An Optimization Method for Wireless Power Transfer System Based on the Principle of Parity-Time Symmetry

Abstract

The present invention proposes an optimization method for a wireless power transfer system based on the parity-time symmetry principle. This method constructs PT-WPT circuit systems with four topological structures, namely S-S type, P-S type, S-P type, and P-P type circuits. According to the size of the load in the application and the quality factor of the transmitting and receiving coils, a suitable topological structure is selected, and through the methods of frequency selection and impedance transformation, the load is transformed to the optimal load to obtain the maximum transmission efficiency. After entering the PT symmetry region, the output power and transmission efficiency of the system remain stable in the PT symmetry region and have strong robustness. The frequency selection and impedance transformation method proposed by the present invention only uses the simplest LC compensation type structure, solves the troubles of frequency tracking, real-time dynamic coupling coefficient identification, and real-time adjustment of the impedance matching network required for traditional magnetic resonance WPT impedance transformation, simplifies the design, and also saves costs.

Description

Technical Field

[0001] The present invention belongs to the field of wireless energy transfer, and particularly relates to an optimization method for a wireless power transfer system based on the parity-time symmetry principle. Background Art

[0002] Wireless Power Transfer (WPT) technology has been widely used in energy supply for many fields such as electric vehicles, implantable medical devices, portable devices, and micro sensors. Among them, magnetic resonance coupling is a WPT technology that has been most studied and applied, and it can achieve medium and short-range transmission. In practical applications, due to the relatively close distance between coils, the coil coupling is strong, resulting in frequency splitting and a decrease in efficiency.

[0003] The WPT technology based on the parity-time (PT) symmetry principle can well solve the problem of efficiency reduction caused by frequency splitting. When the WPT system satisfies the PT symmetry condition, the parity-time symmetric wireless energy transfer (PTsymmetry-WPT, PTs-WPT) system has the characteristic of frequency self-adaptation, and its transmission power and transmission efficiency will be independent of the transmission distance and have strong robustness. It is found that there is a critical value k of the coupling coefficient in the PTs-WPT system. C . When the coupling coefficient is greater than the critical value, the system operates in the PT symmetric state, and the system characteristic frequency values are all real numbers. At this time, the system state variables adjust the operating frequency adaptively to maintain symmetry, and the output power and transmission efficiency remain stable. When the coupling coefficient is less than this critical value k C , the system operates in the PT symmetry broken state, and at this time, the output power and transmission efficiency cannot be kept stable, and the output power and transmission efficiency decrease significantly. The critical point corresponding to this critical coupling coefficient is called the symmetry breaking point.

[0004] The critical coupling coefficient is related to the system loss, and the load impedance corresponding to the critical coupling coefficient k C is called the critical coupling load (R LC ), and the efficiency extreme value at the turning point of the strong and weak coupling regions can be obtained here. The efficiency expression in the weak coupling region of the PTs-WPT system is the same as that of the traditional WPT system, and there is also an efficiency extreme value in the traditional WPT method, and the corresponding load is R Lopt . Under different quality factors of the transmitting and receiving coils, R LC and R Lopt are not necessarily equal. According to the quality factors of the transmitting and receiving coils and the size of the load in the application, a suitable topological structure should be selected, and through frequency selection and impedance transformation methods, the original load can be transformed to the optimal load to obtain the maximum transmission efficiency. Summary of the Invention

[0005] The invention aims to provide an optimization method for a wireless power transmission system based on the parity-time symmetry principle. According to the size of the load and the quality factors of the transmitting and receiving coils, this method selects a suitable topological structure and transforms the load to the corresponding optimal load through impedance transformation, so that the system can obtain the maximum transmission efficiency.

[0006] An optimization method for a wireless power transmission system based on the parity-time symmetry principle includes the following steps:

[0007] Step 1: Construct an optimized wireless power transmission system. The optimized wireless power transmission system includes a transmitting circuit and a receiving circuit; the transmitting circuit includes a negative resistance structure and a first LC resonance circuit connected in a closed loop. The first LC resonance circuit includes a resonance capacitor C1 and a transmitting coil L1. The receiving circuit includes a load RL and a second LC resonance circuit connected in a closed loop. The second LC resonance circuit in the receiving circuit includes a resonance capacitor C2 and a receiving coil L2. The quality factor Q1 of the transmitting coil L1 and the quality factor Q2 of the receiving coil L2 satisfy the relationship Q2≥Q1 + 2 / k C .

