Enhanced Axial Misalignment Tolerance in a 10-kW Autonomous Underwater Vehicle Wireless Charging System Utilizing a Split Solenoid Coupler

This letter presents a 10-kW wireless charging system for autonomous underwater vehicles, utilizing a split solenoid coupler to enhance axial misalignment tolerance. Comparative finite-element analysis with traditional solenoid structures indicates the split solenoid design's superiority in reducing inductance fluctuations, with a 22% reduction in coupling coefficient fluctuation and a 24.8% and 25.6% reduction in self-inductance and mutual inductance fluctuations, respectively, at an 80-mm axial misalignment. Experimental validation of the system demonstrates high efficiency in saltwater environments, achieving a peak efficiency of 96.3% at 7.1 kW and a maximum power output of 10.6 kW at 95.6% efficiency. A tight coupling coefficient of 0.69 along with the split solenoid coupler improves both axial misalignment and system efficiency enabling high-power wireless power transfer in marine environments.

Axial misalignment occurs when the AUVs' receiving coil is not aligned with the transmitting coil in the docking station along their shared central axis, as shown in Fig. 1.This can happen when the AUV is inserted too far or not far enough into the Amr Mostafa is with Tesla Inc., Palo Alto, CA 94304 USA (e-mail: amrmostafa@tesla.com).
Yao Wang is with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 (e-mail: yao.wang@ntu.edu.sg).
Fei Lu and Hua Zhang are with the Department of Electrical and Computer Engineering, Lehigh University, Bethlehem, PA 18015 USA (e-mail: fel324@lehigh.edu;huz524@lehigh.edu).
Color versions of one or more figures in this article are available at https://doi.org/10.1109/TPEL.2024.3431285.
Digital Object Identifier 10.1109/TPEL.2024.3431285docking station, causing the receiving coil to be displaced from the optimal charging position.This misalignment is a common challenge in AUV charging due to the difficulty in achieving perfect alignment between the vehicle and the charging station in marine environments.
In [11], a traditional solenoid coupler structure is utilized for an underwater simultaneous wireless power and data transfer system.While this structure demonstrates good performance, it is still susceptible to power fluctuations under axial misalignment conditions.In contrast, we propose a novel split solenoid coupler structure that consists of four smaller solenoids: two for the transmitter and two for the receiver, with a gap between them.This split arrangement reduces the impact of axial misalignment on the coupling coefficient and self-inductances, leading to enhanced misalignment tolerance and improved power transfer stability compared to the traditional solenoid structure in [11].Finally, the high power transfer capability and efficiency of the split solenoid structure are experimentally validated through a 10-kW IPT prototype in saltwater, demonstrating its practical feasibility and performance in challenging marine environments.
The rest of this letter is organized as follows.Section II provides a detailed description of the split solenoid structure.Section III presents the experimental setup and results, demonstrating an improved axial misalignment performance.Finally, Section IV concludes this letter, summarizing key contributions.

A. Coupler Structure Overview
Fig. 1 shows the proposed design concept of a hull-compatible inductive charger for AUVs.The transmitter (L 1 ) and the

B. Comparison to the Solenoid Structure
Finite-element analysis (FEA) is utilized to examine how gap spacing in a split solenoid structure can enhance axial misalignment tolerance.The tradeoff of this improvement is a marginal decrease in the coupling coefficient when the coils are perfectly aligned.
Fig. 3 compares the split solenoid structure with a traditional solenoid, revealing a 22% reduction in coupling coefficient fluctuation at 80-mm axial misalignment.In addition, the proposed coupler exhibits 24.8% less fluctuation in the primary self-inductance (L 1 ) and 25.6% less fluctuation in the mutual inductance (L M ) at an axial misalignment of 80 mm compared with the conventional coupler, which exhibits a similar trend to the coupling coefficient shown in Fig. 3.The secondary self-inductance (L 2 ) shows similar fluctuations for both the coupler designs, with no significant difference (0%) observed at an axial misalignment of 80 mm.Fig. 4 displays the normalized inductances under axial misalignment, highlighting a significant detuning effect that can impact power transfer efficiency.In AUV applications, where tight coupling is necessary to minimize seawater losses, selfinductance detuning is exacerbated by close transmission distances and large misalignments.The commonly used cylindrical coupler structures in AUVs are particularly susceptible to self-inductance fluctuations due to their geometry, making misalignment tolerant systems difficult to achieve.

