Description function method-based frequency hopping judgment and suppression method for space-time symmetric wireless power transmission system

Abstract

The invention provides a frequency hopping judgment and suppression method for a space-time symmetric wireless power transmission system based on a description function method, and the method employs the description function method and combines the step response of the space-time symmetric wireless power transmission system to determine an actual natural vibration point. Whether frequency hopping occurs in the system is judged by analyzing natural vibration point frequencies of different detuning degrees, and frequency hopping is suppressed by adopting a method of changing compensation topology and / or limiting the variation range of the detuning degrees; for a phase shift control system, whether frequency hopping occurs in the system is judged by analyzing the position of a transfer function selfing point, and frequency hopping is suppressed by adopting a method of limiting the duty ratio of the output voltage of an inverter.

Description

Technical Field

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

[0002] Wireless power transmission technology has the advantages of safety, efficiency and convenience, and has been widely used in consumer electronics, high-voltage energy extraction, electric vehicles, implantable medical and other fields. Wireless power transmission technology based on the principle of parity-time symmetry can overcome the influence of changes in coupling conditions and maintain constant output power and transmission efficiency within a certain transmission distance. The system has the characteristics of high order, time-varying and nonlinearity, which increases the possibility of determining the actual self-oscillation point of the system, determining the possibility of a jump in the operating frequency (i.e., frequency hopping), and the difficulty of simply and effectively suppressing frequency hopping. The inability to determine the actual self-oscillation point causes blindness in system design and debugging, and frequency hopping will increase harmonic components and reduce power utilization and signal sampling accuracy. The existing methods for determining the actual self-oscillation point have the disadvantages of complex calculations and weak versatility, and no in-depth research has been conducted on the mechanism and suppression of the system frequency hopping phenomenon. Summary of the invention

[0003] Therefore, in view of the defects and shortcomings of the prior art, the purpose of the present invention is to provide a method for determining and suppressing frequency hopping in a parity-time symmetric wireless power transmission system based on a describing function method. First, the describing function method is used in combination with the step response of the system to determine the actual self-oscillation point. Then, for a zero-phase angle controlled system, the self-oscillation point frequencies of different detuning degrees are analyzed to determine whether the system will experience frequency hopping, and the frequency hopping is suppressed by changing the compensation topology or limiting the range of detuning degree variation; for a phase-shifted controlled system, the position of the self-intersection point of the transfer function is analyzed to determine whether the system will experience frequency hopping, and the frequency hopping is suppressed by limiting the duty cycle of the inverter output voltage.

[0004] The implementation is based on the following steps: Step S1, establish the circuit model of the system, and draw the Nyquist curve of the transfer function G(jω) and the negative derivative description function -1 / N(I 1 ,α) curve; Step S2, according to the G(jω) curve and -1 / N(I 1,α) curves to determine the theoretical self-oscillation point of the parity-time symmetric wireless power transmission system. 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 have frequency hopping according to the relationship between the self-oscillation point and the resonant frequency under different detuning degrees γ. Step S4, for systems adopting zero phase angle control, frequency hopping can be suppressed by changing the compensation topology or limiting the variation range of the detuning degree γ; Step S5, when the system adopts phase shift control, determine whether the system will have frequency hopping by the position of the self-intersection point of the G(jω) curve; Step S6, for systems adopting phase shift control, calculate the critical angle θ at the self-intersection point of the G(jω) curve 0 and inverter output voltage u 1 The duty cycle critical value D 0 , and set u so that the system does not hop 1 The present invention substantially provides a simple and universal method for determining and suppressing frequency hopping in a parity-time symmetric wireless power transmission system, which can effectively improve the transmission performance and practicality of the system.

[0005] The technical solution specifically adopted by the present invention to solve the technical problem is:

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

[0007] The actual self-oscillation point is determined by using the describing function method combined with the step response of the parity-time symmetric wireless power transmission system:

[0008] For zero phase angle control systems, the frequency of the self-oscillation point with different detuning degrees is analyzed to determine whether the system will experience frequency hopping, and the frequency hopping can be suppressed by changing the compensation topology and / or limiting the range of detuning degree.

[0009] For the phase-shift control system, the position of the self-intersection point of the transfer function is analyzed to determine whether the system will have frequency hopping, and the method of limiting the duty cycle of the inverter output voltage is used to suppress frequency hopping.