[0008] The wireless power transmission system adopts any one of four topological structures. The four topological structures are S-S type, P-S type, P-P type, and S-P type structures. In the S-S type structure, the first LC resonance circuit adopts a capacitor series structure, and the second LC resonance circuit adopts a capacitor series structure; in the P-S type structure, the first LC resonance circuit adopts a capacitor parallel structure, and the second LC resonance circuit adopts a capacitor series structure; in the P-P type structure, the first LC resonance circuit adopts a capacitor parallel structure, and the second LC resonance circuit adopts a capacitor parallel structure; in the S-P type structure, the first LC resonance circuit adopts a capacitor series structure, and the second LC resonance circuit adopts a capacitor parallel structure;

[0009] Step 2: Set the inductance value L2 of the receiving coil L2, its parasitic resistance R2, the load size R L and the critical coupling coefficient k C .

[0010] Step 3: Determine the capacitance value C2 of the resonance capacitor C2. The capacitance value C2 can transform the load to the optimal load.

[0011] When the wireless power transmission system adopts the S-S type or P-S type structure, set the capacitance value C2 of the resonance capacitor C2 as shown in Equation (1):

[0012]

[0013] where k Cis the critical coupling coefficient; L2 is the inductance value of the receiving coil L2; R2 is the parasitic resistance value of the receiving coil L2; R L is the load size.

[0014] When the wireless power transfer system adopts a P-P type or S-P type structure, the capacitance value C2 of the resonant capacitor C2 is set to satisfy the relational expression shown in Equation (2):

[0015]

[0016] Step 3: Adjust the negative resistance structure in the transmitting circuit so that the equivalent resistance value of the negative resistance structure is equal to the equivalent load resistance value of the receiving circuit, obtaining an optimized wireless power transfer system.

[0017] Preferably, when the load RL ≤ 500Ω, the wireless power transfer system adopts an S-S type or P-S type structure. When the load RL > 500Ω, the wireless power transfer system adopts a P-P type or S-P type structure.

[0018] Preferably, when the first LC resonant circuit adopts a capacitor series structure, the resonant capacitor C1 and the transmitting coil L1 are connected in series at both ends of the negative resistance structure; when the first LC resonant circuit adopts a capacitor parallel structure, the resonant capacitor C1 and the transmitting coil L1 are connected in parallel at both ends of the negative resistance structure.

[0019] When the second LC resonant circuit adopts a capacitor series structure, the resonant capacitor C2 and the receiving coil L2 are connected in series at both ends of the load; when the second LC resonant circuit adopts a capacitor parallel structure, the resonant capacitor C2 and the receiving coil L2 are connected in parallel at both ends of the negative resistance structure.

[0020] Preferably, the negative resistance structure includes an operational amplifier and three feedback resistors R t1 、R f1 and R f2 . When the first LC resonant circuit adopts a capacitor series structure, the negative resistance structure adopts a CNIC negative resistance structure; when the first LC resonant circuit adopts a capacitor parallel structure, the negative resistance structure adopts a VNIC negative resistance structure.

[0021] When the negative resistance structure adopts a CNIC negative resistance structure, the inverting input terminal of the operational amplifier is connected to one end of the resistor Rf1; the output terminal of the operational amplifier is connected to the other end of the resistor Rf1 and one end of the resistor Rf2; the non-inverting input terminal of the operational amplifier is connected to the other end of the resistor Rf2 and one end of the resistor Rt1; the other end of the resistor Rt1 and the inverting input terminal of the operational amplifier are respectively the two connection terminals of the negative resistance structure.

[0022] When the negative resistance structure adopts the VNIC negative resistance structure, the inverting input terminal of the operational amplifier is connected to one end of the resistor Rf1 and the resistor Rf2; the output terminal of the operational amplifier is connected to the other end of the resistor Rf1 and one end of the resistor Rt1; the non-inverting input terminal of the operational amplifier is connected to the other end of the resistor Rt1; the other end of the resistor Rf2 and the non-inverting input terminal of the operational amplifier are respectively the two connection terminals of the negative resistance structure.

