Generalized space-time symmetric anti-dislocation wireless power transmission method and system

Abstract

The invention discloses an anti-dislocation wireless power transmission method and system with generalized space time symmetry, and the method comprises the steps: firstly calculating a critical coupling coefficient of a wireless power transmission system, and determining a maximum design value of the radius of a transmitting coil according to the minimum transmission power demand in an application scene; and then establishing a mapping relation between the dislocation parameter and the critical coupling coefficient, and determining a robust working range corresponding to the radius of each transmitting coil according to the mapping relation. And finally, integrating the data and weighing the transmission power and the space robustness according to the data so as to complete the selection of the radius of the transmitting coil, and further determining system element parameters and constructing a complete wireless power transmission system. The system designed according to the method does not need a complex active control circuit, can stably work in a PT symmetric phase within a predetermined dislocation range, and realizes efficient and robust wireless power transmission insensitive to spatial dislocation.

Description

Technical Field

[0001] This application relates to the field of wireless power transmission technology, and more specifically, to a generalized parity-time symmetric anti-misalignment wireless power transmission method and system. Background Technology

[0002] Magnetic-coupled wireless power transfer (MC-WPT) technology can penetrate non-magnetic obstacles to achieve medium-range, high-efficiency contactless power transfer, overcoming the physical limitations of traditional wired power supply and showing significant application potential. In dynamic charging scenarios such as implantable medical devices, the size of the receiver is usually strictly constrained, while the transmitter often uses a larger coil to enhance coupling and ensure power transmission capability. Therefore, asymmetrical coupling structures with transceiver coil sizes have become an important research direction in this scenario. However, during dynamic charging, relative displacement often occurs between the receiver and transmitter coils, including lateral offset and angular deflection, causing fluctuations in the coupling coefficient between them, which in turn leads to instability in the system's output power and transmission efficiency. This is a key challenge currently faced by MC-WPT technology in practical dynamic applications.

[0003] To address coupling fluctuations, traditional MC-WPT systems typically rely on impedance matching networks and frequency tracking control circuits for real-time tuning. This not only increases system complexity and cost but also reduces reliability. In recent years, the parity-time symmetry (PT symmetry) concept, originating from quantum mechanics, has been introduced into wireless power transfer systems. PT-symmetric systems possess a real energy spectrum under specific parameter conditions and exhibit unique frequency adaptive characteristics in dynamic applications: when the system operates in the PT-symmetric phase, even if the coupling coefficient varies within a certain range, the system can maintain stable transmission power and efficiency without requiring active external circuit tuning, thus demonstrating strong robustness against dynamic misalignments. This provides a new approach for simplifying control and achieving robust dynamic wireless power supply.

[0004] Wireless power transfer systems based on PT symmetry exhibit a clear phase transition boundary: when the coupling coefficient is above a critical value, the system is in the PT symmetric phase, and its transmission performance is insensitive to changes in coupling; when the coupling coefficient is below this critical value, the system enters the PT broken phase and cannot maintain stable transmission. Therefore, in the design of dynamic charging systems, it is essential to accurately assess the range of coupling coefficient variations based on the potential spatial misalignment at the receiver, and to design parameters to ensure that the system remains in the PT symmetric phase within the expected misalignment range. This is crucial for achieving robust energy transfer against misalignment. Current methods for designing and optimizing PT symmetric systems for asymmetric coupling structures in conjunction with actual misalignment conditions are still incomplete and require further research. Summary of the Invention

[0005] The purpose of this application is to overcome the shortcomings of existing technologies and provide a generalized parity-time symmetric anti-misalignment wireless power transmission method and system, which can enable the system to operate stably in the PT symmetric phase within a predetermined misalignment range without the need for complex active control, thus achieving efficient and robust wireless power transmission that is insensitive to spatial misalignment.

[0006] The objective of this application is achieved through the following technical solution:

[0007] In a first aspect, this application proposes a generalized parity-time symmetric method for resisting misalignment wireless power transfer, the method comprising: S1. Calculate the critical coupling coefficient of the wireless power transmission system based on the receiver circuit parameters; S2. Determine the maximum design value of the transmitting coil radius based on the minimum transmission power requirement in the application scenario; S3. Set the sweep parameter range. When the transmitting coil and the receiving coil are spatially misaligned, establish a mapping relationship between the misalignment parameter and the critical coupling coefficient. Based on the critical coupling coefficient, determine the robust working range corresponding to the radius of each transmitting coil from the mapping relationship. The misalignment parameter includes the deflection angle and / or lateral offset. S4. Combining the transmission power data and robust operating range data corresponding to each transmitting coil radius, a trade-off is made between transmission power and spatial robustness, and the final transmitting coil radius is selected from the parameter sweep range. S5. Based on the selected transmitting coil radius, determine the system component parameters and construct a complete wireless power transmission system.

[0008] In one possible implementation, the critical coupling coefficient The calculation formula is: , The total loss rate on the receiving side. This is the system's operating angular frequency.

[0009] In one possible implementation, step S2 includes: S21. Set the sweep parameter range for the radius of the transmitting coil; S22. Based on the self-inductance model of a spatial helical coil, calculate the self-inductance coefficient corresponding to different transmitting coil radii within the scan parameter range. ; S23. Calculate the transmission power of the system when it is operating in a parity-time symmetrical phase under different transmitting coil radii; S24. The radius of the transmitting coil corresponding to the minimum transmission power requirement is determined as the maximum design value.

[0010] In one possible implementation, the self-inductance coefficient The calculation formula is: , The permeability of free space, The number of turns of the transmitting coil. The radius of the transmitting coil, is the coefficient of the spatial helical coil.