C. Effect of Self-Inductance Detuning on Output Current
In Fig. 11, this letter selects the series-series topology for simplicity.In the well-aligned case, the resonance is expressed as follows: ( Mutual inductance and equivalent resistance are defined as To analyze detuning, the changes in self-inductances relative to resonance values L 1,0 and L 2,0 are defined as follows: The first harmonic approximation for output current at resonance is further derived as follows: From (4), solving for I 2 yields To simplify the analysis, I 2 can be rewritten as follows: where α is a power scaling factor resulting from self-inductance detuning.If there is no self-inductance detuning, α = 1.From Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.(2), (3), and (5), α is as follows: where two parameters β 1 and β 2 are defined as The load quality factor is defined as L = ω 0 L 2,0 /R Le .In a tightly coupled IPT system, Q L ≈1 for load matching.Based on FEA simulation in Section II-B, Δγ 1 and Δγ 2 are in the range of [0, 0.6] for the proposed coupler, resulting in β 1 <β 2 .
Fig. 6 further shows the effect of inductance detuning on β 1 and β 2 .Since L 1 and L 2 have similar detuning characteristics (from Fig. 4), the inductance variation is set as Δγ = Δγ 1 = Δγ 2 for simplicity.The magnitudes of β 1 and β 2 both positively correlate with k.The blue and red stars show the approximate values of β 1 and β 2 , respectively, at 100-mm axial misalignment.Fig. 7 shows the variation in the magnitude of the scaling factor |α|.In a tightly coupled system (k = 0.8), the inductance detuning results in increased output current based on (6) and

TABLE II IMPLEMENTED MAGNETIC COUPLER DIMENSIONS
consequently power.However, when k = 0.5, the scaling factor |α| contributes to reducing power.It is important to note that the detuning does not result in a reduced overall current since L M is also reduced in (6).
In the aforementioned analysis, the assumption is made that the system operates at resonance when perfectly aligned.However, in practical operation, many designs necessitate a detuning of compensation capacitors to achieve zero-voltage switching (ZVS).To consider capacitor detuning, recalculate L 1,0 and L 2,0 by rewriting (1) as follows: To summarize the design process, (3) can be used to recalculate Δγ 1 and Δγ 2 for each position including a well-aligned case, resulting in (6) that considers both capacitor and selfinductance detuning.

D. Split Unipolar Coupler Implementation
Table II details the split solenoid coupler's structure parameters.The transmitter coil L 1 and the receiver coil L 2 have ferrite lengths of 200 and 150 mm, respectively, extending beyond the coil to shield AUV electronics and minimize seawater leakage losses.
The magnetic coupler is shown in Fig. 8.The primary coil comprises nine turns, while the secondary has five turns.High per turn inductance necessitates half-turns for construction, with each split part of the transmitter having 4.5 turns on opposite sides to maintain symmetry.Fig. 9 illustrates mutual and self-inductances at various misalignments.At 80-mm misalignment, L 1 and L 2 decrease by 31.6% and 25%, respectively, and L M by 38.5%, aligning with FEA results shown in Fig. 4.
The proposed split solenoid coupler is designed for seamless integration within the fiberglass hull of an AUV, providing   inherent protection against the conductive seawater environment.The hollow receiver coil design allows for the efficient placement of AUV components, such as batteries or electronic modules, within the coupler structure.These properties facilitate the integration of the wireless charging system into the existing AUV architectures while minimizing the impact on the vehicle's size and weight.

A. 10-kW Prototype Power-Circulating Testing
Fig. 10 illustrates the saltwater test bench.The power recirculation setup, as shown in Fig. 11, is an arrangement where the rectified dc output of the wireless power transfer system is connected back to the dc input, creating a closed loop for power circulation.This configuration allows the system to effectively serve as its own load, as discussed in [12].The main advantage

TABLE III SPECIFICATIONS OF THE IMPLEMENTED IPT SYSTEM IN THE WELL-ALIGNED CASE
of this approach is that the dc input source only needs to provide the power required to offset system losses, enabling high power testing capability with a lower power demand on the dc source.In this setup, the system behaves as a constant voltage load, continuously recycling the same power.The voltage and current loads observed across all the system components are consistent with those seen in a system operating under a full power dc source.System parameters are given in Table III.Tests were conducted with dc voltages between 100 and 550 V, using a 200-kHz inverter.The magnetic coupler, made from 800-strand 0.1-mm Litz wire, has a coupling coefficient k of 0.69 at a 10-mm transfer distance.It was submerged in 34.9‰ salinity water, with conductivity at 56.7 mS/cm and temperature at 22.4 °C.To manage thermal loads, heat sinks and cooling fans were used.The SiC MOSFETs (C3M0120100K) operate within their continuous current ratings.The rectifier design employs C4D20120D SiC diodes, which are rated for 1200 V and 20-A continuous current.Each diode package contains two diodes, which are connected in parallel, with four packages used for the full-bridge rectifier.

