Multi-degree-of-freedom anti-offset wpt system based on pt symmetry and parameter design method thereof

Abstract

The application relates to the technical field of wireless power transmission, and particularly discloses a multi-degree-of-freedom anti-offset WPT system based on PT symmetry and a parameter design method thereof. The transmission characteristics of a PT-WPT system are utilized to design three square column-shaped transmitting coils which are identical in parameters and three-dimensionally orthogonally arranged, and a circular column-shaped receiving coil which is located in a cubic space formed by the three transmitting coils during operation. The parameters of a coupling mechanism are designed through an NSGA-II algorithm to realize over-coupling under full-direction offset in a designed power transmission area. A self-oscillation inverter and a control strategy are further designed to realize closed-loop control of the system and achieve the design purpose of the PT system. The system can realize constant-power and constant-efficiency output when the receiving coil transmits multi-degree-of-freedom offset, that is, the system has multi-degree-of-freedom anti-offset characteristics. The system does not need to rely on complex topological structures, coupling mechanisms and control strategies, and the complexity of the system is effectively reduced.

Description

Technical Field

[0001] This invention relates to the field of wireless power transmission technology, and in particular to a multi-degree-of-freedom anti-misalignment WPT system based on PT symmetry and its parameter design method. Background Technology

[0002] With the increasing application of wireless power transfer (WPT) technology in more and more small devices, higher requirements are being placed on the multi-degree-of-freedom anti-misalignment and stable high-power and high-efficiency transmission of WPT systems.

[0003] Current common anti-offset techniques typically employ coupling mechanism design and the introduction of control algorithms. Coupling mechanism optimization usually involves multiple aspects, including coil shape, winding method, topology network, and parameter optimization, with the aim of controlling current flow to generate a more uniform spatial magnetic field. However, this design has several drawbacks, such as the system's transmission performance changing with the receiving coil's offset, a small anti-offset region, complex transmitting and receiving coil structures, and generally only being optimized for one target: translational or rotational offset. Control algorithms include dynamic parameter tuning, position detection, and rotating magnetic fields, but complex algorithms increase control difficulty, hindering system miniaturization and cost reduction.

[0004] All the above solutions require compromises on magnetic field uniformity or real-time control. The introduction of parity-time symmetry (PT) technology offers a new paradigm for overcoming this contradiction. PT-WPT technology utilizes the frequency splitting phenomenon when the system operates under overcoupling to automatically adjust the operating frequency to achieve zero-phase angle (ZPA) operation, resulting in constant efficiency and power output, thus achieving anti-offset capability. Researchers at the University of Hong Kong introduced the PT-WPT system into a drone wireless charging system, achieving a transmission efficiency of 93.6% and a power output of 10W. However, this method is limited in terms of offset distance and flexibility. Researchers at the University of Illinois proposed a method to satisfy PT symmetry conditions by adjusting the angle between the transmitting coil and the relay coil, but this method requires additional spatial degrees of freedom, increasing the complexity of the system's spatial structure design. Researchers at South China University of Technology proposed a three-coil PT-WPT system with variable parameters at the transmitting end. By utilizing variable parameter elements, it achieves constant transmission under asymmetric parameter offset, but this design suffers from complex control schemes. Summary of the Invention

[0005] This invention provides a multi-degree-of-freedom anti-misalignment WPT system based on PT symmetry and its parameter design method. The technical problem it solves is that it is not easy to control the WPT system to maintain a constant and high level of transmission efficiency and output power when facing multi-degree-of-freedom misalignment.

[0006] To address the above technical problems, this invention provides a multi-degree-of-freedom anti-offset (WPT) system based on PT symmetry, comprising an inverter, a control module, a transmitting coil circuit, and a receiving coil circuit. The transmitting coil circuit includes three transmitting coil sub-circuits connected in parallel to the control module, corresponding to three square cylindrical transmitting coils. These three transmitting coils have identical parameters and are placed three-dimensionally orthogonally. The receiving coil circuit includes a circular cylindrical receiving coil. During normal operation, the receiving coil is located in the cubic space enclosed by the three transmitting coils. The control module is used to control the operating frequency of the inverter and the operation of the corresponding transmitting coils in a closed loop, based on the output current of the inverter and with the goal of operating the system in a PT symmetric state.

[0007] Preferably, the parameters of the transmitting coil and the receiving coil satisfy the following: within a preset offset range, the coupling coefficient between the operating transmitting coil and the receiving coil is greater than the critical coupling coefficient.

[0008] Preferably, each transmitting coil is spirally wound from a single Litz wire, with half-side length a. tran The turn spacing is d tran The number of turns is n tran The receiving coil is made of two Litz wires wound together, with a radius of r. recv The number of turns is n recv .

