INTRODUCTION
M AGNETIC resonance-based wireless power transfer (WPT) technology brings both convenience and safety [1], [2], [3] to conventional power transmission systems [4], [5], [6], especially for the ones under special operation environments with little accessibility, such as undermining or underwater [7].These properties have brought wide application prospects for underwater applications such as diverse wireless charging systems for underwater electric vehicles [8], [9] or sensor networks [10], [11], wireless lighting, or direct motor drives.Under these operation conditions, the system is usually required with a relatively long-range effective power transmission distance, which may be several times longer than the coupler coil radius.However, the coupling coefficient between the transmitter and the receiver is highly sensitive to their relative positions and will be dropped tremendously as the distance gets longer [12].Currently, one of the viable solutions to this problem is to use relay coils as the repeater to prolong the transmission distance and avoid the significant decay of the output power [13], [14].Researchers have designed and proposed plenty of WPT systems with multiple relay coils with three-coil couplers [15], [16], fourcoil couplers [17], [18], or domino couplers [19], [20].These intermediate coils can effectively increase the system output power for relatively long distances, but on the contrary, the system stability may also become more vulnerable as the coil number increases.Because in principle, the multicoil system usually has much stricter requirements in coupler positions, and the centers for every intermediate coil should all be positioned on the same line.The misalignment in any intermediate coil may result in a quick drop of the coupling strength at that power link, which leads to unexpected power loss and even a fault of the whole system.
Recently, a specially designed coil structure has been proposed for omnidirectional WPT systems [21].This structure is designed with two [22] or three orthogonal coils [23], which are decoupled from each other to form different power transmission paths.It can serve both as a transmitter to realize omnidirectional power transmission through certain current control [23], [24] or as the receiver to allow passive omnidirectional energy pickup [25].The decoupled design establishes two or three separate but complementary power transmission paths for great lateral or angular misalignments which can effectively enlarge the powering area or pickup ranges, and thus increase the system fault tolerance ability.However, this kind of system will still have great output fluctuation in dynamic applications or unstable power transmission environments.Tian et al. [26] propose a multicoil structured energy pick-up unit to reduce this fluctuation by further increasing the coil number of the receiver.But this will also inevitably bring unnecessary reactive power to the system and reduce the system's efficiency.On the other hand, for the multicoil receiver, in certain angular ranges, the resonant magnetic field generated by the different coils will turn from strengthening each other to weakening each other.To avoid these angular dead zones and combine the power from different transmission paths more effectively, the secondary side will need separate filters and extra circuit parts to handle the multiple receiver currents, which may cause further power losses.
To break the dilemma and solve these problems, this article presents an optimized solution for long-range underwater WPT systems with omnidirectional magnetic resonant extenders.The application scenario of the proposed system is presented as shown in Fig. 1.The extender can be easily linked with the engineering ship or mini-submarines and can be submerged in water for usage.For the underwater environment, the water flow and the buoyancy force will be balanced by gravity and the rope tension.To deal with arbitrary water flow direction and velocity, the extender requires at least a 2-D omnidirectionally usable angular range to guarantee the normal operation of the system.Thus, the magnetic resonance extender is also designed with two identical coils which are orthogonal and thus decoupled to each other.On one hand, the two coils can be presumed decoupled for separate compensation and independent operation.On the other hand, by changing the omnidirectional unit to the intermediate part of the system, the magnetic field generated by the two coils can always be compensated by each other at arbitrary angles and the conventional angular dead zones will no longer exist.Thus, the system will not need separate rectifiers and power combination circuits anymore.Theoretical analysis proves under ideal conditions that the proposed extender structure can eliminate the output fluctuation at arbitrary rotation angles, and thus the effect of the water flow can be effectively reduced.For the primary side, the system adopts the LCC-S-S compensated circuit topology to further reduce the fluctuation of the transmitter current.The number of power extenders can also be increased depending on the practical parameters such as the depth of the water or the required power level.Circuit simulation proves that the output current can be maintained constant under idealized conditions.Finite element analysis (FEA) has been conducted for a 100:1 scaleddown system with the extender under a rotation angle ranging from −90 • to +90 • .The results validate that the device can realize a 2-D omnidirectional power transmission for WPT systems.We built an experimental prototype, and the practical testing results further validate the feasibility of the proposed system as well as its superiority in fault-tolerance ability.
Section II will introduce the proposed system design and its omnidirectional output performance.Section III will present both circuit simulation and FEA results for the system evaluation.In Section IV, the experimental prototype is tested for practical operation to further validate the feasibility of the system.At last, a conclusion will be drawn in Section V.