[0023] Preferably, when the optimized wireless power transmission system adopts the S-S type or S-P type structure, the following relational expression is satisfied:

[0024]

[0025] Among them, R f1 is the resistance value of the resistor Rf1; R f2 is the resistance value of the resistor Rf2; R t1 is the resistance value of the resistor Rt1.

[0026] Preferably, when the optimized wireless power transmission system adopts the P-S type structure, the following relational expression is satisfied:

[0027]

[0028] Among them, R f1 is the resistance value of the resistor Rf1; R f2 is the resistance value of the resistor Rf2; R t1 is the resistance value of the resistor Rt1;

[0029] Preferably, when the optimized wireless power transmission system adopts the P-P type, the following relational expression is satisfied:

[0030]

[0031] Among them, R f1 is the resistance value of the resistor Rf1; R f2 is the resistance value of the resistor Rf2; R t1 is the resistance value of the resistor Rt1;

[0032] Preferably, when the wireless power transmission system adopts the P-P type or S-P type structure, the capacitance value C2 of the resonant capacitor C2 is obtained by solving the relational expression (2) using the Shengjin formula.

[0033] Preferably, the expression of the equivalent load resistance value of the receiving circuit described in step three is as follows:

[0034]

[0035] Preferably, the parameters of the resonant capacitor C1 are the same as those of the resonant capacitor C2.

[0036] The beneficial effects of the present invention are as follows:

[0037] 1. Based on the parity-time symmetry principle, the PTs-WPT system of the present invention is designed. After meeting the PT symmetry conditions, the system has the characteristic of frequency self-adaptation. After the system enters strong coupling, it can still maintain stable transmission power and efficiency after the transmission distance changes, and the energy transmission space range is wider.

[0038] 2. Compared with the impedance transformation in traditional WPT, the impedance transformation in the WPT based on PT symmetry of the present invention can obtain the maximum transmission efficiency in the entire load range after the load is equivalent to the optimal load.

[0039] 3. The impedance matching method proposed by the present invention only adopts the simplest LC compensation type structure, and does not require frequency tracking, real-time dynamic coupling coefficient identification, and real-time adjustment of the impedance matching network required in traditional impedance transformation. It simplifies the design and also saves costs. Description of the Drawings

[0040] Figure 1a , 1b , 1c, 1d are respectively the circuit schematic diagrams of the PTs-WPT systems of the four topological structures of the present invention ( Figure 1a corresponding to the S-S type, Figure 1b corresponding to the P-S type, Figure 1c corresponding to the P-P type, Figure 1d corresponding to the S-P type).

[0041] Figure 2a , 2b , 2c, 2d, 2e are respectively the comparison diagrams of the load efficiencies of the traditional WPT system and the PTs-WPT system when the coil quality factor Q takes five different values ( Figure 2a corresponding to the case of "when the Q value is large, Q2>Q1 + 50d", Figure 2b corresponding to the case of "when the Q value is large, Q2<Q1 + 50", Figure 2c corresponding to the case of "when the Q value is small, Q2>Q1 + 50", Figure 2d corresponding to the case of "when the Q value is small, Q2<Q1 + 50"), Figure 2e corresponding to the case of "Q2 = Q1 + 50").

[0042] Figure 3a , 3b , 3c, 3d are respectively the simulation waveform diagrams of the voltage and current of the transmitting circuit and the receiving circuit of the four topological structures of the present invention ( Figure 3a corresponding to the S-S type, Figure 3b corresponding to the P-S type, Figure 3c corresponding to the P-P type, Figure 3d corresponding to the S-P type).

[0043] Figure 4 This is the relationship diagram of the circuit coupling coefficient, transmission efficiency, and output power of the S-S type PTs-WPT system in the present invention. Detailed implementation manners

[0044] To make the objectives, functions, and advantages of the present invention easier to understand, the present invention will be further described below in conjunction with the accompanying drawings and specific embodiments. It should be understood, however, that the present invention can be implemented in various forms, and some exemplary and non-limiting embodiments shown in the accompanying drawings and described below are not intended to limit the present invention to the specific embodiments described.