[0009] Preferably, n tran d tran a tran n recv r recv and the maximum axial offset distance z max To optimize variables, in order to minimize (M) max -M min ), r recv n tran d tran Maximize z max a tran To optimize the objective, M min >M c Determine n as a constraint. tran d tran a tran n recv r recv z max The specific value of M maxM min M c These are the maximum mutual inductance, minimum mutual inductance, and critical mutual inductance between the operating transmitting coil and the receiving coil, respectively.

[0010] Preferably, the control module includes a current sampling unit, a zero-crossing detection unit, a control switching unit, a dead-time generation unit, and a drive circuit sequentially connected between the two bridge arm outputs and four control terminals of the inverter, and also includes a microcontroller connected to the zero-crossing detection unit; the output current of the inverter is input to the current sampling unit, and a zero-crossing signal is generated by the zero-crossing detection unit; one zero-crossing signal generates a PWM wave with dead time through the control switching unit and the dead-time generation unit, and is sent to the drive circuit to drive the inverter to work, thereby forming a closed-loop control and constituting a self-oscillating inverter.

[0011] Preferably, the control module further includes a coil switching unit connecting the current sampling unit, the microcontroller, and the transmitting coil circuit. Another zero-crossing signal is sent to the microcontroller to detect the real-time operating frequency of the system and determine whether to perform coil switching. If coil switching is required, the microcontroller sends a signal to the coil switching unit to execute the transmitting coil switching operation.

[0012] The microcontroller sends a signal to the coil switching unit to execute the transmitting coil switching operation, specifically:

[0013] When the microcontroller determines, based on the system operating frequency, that the receiving coil has shifted due to rotation, and the dihedral angle between the plane of the receiving coil and the plane of the transmitting coil exceeds a critical value, it sends a signal to the coil switching unit to switch to another transmitting coil whose angle with the plane of the receiving coil is less than the critical value.

[0014] This invention also provides a parameter design method for a PT-symmetric multi-degree-of-freedom anti-migratory WPT system, the key of which includes the following steps:

[0015] Determine the application context and topology;

[0016] Set the offset parameter in a high-dimensional space;

[0017] Set optimization variables, including the number of turns n of the transmitting coil. tran , turn spacing d tran Half-side length a tran The number of turns n of the receiving coil recv radius r recv and the maximum axial offset distance z max ;

[0018] Define the objective function: minimize (M max -M min), r recv n tran d tran and maximizing z max a tran ;

[0019] Set constraints: M min >M c ;

[0020] The improved NSGA-II algorithm was used to determine multiple sets of optimization variable values;

[0021] Design an evaluation function to optimize and filter multiple sets of optimization variable values, and obtain a set of optimization variable values;

[0022] Perform simulation verification on a set of optimized variable values ​​to determine whether they meet the design objectives. If they do, output the optimized variable values; otherwise, return to the previous step to perform simulation verification on the next set of optimized variable values.

[0023] Furthermore, an improved NSGA-II algorithm is used to determine multiple sets of optimization variable values, specifically including the following steps:

[0024] Set up optimization variables, objective function, and a high-dimensional parameter space for test points;

[0025] Set the parameters for the improved NSGA-II;

[0026] Algorithm initialization;

[0027] Calculate the objective function and constraints;

[0028] Perform environmental selection: non-dominated sorting, crowded sorting;

[0029] The population convergence progress is detected at this time, and the relevant parameters are adaptively and nonlinearly adjusted using the Sigmoid function;

[0030] The offspring population is generated through selection, crossover, and mutation;

[0031] Merge populations and select environments;

[0032] Determine if the number of iterations has reached the maximum number of algebras. If so, derive the current multiple sets of optimization variable values. Otherwise, return to the step of calculating the objective function and constraints for the next iteration.

[0033] Furthermore, the relevant parameters are adaptively and nonlinearly adjusted according to the following formula:

[0034]

[0035] Where k is the adjustment factor, FeasiblePopSize is the number of current feasible solutions, PopSize is the population size, Iteration is the current iteration number, Generation is the upper limit of the number of iterations, Ratio is the current convergence progress of the algorithm, SBX is the distribution exponent of the simulated binary crossover operator, σ is the mutation intensity, and p Mutation p is the mutation probability. Crossover Let F represent the crossover probability, where F represents SBX, σ, and p. Mutation p Crossover Four parameters, F| max and F| min The maximum and minimum values ​​of the range of variation set for the above four parameters.