B. Well-Aligned Power Transfer Capability
Fig. 12 displays waveforms at zero-phase-angle operation with matched input and output voltages V DC = V out = 550 V, yielding 8.63-kW output power and 96.27% efficiency in saltwater.Fig. 13 indicates that within a V DC = V out = 100-550 V range, power spans 0.28-8.63kW.Peak efficiencies are 96.99% at 5.13 kW in air and 96.29% at 7.14 kW in saltwater, 0.7% discrepancy due to saltwater's ion-induced eddy current losses.Fig. 15 presents efficiency under misalignment.At 80 mm, efficiency drops by 1.31% in air and 4.9% in saltwater, with the efficiency gap between the two widening from 0.7% to 4.28%.In addition, it details the power loss distribution in saltwater at 0-mm misalignment with an input voltage of 550 V and an output power of 8.63 kW.

C. Axial Misaligned Power Transfer Performance
Fig. 14 demonstrates how axial misalignment affects output power at various input voltages.At an input voltage of 550 V and an axial misalignment of 50 mm, the system achieves a peak output power of 10.6 kW, highlighting its high power transfer capability under misalignment conditions.As shown in Fig. 15, high power transfer is maintained with a small efficiency drop from 96.27% to 95.72%, demonstrating system robustness to axial misalignment.

D. Power Loss Analysis
In the power circulating setup, the input voltage V DC equals the output voltage V out .At the steady state, the input power from the dc source represents the total system losses.To measure system efficiency, a Chroma 62024P dc power supply provided input power, with voltage measurements validated by a Keithley DMM6500 multimeter.Output current was measured using a Tektronix TCP0030A current probe and a Tektronix 5 Series oscilloscope.Since the power loss is measured independently of the output current, any error in the current probe accuracy will have a minimal effect on the calculated efficiency.
Fig. 16 presents a breakdown of the power losses in each component when operating in saltwater with a well-aligned coupler, at an input and output voltage of 550 V, a switching frequency of 200 kHz, and an output power level of 8.6 kW.The figure reveals that the main losses occur in the magnetic coupler (L 1 and L 2 ), accounting for 53% of the total losses.The inverter contributes to 23% of the losses, followed by the rectifier at 19% and the capacitors (C 1 and C 2 ) at 5%.

IV. CONCLUSION
This letter presents a split solenoid coupler structure to improve axial misalignment tolerance for AUVs without compromising rotational performance compared to a traditional solenoid structure.A 10-kW IPT prototype is implemented in saltwater, achieving a peak power level of 10.6 kW with efficiency of 95.6% and a peak efficiency of 96.3% at 7.1 kW.Besides, the experimental results show that the proposed coupler only has 0.7% efficiency difference in saltwater compared to the air condition at a well-aligned position.

Manuscript received 9
April 2024; revised 11 May 2024 and 19 June 2024; accepted 7 July 2024.Date of publication 19 July 2024; date of current version 4 September 2024.This work was supported by the National Science Foundation under Grant 2301637.(Corresponding author: Hua Zhang.)

Fig. 2 .
Fig. 2. Proposed split solenoid magnetic coupler structure, showing the details and different viewing angles.(a) Side view of the coupler.(b) Front view of the coupler.

Fig. 14
Fig. 14 demonstrates how axial misalignment affects output power at various input voltages.A 50-mm misalignment results

Fig. 12 .
Fig. 12. Experimental waveforms in saltwater at the well-aligned position with k = 0.69, V DC = V out = 550 V, and P out = 8.63 kW.

Fig. 13 .
Fig. 13.Experimental output power and DC-DC efficiency at the well-aligned position, comparing the performance in the air and saltwater conditions.

Fig.
Fig. Experimental output power at misalignment in saltwater environment.

Fig. 15 .
Fig. 15.Experimental DC-DC efficiency at misalignment in the air and saltwater environments, showing that the misalignment can cause efficiency drop in saltwater.

Fig. 16 .
Fig. 16.Power loss distribution of components at well aligned 8.63 kW in seawater.The L 1 and L 2 loss includes both the conduction/magnetic loss in the coupler and the eddy current loss in the seawater environment.