[0045] An optimization method for a wireless power transfer system based on the parity-time symmetry principle, which transforms the original load to the optimal load according to the size of the load in the application and the quality factors of the transmitting coil and the receiving coil, so as to obtain the maximum transmission efficiency. The optimized wireless power transfer system includes a primary-side transmitting circuit and a secondary-side receiving circuit. The transmitting circuit includes a negative resistance structure and a first LC resonant circuit, and the receiving circuit includes a load and a second LC resonant circuit.

[0046] In the receiving circuit, when the load is a small resistor, the receiving circuit is usually selected to adopt a capacitor series structure to form a series resonant circuit; when the load is a large resistor, the receiving circuit is usually selected to adopt a capacitor parallel structure to form a parallel resonant circuit. In the transmitting circuit, the same resonant mode as the receiving circuit is usually selected, or a different resonant mode from the receiving circuit can also be selected, but the resonant frequency of the transmitting circuit should be consistent with that of the receiving circuit. Therefore, a total of four topological structures, namely series-series (S-S) type, parallel-series (P-S) type, parallel-parallel (P-P) type, and series-parallel (S-P) type, can be formed.

[0047] According to the requirements of the parity-time symmetry principle, a negative resistance needs to be implemented in the transmitting circuit. The implementation of the negative resistance can be achieved by a positive feedback circuit, can be built with an operational amplifier, or can be achieved by an inverter circuit including feedback. The negative resistance structure built with an operational amplifier mainly includes a negative impedance converter (NIC) combined with a positive resistance. The specific method adopted can be a current-inversion NIC (CNIC) or a voltage-inversion NIC (VNIC). Both negative resistance structures include an operational amplifier and adjustment resistors R t1 , feedback resistor R f1 , feedback resistor R f2, the overall negative resistance structure circuit will be equivalent to a negative resistance whose absolute value is equal to the equivalent load value. The connection methods of the two structures of negative resistance circuits are different, and the resistance values ​​of the three adjustment feedback resistors also need to be adjusted according to the application and structure, so that the system can self-oscillate.

[0048] Four embodiments are described for four topological structures of the optimized wireless power transmission system:

[0049] Example 1: Construction and optimization of SS-type PTs-WPT system

[0050] Example 2: Construction and optimization of a PTs-WPT system with a PS structure

[0051] Example 3: Construction and optimization of PTs-WPT system with PP structure

[0052] Example 4: Construction and optimization of a PTs-WPT system with SP structure

[0053] Example 1

[0054] A wireless power transmission system optimization method based on the parity-time symmetry principle is as follows:

[0055] Based on the principle of parity-time symmetry, an SS-type PTs-WPT wireless power transmission system is constructed. Both the sending circuit and the receiving circuit are S-type structures, and the negative resistance structure is CNIC type. The circuit diagram is shown in Figure 1a As shown, it is composed of a transmitting circuit and a receiving circuit. The transmitting circuit includes a CNIC negative resistance structure composed of an operational amplifier, a resonant capacitor C1, a transmitting coil L1 and a coil parasitic resistance R1; the receiving circuit is composed of a load resistor R L , resonant capacitor C2, receiving coil L2 and coil parasitic resistance R2. The inductance, capacitance, parasitic internal resistance and resonant frequency of the transmitting circuit and the receiving circuit are the same.

[0056] like Figure 1a As shown, the resonant capacitor C1 and the transmitting coil L1 form a first LC resonant circuit. The CNIC negative resistance structure is composed of an operational amplifier and three feedback resistors R t1 , R f1 and R f2 The inverting input terminal of the operational amplifier is connected to one end of the resistor Rf1; the output terminal of the operational amplifier is connected to the other end of the resistor Rf1 and one end of the resistor Rf2; the non-inverting input terminal of the operational amplifier is connected to the other end of the resistor Rf2 and one end of the resistor Rt1; the other end of the resistor Rt1 and the inverting input terminal of the operational amplifier are two terminals of the negative resistance structure. The two terminals are connected to the first LC resonant circuit; see Figure 1aIn the circuit diagram, the CNIC negative resistance structure can be equivalent to a negative resistance -R0, and its value should be equal to the load resistance of the receiving circuit. The equivalent resistance of the CNIC negative resistance is as follows:

[0057]

[0058] According to the different value cases of the quality factors of the transmitting and receiving coils, compare R LC and R Lopt to find the optimal load corresponding to the maximum transmission efficiency, as follows:

[0059] Give the expression of the transmission efficiency of the PTs-WPT system. The transmission efficiency is the ratio of the output power on the load to the input power at the negative resistance end:

[0060]

[0061] It can be seen from the formula that in the strong coupling region, as the load increases, the transmission efficiency increases, and reaches the peak at the critical coupling load R C corresponding to the critical coupling point k LC . After entering the weak coupling region, the efficiency expression is the same as that of the traditional WPT, and the efficiency has a non-linear relationship with the load. When taking the derivative of η S-S with respect to R L , there is an optimal load R Lopt that makes the transmission efficiency η S-S reach the maximum value.

[0062] The expression of R Lopt is as follows:

[0063]

[0064] Among them, Q1 and Q2 are the quality factors of the transmitting coil and the receiving coil, Q1 = ω1L1 / R1, Q2 = ω2L2 / R2.

[0065] According to the expression of the critical coupling point k C under the PT symmetry condition, the expression of the corresponding critical load R LC can be obtained:

[0066] R LC = k C ω2L2 - R2 = R2(k C Q2 - 1)

[0067] When k = k C , the magnitude relationship between R Lopt and R LC for different Q1 and Q2 values is as follows:

[0068]

[0069]

[0070]

[0071] Select the same structural parameters and different Q values, and draw the relationship diagram of the load R L and the transmission efficiency η, as shown in Figures 2a - 2e the figure. In the figure, the coupling coefficient k is set to 0.04, and the corresponding 2 / k = 50. The R Lopt point corresponds to the maximum vertex of the traditional WPT, and the R LC point corresponds to the critical point of strong and weak coupling of the PTs-WPT system. The following conclusions can be obtained:

[0072] When Q2 < Q1 + 2 / k, R LC < R Lopt , the maximum transmission efficiency is at the R Lopt point, and the optimal load is R Lopt . At this time, to obtain a greater transmission efficiency for the PTs-WPT system, the load should be selected to be transformed to R Lopt .

[0073] When Q2 = Q1 + 2 / k, R LC = R Lopt , and at this time the load can be arbitrarily transformed to R LC or R Lopt , and the maximum transmission efficiency of the system can be obtained.

[0074] When Q2 > Q1 + 2 / k, R LC > R Lopt , the maximum transmission efficiency is at the R LC point, and the optimal load is R LC . At this time, the maximum transmission efficiency of the PTs-WPT system is at the R LC point, and the load should be selected to be transformed to R LC .

[0075] When the Q value is large, the corresponding efficiency difference between R LC and R Lopt is small, and the overall efficiency is large; when the Q value is small, the corresponding efficiency difference between R LC and R Lopt is large, and the overall efficiency is small.

[0076] Similarly, the other three topological structures (i.e., P-P, S-P, and P-S) can obtain the same results as the S-S structure. Transform the load to R LoptObtaining the maximum transmission efficiency is the same as the impedance matching method of traditional WPT systems, so no specific description will be given here. Only for the case of Q2≥Q1+2 / k, the method of transforming the load to the critical load R LC will be specifically elaborated.

[0077] First, the steps of the load transformation method for the S-S type PTs-WPT system circuit are as follows:

[0078] First, determine the circuit structure parameters: Determine the inductance value L2 of the receiving coil, the load size R L and the parameter values of the critical coupling coefficient k C .

[0079] Then, according to the k at the critical coupling point under the PT symmetry condition C expression:

[0080]

[0081] Let R L =R LC , corresponding to k C there is an optimal resonance frequency, and an expression for this optimal resonance frequency ω2 can be obtained:

[0082]

[0083] The corresponding resonance capacitor C2 can be obtained as follows:

[0084]

[0085] By changing this resonance capacitor C2, the resonance frequency ω2 of the resonance system can be changed, and the original load can be changed to the critical coupling load R LC of the corresponding structure, and the maximum transmission efficiency of this structure can be obtained.