[0036] Furthermore, the evaluation function S value Designed as follows:

[0037]

[0038] Among them, W P * To represent a tran / r recv , z max / a tran a tran / n tran d tran Three functions, W P * For W P The normalized value.

[0039] This invention provides a PT-symmetric multi-degree-of-freedom anti-migration (WPT) system and its parameter design method. Utilizing the transmission characteristics of the PT-WPT system, three square cylindrical transmitting coils with identical parameters are designed and placed orthogonally in three dimensions (x, y, and z directions). A circular cylindrical receiving coil is located within the cubic space formed by the three transmitting coils during operation. The coupling mechanism parameters are designed using the NSGA-II algorithm to achieve overcoupling under omnidirectional misalignment within the designed power transfer region. A self-oscillating inverter and control strategy are then designed to achieve closed-loop control of the system, fulfilling the design objectives of the PT system. This results in constant power and constant efficiency output when the receiving coil transmits at multiple degrees of freedom, demonstrating the system's multi-degree-of-freedom anti-migration characteristics. When operating in PT-symmetric mode, the PT-WPT system can spontaneously adjust its operating frequency to its intrinsic frequency to achieve zero-amplitude offset (ZPA), achieving multi-degree-of-freedom anti-migration without the need for complex topology, coupling mechanisms, and control strategies, effectively reducing system complexity. Attached Figure Description

[0040] Figure 1This is the equivalent circuit diagram of the two-coil PT-WPT system provided in the embodiment of the present invention;

[0041] Figure 2 This is the equivalent circuit diagram of the multi-degree-of-freedom anti-offset WPT system based on PT symmetry provided in the embodiments of the present invention;

[0042] Figure 3 This is a perspective view of the magnetic coupling mechanism provided in an embodiment of the present invention;

[0043] Figure 4 This is a flowchart of the parameter design method for a PT-symmetric multi-degree-of-freedom anti-migrating WPT system provided in an embodiment of the present invention;

[0044] Figure 5 This is a diagram showing the mutual inductance between the receiving coil and the transmitting coil when the receiving coil undergoes multi-degree-of-freedom offset, as provided in an embodiment of the present invention.

[0045] Figure 6 This is a waveform diagram of the PT-WPT system during operation provided in this embodiment of the invention;

[0046] Figure 7 This is a dynamic response waveform diagram of the PT-WPT system during hot start and transmitter coil switching provided in the embodiment of the present invention;

[0047] Figure 8 This is a comparison chart of experimental and theoretical values ​​of the system output performance when the receiving coil is shifted at various positions, provided by an embodiment of the present invention.

[0048] Figure 9 This is a diagram showing the system output performance when the receiving coil rotates at the maximum offset point (25,25,25), as provided in an embodiment of the present invention. Detailed Implementation

[0049] The embodiments of the present invention are described in detail below with reference to the accompanying drawings. The embodiments are given for illustrative purposes only and should not be construed as limiting the present invention. The accompanying drawings are for reference and illustration only and do not constitute a limitation on the scope of patent protection of the present invention, because many changes can be made to the present invention without departing from the spirit and scope of the present invention.

[0050] Figure 1 This is an embodiment of the design of a multi-degree-of-freedom anti-offset wireless power transfer system based on parity-time symmetry technology, using the equivalent circuit diagram of a two-coil PT-WPT system. The constant power and constant efficiency performance of the PT-WPT system operating in the PT symmetry state in this invention is based on the analysis of the energy transfer mechanism and output performance of the two-coil PT-WPT system. Considering the symmetry between the power supply and load resistance after PT symmetry transformation, the inverter can be considered as a negative resistor, such as... Figure 1 China-Rs As shown, it naturally possesses the characteristics of ZPA, which is realized in the experimental prototype using a self-oscillating inverter. Figure 1 In the diagram, L1 is the transmitting coil inductance, C1 is the transmitting coil capacitance, and r1 is the transmitting coil internal resistance; L2 is the receiving coil inductance, C2 is the receiving coil capacitance, r2 is the receiving coil internal resistance, and R... load M is the load resistance. 12 This refers to the mutual inductance between the transmitting coil and the receiving coil.

[0051] Critical coupling rate κ of a two-coil PT-WPT system c =γ 20 +γ load (γ load γ is the load loss rate. 20 (where k is the loss rate of the receiving coil, i.e., the critical coupling coefficient) c With critical mutual inductance M c for:

[0052]

[0053] ω0 is the system's natural angular frequency. When the coupling coefficient k of the transmitting and receiving coils > k c When the system is in a PT-symmetric state, the amplitude values ​​of the coupling modes at both ends of the system are the same, which are:

[0054]

[0055] γ1 is the loss rate of the transmitting coil, γ2 is the loss rate of the receiving coil, a1 is the coupled mode of the transmitting coil, a2 is the coupled mode of the receiving coil, and G is the gain rate of the negative resistor (i.e., the self-oscillating inverter).