A. Circuit Analysis
The proposed system configuration is shown in Fig. 2(a) and its equivalent circuit is presented in Fig. 2(b).The two orthogonal coils in the proposed power extender can be decoupled from each other.To realize the zero-phase operation of the proposed system, the compensation circuits shown in Fig. 2 where the series-connected inductor of the primary side is denoted by L s , and the two capacitors of the primary side are denoted by C p1 and C p2 , respectively.The inductance of the transmitter coil is denoted by L t .The inductance of the repeater coil, the receiver coil, and their corresponding compensation capacitors are denoted by L e , C e , L r , and C r respectively.The equivalent load resistance has the name R l .The resonant angular frequency of the system is denoted by ω [27].Under this condition, for the primary side, the transmitter current is irrelevant to the load variance, whose value can be achieved through where Z ref represents the impedance reflected from the secondary side to the transmitter.Equation ( 2) depicts that the LCC-compensated circuit forms a stabilized current source, and the transmitter current will not be influenced by the variance of the mutual inductance values.In the time domain, assume the transmitter current and the load current are expressed by where ϕ r is the phase angle of the output current.The circuit equations of the power extender coils can thus be obtained as follows: Similarly, the receiver circuit equation can be derived as follows: where i e1 and i e2 denote the currents of the two repeater coils in the time domain, respectively.The equivalent load resistance and the parasite resistance of the receiver coil are called R l and R r , respectively.The mutual inductance between the transmitter and the receiver is denoted by M tr and that between the repeater coil and transmitter or receiver coils are named M ti and M ri (i = 1 or 2), respectively.Combining (3)- (7), it yields Thus, the magnitude of the load current can be derived as follows: Its phase angle can be obtained through

B. Omnidirectional Power Transmission Performance
As discussed in previous research [28], [29], the mutual inductance values of two coaxial circular coils can be approximately regarded as a function of the inclined angle of the coil axis.The FEA results of the mutual inductance variance between the two circular coils shown in Fig. 3(a) are analyzed.For constant input current in the transmitter, the variance of the induced voltage can be presented as shown in Fig. 3(b).The positive or negative sign of the voltage indicates that the phase angle of the induced voltage is lagging or leading the input current for 90 • respectively.As depicted, the induced voltage at the secondary side with different angular positions of the receiver varies as a sinusoidal waveform.Based on this phenomenon, when the sizes of the two coils in the power extender are identical, for simplicity analysis, the mutual inductance values in the system approximately satisfy sin θ (11) where θ is the rotation angle of the coil axis.M to and M r o refer to the mutual inductance between the intermediate coil and the transmitter or receiver under the coaxial position, respectively.
For two identical coils, the integrated resistances of the two circuits can be regarded as the same, which yields Combining ( 11) and ( 12), ( 9) and ( 10) can further simplify the equations to Per ( 13) and ( 14), neither the magnitude nor the phase angle of the receiver current will be affected by the rotation angle of the magnetic resonant extender for the fixed system configuration.
The system can thus achieve stable output.Making use of (2), it can be derived as follows: The two currents of the magnetic resonant extender can be derived by (16), as shown at the bottom of the next page, where Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.The phase deviation of the repeater currents can be derived as follows: The system efficiency can be calculated by (19), as shown at the bottom of the page.Per ( 15) and ( 19), the system output performance and transmission efficiency are both insensitive to extender misalignments.During the period 0 ≤ ωt ≤ π /2, the current flow directions of the coupler coils are compared with the winding directions of extender coils at −45 • and +45 • misalignments.The results presented as shown in Fig. 4(a), where the winding directions, current increment directions, and magnetic field increment directions are denoted by blue, green, and red arrows, respectively.The phase diagram of the system is presented as shown in Fig. 4(b).For two adjacent quadrants of the rotation angle, the different winding directions will not influence the combined resonant magnetic field.Thus, the phases of transmitter and receiver currents will always be presumed constant.In addition, the phase angle of the receiver current ϕ r is determined by the coupling strength between the coupler coils, and the inner resistances of the extender coils, whose value is usually relatively small.On the other hand, the mutual inductance between the transmitter and receiver is also relatively small compared to M to and M r o .Therefore, under these circumstances, the output current will always be approximately in the opposite phase from the transmitter current.For more idealized cases, specifically under long-range operations when the mutual inductance between the transmitter and the receiver is much weaker than that with intermediate coils, i.e., M tr is negligible and can be approximately regarded as equal to zero, the current of the power extender coils can be further simplified as follows: Similarly, the receiver current Thus, the output power follows: The transmission efficiency of the system can then be further simplified as follows: It should be noted that these characteristics only stand for the most ideal case and can only be used for an estimation of the system output.In practical operation, the two coils in the resonant extender cannot be identical, and the mutual inductance will also be affected by other interferences.On the other hand, the cross-coupling effect is another important factor that will influence the magnitude and phase angle of the output current.