[0086] Technical effect verification:

[0087] To verify the effectiveness of the S-S type PTs-WPT system and its frequency selection method proposed in the above embodiments, we use Multisim software to build a model of the system.

[0088] Based on the adaptive characteristics of the PTs-WPT system and the self-excitation oscillation conditions of the amplifier circuit, the resistance value of the S-S structure negative resistance circuit should satisfy:

[0089]

[0090] Therefore, the parameter settings are: R f1 =20Ω, R f2 =47Ω, R t1 =510Ω, k C= 0.04, R L = 20 Ω, R1 = R2 = 0.25 Ω, L1 = L2 = 2.325 mH. Solving the resonant capacitor C2 = C1 = 9.072 nF according to the above formula, the theoretically calculated efficiency is 97.59%, and the coupling coefficient range is 0.0021 - 0.3. The operational amplifier model selected is ADA4000-1AZR. Figure 3a is the simulation waveform diagram of current-to-voltage conversion of the S-S type circuit's transmitting circuit and receiving circuit. It can be seen that after entering the PT symmetric state, the voltage amplitude of the receiving circuit is almost the same as that of the transmitting circuit. Figure 4 is the relationship diagram of the coupling coefficient, transmission efficiency, and output power of the S-S type circuit. The corresponding critical coupling coefficient during simulation is 0.04 set initially. After reaching the critical coupling point and entering the strong coupling region, the system's transmission efficiency and output power remain stable, and the efficiency is as high as over 90%. It can be seen that the simulation is consistent with the theory.

[0091] Embodiment 2

[0092] An optimization method for a wireless power transfer system based on the parity-time symmetry principle. In this embodiment, a P-S type PTs-WPT wireless power transfer system is constructed. The transmitting circuit is of P type structure, the receiving circuit is of S type structure, and the negative resistance structure selects the VNIC type. The circuit schematic diagram is as Figure 1b shown. The construction and frequency selection method of the P-S type PTs-WPT system are the same as those of the above S-S type, only the transmitting circuit is different.

[0093] As Figure 1b shown, the VNIC type negative resistance structure consists of an operational amplifier and three feedback resistors R t1 , R f1 and R f2 . One end of the feedback resistor Rf1 and the feedback resistor Rf2 is connected to the inverting input terminal of the operational amplifier; the other end of the feedback resistor Rf1 and one end of the resistor Rt1 are connected to the output terminal of the operational amplifier; the other end of the resistor Rt1 is connected to the non-inverting input terminal of the operational amplifier; the other end of the feedback resistor Rf2 and the non-inverting input terminal of the operational amplifier are respectively the two connection terminals of the negative resistance structure. These two connection terminals are connected to the first LC resonant circuit.

[0094] Refer to Figure 1b for the schematic diagram in it. The entire circuit is also equivalent to a negative resistor -R0, and its value should be equal to the load resistor after the receiving circuit is equivalent. The equivalent resistance of the VNIC negative resistor is:

[0095]

[0096] Technical effect verification:

[0097] When performing simulations using Application Example 2, based on the adaptive characteristics of the PTs-WPT system and the self-excitation oscillation conditions of the amplifier circuit, the resistance values of the P-S structure negative resistance circuit should satisfy:

[0098]

[0099] Therefore, the resistance values of the three resistors in the negative resistance structure are different from those set in Example 1, and the values are: R f1 = 3.5 kΩ, R f2 = 6.5 kΩ, R t1 = 5 kΩ. The structural parameters of other transmitting and receiving circuits are the same as those set in Example 1.

[0100] For the simulation results, see Figure 3b , the simulation waveform diagram of the voltages of the transmitting and receiving circuits of the P-S type circuit is the same as that of the S-S type. After entering the PT symmetric state, the voltage amplitude of the receiving circuit is the same as that of the transmitting circuit. The relationship diagram of the coupling coefficient with the transmission efficiency and output power is the same as the result obtained in Example 1, as shown in Figure 4 .