[0011] In one possible implementation, step S3 includes: S31. Based on the improved mutual inductance model, calculate the mutual inductance coefficient between the transmitting coil and the receiving coil under different transmitting coil radii and different spatial misalignments. This establishes the first mapping relationship between the misalignment parameter and the mutual inductance coefficient. S32, combined with mutual inductance coefficient and the self-inductance of the transmitting coil Self-inductance of the receiving coil Calculate the coupling coefficient Establish a second mapping relationship between misaligned parameters and coupling coefficients; S33, with critical coupling coefficient As a threshold, the coupling coefficient is determined from the second mapping relationship to be equal to... The critical misalignment parameter corresponding to the time is used to define the robust operating range corresponding to the radius of each transmitting coil.

[0012] In one possible implementation, the calculation formula for the improved mutual inductance model is as follows: ; in, , These are the number of turns of the transmitting coil and the receiving coil, respectively. , The first The first transmitting coil turn and the first Differential line element of one receiving coil turn, The distance between the two differential line elements is denoted as .

[0013] In one possible implementation, step S5 includes: S51. Wind the transmitting coil according to the selected transmitting coil radius and measure the corresponding self-inductance. ; S52, According to the resonance condition Calculate the compensation capacitor value of the original loop. The calculation formula is: ; S53. Construct a negative resistance circuit; S54, Negative resistor, compensation capacitor , transmitting coil The equivalent series resistances are connected in sequence to form the primary loop; Load resistor and compensation capacitor Receiver coil The equivalent series resistances are connected in sequence to form the secondary circuit, which together form a wireless power transmission system.

[0014] In one possible implementation, the negative resistance circuit is implemented by a non-inverting amplifier circuit, which includes an operational amplifier and a first resistor. First feedback resistor Second feedback resistor ; The first resistor It is connected between the non-inverting input and the output of the operational amplifier; First feedback resistor It is connected between the inverting input and output of the operational amplifier; Second feedback resistor It is connected between the inverting input of the operational amplifier and the reference ground.

[0015] Secondly, this application proposes a generalized parity-time symmetric anti-misalignment wireless power transfer system, the anti-misalignment wireless power transfer system comprising: The primary circuit includes a negative resistor and a compensation capacitor connected in sequence. , transmitting coil and equivalent series resistance The primary loop resonates at angular frequency ; The secondary circuit includes a load resistor and a compensation capacitor connected in sequence. Receiver coil and equivalent series resistance The secondary circuit resonates at angular frequency ; The negative resistor value is configured such that the system gain equals the total loss on the receiving side, ensuring that when the coupling coefficient... Greater than or equal to the critical coupling coefficient At that time, the system operates in a parity-time symmetric phase.

[0016] In one possible implementation, the transmitting coil With receiving coil All are spatial spiral coils with different inductance values, forming an asymmetric coupling structure.

[0017] The main solution and its various further alternatives described above can be freely combined to form multiple solutions, all of which are solutions that can be adopted and are claimed in this application; furthermore, the (non-conflicting alternatives) can also be freely combined with each other and with other alternatives. Those skilled in the art, after understanding the solution of this application, will realize from the prior art and common general knowledge that there are many combinations, all of which are technical solutions to be protected in this application, and will not be exhaustively listed here.

[0018] This application discloses a generalized parity-time symmetric wireless power transfer method and system resistant to spatial misalignment. First, the critical coupling coefficient of the wireless power transfer system is calculated, and the maximum design value of the transmitting coil radius is determined based on the minimum transmission power requirement in the application scenario. Then, a mapping relationship between misalignment parameters and the critical coupling coefficient is established, and the robust operating range corresponding to each transmitting coil radius is determined accordingly. Finally, the above data is integrated, and the transmission power and spatial robustness are weighed to complete the selection of the transmitting coil radius, thereby determining the system component parameters and constructing a complete wireless power transfer system. The system designed according to this method does not require complex active control circuitry and can operate stably in the PT-symmetric phase within a predetermined misalignment range, achieving efficient and robust wireless power transfer that is insensitive to spatial misalignment. Attached Figure Description

[0019] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 The diagram shows a flowchart of a generalized parity-time symmetric anti-misalignment wireless power transfer method proposed in an embodiment of this application.

[0021] Figure 2 A schematic diagram of a generalized parity-time symmetric anti-misalignment wireless power transfer system proposed in an embodiment of this application is shown.

[0022] Figure 3 The equivalent circuit diagram of the wireless power transfer system proposed in the embodiments of this application is shown.

[0023] Figure 4 A geometrical schematic diagram of the mutual inductance model proposed in an embodiment of this application is shown.

[0024] Figure 5 The diagram shows the mapping relationship between the coupling coefficient and the deflection angle when the coil radius is 80 mm.

[0025] Figure 6The diagram shows the trade-off between coil radius and system performance under angular deflection.

[0026] Figure 7 The diagram illustrates the trade-off between coil radius and system performance under lateral offset.

[0027] Figure 8 A schematic diagram showing the system's transmission power and transmission efficiency when the receiving coil undergoes angular deflection is shown.

[0028] Figure 9 A schematic diagram of the system's transmission power and transmission efficiency is shown when the receiving coil is laterally offset.

[0029] Figure 10 A schematic diagram showing the transmission power and transmission efficiency of the system under lateral offset when the receiving coil angle is deflected by 60° is shown.

[0030] Figure 11 The diagram shows the operating frequency under different deflection angles when the radius of the transmitting coil is 80 mm.

[0031] Figure 12 The diagram shows the voltage of the system constructed in this embodiment under different angular misalignments.

[0032] Figure 13 The graph shows the transmission efficiency curves obtained experimentally when the receiving coil is deflected at different angles. Detailed Implementation

[0033] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. This application can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, unless otherwise specified, the following embodiments and features in the embodiments can be combined with each other.

[0034] Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0035] In existing technologies, magnetically coupled wireless power transfer (MC-WPT) can overcome the influence of non-magnetic obstacles and achieve efficient mid-range contactless power transfer, showing significant application potential in dynamic charging scenarios such as implantable medical devices. These scenarios typically require strictly limited receiving coil size, while the transmitting coil size is larger to enhance coupling; therefore, research on asymmetric coupling structures is particularly crucial. During dynamic charging, spatial misalignment between coils leads to changes in the coupling coefficient, thus affecting transmission efficiency and power stability. Traditional MC-WPT systems often require additional control such as impedance matching and frequency tracking to maintain performance, while systems based on parity-time symmetry (PT symmetry) possess frequency adaptive characteristics, achieving robust transmission performance within a certain range of coupling coefficient fluctuations.