[0056] The system's intrinsic frequency at this time is:

[0057]

[0058] Among them κ 12 for:

[0059]

[0060] At this time, the system input power P in Output power P out And the transmission efficiency η is:

[0061]

[0062] All three are constant values.

[0063] It can be seen that when the coupling coefficient k between the transmitting coil and the receiving coil is greater than the critical coupling coefficient k... cWhen in an overcoupled state, the system spontaneously enters the PT-WPT operating state. At this point, regardless of how k changes, the system can spontaneously change its operating frequency to achieve ZPA (Zero-Parallelism), maintaining constant output power and transmission efficiency, thus achieving anti-offset performance. Based on the above theoretical analysis, if the coupling mechanism can be designed so that when the receiving coil experiences multi-degree-of-freedom offset within a certain range, the system coupling coefficient can always be guaranteed to be greater than the critical coupling coefficient, then the transmission performance of the PT-WPT system can be utilized to construct a WPT system with multi-degree-of-freedom anti-offset performance.

[0064] Therefore, embodiments of the present invention design a multi-degree-of-freedom anti-migratory WPT system based on PT symmetry, such as... Figure 2 The system equivalent diagram shows that the system includes an inverter (full-bridge inverter), a control module, a transmitting coil circuit, and a receiving coil circuit. The transmitting coil circuit includes three transmitting coil sub-circuits connected in parallel to the control module, corresponding to three square cylindrical transmitting coils (the transmitting coil L in the x-direction). tran-x y-direction transmitting coil L tran-y The transmitting coil L in the z-direction tran-z The three transmitting coils have identical parameters and are placed orthogonally in three dimensions. The series compensation capacitors used are denoted as C. tran-x C tran-y C tran-z The receiving coil circuit includes the receiving coil L. recv Series compensation capacitor C recv Load resistance R load Receiving coil L recv It is cylindrical in shape, and during normal operation, the receiving coil is located in the cubic space enclosed by the three transmitting coils. The mutual inductance between the three transmitting coils and the receiving coil is denoted as M. x-recv M y-recv M z-recv .

[0065] A 3D view of the magnetic coupling mechanism is shown below. Figure 3 As shown. Each transmitting coil is spirally wound from a single Litz wire, with half-side length a. tran The turn spacing is d tran The number of turns is n tran The receiving coil is made of two Litz wires wound together, with a radius of r. recv The turn spacing is d recv The number of turns is n recv .

[0066] The control module is used to control the inverter's operating frequency in a closed loop, based on the inverter's output current and with the system operating in a PT symmetrical state as the target, and to control which transmitting coil is connected to the inverter. Specifically, as shown... Figure 2As shown, the control module includes a current sampling unit, a zero-crossing detection unit, a control switching unit, a dead-time generation unit, and a drive circuit, sequentially connected between the two bridge arm outputs and four control terminals of the inverter. It also includes a microcontroller connected to the zero-crossing detection unit, and a coil switching unit connecting the current sampling unit, the microcontroller, and the transmitting coil circuit. The inverter output current is input to the current sampling unit, and a zero-crossing signal is generated by the zero-crossing detection unit. One zero-crossing signal is used by the control switching unit and the dead-time generation unit to generate a PWM wave with a dead time, which is then sent to the inverter drive circuit to drive the full-bridge inverter, thus forming a closed-loop control and constituting a self-oscillating inverter. The other zero-crossing signal is sent to the microcontroller (STM32F103RCT6), which uses a frequency detection program to detect the real-time operating frequency of the system and determine whether coil switching is required. If coil switching is needed, the microcontroller sends a signal to the coil switching unit to control the AC switch to turn on and off, executing the transmitting coil switching operation. Since the transmission efficiency and output power of the system are independent of the coupling coefficient when the system is operating in PT symmetric state, the PT-WPT system can always maintain constant output power and transmission efficiency when the receiving coil is in an overcoupled state and is offset by multiple degrees of freedom, thus achieving anti-offset.

[0067] The omnidirectional wireless power transmission area is designed as a cubic space with a side length of D, centered on the center of the transmitting coil. The receiving coil can be offset within this space with any number of degrees of freedom, and the system can maintain constant transmission efficiency and output power. In this example, only one transmitting coil is active at a time. For this active transmitting coil, when the receiving coil rotates and the dihedral angle between the planes of the receiving and transmitting coils exceeds a critical value (at which point the coupling coefficient k is less than the critical coupling coefficient k...), the system will... c The microcontroller controls the coil switching unit to switch to another transmitting coil whose angle with the receiving coil plane is less than the critical value. Since the parameters of the three transmitting coils are the same, the transmitting coil is overcoupled with the receiving coil at this time, and the system resumes to work in PT symmetry state, thereby achieving multi-degree-of-freedom anti-migration.