[0010] Furthermore, the method of determining the actual self-oscillation point by using the description function method and combining the step response of the parity-time symmetric wireless power transmission system is as follows: drawing the Nyquist curve of the transfer function G(jω) of the linear link of the circuit model of the parity-time symmetric wireless power transmission system and the negative inverse description function -1 / N(I 1 ,α) curve; According to the G(jω) curve and -1 / N(I 1 ,α) The distribution relationship and intersection position of the curves are used to determine the theoretical self-oscillation point of the parity-time symmetric wireless power transmission system.

[0011] Furthermore, if there are multiple theoretical self-oscillation points, 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 Laplace transform and inverse transform are used to solve the inverter output current i 1 Substituting the system electrical parameters into the step response, the post-disturbance current i 1 The frequency f′ of the waveform corresponding to the first zero crossing point is compared with the frequency corresponding to the theoretical self-oscillation point, and the theoretical self-oscillation point to which the current f′ is closer is taken as the actual self-oscillation point.

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

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

[0014] Furthermore, the specific implementation method of the phase-shift control system for determining whether the system will experience frequency hopping by analyzing the position of the self-intersection point of the transfer function is as follows: drawing Nyquist diagrams of different detuning degrees γ, including γ<1, γ=1 and γ>1; determining whether the system will experience frequency hopping according to the position of the self-intersection point S of the G(jω) curve: if S is in the region of 0<θ<π / 2, it is determined that frequency hopping may occur; if S is in the region of -π / 2≤θ≤0, frequency hopping will not occur; wherein θ is the inverter output voltage u 1 and current i 1 The phase difference is -π / 2≤θ≤π / 2.

[0015] Furthermore, the specific implementation method of limiting the duty cycle of the inverter output voltage to suppress frequency hopping is: using the coordinates (a, jb) of the intersection point S of the G(jω) curve, and then calculating the inverter output voltage u corresponding to point S 1 and current i 1 The critical value of phase difference θ 0 =arctan(b / a), and then use θ 0 =(1-D 0 )π / 2 to find the inverter output voltage u 1The critical value of duty cycle D 0 , according to the system's requirements for the working frequency band, set the system so that the frequency hopping does not occur 1 The duty cycle D range is used to achieve frequency hopping suppression.

[0016] Compared with the existing methods, the method for determining and suppressing frequency hopping of the present invention does not need to solve the state equation, the calculation difficulty is not affected by the system order, is applicable to systems of various topological structures, has low complexity and good versatility. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

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

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

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

[0022] Figure 5 It is a Nyquist diagram of a series-series parity-time symmetric wireless power transmission system using phase shift control according to an embodiment of the present invention.

[0023] Figure 6 4 is a diagram showing the relationship between the inverter output voltage and current phase difference and the inverter output voltage duty cycle according to an embodiment of the present invention.

[0024] Figure 7 Schematic diagram of an experimental device according to an embodiment of the present invention.

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

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

[0027] Fig.10 It is a waveform diagram of a frequency hopping suppression experiment by limiting the duty ratio when γ < 1 according to an embodiment of the present invention. DETAILED DESCRIPTION

[0028] In order to make the features and advantages of this patent more obvious and easy to understand, the following embodiments are specifically described in detail as follows:

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

[0030] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0031] The embodiment of the present invention provides a detailed introduction to the frequency hopping determination and suppression method of a parity-time symmetric wireless power transmission system based on a describing function method: firstly, a circuit model of the system is established, and the Nyquist curve of the transfer function G(jω) and the negative derivative describing function -1 / N(I 1 ,α) curve; then according to the G(jω) curve and -1 / N(I 1 ,α) curves to determine the actual self-oscillation point of the parity-time symmetric wireless power transmission system. If the system has multiple theoretical self-oscillation points, the actual self-oscillation point needs to be further determined. Then, the control strategy adopted by the system is determined. If the system adopts zero-phase angle control, the relationship between the self-oscillation 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, the frequency hopping is suppressed by changing the compensation topology or limiting the variation range of the detuning degree γ. If the system adopts phase shift control, the position of the self-intersection point of the G(jω) curve is used to determine whether the system will experience frequency hopping. If the system will experience frequency hopping, the critical angle θ at the self-intersection point of the G(jω) curve is calculated. 0 and inverter output voltage u 1 The duty cycle critical value D 0 , and set u so that the system does not hop 1 The duty cycle D range can achieve frequency hopping suppression. Figure 1 As shown, the specific steps include:

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

[0033] First, the structure of the parity-time symmetric wireless power transmission system is simplified to a typical form in which a nonlinear link N consisting of a high-frequency inverter and a linear link G(s) consisting of an LC resonant circuit are connected in series, as shown in Figure 2 As shown. Among them, the inverter output current i 1 The effective value is I1 , inverter output voltage u 1 The effective value of the fundamental component is U 1 and set up and u 1 with i 1 The phase difference is θ = π-α. The natural resonant angular frequencies of the primary and secondary sides are The detuning degree γ represents the degree of detuning of the system and γ=ω 1 / ω 2 The relationship between angular frequency ω and frequency f is ω=2πf.

[0034] Then, according to circuit theory, the description function N(I 1 ,α) and the transfer function G(jω) of the linear link. Figure 3 As an example, the tandem-tandem parity-time symmetric wireless power transmission system shown in FIG. 1 ,α) and G(jω) are as follows:

[0035]

[0036] Since the characteristic equation of the closed-loop system is 1+N(I 1 ,α)G(jω)=0, therefore G(jω)=-1 / N(I 1 ,α). Among them, -1 / N(I 1 ,α) is called the negative inverse description function of the nonlinear characteristic, as shown below:

[0037]

[0038] Finally, we plot the Nyquist curve of G(jω) and the negative inverse description function -1 / N(I 1 ,α) curve, such as Figure 4 As shown. In practical applications, PT-WPT systems work in the parity-time symmetric region (strong coupling region) to utilize their robustness to obtain constant and efficient output performance. At the same time, the parasitic resistance of the coil and capacitor is generally not negligible, that is, R 10,20 ≠0, so the research object of the present invention is the parity-time symmetric wireless power transmission system that meets the above conditions.

[0039] Step (2): Determine the actual self-oscillation point of the system:

[0040] According to the describing function method, the area surrounded by the G(jω) curve is the unstable area, and the area not surrounded by the G(jω) curve is the stable area. 1 ,α) The intersection point of the curve is set to P. If the -1 / N(I 1,α) curve along the amplitude I 1 The direction of increase is from the unstable region to the stable region, then point P is the theoretical self-oscillation point. Taking the zero phase angle controlled series-series parity-time symmetric wireless power transmission system as an example, its Nyquist diagram is as follows Figure 4 As shown. Since zero phase angle control is adopted, θ=0, that is, α=π and the negative inverse description function is -1 / N(I 1 ,π). Therefore, the G(jω) curve (blue solid line with arrow) is similar to -1 / N(I 1 There are three intersection points of the curve (red solid line with arrows), and the corresponding frequencies are ω, L ,ω M and ω H . Among them ω L <ω M And ω H >ω M , if the angular frequency is greater than ω M The system is said to work in the high-frequency branch, and the angular frequency is less than ω M The system is said to operate 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 is surrounded by the G(jω) curve, so ω M The corresponding point (hollow circle) is not a natural vibration point. L and ω H are not surrounded by the G(jω) curve, so ω L and ω H The corresponding points (the two overlapping solid circles) are the theoretical self-oscillation points of the system. Figure 4 (b) It can be seen that when γ>1, due to ω M and ω H is surrounded by the G(jω) curve, so ω M and ω H The corresponding points (hollow circles) are not natural vibration points. L is not surrounded by the G(jω) curve, so ω L The corresponding point (heavy solid circle) is the only theoretical self-oscillation point of the system. Figure 4 (c) It can be seen that when γ<1, due to ω M and ω L is surrounded by the G(jω) curve, so ω M and ω L The corresponding points (hollow circles) are not natural vibration points. H is not surrounded by the G(jω) curve, so ω H The corresponding point (solid circle) is the only theoretical self-oscillation point of the system.