[0036] The concept of PT symmetry originates from quantum mechanics. Its application in wireless power transfer allows a system to operate in a PT-symmetric phase when the coupling coefficient is above a critical value. In this phase, even if coupling changes occur, the system can maintain stable power transmission and efficiency. Conversely, if the coupling coefficient falls below the critical value and enters a broken phase, performance becomes difficult to maintain. To address the misalignment problem in dynamic charging, the range of coupling coefficient variation needs to be evaluated based on the potential spatial displacement of the receiving coil. This guides the design of systems based on generalized PT symmetry, ensuring they always operate in the PT-symmetric phase, thereby achieving robust power transfer resistant to misalignment.

[0037] To ensure that the system can always operate in the PT symmetric phase within a wide range of misalignment, the relevant parameters need to be designed with this as the goal. This application proposes a generalized parity-time symmetric anti-misalignment wireless power transfer method and system. It improves the mutual inductance calculation model between spatial spiral coils and optimizes the parameters of source components such as the transmitting coil and compensation capacitor according to the spatial misalignment range of the receiver and the minimum transmission power requirement of the system under dynamic charging scenarios. This enables the system to have both robustness and reasonable transmission power. The following is a detailed description of the method.

[0038] Please refer to Figure 1 , Figure 1 The diagram illustrates a flowchart of a generalized parity-time symmetric anti-misalignment wireless power transfer method proposed in an embodiment of this application. This method is applied to a generalized parity-time symmetric anti-misalignment wireless power transfer system. Figure 2 This illustration shows a schematic diagram of a generalized parity-time symmetric anti-misalignment wireless power transfer system according to an embodiment of this application. The system includes: The primary circuit includes a negative resistor and a compensation capacitor connected in sequence. , transmitting coil and equivalent series resistance The primary loop resonates at angular frequency ; The secondary circuit includes a load resistor and a compensation capacitor connected in sequence. Receiver coil and equivalent series resistance The secondary circuit resonates at angular frequency ; The negative resistor value is configured such that the system gain equals the total loss on the receiving side, ensuring that when the coupling coefficient... Greater than or equal to the critical coupling coefficient At that time, the system operates in a parity-time symmetric phase.

[0039] The system consists of a primary circuit and a secondary circuit. The primary circuit includes a negative resistor. Parallel resonant capacitor Primary inductor coil The equivalent series resistance of the primary coil The secondary circuit includes the load resistor. Parallel resonant capacitor Secondary inductor coil The equivalent series resistance of the secondary coil In a parity-time symmetric two-coil wireless power transfer system, the negative resistance... The DC signal input from the DC power supply is converted into an AC signal; energy is coupled through the primary inductor coil via a magnetic field. Transmitted to the secondary inductor coil For ease of theoretical analysis, Figure 3 The equivalent circuit schematic of the wireless power transfer system proposed in this application is shown. Figure 2 It can be equivalent to Figure 3 .set up and Let represent the energy mode amplitude values ​​on the transmitting and receiving sides, respectively; the coupling coefficient between the transmitting and receiving coils is k; the natural resonant angular frequency on the transmitting side is , and the parasitic loss rate of the circuit is . The loop's own gain is The natural resonant angular frequency of the receiving side is , and the parasitic loss rate of the circuit is . The load loss rate The energy coupling rate is a function of the distance between the transmitter and receiver. Sometimes, The difference in physical dimensions between the primary and secondary coils usually results in a difference in their inductance values. Here, we define the ratio of the primary to secondary coil inductance values. To ensure that the resonant frequencies of the source and receiver are the same during system design, the ratio of the primary-side parallel resonant capacitor value to the secondary-side parallel capacitor value is: .

[0040] The coupled-mode equations of the system are listed as follows: Define the gain rate Loss rate , This represents the energy level within each resonator, where m=1 represents the transmitting end and m=2 represents the receiving end. Solving for the characteristic frequency yields the characteristic equation: The equation contains both real and imaginary parts. By setting both the real and imaginary parts to 0 and solving the equation simultaneously, we can obtain the essential frequency and then analyze the system's operating state.

[0041] when At this time, the system operates in the broken phase, and the system's eigenfrequency is . The gain-loss relationship is as follows The energy modulus ratio is Further derivation yields the voltage magnitude ratio between the load and source terminals as follows: ; At this point, the transmission efficiency can be expressed as: , To dissipate the equivalent series resistance in the transmitting coil Joule heat loss on the surface. To dissipate the equivalent series resistance of the receiving coil Joule heat loss on the surface. Supply to load resistor The effective power.

[0042] When the system operates in the broken phase of the PT, the voltage amplitude ratio changes with the coupling coefficient, which is not an ideal operating state.

[0043] when The system operates in PT-symmetric phase, at which point the system's eigenfrequency is given, and the gain-loss relationship is given. The energy modulus ratio is Further derivation yields the voltage magnitude ratio between the load and source terminals as follows: ; At this point, the transmission efficiency can be expressed as: ; When the system operates in the PT phase, the voltage amplitude ratio remains constant and is independent of the coupling coefficient. This represents the ideal operating state for an anti-misalignment wireless power transfer system.

[0044] transmitting coil With receiving coil All are spatial spiral coils with different inductance values, forming an asymmetric coupling structure.

[0045] In the wireless power transmission system, the transmitting coil With receiving coil Both employ a space spiral coil structure. Their physical dimensions and inductance values ​​are designed to be different, thus forming an asymmetric magnetic coupling structure. This asymmetric design is particularly suitable for applications with strictly limited space at the receiving end, where the receiving coil... Miniaturization is required, and the transmitting coil It can then have a larger size so that it can still establish and maintain a sufficiently strong magnetic coupling under conditions of large spatial spacing or misalignment.

