Frequency hopping judgment and suppression method for parity-time symmetry wireless power transmission system

Abstract

The application provides a parity-time symmetry wireless power transmission system frequency hopping judgment and suppression method based on a description function method, adopts the description function method and combines a step response of the parity-time symmetry wireless power transmission system to determine an actual self-oscillation point; for a system of zero phase angle control, whether frequency hopping occurs is judged by analyzing self-oscillation point frequencies of different detunings, and the frequency hopping is suppressed by changing a compensation topology and / or limiting a detuning variation range; for a system of phase shift control, whether frequency hopping occurs is judged by analyzing a self-intersection position of a transfer function, and the frequency hopping is suppressed by limiting an output voltage duty cycle of an inverter.

Description

Technical Field

[0001] This invention belongs to the technical fields of nonlinear system stability analysis and wireless power transmission, specifically relating to a method for frequency hopping determination and suppression in parity-time symmetric wireless power transmission systems based on the describing function method. Background Technology

[0002] Wireless power transfer technology boasts advantages such as safety, efficiency, and convenience, and has been widely applied in consumer electronics, high-voltage power extraction, electric vehicles, and implantable medical devices. Based on the parity-time symmetry principle, wireless power transfer technology can overcome the influence of changing coupling conditions, maintaining constant output power and transmission efficiency over a certain transmission distance. However, this system exhibits high-order, time-varying, and nonlinear characteristics, increasing the difficulty of determining the system's actual self-oscillation point, identifying frequency jumps (i.e., frequency hopping), and effectively suppressing frequency hopping. The inability to determine the actual self-oscillation point leads to blind design and debugging of the system, while frequency hopping increases harmonic components and reduces power utilization and signal sampling accuracy. Existing methods for determining the actual self-oscillation point suffer from computational complexity and weak universality, and in-depth research on the mechanism and suppression of frequency hopping phenomena in systems has not yet been conducted. Summary of the Invention

[0003] Therefore, addressing the shortcomings and deficiencies of existing technologies, the present invention aims to provide a method for determining and suppressing frequency hopping in parity-time symmetric wireless power transfer systems based on the describing function method. First, the describing function method, combined with the system's step response, is used to determine the actual natural resonant point. Then, for systems with zero-phase angle control, the natural resonant point frequencies at different detuning degrees are analyzed to determine whether frequency hopping will occur, and frequency hopping is suppressed by changing the compensation topology or limiting the range of detuning degree variation. For systems with phase-shift control, the self-intersection position of the transfer function is analyzed to determine whether frequency hopping will occur, and frequency hopping is suppressed by limiting the inverter output voltage duty cycle.

[0004] The implementation is based on the following steps: Step S1: Establish the circuit model of the system and plot the Nyquist curve of the transfer function G(jω) and the curve of the negative derivative describing function -1 / N(I1,α) on the complex plane; Step S2: Determine the theoretical self-oscillation point of the parity-time symmetric wireless power transmission system based on the mutual distribution relationship between the G(jω) curve and the -1 / N(I1,α) curve. If the system has multiple theoretical self-oscillation points, the actual self-oscillation point needs to be further determined; Step S3: When the system adopts zero-phase angle control, determine whether the system will experience frequency hopping based on the relationship between the self-oscillation point and the resonant frequency under different detuning degrees γ. Step S4: For systems using zero-phase angle control, frequency hopping is suppressed by changing the compensation topology or limiting the range of detuning γ. Step S5: When the system uses phase-shift control, the position of the intersection point of the G(jω) curve determines whether frequency hopping will occur. Step S6: For systems using phase-shift control, frequency hopping is suppressed by calculating the critical angle θ0 at the intersection point of the G(jω) curve and the critical duty cycle D0 of the inverter output voltage u1, and setting a range for the duty cycle D of u1 that prevents frequency hopping. This invention essentially provides a simple and universal method for determining and suppressing frequency hopping in parity-time symmetric wireless power transmission systems, effectively improving the transmission performance and practicality of the system.

[0005] The specific technical solution adopted by this invention to solve its technical problem is as follows:

[0006] A method for frequency hopping determination and suppression in parity-time symmetric wireless power transfer systems based on the describing function method:

[0007] The actual natural points are determined using the describing function method combined with the step response of the parity-time symmetric wireless power transfer system.