[0068] For a cylindrical receiving coil, its unit normal vector is denoted as m = (m x ,m y ,m z If the z-axis is the central axis and parallel to the xOy plane, then the unit normal vector of the receiving coil is (0,0,1). The pitch angle offset of the receiving coil in the xOy plane is equivalent to the angle between its normal vector and the z-axis:

[0069] <(m x ,m y ,m z ),(0,0,1)>=m z ,

[0070] Since m is a unit normal vector, we have:

[0071]

[0072] Therefore, by the Cauchy-Schwarz inequality, we have:

[0073]

[0074] That is, the maximum angle between the normal vector and the z-axis is arccos(m) z = 54.7°≈55°. Therefore, it is only necessary to optimize the coupling mechanism parameters through the algorithm to ensure that the overcoupling state can still be maintained when the elevation angle of the receiving coil deviates by a critical value of 55°.

[0075] To ensure the symmetry of the parameters of the three transmitting coils and reduce the effective energy transfer redundancy region, the sphere S containing the unit normal vector of the receiving coil can be... 2 Construct the following complete spherical rectangle partition with intersection measure of 0:

[0076]

[0077] The coordinate transformation relationship between the normal vector and the rotational offset of the receiving coil is as follows (taking P as P). z For example:

[0078]

[0079] The spherical rectangular partition is transformed to the uv coordinate system, and the mapping relationship is as follows (taking P as the coordinate system). z For example:

[0080]

[0081] The spherical rectangle is a rectangle in the uv coordinate system, and algorithms can be applied to optimize the relevant parameters.

[0082] To ensure that the coupling coefficient k between the transmitting coil and the receiving coil is greater than the critical coupling coefficient k within a preset offset range. c The parameters of the coupling mechanism need to be optimized to ensure that the transmitting and receiving coils can maintain overcoupling when the receiving coil undergoes translational shift within ±55° of elevation and rotational shift within 360° of azimuth within the space on either side of a single transmitting coil. For a transmitting coil with three orthogonal directions, the receiving coil can then perform multi-free omnidirectional shifts within the cubic space enclosed by the transmitting coils. The optimization variable is chosen as the number of turns n of the transmitting coil. tran , turn spacing d tran Half-side length a tran The number of turns n of the receiving coilrecv radius r recv and the maximum offset distance z in the z-axis direction max (Since the maximum offset distance is the same for each axis, we take the z-axis as an example); the optimization objective is to minimize (M max -M min ), r recv n tran d tran Maximize z max a tran M max M min These represent the maximum and minimum mutual inductance between the transmitting and receiving coils, respectively.

[0083] Therefore, this invention also provides a parameter design method for a PT-symmetric multi-degree-of-freedom anti-migratory WPT system, the process of which is as follows: Figure 4 As shown, the process includes several major steps: model building, parameter optimization, and parameter selection.

[0084] like Figure 4 As shown, the establishment of the model mainly includes determining the application background and topology, that is, determining the system parameters other than the optimization variables and the design purpose.

[0085] like Figure 4 As shown, the model establishment includes:

[0086] Determine the application context to determine the range of values ​​for the optimization variables;

[0087] The topology is determined to be SS topology.

[0088] Parameter optimization includes:

[0089] Set the offset parameter in high-dimensional space:

[0090]

[0091] Where x, y, and z are translation offset parameters, and u and v are pitch angle θ and azimuth angle, respectively. The rotation offset parameters after coordinate transformation;

[0092] Set optimization variables, including the number of turns n of the transmitting coil. tran , turn spacing d tran Half-side length a tran The number of turns n of the receiving coil recv radius r recv and the maximum offset distance z in the z-axis direction max ;

[0093] Define the objective function: minimize (M max -M min ), rrecv n tran d tran and maximizing z max a tran ;

[0094] Set constraints: M min >M c ;

[0095] An improved NSGA-II algorithm was used to determine multiple sets of optimization variable values.

[0096] The specific steps for determining multiple sets of optimization variable values ​​using the improved NSGA-II algorithm include:

[0097] Set up optimization variables, objective function, and a high-dimensional parameter space for test points;

[0098] Set the parameters for the improved NSGA-II: maximum number of iterations, population size, crossover probability, mutation probability, mutation strength, simulated binary crossover operator (SBX) distribution index, crossover probability, number of sampling points, number of optimization variables, upper and lower limits of optimization variables, number of objective functions, number of constraints, etc.