[0046] A generalized parity-time symmetric method for resisting misalignment wireless power transfer includes: S1. Calculate the critical coupling coefficient of the wireless power transmission system based on the receiver circuit parameters.

[0047] Critical Coupling Coefficient The calculation formula is: , The total loss rate on the receiving side. This is the system's operating angular frequency.

[0048] System stability and operating phase (PT-symmetric phase or broken phase) are directly determined by the coupling coefficient. Total loss rate on the receiving side The relative size determines this. When the system satisfies... When the system operates in the PT symmetrical phase, the system gain will be [value missing]. Equal to the total loss rate on the receiving side (Right now Transmission power and efficiency remain constant when the coupling coefficient fluctuates. Conversely, when When the system enters the broken phase, its transmission performance will fluctuate drastically with changes in the coupling coefficient. Therefore, to accurately define the range of coupling coefficients within which the system can maintain stable energy transmission, the critical coupling coefficient is defined as the coupling coefficient at the point where the system transitions from the PT-symmetric phase to the broken phase, i.e., when k=γ. .

[0049] S2. Determine the maximum design value of the transmitting coil radius based on the minimum transmission power requirement in the application scenario; In step S2, under an asymmetric coupling structure, increasing the size of the transmitting coil will improve the coupling strength between the coils, thereby increasing the transmission power. However, an excessively large coil size is not only impractical but may also lead to a decrease in the actual transmission power of the system at a specific operating point. Therefore, by establishing a quantitative relationship between the transmitting coil radius and the theoretical transmission power when the system operates in a parity-time symmetric phase, systematic calculations are performed within a preset radius parameter range.

[0050] In one possible implementation, step S2 includes: S21. Set the sweep parameter range for the radius of the transmitting coil; S22. Based on the self-inductance model of a spatial helical coil, calculate the self-inductance coefficient corresponding to different transmitting coil radii within the scan parameter range. ; S23. Calculate the transmission power of the system when it is operating in a parity-time symmetrical phase under different transmitting coil radii; S24. The radius of the transmitting coil corresponding to the minimum transmission power requirement is determined as the maximum design value.

[0051] Self-inductance coefficient The calculation formula is: , The permeability of free space, The number of turns of the transmitting coil. The radius of the transmitting coil, is the coefficient of the spatial helical coil.

[0052] Step S2 quantifies the relationship between transmitted power and the radius of the transmitting coil through a systematic parameter scan (parameter sweep), thereby determining the maximum design value of the transmitting coil radius based on the minimum transmitted power requirements of the application scenario. This sets a crucial upper limit boundary for balancing power transmission capability and spatial robustness. First, a reasonable range of transmitting coil radius parameters is set based on the receiver size and expected design space. Second, the self-inductance coefficient of the transmitting coil corresponding to different radii within this range is calculated based on the self-inductance model of a spatial helical coil. The coefficient of the spatial helical coil is: ,in , The height of the space spiral coil is represented by the distance between the turns of the transmitting coil. The diameter of a single turn is ; , for The first kind of complete elliptic integral, for Complete elliptic integrals of the second kind.

[0053] Next, based on PT symmetry theory, the load transmission power corresponding to different transmitting coil radii is calculated when the system operates in parity-time symmetric phase. Its calculation formula is ,in Represents the energy amplitude value at the receiving end. This represents the load loss rate. The final transmission power will be... Compared with the preset minimum transmission power requirement, it will meet The radius of the transmitting coil that corresponds to the minimum required value is formally determined as the maximum design value, and the radius scan range is updated accordingly.

[0054] S3. Set the parameter range. When the transmitting coil and receiving coil are spatially misaligned, establish the mapping relationship between the misalignment parameter and the critical coupling coefficient. Based on the critical coupling coefficient, determine the robust working range corresponding to the radius of each transmitting coil from the mapping relationship. The misalignment parameter includes the deflection angle and / or lateral offset.

[0055] For each candidate transmit coil radius within a defined scan parameter range, an accurate physical model is established to quantify the impact of spatial misalignment on system stability. First, based on an improved mutual inductance model incorporating geometric details such as turn spacing and wire diameter, the mutual inductance coefficient and corresponding actual coupling coefficient between the receive coil and the transmit coil are calculated when the receive coil experiences different deflection angles and / or lateral offsets relative to the transmit coil. Then, this calculated actual coupling coefficient, which varies continuously with the misalignment parameters, is compared and mapped to a pre-determined critical coupling coefficient for the system. Through this mapping, the set of misalignment parameters corresponding to the actual coupling coefficient being exactly equal to the critical coupling coefficient for each specific transmit coil radius can be clearly identified. This set of parameters defines the spatially robust operating range within which the system can maintain parity-time symmetric phase and thus ensure stable transmission performance for that transmit coil size.

[0056] The steps in S3 include: S31. Based on the improved mutual inductance model, calculate the mutual inductance coefficient between the transmitting coil and the receiving coil under different transmitting coil radii and different spatial misalignments. This establishes the first mapping relationship between the misalignment parameter and the mutual inductance coefficient. S32, combined with mutual inductance coefficient and the self-inductance of the transmitting coil Self-inductance of the receiving coil Calculate the coupling coefficient Establish a second mapping relationship between misaligned parameters and coupling coefficients; S33, with critical coupling coefficient As a threshold, the coupling coefficient is determined from the second mapping relationship to be equal to... The critical misalignment parameter corresponding to the time is used to define the robust operating range corresponding to the radius of each transmitting coil.