[0008] For zero-phase angle controlled systems, frequency hopping is determined by analyzing the natural frequency of different detuning degrees, and frequency hopping is suppressed by changing the compensation topology and / or limiting the range of detuning degree variation.

[0009] For phase-shift control systems, frequency hopping is determined by analyzing the self-intersection position of the transfer function, and frequency hopping is suppressed by limiting the duty cycle of the inverter output voltage.

[0010] Furthermore, the method of determining the actual natural point of the parity-time symmetric wireless power transfer system by employing the describing function method in conjunction with the step response of the parity-time symmetric wireless power transfer system is as follows: Plot the Nyquist curve of the transfer function G(jω) of the linear element and the curve of the negative reciprocal describing function -1 / N(I1,α) of the nonlinear element on the complex plane; determine the theoretical natural point of the parity-time symmetric wireless power transfer system based on the distribution relationship and intersection position of the G(jω) curve and the -1 / N(I1,α) curve.

[0011] Furthermore, if multiple theoretical self-oscillation points exist, the actual self-oscillation point is determined by calculating the frequency of the disturbance signal: based on the differential equation of the parity-time symmetric wireless power transmission system, the step response of the inverter output current i1 is solved using Laplace transform and inverse transform. Substituting the system electrical parameters, the frequency f′ of the waveform corresponding to the current i1 after the disturbance at the first zero crossing is obtained. The frequency f′ is compared with the frequency corresponding to the theoretical self-oscillation point, and the theoretical self-oscillation point that is closer to the current f′ is taken as the actual self-oscillation point.

[0012] Furthermore, the specific implementation method for determining whether the system will experience frequency hopping by analyzing the natural frequency of different detuning degrees in the zero-phase angle control system is as follows: draw Nyquist plots for different detuning degrees γ to obtain the corresponding natural frequencies, including γ < 1, γ = 1, and γ > 1; if the frequency corresponding to the system's natural frequency is always in the high-frequency branch or always in the low-frequency branch as γ changes, it is determined that frequency hopping will not occur; if the frequency corresponding to the system's natural frequency is sometimes in the high-frequency branch and sometimes in the low-frequency branch as γ changes, it is determined that frequency hopping may occur.

[0013] Furthermore, the specific implementation method for suppressing frequency hopping by changing the compensation topology is as follows: the series-series or parallel-parallel compensation topology is changed to a series-parallel or parallel-series compensation topology. If a series-series or parallel-parallel compensation topology is required, frequency hopping suppression can be achieved by limiting the variation range of γ.

[0014] Furthermore, the specific implementation method for determining whether the system will experience frequency hopping by analyzing the position of the transfer function's self-intersection point for phase-shift control is as follows: draw Nyquist plots for different detuning degrees γ, including γ < 1, γ = 1, and γ > 1; determine whether the system will experience frequency hopping based on the position of the self-intersection point S of the G(jω) curve: if S is located in the region 0 < θ < π / 2, it is determined that frequency hopping may occur; if S is located in the region -π / 2 ≤ θ ≤ 0, frequency hopping will not occur; where θ is the phase difference between the inverter output voltage u1 and current i1 and -π / 2 ≤ θ ≤ π / 2.

[0015] Furthermore, the specific implementation method of suppressing frequency hopping by limiting the inverter output voltage duty cycle is as follows: using the coordinates (a, jb) of the self-intersection point S of the G(jω) curve, the critical value θ0 = arctan(b / a) of the phase difference between the inverter output voltage u1 and the current i1 corresponding to point S is calculated. Then, the critical value D0 of the inverter output voltage u1 duty cycle is obtained by using θ0 = (1-D0)π / 2. Based on the system's requirements for the operating frequency band, the range of the u1 duty cycle D that prevents the system from hopping is set, thereby achieving frequency hopping suppression.

[0016] Compared to existing methods, the method for determining and suppressing frequency hopping in this invention does not require solving state equations, the computational difficulty is not affected by the system order, it is applicable to systems with various topologies, and it has low complexity and good versatility. Attached Figure Description

[0017] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0018] Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention.

[0019] Figure 2 This is a structural diagram of a parity-time symmetric wireless power transfer system according to an embodiment of the present invention.

[0020] Figure 3 This is a circuit diagram of a series-to-series parity-time symmetric wireless power transfer system according to an embodiment of the present invention.