III. SYSTEM EVALUATION
A. Circuit Simulation Similar to the receiver side, the reflected impedance is also insensitive to the rotation angle of the magnetic resonant extender.Thus, the primary side will also be quite stable with different angular misalignments of the extender.Fig. 5 illustrates the system output performance versus different system parameters for a transmitter current of 1.5 A. Based on the circuit topology of Fig. 2(b), Fig. 6 presents simulation waveforms for various system mutual inductance values.Table I in turn lists the key electrical parameters.For three different cases, the mutual inductance values are calculated based on the rotation angle of the power extender and its corresponding FEA results, as specified in Table II.As illustrated by the input waveforms in Fig. 6(a), the system can maintain a zero-phase operation.The transmitter current is 90 • lagging the input current.For the fixed input voltage of 25 V, the transmitter current can always maintain a constant output, and the rms values of the magnetic flux density of the receiver coil for the four different angular positions are approximately equal.With different mutual inductance values, the output current can also Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

TABLE I SYSTEM PARAMETERS TABLE II MUTUAL INDUCTANCE
be stabilized at about 1 A, which agrees with the theoretical analysis.According to the above analysis for ideal conditions, the reflected impedance on the primary side follows:

B. FEA Results
The FEA results of the system for the resonant extender with 0 • , ±30 • , and ±60 • angular positions are compared and presented in Fig. 7.The slight discrepancy in the magnetic field distribution is probably caused by the modeling error.The outside coil is designed to be slightly bigger than the inside coil to avoid overlap of the coil models, which is inevitable.Consistent with the circuit analysis results, the phase angle of the receiver current is approximately 180 • lagging behind the transmitter current, and its magnitude is independent of the rotation angle of the power extender.As depicted by the comparison results in Figs. 4 and 7, for two adjacent quadrants, the relative turning direction between the repeater coil and the coupler coils will be at least flipped once.However, the physical angle will not influence the Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.output level.The induced electrical magnetic force at the receiver side, which is induced by the two orthogonal coils in the power extender will always be enhancing each other no matter the physical angle or the turning direction of the coils.Based on the symmetric characteristic of the model, this result validates that the proposed power extender is workable for 2-D omnidirectional angular ranges.