[0057] The calculation formula for the improved mutual inductance model is as follows: ; in, , These are the number of turns of the transmitting coil and the receiving coil, respectively. , The first The first transmitting coil turn and the first Differential line element of one receiving coil turn, The distance between the two differential line elements is denoted as . It refers to the first Closed integration path of the turn-emitting coil. It refers to the first Closed integration path of the receiving coil Figure 4 The diagram illustrates the geometrical schematic of the mutual inductance model proposed in this application. First, for each transmitting coil radius within the scan range, an improved mutual inductance model is used to calculate the mutual inductance coefficient between the transmitting and receiving coils under different deflection angles and lateral offsets. In the improved mutual inductance model… and They represent The first transmitting coil turn and the first The differential line elements of each receiving coil turn can be represented as follows: ; ; In the above formula and These represent the radii of the transmitting and receiving coils, respectively. This represents the rotation angle of the receiving coil along the Y-axis. The distance between them is represented as: ; Among them are: and , which respectively represent the axial position of a single turn relative to its respective coil centroid, where and These represent the turn spacing of the transmitting coil and the receiving coil, respectively. Indicates along the x-axis Lateral displacement.

[0058] The improved model fully considers the geometric characteristics of the spatial helical coil, thus establishing the first mapping relationship between the misalignment parameter and the mutual inductance coefficient. Then, it combines this with the obtained coil self-inductance coefficient... and Through formula The mutual inductance coefficient is converted into a coupling coefficient that determines the operating state of the system. This ultimately establishes a precise second mapping relationship between the misalignment parameters and the coupling coefficients. Finally, the critical coupling coefficient is determined. As a threshold for determining whether the system has exited the PT-symmetric phase, the coupling coefficient is obtained by interpolation from the second mapping relationship described above. The critical deflection angle corresponding to the time ( ) and critical lateral offset ( These two critical values ​​together define the robust operating range within which the system can maintain stable energy transfer at each transmitting coil radius.

[0059] S4. Combining the transmission power data and robust operating range data corresponding to each transmitting coil radius, a trade-off is made between transmission power and spatial robustness, and the final transmitting coil radius is selected from the parameter sweep range.

[0060] Step S4, based on the specific requirements of the actual application scenario, comprehensively weighs the calculated transmission power data corresponding to each transmitting coil radius against the determined robust operating range corresponding to each radius (defined by the critical deflection angle and critical lateral offset), thereby selecting the final transmitting coil radius from the scan range. This reveals the competitive relationship between transmitting coil radius, transmission power, and spatial robustness. Increasing the transmitting coil radius can effectively extend the robust operating range of the system, but at the same time, the maximum transmission power achievable by the system under parity-time symmetry will decrease accordingly. Therefore, designers need to make decisions based on the specific priorities of the dynamic charging scenario: if the application scenario has extremely high tolerance for spatial misalignment, a larger radius transmitting coil should be selected to prioritize robustness; conversely, if there are high requirements for transmission power and the misalignment range is relatively controllable, a smaller radius coil can be selected to maximize power output.

[0061] S5. Based on the selected transmitting coil radius, determine the system component parameters and construct a complete wireless power transmission system.

[0062] Step S5, based on the finally selected transmitting coil radius, first determines its actual inductance value through measurement or the self-inductance model, and then calculates the required parallel compensation capacitor value for the transmitting end based on the system operating frequency. Simultaneously, an active circuit consisting of an operational amplifier and external resistors is constructed to achieve the required equivalent negative resistance in the transmitting loop, used to accurately compensate for system losses and provide gain. Finally, the DC power supply, negative resistance circuit, and... and The transmitting and receiving resonant networks, along with the load, are connected according to a predetermined circuit topology, thus completing the physical construction of a complete wireless power transmission system based on the principle of generalized parity-time symmetry. This step transforms all the key parameters obtained in the aforementioned design process into specific physical components and circuit connections, ultimately realizing a system.

[0063] In one possible implementation, step S5 includes: S51. Wind the transmitting coil according to the selected transmitting coil radius and measure the corresponding self-inductance. ; S52, According to the resonance condition Calculate the compensation capacitor value of the original loop. The calculation formula is: ; S53. Construct a negative resistance circuit; S54, Negative resistor, compensation capacitor , transmitting coil The equivalent series resistances are connected in sequence to form the primary loop; Load resistor and compensation capacitor Receiver coil The equivalent series resistances are connected in sequence to form the secondary circuit, which together form a wireless power transmission system.

[0064] Step S5: Based on the selected final transmitting coil radius, complete the physical construction and parameter determination of the entire wireless power transmission system. First, wind the transmitting coil according to the selected radius and actually measure its self-inductance. Next, to ensure the system resonant frequency is consistent ( According to the formula Calculate the compensation capacitor value of the primary loop; then construct the core negative resistor. It consists of an operational amplifier and resistors. Feedback resistor and This is achieved using a non-inverting amplifier circuit, and the specific connection relationship of this circuit is as follows: resistors The feedback resistor is connected between the non-inverting input and the output of the operational amplifier. The feedback resistor is connected between the inverting input and output of the operational amplifier. It is connected between the inverting input of the operational amplifier and the reference ground; finally, system integration is performed, including the negative resistor and compensation capacitor. , transmitting coil The load resistor and its equivalent series resistance are connected in sequence to form the primary circuit, while the load resistance is also connected. Compensation capacitor Receiver coil The circuit and its equivalent series resistance are connected in sequence to form the secondary circuit, together forming a complete wireless power transmission system.

[0065] As a preferred embodiment, both the primary and secondary coils are spatial spiral coils. In the initial operating state of the system, the primary and secondary coils are parallel to each other and their centerlines coincide to ensure optimal initial coupling conditions. This achieves a complete transformation from design parameters and component calculations to the construction of the physical system, ultimately enabling the system to possess the theoretically designed anti-misalignment performance.

[0066] The negative resistance circuit is implemented by a non-inverting amplifier circuit, which includes an operational amplifier and a first resistor. First feedback resistor Second feedback resistor ; The first resistor It is connected between the non-inverting input and the output of the operational amplifier; First feedback resistor It is connected between the inverting input and output of the operational amplifier; Second feedback resistor It is connected between the inverting input of the operational amplifier and the reference ground.