[0042] Under certain parameters and working conditions, the system generally has only one theoretical self-oscillation point, which is also the actual self-oscillation point. However, when γ = 1, the series-series parity-time symmetric wireless power transmission system has two theoretical self-oscillation points. It is necessary to further determine the only actual self-oscillation point. The specific steps are as follows:

[0043] First, it is reasonable to assume that the inverter output voltage u 1 is the step signal acting on the primary circuit, and then write the differential equation of the system and use Laplace transform and inverse transform to obtain the inverter output current i 1 The step response is as follows, where a 1,2 , b 1,2 、c 1,2 and d 1,2 are all real numbers:

[0044]

[0045] Next, substitute the system electrical parameters to obtain the disturbance i 1 The frequency f' of the waveform corresponding to the first zero crossing point is then compared with the frequency corresponding to the theoretical self-oscillation point, and the theoretical self-oscillation point closer to f' is the actual self-oscillation point. Figure 3 The series-series (SS) system parameters shown are L 1,2 =118.81μH,C 1,2 =5.32nF, R 10,20 =0.2Ω, R L =10Ω, the solution is that when the system starts, i 1 (t) The frequency of the waveform corresponding to the first zero crossing point is f′=211.9kHz. M =200.2kHz, so f′>f M Therefore, the corresponding ω′ is closer to ω H , so although the system has two theoretical self-oscillation points ω L and ω H , but only ω H is the actual self-oscillation point, that is, in actual applications, the system automatically chooses to work at ω H Place.

[0046] The same method is used to determine the self-oscillation points of the series-parallel (SP), parallel-parallel (PP) and parallel-series (PS) systems in the parity-time symmetry region (strong coupling region), as shown in the following table, where √ represents the self-oscillation 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 the system using zero phase angle control will experience frequency hopping:

[0050] When the parity-time symmetric wireless power transmission system adopts zero phase angle control, the Nyquist diagrams of different detuning degrees γ are first drawn, including γ < 1, γ = 1 and γ > 1; then the actual self-oscillation points corresponding to different γ are obtained respectively by the method of step (2); if the frequency corresponding to the self-oscillation point of the system is always located in the high frequency branch (ω H ) or always located in the low-frequency branch (ω L ) the system will not hop. If the frequency corresponding to the self-oscillation point of the system is located in the high-frequency branch (ω H ) and some are located in the low-frequency branch (ω L ) the system may experience frequency hopping.

[0051] As shown in Table 1, when the detuning degree γ changes, the self-oscillation point of the SP type system is always located at the high frequency branch, while the self-oscillation point of the PS type system is always located at the low frequency branch, so the SP and PS type systems will not hop. However, for the SS and PP type systems, when the detuning degree γ changes, some of the self-oscillation points of the system are located at the high frequency branch (ω H ) and some are located in the low-frequency branch (ω L ), so the system may experience frequency hopping.

[0052] Step (4): Realize frequency hopping suppression of zero phase angle control system:

[0053] Based on the analysis of step (3), for the parity-time symmetric wireless power transmission system using zero phase angle control, if the detuning degree γ will change due to the needs of the application, a series-parallel (SP) or parallel-series (PS) compensation topology can be used to achieve frequency hopping suppression. If it is required to use a compensation topology that may cause frequency hopping, such as a series-series (SS) and parallel-parallel (PP) system, 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 the parity-time symmetric wireless power transmission system adopts phase shift control, the Nyquist diagrams of different detuning degrees γ are first drawn, including γ < 1, γ = 1 and γ > 1. Taking the series-series (SS) system with phase shift control as an example, its Nyquist diagram is as follows Figure 5 As shown. Since phase shift control is adopted, 0<θ≤π / 2, that is, π / 2<α<π (area I). ​​Where θ is the inverter output voltage u 1 and current i 1 The phase difference is -π / 2≤θ≤π / 2. For different θ(θ1 <θ 2 <θ 3 ), G(jω) curve and -1 / N(I 1 ,α) curves have 3 intersection points. G(jω) curve has one self-intersection point S.

[0056] Depend on Figure 5 (a) and (b) show that when the detuning degree is γ=1 and γ>1 respectively, the self-intersection point S of the G(jω) curve is located in the region II of π≤α<3π / 2. Therefore, for different θ(θ 1 <θ 2 <θ 3 ), the self-oscillation points are all located on the high-frequency branch (ω H ,ω′ H and ω″ H ), so the system will not have frequency hopping. 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 of π / 2<α<π. Let the critical value corresponding to point S be θ 0 , when θ<θ 0 That is, θ = θ 1，2 The self-oscillation points of the system are ω L and ω′ L are all located on the low-frequency branch, and when θ>θ 0 That is, θ = θ 3 The self-oscillation point of the system is ω″ H is located on the high frequency branch. Therefore, when θ changes, the system may experience frequency hopping.