[0099] Algorithm initialization;

[0100] Calculate the objective function and constraints;

[0101] Perform environmental selection: non-dominated sorting, crowded sorting;

[0102] The population convergence progress is detected at this point, and the relevant parameters (mutation intensity, SBX distribution index, mutation probability, crossover probability, etc.) are adaptively and nonlinearly adjusted using the Sigmoid function:

[0103]

[0104] Where k is the adjustment factor, FeasiblePopSize is the number of current feasible solutions, PopSize is the population size, Iteration is the current iteration number, Generation is the upper limit of the number of iterations, Ratio is the current convergence progress of the algorithm, SBX is the distribution exponent of the simulated binary crossover operator, σ is the mutation intensity, and p Mutation p is the mutation probability. Crossover Let F represent the crossover probability, where F represents SBX, σ, and p. Mutation p Crossover Four parameters, F| max and F| min The maximum and minimum values ​​of the range of variation set for the above four parameters.

[0105] The offspring population is generated through selection, crossover, and mutation;

[0106] Merge populations and select environments;

[0107] Determine if the number of iterations has reached the maximum number of algebras. If so, derive the current multiple sets of optimization variable values. Otherwise, return to the step of calculating the objective function and constraints for the next iteration.

[0108] like Figure 4 As shown, the parameter selection process includes the following steps:

[0109] Design the evaluation function S value :

[0110]

[0111] Among them, W P * To represent a tran / r recv , z max / a tran a tran / n tran d tran Three functions, W P * For W P The normalized value.

[0112] Optimize and filter multiple sets of optimization variable values ​​to obtain a single set of optimization variable values;

[0113] Maxwell and Simulink are used to simulate and verify a set of optimized variable values ​​to determine whether they meet the design objectives. If they do, the optimized variable value is output; otherwise, the process returns to the previous step to simulate and verify the next set of optimized variable values.

[0114] An experimental prototype was built, and the omnidirectional wireless power transmission area was designed as a cubic space with a center side length D = 50 cm of the transmitting coil cube. The system's natural frequency was set to f0 = 82.5 kHz (so that the operating frequency would be around 85 kHz when the system operates in PT symmetry mode). A self-oscillating inverter provided DC power supply U. cd =20V, using Litz wire with a diameter of 2.8mm to wind the transmitting and receiving coils, and following the above parameter design process, a set of optimized variable values ​​can be obtained: a tran =39.785cm, n tran =24,d tran =7.36cm, r recv =14.465cm, n recv =30. Therefore, the self-inductance L of the transmitting coil is... tran =742.08μH, internal resistance R tran =3.5Ω; Self-inductance of the receiving coil Lrecv =462.87μH, internal resistance R recv =0.5Ω; Load resistance R load =5Ω; Critical mutual inductance of the system M c =13.43μH, critical coupling coefficient k c =0.0232; Theoretical transmission efficiency η = 65.11%.

[0115] Figure 5 This describes the change in mutual inductance of the system when the receiving coil undergoes multi-degree-of-freedom offset in the offset space, as described in this invention. Figure 5 (a) shows the change in mutual inductance between the transmitting and receiving coils when the receiving coil is translated and offset on the first octant coordinate plane within the offset space cube; Figure 5 Figures (b) and (c) show the changes in mutual inductance between the transmitting and receiving coils when the receiving coil rotates at the origin (0,0,0) and the maximum translational offset point (25,25,25), respectively (in centimeters / cm). Figure 5 It can be seen that when the receiving coil undergoes multi-degree-of-freedom offset, its mutual inductance with the transmitting coil is always greater than the critical mutual inductance, maintaining an over-coupling state, which proves that the parameter optimization scheme meets the design requirements.

[0116] like Figure 6 These are waveform diagrams of the system operating at different intrinsic frequencies in this invention. Figure 6 (a) is the high-frequency branch. Figure 6 (b) is the low-frequency branch. (From...) Figure 6 It can be seen that the system can spontaneously operate at the intrinsic frequency and achieve ZPA, which proves the effectiveness of the self-oscillating inverter closed-loop control designed in the invention, as well as the rationality and effectiveness of the self-oscillating inverter being equivalent to a negative resistor.