[0067] The non-inverting amplifier circuit includes an operational amplifier and a first resistor. First feedback electricity Second feedback resistor The first resistor One end of the first feedback resistor is connected to the non-inverting input of the operational amplifier, and the other end is connected to the output of the operational amplifier, forming part of the gain setting network. The second feedback resistor is connected between the inverting input and output terminals of the operational amplifier. This is then connected between the inverting input of the operational amplifier and the reference ground. Through proper configuration... , and The circuit can present a controllable equivalent negative resistance value at the equivalent port of the transmitting resonant circuit. This allows for precise compensation of the system's inherent losses and provides the necessary gain to maintain parity-time symmetry.

[0068] In one possible embodiment, the minimum transmission power required in the dynamic charging scenario of this application is 0.1mW. Since there are limitations on the receiver size and required operating frequency, the receiver coil size and its circuit parameters are given as shown in Tables 1 and 2, respectively. Here, it is assumed that the transmitting coil has 25 turns, and the coil turn spacing and the use of Litz wire are the same as those of the receiving coil.

[0069] Table 1

[0070] Table 2

[0071] During dynamic charging, spatial misalignment, including angular deflection and lateral offset, may occur at the receiving end. Therefore, when designing a wireless power transmission system, a technical solution is needed to characterize the system's operating range and transmission power for stable energy transmission, thereby guiding designers to balance robustness and transmission performance when selecting system component parameters.

[0072] S1. Calculate the critical coupling coefficient of the wireless power transmission system based on the receiver circuit parameters. .

[0073] definition The coupling coefficient corresponding to this time is the critical coupling coefficient. The formula is: ; Calculated based on the data in Table 2 .

[0074] S2. Determine the maximum design value of the transmitting coil radius based on the minimum transmission power requirement in the application scenario.

[0075] Since the receiving coil radius is 50mm, the initial transmitting coil radius sweep parameter range is set to (25, 200) in millimeters, and the self-inductance coefficient of the transmitting coil is calculated for different radii.

[0076] The formula for calculating the self-inductance coefficient is: .

[0077] The following formula is used to calculate the transmitted power of the system when operating in PT symmetrical phase for different transmitting coil radii: ; The radius of the transmitting coil corresponding to the system whose transmission power equals the minimum transmission power requirement is determined, and this radius is taken as the maximum design value. The calculation results from B2 show that the maximum design radius is 120 mm. Therefore, the radius scan parameter range for subsequent steps is updated to (25, 120), in millimeters.

[0078] S3. Set the parameter range. When the transmitting coil and the receiving coil are spatially misaligned, establish a mapping relationship between the misalignment parameter and the critical coupling coefficient. Based on the critical coupling coefficient, determine the robust working range corresponding to the radius of each transmitting coil from the mapping relationship. The misalignment parameter includes the deflection angle and / or lateral offset.

[0079] First, based on the obtained radius scan parameter range, we analyze the change in mutual inductance coefficient of the WPT system when spatial misalignment occurs under different transmitting coil radii, and establish the mapping relationship between deflection angle and lateral offset and mutual inductance coefficient.

[0080] Combining the mutual inductance and self-inductance results above, the coupling coefficient change of the WPT system under different transmitting coil radii is calculated when spatial misalignment occurs, thereby establishing the mapping relationship between deflection angle and lateral offset and coupling coefficient.

[0081] The coupling coefficient between coils can be obtained from the self-inductance and mutual inductance, and its formula is as follows: .

[0082] critical coupling coefficient As an index, the mapping relationship of each emission radius is retrieved using linear interpolation to find the coupling coefficient equal to... The corresponding deflection angle and lateral offset are used as the critical value to establish the critical deflection angle. and critical lateral offset The mapping relationship between the launch radius and the launch radius.

[0083] S4. Combining the transmission power data and robust operating range data corresponding to each transmitting coil radius, a trade-off is made between transmission power and spatial robustness, and the final transmitting coil radius is selected from the parameter sweep range.

[0084] By combining the transmission power data corresponding to the system operating in the PT symmetrical phase under different transmitting coil radii, as well as the mapping relationship between the critical deflection angle and critical lateral offset and the transmitting coil radius, a trade-off between transmission power and robust operating range is made according to the actual application scenario, and then a suitable transmitting coil radius is selected.

[0085] The trade-offs in this step have all been discussed. Figure 6 and Figure 7 It was presented in the middle, Figure 6 The diagram illustrates the trade-off between coil radius and system performance under angular deflection. Figure 7 The diagram illustrates the trade-off between coil radius and system performance under lateral offset. Figure 5 The diagram shows the mapping relationship between the coupling coefficient and the deflection angle when the coil radius is 80mm. Figure 5 The solid line clearly shows the critical angle. The relationship with the radius of the transmitting coil. When the radius is less than 45mm, the system cannot enter the PT symmetrical phase due to insufficient coupling. Critical angle. It increases steadily with the radius starting from 45mm, reaching its peak at 120mm. Figure 7 The different behavioral characteristics under lateral misalignment were revealed: when the coil radius exceeds 45mm, the critical lateral offset... It increases monotonically with radius, but its growth rate gradually slows down. Figure 6 and Figure 7 In the diagram, the dashed lines confirm that the output power at the singular point decreases as the coil radius increases.

[0086] Therefore, careful trade-offs must be made when designing the transmit coil size: while increasing the coil size to over 45mm can significantly improve spatial robustness, it will simultaneously reduce output power. The 45–120mm range identified in the study constitutes the optimal design window, achieving the most favorable balance among the aforementioned competing objectives.