[0021] Figure 4 This is a Nyquist plot of a series-to-series parity-time symmetric wireless power transfer system using zero-phase-angle control, according to an embodiment of the present invention.

[0022] Figure 5 This is a Nyquist plot of a series-to-series parity-time symmetric wireless power transfer system employing phase-shift control, according to an embodiment of the present invention.

[0023] Figure 6 This is a graph showing the relationship between the phase difference between the inverter output voltage and current and the duty cycle of the inverter output voltage in an embodiment of the present invention.

[0024] Figure 7 This is a schematic diagram of the experimental apparatus according to an embodiment of the present invention.

[0025] Figure 8 This is an experimental waveform diagram of switching duty cycle without frequency hopping when γ>1 according to an embodiment of the present invention.

[0026] Figure 9 This is a waveform diagram of the frequency hopping experiment with switching duty cycle when γ < 1 according to an embodiment of the present invention.

[0027] Figure 10 This is a waveform diagram of the experiment on limiting duty cycle to suppress frequency hopping when γ < 1 in an embodiment of the present invention. Detailed Implementation

[0028] To make the features and advantages of this patent more apparent and understandable, specific embodiments are provided below for detailed explanation:

[0029] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used in this specification have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0030] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0031] This invention provides a detailed description of a method for determining and suppressing frequency hopping in a parity-time symmetric wireless power transfer system based on the describing function method: First, a circuit model of the system is established, and the Nyquist curve of the transfer function G(jω) and the curve of the negative derivative describing function -1 / N(I1,α) are plotted on the complex plane. Then, the actual natural resonant point of the parity-time symmetric wireless power transfer system is determined based on the mutual distribution relationship between the G(jω) curve and the -1 / N(I1,α) curve. If the system has multiple theoretical natural resonant points, the actual natural resonant point needs to be further determined. Next, the control strategy adopted by the system is determined. If the system adopts zero-phase control, the relationship between the natural resonant point and the resonant frequency under different detuning degrees γ is used to determine whether the system will experience frequency hopping. If the system will experience frequency hopping, frequency hopping is suppressed by changing the compensation topology or limiting the range of detuning degree γ. If the system uses phase-shift control, the position of the intersection point of the G(jω) curve determines whether frequency hopping will occur. If frequency hopping is expected, the critical angle θ0 at the intersection point of the G(jω) curve and the critical duty cycle D0 of the inverter output voltage u1 are calculated. A range of the duty cycle D of u1 is then set to prevent frequency hopping, thus suppressing it. Figure 1 As shown, the specific steps include:

[0032] Step (1): Establish the system circuit model and draw the Nyquist plot;

[0033] First, the structure of a parity-time symmetric wireless power transfer system is simplified to a typical form consisting of a nonlinear element N composed of a high-frequency inverter and a linear element G(s) composed of an LC resonant circuit connected in series, as follows: Figure 2 As shown. The effective value of the inverter output current i1 is I1, and the effective value of the fundamental component of the inverter output voltage u1 is U1. set up and The phase difference between u1 and i1 is θ = π - α. The natural resonant angular frequencies of the primary and secondary sides are respectively... and The detuning degree γ represents the degree of detuning of the system and γ = ω1 / ω2. The relationship between angular frequency ω and frequency f is ω = 2πf.

[0034] Then, based on circuit theory, the describing function N(I1,α) of the nonlinear element and the transfer function G(jω) of the linear element are written. Figure 3 Taking the series-to-series parity-time symmetric wireless power transfer system as an example, N(I1,α) and G(jω) are shown below:

[0035]

[0036] Since the characteristic equation of the closed-loop system is 1 + N(I1,α)G(jω) = 0, therefore G(jω) = -1 / N(I1,α). Here, -1 / N(I1,α) is called the negative reciprocal describing function of the nonlinear characteristic, as shown below:

[0037]

[0038] Finally, the Nyquist curve of G(jω) and the curve of the negative reciprocal describing function -1 / N(I1,α) are plotted on the complex plane, as shown below. Figure 4 As shown. In practical applications, PT-WPT systems operate in the parity-time symmetric region (strong coupling region) to utilize their robustness and achieve constant and efficient output performance. Meanwhile, the parasitic resistance of the coil and capacitor is generally not negligible, i.e., R... 10,20 Since ≠0, the research object of this invention is a parity-time symmetric wireless power transmission system that meets the above conditions.