[0057] Step (6): Realize frequency hopping suppression of phase shift control system:

[0058] Based on the analysis of step (5), if the system may experience frequency hopping, first obtain the coordinates (a, jb) of the intersection point S of the G(jω) curve on the Nyquist diagram, and then calculate the inverter output voltage u corresponding to point S 1 and current i 1 The critical value of phase difference θ 0 =arctan(b / a), then use θ 0 =(1-D 0 )π / 2 to find the inverter output voltage u 1 The critical value of duty cycle D 0 Finally, according to the system's requirements for the working frequency band, the u setting is set so that the system will not hop 1 The duty cycle D range is used to suppress frequency hopping. 0 =(1-D 0 )π / 2 can be obtained by Figure 6 Derivation.

[0059] Example verification

[0060] In order to verify the frequency hopping determination and suppression method of the parity-time symmetric wireless power transmission system proposed in this invention, a series-series system experimental platform was built. Figure 7 The transmitting end includes a DC power supply, a full-bridge inverter, and a transmitting coil L 1 and compensation capacitor C 1 The receiving end includes a receiving coil L 2 , compensation capacitor C 2 , rectifier and electronic load R L . Tuning capacitor C 3 Used to adjust the detuning degree of the system. Current transformers and high-speed comparators are used to sample the zero-crossing point of the primary current, and the sampling 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 natural resonant frequency of the primary LC circuit is close to f 0 =200.2kHz.

[0061] Table 2 Experimental parameters

[0062] Symbol / Unit Numeric Symbol / Unit Numeric <![CDATA[L 1 / μH]]> 118.81 <![CDATA[R 10 / Oh]]> 0.2 <![CDATA[L 2 / μH]]> 118.85 <![CDATA[R 20 / Oh]]> 0.2 <![CDATA[C 1 / nF]]> 5.32 <![CDATA[R L / Oh]]> 10 <![CDATA[C 2 / nF]]> 5.32 <![CDATA[k C ]]> 0.068 <![CDATA[C 3 / nF]]> 5.1 k 0.3

[0063] The parity-time symmetric wireless power transmission system uses phase shift control. First, select C 3 and C 2 As the compensation capacitors of the primary and secondary sides respectively, γ=1.02, such as Figure 8 As shown. 1 When the duty cycle D = 0.9, the operating frequency of the system is 222.2kHz, which is located in the high frequency branch. Figure 8 The expanded waveform at ① is shown in the figure. When D switches from 0.9 to 0.6, its transient state is shown in the expanded waveform at ②. When D = 0.6, the system stabilizes at 225.2kHz and is also located in the high-frequency branch, as shown in the expanded waveform at ③. This is consistent with the rule that the SS type system with phase shift control will not have frequency hopping when γ>1 as analyzed in step (5).

[0064] Next, select C 1 and C 3 As the compensation capacitors of the primary and secondary sides respectively, γ=0.98. Fig. 9 It can be seen that when D = 0.9, the operating frequency of the system is 183.2kHz located in the low-frequency branch, as shown in the expanded waveform at ①. When D switches from 0.9 to 0.6, its transient state is shown in the expanded waveform at ②. When D = 0.6, the system stabilizes at 230.8kHz located in the high-frequency branch, as shown in the expanded waveform at ③. This is consistent with the rule that the SS type system with phase shift control will experience frequency hopping when γ < 1 as analyzed in step (5).

[0065] Finally, keeping γ = 0.98, the coordinates of the intersection point S of the G(jω) curve on the complex plane are (0.089, -j0.027) from the Nyquist plot, so θ 0 =29.67°, using θ 0 =(1-D 0 )π / 2 can be used to find the critical value of the duty cycle D 0 =0.67. Fig.10 It can be seen that when D = 0.9, the operating frequency of the system is 185.2kHz, which is located in the low-frequency branch, as shown in the expanded waveform at ①. When D switches from 0.9 to 0.7, its transient state is shown in the expanded waveform at ②. When D = 0.7, the system stabilizes at 187.3kHz and is still located in the low-frequency branch, without frequency hopping, as shown in the expanded waveform at ③. It can be seen that the reasonable selection of the range of D mentioned in step (6) can effectively suppress frequency hopping.