IV. EXPERIMENTS
The experimental prototype is established with the very coil sizes and electrical parameters specified in Fig. 7(a) and Table I.The platform is presented as shown in Fig. 8.The coupler coils are fabricated with 1-mm Litz wire to reduce ac losses.Identical to the circuit simulations, the proposed omnidirectional magnetic resonance extender is positioned at 30 • , 45 • , and 60 • angular positions for three different test cases.The distance between the transmitter and the receiver coil centers is 278 mm, which is three times the radius of each of the coupling coils.The measured input and output waveforms are presented in Fig. 9.As depicted, the LCC-S-S network can successfully realize the zero-phase operation of the system.For 25 V input voltage, the transmitter current can be stabilized as 1 A under different positions of the magnetic resonance extender.For the three test cases, the repeater current changes according to the rotation.Because of the existence of the cross-coupling effect, the load current is not in the exact opposite phase with the transmitter coil.However, the magnitude can be stabilized at approximately as desired.It should be noted that as a typical issue in 3-coil systems, the current in the repeater could be quite big, this phenomenon will be more obvious when it is positioned too close to the Tx coil.Thus, the distance between the extender and the transmitter/receiver should be carefully determined.On the other hand, since the intermediate device will carry the biggest currents in the system, it is also important to consider the trade-off between the overall power losses and the manufacturing costs for different coil type choices.Fig. 10 compares the output power variance with the different angular and lateral positions of the magnetic resonance extender.First, with the fixed position of the extender (Ex), its rotation angle always has only a marginal influence on the output power.Second, when the extender moves from the transmitter (Tx) coil to the receiver (Rx) coil, the output power will be decreased constantly.This is because the mutual inductance between the Tx and the repeater is dropping, while that between the Rx and the repeater is rising, which is consistent with the analytical results expressed by (15).The test results of the output power with the extender positioned with a certain lateral misalignment from the central between the Tx and Rx coils are depicted in Fig. 10(b).The output power be dropped from about 15 to 4 W with the Ex-displacement increased from 0 to 150 To the system performance, the efficiency variance versus the output and the distance between the extender and the transmitter coil when the extender is positioned with a 60 • rotation angle are presented as shown in Fig. 11.The test of the normalized system output power under 25 W input power versus angular of the extender, when it is positioned at the central point, are presented with the comparison to the conventional 1-to-1 WPT system, as depicted in Fig. 12

+90
• .Even at the worst angular positions, the system can still maintain over 60% transmission efficiency.For the best cases, the output power can reach 17.7 W with an efficiency exceeding 70%.In addition, since the presented system is completely linear, the output power can be easily further increased with the raised input current and voltage.For example, 1.5 kW output power will only require the input voltage and the transmitter current to be increased to about 250 V, 10 A accordingly.
V. CONCLUSION This article presents an optimized solution for long-range underwater WPT systems with omnidirectional magnetic resonant extenders.With the decoupled coil structure, the presented magnetic resonance extender effectively prolongs the transmission distance and efficiency for long-range underwater wireless power transfer systems.The system is designed with two complementary power transmission paths which are com-patible with separate compensation designs and independent operations.In addition, by changing the omnidirectional unit to the intermediate part of the system, the magnetic field generated by the two coils can always be compensated by each other at arbitrary angles which solves the conventional angular dead zones issue.Thus, the system will not need separate rectifiers and power combination circuits anymore.The LCC-S-S compensation circuit enables the system with a highly stable primary current, which further improves the fault tolerance ability of the system to adapt to the unstable underwater environment.The biggest advantage of the extender is that its angular position will not influence the system stability, while its existence will always enhance the coupling strength and increase the output power.On the other hand, the extender does not require any active components and can be easily deployed at a very low cost.Thus, it is possible to have multiple of them in the system to further enlarge the coupling ranges and strength in 1-to-1, 1-to-many, or many-to-many WPT systems.
Both circuit simulation and FEA results validate that the proposed omnidirectional unit can have a homogeneous resonant extending effect at arbitrary angular positions, and the system has a stable output current in both magnitude and phase angle.The experimental prototype successfully transferred 15 W wireless power over a distance of about three times the radii of the coupler coils.Compared to conventional 1-to-1 WPT systems, the efficiency is effectively raised from 17.6% to 70.8%, which validates the effectiveness of the proposed system.

Fig. 5 .
Fig. 5. System output performance in dependence on key parameters.(a) Frequency.(b) Mutual inductance between transmitter and intermediate coil.(c) Mutual inductance between receiver and intermediate coil.(d) Load resistance.

Fig. 10 .
Fig. 10.Output power variance against (a) position of the extender on the central line and (b) lateral misalignment of the extender from the central point.

Fig. 11 .
Fig. 11.variance versus (a) output power and (b) distance between the extender and Tx coil.

Fig. 12 .
Fig. 12.Comparison results of output power versus rotation angle under 25 W input power.