[0039] Step (2): Determine the actual natural vibration point of the system:

[0040] According to the describing function method, the region enclosed by the G(jω) curve is the unstable region, while the region not enclosed by the G(jω) curve is the stable region. Let P be the intersection of the G(jω) curve and the -1 / N(I1,α) curve. If the -1 / N(I1,α) curve at point P moves from the unstable region to the stable region along the direction of increasing amplitude I1, then point P is the theoretical natural point. Taking a zero-phase-angle controlled series-to-series parity-time symmetric wireless power transfer system as an example, its Nyquist plot is as follows... Figure 4 As shown. Since zero-phase control is used, θ = 0, i.e., α = π, and the negative reciprocal describing function is -1 / N(I1,π). Therefore, the G(jω) curve (the solid blue line with arrows) intersects the -1 / N(I1,π) curve (the solid red line with arrows) at three points, corresponding to frequencies from smallest to largest: ω... L ω M and ω H Where ω L <ω M And ω H >ω M If the angular frequency is greater than ω M This is called the system operating in the high-frequency branch, where the angular frequency is less than ω. MThis is called the system operating in the low-frequency branch.

[0041] Depend on Figure 4 (a) It can be seen that when the detuning degree γ=1, due to ω M Enclosed by the G(jω) curve, therefore ω M The corresponding point (the hollow circle) is not a point of natural vibration. And ω... L and ω H None of them are enclosed by the G(jω) curve, therefore ω L and ω H The corresponding points (the two overlapping solid circles) are the theoretical natural vibration points of the system. Figure 4 (b) It can be seen that when γ>1, due to ω M and ω H Enclosed by the G(jω) curve, therefore ω M and ω H The corresponding points (hollow circles) are not self-oscillating points. And ω L It is not enclosed by the G(jω) curve, therefore ω L The corresponding point (the double solid circle) is the system's unique theoretical natural vibration point. (From...) Figure 4 (c) It can be seen that when γ < 1, due to ω M and ω L Enclosed by the G(jω) curve, therefore ω M and ω L The corresponding points (hollow circles) are not self-oscillating points. And ω H It is not enclosed by the G(jω) curve, therefore ω H The corresponding point (solid circle) is the system's only theoretically natural point.

[0042] Under given parameters and operating conditions, a system generally has only one theoretical natural point of vibration, which is also the actual natural point of vibration. However, when γ = 1, a series-series parity-time symmetric wireless power transfer system has two theoretical natural points of vibration, and it is necessary to further determine the unique actual natural point of vibration. The specific steps are as follows:

[0043] First, we reasonably assume that the inverter output voltage u1 during a disturbance is a step signal acting on the primary circuit. Then, we write the differential equation of the system and use the Laplace transform and inverse transform to obtain the step response of the inverter output current i1, as shown below, where a 1,2 b 1,2 c 1,2 and d 1,2 All are real numbers:

[0044]

[0045] Next, substituting the system electrical parameters, the frequency f′ of the waveform corresponding to i1 at the first zero-crossing point after the disturbance is obtained. Then, f′ is compared with the frequency corresponding to the theoretical natural vibration point; the theoretical natural vibration point that is closer to f′ is the actual natural vibration point. For example... Figure 3 The parameters of the series-to-series (SS) system shown are L 1,2 =118.81μH, C 1,2 =5.32nF, R 10,20 =0.2Ω, R L When Ω = 10Ω, the frequency f′ of the waveform corresponding to the first zero-crossing point of i1(t) at the start-up of the system is found to be 211.9kHz. Since f M =200.2kHz, therefore f′>f M Therefore, the corresponding ω′ is closer to ω. H Therefore, although the system has two theoretical natural points ω L and ω H But only ω H It is the actual natural vibration point, that is, the point at which the system automatically selects to operate in practical applications. H Place.

[0046] The same method was used to determine the natural vibration points of series-parallel (SP), parallel-parallel (PP), and parallel-series (PS) systems in the parity-time symmetric region (strong coupling region), as shown in the table below, where √ indicates the natural vibration point.