[0087] To illustrate the impact of coil size on system performance under spatial misalignment conditions, LTspice circuit simulations were used to characterize the variations in output power and transmission efficiency of the WPT system for three typical misalignment scenarios (angular misalignment, lateral misalignment, and combined misalignment). These simulation results visually demonstrate the performance trade-offs that must be considered in WPT system design. Figure 8 A schematic diagram illustrating the system's transmission power and efficiency when the receiving coil undergoes angular deflection is shown. Figure 8 As shown in the pure angular misalignment case, all coil sizes maintain stable performance within the range of 0° to 30°. However, when the angle exceeds 45°, performance diverges significantly: the 50mm coil experiences the most rapid performance degradation, while larger coils exhibit progressively increasing angular stability. Notably, the 120mm coil maintains stable power delivery and high efficiency even at a 60° misalignment, although its maximum output power decreases. Figure 9 This diagram illustrates the system's transmission power and efficiency when the receiving coil is laterally offset. Figure 9 As shown in the diagram, the performance of the 50mm coil drops sharply when the lateral misalignment exceeds 8cm. In stark contrast, the 120mm coil maintains stable and efficient operation even with lateral misalignments up to 12cm, representing a substantial improvement in its space tolerance.

[0088] Figure 10 The diagram illustrates the system's transmission power and efficiency under lateral offset with a 60° deflection of the receiving coil. While the 50mm coil achieves the highest output power within a limited offset range, its performance exhibits significant instability and drastic fluctuations. In contrast, the 120mm coil maintains high transmission efficiency and stable power output throughout the entire test range.

[0089] A systematic comparison of coil performance under different misalignment scenarios yields two main conclusions. First, larger coils (80–120 mm) consistently offer superior robustness and efficiency retention. Therefore, designers face a clear trade-off: using smaller coils maximizes power transfer, while larger coils ensure spatial robustness; the optimal choice depends on specific application requirements.

[0090] In this case, the robust operating range and transmission power are relatively high when the transmitting coil radius is 80mm. Therefore, after comprehensive consideration, 80mm was selected as the transmitting coil radius.

[0091] S5. Based on the selected transmitting coil radius, determine the system component parameters and construct a complete wireless power transmission system.

[0092] The transmitting coil was wound using the selected coil radius of 80mm, and its self-inductance was then measured. Calculate the compensation capacitor value. To ensure the resonant frequency of the transmitter , The calculation formula is: Calculations show that... The value is 1.18 nF.

[0093] Constructing negative resistance The negative charge bank structure consists of a non-inverting amplifier circuit, which includes an operational amplifier and resistors. Feedback resistor and feedback resistor .resistance Connected to the non-inverting input and output of the operational amplifier; feedback resistor Connected to the inverting input and output of the operational amplifier; feedback resistor It is connected to the inverting input of the operational amplifier and the reference ground.

[0094] Construct the system circuit based on the results of the above steps. The non-inverting input of the operational amplifier is connected to one end of the primary-side LC resonant circuit, and the other end of the primary-side LC resonant circuit is connected to ground. A load resistor is connected in parallel across the secondary-side LC resonant circuit. .

[0095] The circuit parameters of the final designed wireless power transfer system are summarized in Table 3: Table 3

[0096] To verify the transmission performance of the wireless power transmission system designed based on this invention, a prototype system was built and tested.

[0097] During system operation, as the deflection angle α of the receiving coil is changed, the changes in the coupling coefficient between the coupled structures are measured as follows: Figure 5 The triangular scatter plot shows that, within the angular deflection range of 0° to 30°, the coupling coefficient k exhibits a slow, linear decay; beyond 30°, the slope of the decay curve increases. In traditional WPT systems, this coupling deterioration beyond the critical angle severely disrupts power transmission stability.

[0098] Figure 11 The diagram shows the operating frequency at different deflection angles when the radius of the transmitting coil is 80 mm. It shows the evolution of the system's intrinsic frequency and observes the evolution of the PT symmetric phase toward the broken phase as the angle deflection increases.

[0099] Figure 12 The diagram illustrates the voltage distribution of the system constructed in this embodiment under different angular misalignments. The system exhibits nearly identical voltage distributions at deflection angles of 0°, 30°, and 60°, with relatively small variations in the amplitude ratio of the primary coil voltage to the secondary coil voltage. This indicates that even with angular deflection of the receiving coil within a certain range, resulting in a small change in the coupling coefficient (see [reference needed]). Figure 4 Even when a significant drop occurs, the system still exhibits stable transmission performance in the symmetrical phase of the PT. However, when the angle deflection is 80°, the output voltage decreases, and the system's output power is limited under this large deflection condition.

[0100] Figure 13 The graph shows the transmission efficiency curves obtained experimentally when the receiving coil is deflected at different angles. It can be seen that the proposed system can achieve stable power transmission within a deflection range of 0° to 60°, maintaining a transmission efficiency above 94.5%. Although the system's transmission efficiency begins to decrease significantly beyond 60°, it can still be seen from the graph that the transmission efficiency remains above 90% within a large angle offset range of up to 75°. This demonstrates the excellent robustness of the system constructed in this embodiment to spatial variations and highlights its operational advantages under practical wireless power transmission conditions.

[0101] Compared with the prior art, the embodiments of this application have the following beneficial effects: First, the spatial spiral coil mutual inductance model, by fully considering geometric details such as coil turn spacing and wire diameter, establishes an accurate mapping relationship between coil spatial pose and coupling coefficient, effectively overcoming the error problem caused by simplification in traditional models, and providing a reliable theoretical tool for performance analysis in dynamic misalignment scenarios.

[0102] Secondly, it provides freedom and performance assurance in asymmetric coil size design. This method allows the transmitting and receiving coils to use different sizes, broadening its application range in constrained scenarios such as implantable devices, and ensuring high coupling strength and reasonable transmission power under dynamic misalignment conditions through parameter optimization.

[0103] Third, it achieves stable transmission without complex active control. The system designed based on the principle of generalized parity-time symmetry has frequency adaptive characteristics. It can maintain stable transmission power and efficiency within a predetermined misalignment range without the need for additional impedance matching or frequency tracking circuits near the operating point, which significantly improves the robustness and reliability of the system.

[0104] Fourth, the quantitative trade-off between power and robustness is clarified. Through systematic parameter scanning and mapping analysis, this method intuitively reveals the specific impact of the transmitting coil size on transmission capability and spatial tolerance, providing designers with a clear decision-making basis for targeted optimization based on actual application requirements, thereby achieving optimal system performance configuration.