[0117] like Figure 7 This is a dynamic response diagram of the system during hot start and coil switching. When the receiving coil deflects too much, causing undercoupling between it and the currently operating transmitting coil, the microcontroller detects the system's operating frequency to identify whether the system is in a PT-symmetric state, and then switches the transmitting coil to bring the system back to PT-symmetric operation. To ensure stable system startup, the microcontroller outputs a PWM signal to keep the system operating at its natural frequency for 50ms for hot start. Subsequently, the negative feedback signal path is activated, and the system enters a self-oscillation state, identifying and switching the optimal operating coil. The system spends 48ms and 78ms in the two non-optimal operating coils, respectively. When the optimal coil is in operation, the system switches and stabilizes in PT-symmetric operation in 24ms.

[0118] like Figure 8It is a line graph comparing the system transmission efficiency, output power, and operating frequency with theoretical values ​​when the receiving coil undergoes translational shift. Figure 8 Figures (a)-(c) are comparison charts of experimental, simulated, and theoretical values ​​of the system's output power and transmission efficiency when the receiving coil undergoes translational shift. Figure 8 (d) represents the path of the center point during the translational offset of the receiving coil: (0,0,0)→(25,0,0)→(25,25,0)→(25,25,25) (coordinate units are centimeters / cm). Figure 8 It can be seen that when the receiving coil is shifted, the system transmission performance can remain constant, with an average transmission efficiency of 63.19% and an average output power of 16.20W. The experimental results are in good agreement with the theoretical values.

[0119] like Figure 9 This is a graph (in centimeters / cm) showing the system transmission efficiency and output power when the receiving coil experiences a combined offset of a azimuth angle within 360° and a pitch angle within ±55° at the maximum translation offset point (25,25,25). Figure 9 It can be seen that when the receiving coil rotates and deflects, the system transmission performance can remain constant, with an average transmission efficiency of 62.60% and an average output power of 16.12W. The experimental results are in good agreement with the theoretical values.

[0120] It should be noted that the above-mentioned topology, optimized variable values, DC input voltage, load resistance value, system operating frequency, etc. are only examples and do not constitute a limitation on the scope of protection of this invention.

[0121] In summary, the multi-degree-of-freedom anti-migration WPT system and its parameter design method based on PT symmetry provided by this invention utilizes the transmission characteristics of the PT-WPT system. It designs three square cylindrical transmitting coils with identical parameters, placed three-dimensionally orthogonally (x, y, and z directions), and a circular cylindrical receiving coil located within the cubic space formed by the three transmitting coils during operation. The coupling mechanism parameters are designed using the NSGA-II algorithm to achieve over-coupling under omnidirectional misalignment within the designed power transfer region. A self-oscillating inverter and control strategy are then designed to achieve closed-loop control of the system, fulfilling the design objectives of the PT system. This results in constant power and efficiency output when the receiving coil exhibits multi-degree-of-freedom migration, demonstrating the system's multi-degree-of-freedom anti-migration characteristics. Experimental results show that when the STM32 microcontroller detects that the system's real-time operating frequency is in a non-PT symmetric state, the control coil switching module can switch to the optimal transmitting coil and achieve stability within a maximum of 150ms. This invention not only improves the system's multi-degree-of-freedom anti-migration capability but also achieves omnidirectional wireless power transmission with constant output power and transmission efficiency during multi-degree-of-freedom migration.

[0122] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A multi-degree-of-freedom anti-migratory WPT system based on PT symmetry, characterized in that: It includes an inverter, a control module, a transmitting coil circuit, and a receiving coil circuit; the transmitting coil circuit includes three transmitting coil sub-circuits connected in parallel to the control module, corresponding to three square cylindrical transmitting coils, which have the same parameters and are placed three-dimensionally orthogonally; the receiving coil circuit includes a circular cylindrical receiving coil; during normal operation, the receiving coil is located in the cubic space enclosed by the three transmitting coils; The control module is used to control the operating frequency of the inverter in a closed loop, based on the output current of the inverter, with the goal of the system operating in a PT symmetrical state, and to control the operation of the corresponding transmitting coil. Each transmitting coil is spirally wound from a single Litz wire, with half-side length a. tran The turn spacing is d tran The number of turns is n tran The receiving coil is made of two Litz wires wound together, with a radius of r. recv The number of turns is n recv ; With n tran d tran a tran n recv r recv and the maximum axial offset distance z max To optimize variables, in order to minimize (M) max -M min ), r recv n tran d tran Maximize z max a tran To optimize the objective, M min >M c Determine n as a constraint. tran d tran a tran n recv r recv z max The specific value of M max M min M c These are the maximum mutual inductance, minimum mutual inductance, and critical mutual inductance between the operating transmitting coil and the receiving coil, respectively.