[0047] Table 1 Frequency selection rules of zero-phase-angle controlled PT-WPT system (strong coupling region, R 10,20 ≠0)

[0048]

[0049] Step (3): Determine whether frequency hopping will occur in the system using zero-phase control:

[0050] When a parity-time symmetric wireless power transfer system employs zero-phase control, firstly, Nyquist plots for different detuning degrees γ are drawn, including γ < 1, γ = 1, and γ > 1; then, the actual natural vibration points corresponding to different γ values ​​are obtained using the method in step (2); if the frequency corresponding to the system's natural vibration point always lies in the high-frequency branch (ω) as γ changes. H ) or always located in the low-frequency branch (ω) L If the system will not experience frequency hopping, and if the frequency corresponding to the system's natural vibration point is located in the high-frequency branch (ω) as γ changes... H Some are located in the low-frequency branch (ω) L If this occurs, frequency hopping may happen in the system.

[0051] As shown in Table 1, when the detuning degree γ changes, the natural point of the SP type system is always located in the high-frequency branch, while the natural point of the PS type system is always located in the low-frequency branch. Therefore, the SP and PS type systems do not experience frequency hopping. However, for the SS and PP type systems, when the detuning degree γ changes, some of the system's natural points are located in the high-frequency branch (ω). H Some are located in the low-frequency branch (ω) L Therefore, frequency hopping may occur in the system.

[0052] Step (4): Achieve frequency hopping suppression in the zero-phase control system:

[0053] Based on the analysis in step (3), for parity-time symmetric wireless power transfer systems using zero-phase-angle control, if the detuning degree γ changes due to application requirements, a series-parallel (SP) or parallel-series (PS) compensation topology can be used to suppress frequency hopping. If a compensation topology that may cause frequency hopping, such as a series-series (SS) or parallel-parallel (PP) system, is required, frequency hopping suppression can be achieved by limiting the range of γ.

[0054] Step (5): Determine whether frequency hopping will occur in the system using phase-shift control.

[0055] When a parity-time symmetric wireless power transfer system employs phase-shift control, the Nyquist plots for different detuning degrees γ are first plotted, including γ < 1, γ = 1, and γ > 1. Taking a series-to-series (SS) system with phase-shift control as an example, its Nyquist plot is as follows: Figure 5 As shown. Due to the use of phase-shift control, 0 < θ ≤ π / 2, i.e., π / 2 < α < π (region I). Here, θ is the phase difference between the inverter output voltage u1 and current i1, and -π / 2 ≤ θ ≤ π / 2. For different θ values ​​(θ1 < θ2 < θ3), the G(jω) curve intersects the -1 / N(I1,α) curve at three points. The G(jω) curve has one self-intersection point S.

[0056] Depend on Figure 5 From (a) and (b), we can see that when the detuning degrees are γ=1 and γ>1 respectively, the self-intersection point S of the G(jω) curve is located in region II, where π≤α<3π / 2. Therefore, for different θ (θ1<θ2<θ3), the self-intersection point is located on the high-frequency branch (ω). H , ω′ H and ω″ H Therefore, frequency hopping will not occur in the system. Figure 5 (c) It can be seen that when the detuning degree γ < 1, the self-intersection point S of the G(jω) curve is located in the region I where π / 2 < α < π. Let the critical value corresponding to point S be θ0, when θ < θ0, i.e., θ = θ 1，2 The natural vibration points of the system are respectively ω L and ω′ LAll are located on the low-frequency branch, and when θ > θ0, i.e., θ = θ3, the natural point of the system is ω″. H It is located on the high-frequency branch. Therefore, frequency hopping may occur in the system when θ changes.

[0057] Step (6): Implement frequency hopping suppression in the phase-shifting control system:

[0058] Based on the analysis in step (5), if frequency hopping is possible in the system, first obtain the coordinates (a, jb) of the self-intersection point S of the G(jω) curve on the Nyquist plot. Then, calculate the critical value θ0 = arctan(b / a) of the phase difference between the inverter output voltage u1 and current i1 corresponding to point S. Next, use θ0 = (1-D0)π / 2 to calculate the critical value D0 of the duty cycle of the inverter output voltage u1. Finally, set the range of the duty cycle D of u1 that prevents frequency hopping according to the system's requirements for the operating frequency band, thereby achieving frequency hopping suppression. Wherein, θ0 = (1-D0)π / 2 can be obtained from... Figure 6 Derivation.