[0105] In summary, this application discloses a generalized parity-time symmetric wireless power transfer method and system resistant to spatial misalignment. First, the critical coupling coefficient of the wireless power transfer system is calculated, and the maximum design value of the transmitting coil radius is determined based on the minimum transmission power requirement in the application scenario. Then, a mapping relationship between misalignment parameters and the critical coupling coefficient is established, and the robust operating range corresponding to each transmitting coil radius is determined accordingly. Finally, the above data is integrated, and the transmission power and spatial robustness are weighed to complete the selection of the transmitting coil radius, thereby determining the system component parameters and constructing a complete wireless power transfer system. The system designed according to this method does not require complex active control circuitry and can operate stably in the PT-symmetric phase within a predetermined misalignment range, achieving efficient and robust wireless power transfer that is insensitive to spatial misalignment.

[0106] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A generalized parity-time symmetric method for resisting misalignment wireless power transfer, characterized in that, The method includes: S1. Calculate the critical coupling coefficient of the wireless power transmission system based on the receiver circuit parameters; S2. Determine the maximum design value of the transmitting coil radius based on the minimum transmission power requirement in the application scenario; S3. Set the sweep parameter range. When the transmitting coil and the receiving coil are spatially misaligned, establish the mapping relationship between the misalignment parameter and the critical coupling coefficient. Based on the critical coupling coefficient, determine the robust working range corresponding to the radius of each transmitting coil from the mapping relationship. The misalignment parameter includes the deflection angle and / or lateral offset. S4. Combining the transmission power data and robust operating range data corresponding to each transmitting coil radius, a trade-off is made between transmission power and spatial robustness, and the final transmitting coil radius is selected from the parameter sweep range. S5. Based on the selected transmitting coil radius, determine the system component parameters and construct a complete wireless power transmission system.

2. The anti-misalignment wireless power transmission method as described in claim 1, characterized in that, Critical Coupling Coefficient The calculation formula is: , The total loss rate on the receiving side. This is the system's operating angular frequency.

3. The anti-misalignment wireless power transmission method as described in claim 1, characterized in that, The steps of S2 include: S21. Set the sweep parameter range for the radius of the transmitting coil; S22. Based on the self-inductance model of a spatial helical coil, calculate the self-inductance coefficient corresponding to different transmitting coil radii within the scan parameter range. ; S23. Calculate the transmission power of the system when it is operating in a parity-time symmetrical phase under different transmitting coil radii; S24. The radius of the transmitting coil corresponding to the minimum transmission power requirement is determined as the maximum design value.

4. The anti-misalignment wireless power transmission method as described in claim 3, characterized in that, Self-inductance coefficient The calculation formula is: , The permeability of free space, The number of turns of the transmitting coil. The radius of the transmitting coil, is the coefficient of the spatial helical coil.

5. The anti-misalignment wireless power transmission method as described in claim 1, characterized in that, The steps in S3 include: S31. Based on the improved mutual inductance model, calculate the mutual inductance coefficient between the transmitting coil and the receiving coil under different transmitting coil radii and different spatial misalignments. This establishes the first mapping relationship between the misalignment parameter and the mutual inductance coefficient. S32, combined with mutual inductance coefficient and the self-inductance of the transmitting coil Self-inductance of the receiving coil Calculate the coupling coefficient Establish a second mapping relationship between misaligned parameters and coupling coefficients; S33, with critical coupling coefficient As a threshold, the coupling coefficient is determined from the second mapping relationship to be equal to... The critical misalignment parameter is used to define the robust operating range corresponding to the radius of each transmitting coil.

6. The anti-misalignment wireless power transmission method as described in claim 1, characterized in that, The calculation formula for the improved mutual inductance model is as follows: ； in, , These are the number of turns of the transmitting coil and the receiving coil, respectively. , The first The first transmitting coil turn and the first Differential line element of one receiving coil turn, The distance between the two differential line elements is denoted as .

7. The anti-misalignment wireless power transmission method as described in claim 1, characterized in that, The steps in S5 include: S51. Wind the transmitting coil according to the selected transmitting coil radius and measure the corresponding self-inductance. ; S52, According to the resonance condition Calculate the compensation capacitor value of the original loop. The calculation formula is: ; S53. Construct a negative resistance circuit; S54, Negative resistor, compensation capacitor , transmitting coil The equivalent series resistances are connected in sequence to form the primary loop; Load resistor and compensation capacitor Receiver coil The equivalent series resistances are connected in sequence to form the secondary circuit, which together form a wireless power transmission system.

8. The anti-misalignment wireless power transmission method as described in claim 7, characterized in that, The negative resistance circuit is implemented by a non-inverting amplifier circuit, which includes an operational amplifier and a first resistor. First feedback resistor Second feedback resistor ; The first resistor It is connected between the non-inverting input and the output of the operational amplifier; First feedback resistor It is connected between the inverting input and output of the operational amplifier; Second feedback resistor It is connected between the inverting input of the operational amplifier and the reference ground.

9. A generalized parity-time symmetric anti-misalignment wireless power transfer system, characterized in that, The anti-misalignment wireless power transmission system includes: The primary circuit includes a negative resistor and a compensation capacitor connected in sequence. , transmitting coil and equivalent series resistance The primary loop resonates at angular frequency ; The secondary circuit includes a load resistor and a compensation capacitor connected in sequence. Receiver coil and equivalent series resistance The secondary circuit resonates at angular frequency ; The negative resistor value is configured such that the system gain equals the total loss on the receiving side, ensuring that when the coupling coefficient... Greater than or equal to the critical coupling coefficient At that time, the system operates in a parity-time symmetric phase.

10. The anti-misalignment wireless power transmission system as described in claim 9, characterized in that, transmitting coil With receiving coil All are spatial spiral coils with different inductance values, forming an asymmetric coupling structure.

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