[0066] The above is only a preferred embodiment of the present invention, and does not limit the present invention in other forms. Any technician familiar with the profession may use the above disclosed technical content to change or modify it into an equivalent embodiment with equivalent changes. However, any simple modification, equivalent change and modification made to the above embodiment according to the technical essence of the present invention without departing from the technical solution of the present invention still belongs to the protection scope of the technical solution of the present invention.

[0067] This patent is not limited to the above-mentioned optimal implementation mode. Anyone can derive other various forms of frequency hopping determination and suppression methods for parity-time symmetric wireless power transmission systems based on the description function method under the inspiration of this patent. All equal changes and modifications made according to the scope of the patent application of the present invention should be covered by this patent.

Claims

1. A method for frequency hopping determination and suppression of a parity-time symmetric wireless power transmission system based on a describing function method, characterized in that: The actual self-oscillation point is determined by using the describing function method combined with the step response of the parity-time symmetric wireless power transmission system: For zero phase angle control systems, the frequency of the self-oscillation point with different detuning degrees is analyzed to determine whether the system will experience frequency hopping, and the frequency hopping can be suppressed by changing the compensation topology and / or limiting the range of detuning degree. For the phase-shift control system, the position of the self-intersection point of the transfer function is analyzed to determine whether the system will have frequency hopping, and the method of limiting the duty cycle of the inverter output voltage is used to suppress frequency hopping.

2. The method for frequency hopping determination and suppression of a parity-time symmetric wireless power transmission system based on a describing function method according to claim 1, characterized in that: The method for determining the actual self-oscillation point by using the description function method and combining the step response of the parity-time symmetric wireless power transmission system is as follows: drawing the Nyquist curve of the transfer function G(jω) of the linear link of the circuit model of the parity-time symmetric wireless power transmission system and the curve of the negative inverse description function -1 / N(I1,α) of the nonlinear link on the complex plane; and determining the theoretical self-oscillation point of the parity-time symmetric wireless power transmission system according to 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 a parity-time symmetric wireless power transmission system based on a describing function method according to claim 2, characterized in that: If there are multiple theoretical self-oscillation points, 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 Laplace transform and inverse transform are used to solve the step response of the inverter output current i1, and the system electrical parameters are substituted to obtain the frequency f′ of the waveform corresponding to the first zero crossing point of the current i1 after the disturbance. 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.

4. The method for frequency hopping determination and suppression of a parity-time symmetric wireless power transmission system based on a describing function method according to claim 1, characterized in that: The specific implementation method for the zero phase angle control system is to determine whether the system will experience frequency hopping by analyzing the self-oscillation point frequencies of different detuning degrees: draw Nyquist diagrams of different detuning degrees γ to obtain corresponding self-oscillation points, including γ<1, γ=1 and γ>1; if as γ changes, the frequency corresponding to the system self-oscillation point is always located in the high-frequency branch or always located in the low-frequency branch, it is determined that frequency hopping will not occur; if as γ changes, the frequency corresponding to the system self-oscillation point is located in the high-frequency branch or in the low-frequency branch, it is determined that frequency hopping may occur.

5. The method for frequency hopping determination and suppression of parity-time symmetric wireless power transmission system based on describing function method according to claim 1, characterized in that: The specific implementation method of suppressing frequency hopping by changing the compensation topology is: changing 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 transmission system based on describing function method according to claim 1, characterized in that: The specific implementation method of the phase shift control system for determining whether the system will have frequency hopping by analyzing the position of the self-intersection point of the transfer function is as follows: drawing Nyquist diagrams of different detuning degrees γ, including γ<1, γ=1 and γ>1; determining whether the system will have frequency hopping according to the position of the self-intersection point S of the G(jω) curve: if S is in the region of 0<θ<π / 2, it is determined that frequency hopping may occur; if S is in the region of -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.

7. The method for frequency hopping determination and suppression of a parity-time symmetric wireless power transmission system based on a describing function method according to claim 2, characterized in that: The specific implementation method of the method of limiting the duty cycle of the inverter output voltage to suppress frequency hopping is: using the coordinates (a, jb) of the intersection point S of the G(jω) curve, and then calculating the critical value θ0=arctan(b / a) of the phase difference between the inverter output voltage u1 and the current i1 corresponding to the point S, and then using θ0=(1-D0)π / 2 to calculate the critical value D0 of the duty cycle of the inverter output voltage u1, according to the system's requirements for the working frequency band, set the range of the duty cycle D of u1 so that the system will not hop, thereby achieving frequency hopping suppression.

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