[0059] Instance verification

[0060] To verify the frequency hopping determination and suppression method for parity-time symmetric wireless power transfer systems proposed in this invention, a series-to-series system experimental platform was built, such as... Figure 7 As shown. The transmitting end includes a DC power supply, a full-bridge inverter, a transmitting coil L1, and a compensation capacitor C1. The receiving end includes a receiving coil L2, a compensation capacitor C2, a rectifier, and an electronic load R. L Tuning capacitor C3 is used to adjust the system's detuning. A current transformer and a high-speed comparator are used to sample the zero-crossing point of the primary current, and the sampled information is sent to the DSP chip to generate the required pulse-width modulation drive signal, which is used to adjust the duty cycle of the full-bridge inverter output voltage. Table 2 lists the electrical parameters of the experimental prototype. The inherent resonant frequencies of the primary LC circuits are all close to f0 = 200.2 kHz.

[0061] Table 2 Experimental parameters

[0062] Symbols / Units numerical values Symbols / Units numerical values <![CDATA[L1 / μH]]> 118.81 <![CDATA[R 10 / Oh]]> 0.2 <![CDATA[L2 / μH]]> 118.85 <![CDATA[R 20 / Oh]]> 0.2 <![CDATA[C1 / nF]]> 5.32 <![CDATA[R L / Oh]]> 10 <![CDATA[C2 / nF]]> 5.32 <![CDATA[k C ]]> 0.068 <![CDATA[C3 / nF]]> 5.1 k 0.3

[0063] The parity-time symmetric wireless power transfer system employs phase-shift control. First, C3 and C2 are selected as compensation capacitors for the primary and secondary sides, respectively, then γ = 1.02. Figure 8 As shown. When the duty cycle D of u1 is 0.9, the system's operating frequency is 222.2kHz, which is located in the high-frequency branch, as... Figure 8The expanded waveform at point ① is shown. When D switches from 0.9 to 0.6, its transient state is shown in the expanded waveform at point ②. The system stabilizes at 225.2kHz when D = 0.6, which is also in the high-frequency branch, as shown in the expanded waveform at point ③. This is consistent with the rule analyzed in step (5) that the SS-type phase-shift controlled system will not hop frequency when γ > 1.

[0064] Secondly, selecting C1 and C3 as the compensation capacitors for the primary and secondary sides respectively, then γ = 0.98. From Figure 9 It can be seen that when D = 0.9, the system's operating frequency is 183.2 kHz, located in the low-frequency branch, as shown in the expanded waveform at point ①. When D switches from 0.9 to 0.6, its transient state is shown in the expanded waveform at point ②. The system stabilizes at 230.8 kHz when D = 0.6, located in the high-frequency branch, as shown in the expanded waveform at point ③. This is consistent with the frequency hopping rule of the phase-shift controlled SS-type system analyzed in step (5) when γ < 1.

[0065] Finally, keeping γ = 0.98, the coordinates of the intersection point S of the G(jω) curve in the complex plane are (0.089, -j0.027) obtained from the Nyquist plot. Therefore, θ0 = 29.67°. Using θ0 = (1-D0)π / 2, the critical value of the duty cycle, D0 = 0.67, can be calculated. Figure 10 It can be seen that when D = 0.9, the system's operating frequency is 185.2 kHz, located in the low-frequency branch, as shown in the expanded waveform at point ①. When D switches from 0.9 to 0.7, its transient state is shown in the expanded waveform at point ②. When D = 0.7, the system stabilizes at 187.3 kHz, still located in the low-frequency branch, without frequency hopping, as shown in the expanded waveform at point ③. It is evident that by reasonably selecting the range of D as mentioned in step (6), frequency hopping can be effectively suppressed.

[0066] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

[0067] This patent is not limited to the above-described preferred embodiments. Anyone can derive other forms of frequency hopping determination and suppression methods for parity-time symmetric wireless power transfer systems based on the describing function method under the guidance of this patent. All equivalent changes and modifications made within the scope of this patent application shall fall within the scope of this patent.

Claims

1. A method for frequency hopping determination and suppression in parity-time symmetric wireless power transfer systems based on the describing function method, characterized in that: The actual natural points are determined using the describing function method combined with the step response of the parity-time symmetric wireless power transfer system. For zero-phase angle controlled systems, frequency hopping is determined by analyzing the natural frequency of different detuning degrees, and frequency hopping is suppressed by changing the compensation topology and / or limiting the range of detuning degree variation. For phase-shift control systems, frequency hopping is determined by analyzing the transfer function of the linear element in the system circuit model at the intersection point. Frequency hopping is then suppressed by limiting the duty cycle of the inverter output voltage.