2. The multi-degree-of-freedom anti-migratory WPT system based on PT symmetry according to claim 1, characterized in that, The parameters of the transmitting coil and the receiving coil satisfy the following: within a preset offset range, the coupling coefficient between the operating transmitting coil and the receiving coil is greater than the critical coupling coefficient.

3. The multi-degree-of-freedom anti-migratory WPT system based on PT symmetry according to claim 1, characterized in that: The control module includes a current sampling unit, a zero-crossing detection unit, a control switching unit, a dead-time generation unit, and a drive circuit, sequentially connected between the two bridge arm outputs and four control terminals of the inverter. It also includes a microcontroller connected to the zero-crossing detection unit. The output current of the inverter is input to the current sampling unit, and a zero-crossing signal is generated by the zero-crossing detection unit. One zero-crossing signal generates a PWM wave with a dead time through the control switching unit and the dead-time generation unit, and is sent to the drive circuit to drive the inverter to work, thereby forming a closed-loop control and constituting a self-oscillating inverter.

4. The multi-degree-of-freedom anti-migratory WPT system based on PT symmetry according to claim 3, characterized in that: The control module also includes a coil switching unit that connects the current sampling unit, the microcontroller and the transmitting coil circuit. Another zero-crossing signal is sent to the microcontroller to detect the real-time operating frequency of the system and determine whether to perform coil switching. If coil switching is required, the microcontroller sends a signal to the coil switching unit to perform the transmitting coil switching operation. The microcontroller sends a signal to the coil switching unit to execute the transmitting coil switching operation, specifically: When the microcontroller determines, based on the system operating frequency, that the receiving coil has shifted due to rotation and the dihedral angle between the plane of the receiving coil and the plane of the transmitting coil exceeds a critical value, it sends a signal to the coil switching unit to switch to another transmitting coil whose angle with the plane of the receiving coil is less than the critical value.

5. A parameter design method for a PT-symmetric multi-degree-of-freedom anti-migratory WPT system, wherein the method is applied to the PT-symmetric multi-degree-of-freedom anti-migratory WPT system as described in any one of claims 1 to 4, characterized in that, Including the following steps: Set optimization variables, including the number of turns n of the transmitting coil. tran , turn spacing d tran Half-side length a tran The number of turns n of the receiving coil recv radius r recv and the maximum axial offset distance z max ; Define the objective function: minimize (M max -M min ), r recv n tran d tran and maximizing z max a tran ; Set constraints: M min >M c ; The improved NSGA-II algorithm was used to determine multiple sets of optimization variable values; Design an evaluation function to optimize and filter multiple sets of optimization variable values, and obtain a set of optimization variable values; Perform simulation verification on a set of optimized variable values ​​to determine whether they meet the design objectives. If they do, output the optimized variable values; otherwise, return to the previous step to perform simulation verification on the next set of optimized variable values.

6. The parameter design method for a PT-symmetric multi-degree-of-freedom anti-migratory WPT system according to claim 5, characterized in that, The improved NSGA-II algorithm is used to determine multiple sets of optimization variable values, specifically including the following steps: Set up optimization variables, objective function, and a high-dimensional parameter space for test points; Set the parameters for the improved NSGA-II; Algorithm initialization; Calculate the objective function and constraints; Perform environmental selection: non-dominated sorting, crowded sorting; The population convergence progress is detected at this time, and the relevant parameters are adaptively and nonlinearly adjusted using the Sigmoid function; The offspring population is generated through selection, crossover, and mutation; Merge populations and select environments; Determine if the number of iterations has reached the maximum number of algebras. If so, derive the current multiple sets of optimization variable values. Otherwise, return to the step of calculating the objective function and constraints for the next iteration.

7. The parameter design method for a PT-symmetric multi-degree-of-freedom anti-migratory WPT system according to claim 6, characterized in that, The relevant parameters are adaptively and nonlinearly adjusted according to the following formula: ， Where k is the adjustment factor, FeasiblePopSize is the number of current feasible solutions, PopSize is the population size, Iteration is the current iteration number, Generation is the upper limit of the number of iterations, Ratio is the current convergence progress of the algorithm, SBX is the distribution exponent of the simulated binary crossover operator, σ is the mutation intensity, and p Mutation p is the mutation probability. Crossover Let F represent the crossover probability, where F represents SBX, σ, and p. Mutation p Crossover Four parameters, F| max and F| min The maximum and minimum values ​​of the range of variation set for the above four parameters.

8. The parameter design method for a PT-symmetric multi-degree-of-freedom anti-migratory WPT system according to claim 7, characterized in that, The evaluation function S value Designed as follows: ， Among them, W P * To represent a tran / r recv , z max / a tran a tran / n tran d tran Three functions, W P * For W P The normalized value.

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