2. The method for frequency hopping determination and suppression in parity-time symmetric wireless power transfer systems based on the describing function method according to claim 1, characterized in that: The method for determining the actual self-oscillation point of the parity-time symmetric wireless power transfer system by employing the describing function method and combining it with the step response of the parity-time symmetric wireless power transfer system is as follows: Plot the Nyquist curve of the transfer function G(jω) of the linear element and the curve of the negative reciprocal describing function -1 / N(I1,α) of the nonlinear element on the complex plane, where ω is the angular frequency and I1 is the effective value of the inverter output current i1; determine the theoretical self-oscillation point of the parity-time symmetric wireless power transfer system based on the distribution relationship and intersection position of the G(jω) curve and the -1 / N(I1,α) curve.

3. The method for frequency hopping determination and suppression of parity-time symmetric wireless power transfer systems based on the describing function method according to claim 2, characterized in that: If multiple theoretical self-oscillation points exist, the actual self-oscillation point is determined by calculating the frequency of the disturbance signal: Based on the differential equation of the parity-time symmetric wireless power transmission system, the step response of the inverter output current i1 is solved using Laplace transform and inverse transform. Substituting the system electrical parameters, the frequency f′ of the waveform corresponding to the current i1 after the disturbance at the first zero crossing is obtained. The frequency f′ is compared with the frequency corresponding to the theoretical self-oscillation point, and the theoretical self-oscillation point with the frequency f′ closer is taken as the actual self-oscillation point.

4. The method for frequency hopping determination and suppression of parity-time symmetric wireless power transfer systems based on the describing function method according to claim 1, characterized in that: The specific implementation method for determining whether the system will experience frequency hopping by analyzing the natural frequencies of different detuning degrees in the zero-phase angle control system is as follows: draw Nyquist plots for different detuning degrees γ to obtain the corresponding natural frequencies, including γ < 1, γ = 1, and γ > 1; if the frequency corresponding to the system's natural frequency is always in the high-frequency branch or always in the low-frequency branch as γ changes, it is determined that frequency hopping will not occur; if the frequency corresponding to the system's natural frequency is sometimes in the high-frequency branch and sometimes in the low-frequency branch as γ changes, it is determined that frequency hopping may occur.

5. The method for frequency hopping determination and suppression of parity-time symmetric wireless power transfer systems based on the describing function method according to claim 1, characterized in that: The specific implementation method of suppressing frequency hopping by changing the compensation topology is as follows: change the series-series or parallel-parallel compensation topology to a series-parallel or parallel-series compensation topology.

6. The method for frequency hopping determination and suppression of parity-time symmetric wireless power transfer systems based on the describing function method according to claim 1, characterized in that: The specific implementation method for determining whether the system will hop frequency by analyzing the transfer function of the linear element in the system circuit model for phase-shift control is as follows: draw Nyquist plots for different detuning degrees γ, including γ < 1, γ = 1, and γ > 1; determine whether the system will hop frequency based on the position of the self-intersection point S of the G(jω) curve: if S is located in the region 0 < θ < π / 2, it is determined that hopping frequency may occur; if S is located in the region -π / 2 ≤ θ ≤ 0, hopping frequency will not occur. Where θ is the phase difference between the inverter output voltage u1 and current i1, and -π / 2≤θ≤π / 2.

7. The method for frequency hopping determination and suppression of parity-time symmetric wireless power transfer systems based on the describing function method according to claim 2, characterized in that: The specific implementation method of suppressing frequency hopping by limiting the duty cycle of the inverter output voltage is as follows: using the coordinates (a, jb) of the intersection point S of the G(jω) curve, the critical value θ0 = arctan(b / a) of the phase difference between the inverter output voltage u1 and the current i1 corresponding to point S is calculated. Then, the critical value D0 of the duty cycle of the inverter output voltage u1 is obtained by using θ0 = (1-D0)π / 2. Based on the system's requirements for the operating frequency band, the range of the duty cycle D of u1 that prevents the system from hopping is set, thereby achieving frequency hopping suppression.

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