[0101] In addition, the other receiving circuit frequency selection methods in this embodiment are the same as those in Example 1, and will not be elaborated here.

[0102] Example 3

[0103] An optimization method for a wireless power transfer system based on the parity-time symmetry principle. In this embodiment, a P-P type PTs-WPT wireless power transfer system is constructed. Both the transmitting circuit and the receiving circuit are of P type structure, and the circuit schematic diagram is as shown in Figure 1c . In this embodiment, the negative resistance structure is the same as that in Example 2, and the VNIC type negative resistance structure is adopted.

[0104] Furthermore, the method steps for the receiving circuit to perform impedance transformation and frequency selection for the load are specifically as follows:

[0105] 1. Solve for the parallel capacitance value for LC impedance matching

[0106] (1) Fix the structural parameters of the circuit: inductance L2, load R L , critical coupling coefficient k C is determined, ω2 is not determined and will change with the value of C2. According to the R of the PT symmetry condition LC and the equivalent R L ', an equation of degree three is obtained by equating both sides, and the solution of C2 is obtained, and then the value of ω2 is obtained.

[0107] (2) List the equation and solve

[0108] According to the k at the EP point of the PT symmetry condition CThe formula determines the critical coupling load R at this point LC , and impedance transformation is carried out through the parallel resonance capacitor C2 to make R L equivalent to R L '. From the PT symmetry condition and the parallel-to-series equivalent formula, the following two equations are obtained:

[0109] R LC = k C ω2L2 - R2

[0110]

[0111] The above two equations are equal, R L ' = R LC , and the following equation is obtained

[0112]

[0113] Substitute ω2 with . ω2 changes with C2. A cubic equation can be obtained. Regarding as the solution x of the equation

[0114]

[0115] Solve according to Shengjin's formula, and list the discriminant △ of the cubic equation for having solutions.

[0116]

[0117] The present invention first determines the inductance values L1 = L2 of the transmitting coil and the receiving coil, the parasitic resistances R1 = R2 of the coils, and the critical coupling coefficient k C as constants according to the application background of the PTs-WPT system, optimizes the load R L , and on the basis of making the equation have solutions, determines the range of R L , that is, only R L is a variable in this discriminant △ for having solutions.

[0118] After that, the solution of C2 can be obtained by using Shengjin's formula with the Mmatlab software.

[0119] 2. Scope of application of this method:

[0120] According to Shengjin's discriminant method, when △>0, a pair of conjugate imaginary root solutions (discarded) and a real root solution are obtained. This unique real root solution obtains a C2 value that is too small. When R L is small, (ω2C2R L ) 2 <<1, making R L '≈R L , and it is impossible to connect a relatively large resistor R LEquivalent to a smaller resistance value R LC At this point. Therefore, this unique real solution is also discarded. Therefore, only when △ is not greater than 0 can a suitable solution C2 be obtained.

[0121] In addition, an image can be drawn from the cubic equation and the discriminant △ of the solution. When k C takes a fixed value, the larger the value of R L is, the smaller C2 becomes, the critical load resistance value R LC becomes larger, so that the efficiency is closer to 1, and the resonant angular frequency ω and the resonant frequency F also become larger. However, if R L is too large, making C2 too small is equivalent to an open circuit, and the resonant frequency is too large, which will damage the circuit. In high-frequency circuits, many parasitic parameters will be generated, having a great impact on the circuit system. Therefore, considering the actual circuit, R L cannot be too large.

[0122] To sum up, there is an applicable range for R L in this method. When k C is determined, due to the limitation that △ is not greater than 0, there will be a minimum value for R L . Due to the influence of high frequency, there will also be an applicable maximum value for R L . The minimum value and the maximum value here should be determined according to the actual circuit parameters.

[0123] 3. List the efficiency expression

[0124] According to the series equivalent formula method: the parallel P-P structure is equivalent to the series S-S structure, and the equivalent negative resistance and the equivalent load resistance are:

[0125]

[0126] The equivalent capacitances of the transmitting circuit and the receiving circuit are:

[0127]

[0128] Substitute the equivalent resistance and capacitance into the circuit efficiency formula of the S-S structure, and the efficiency is obtained as:

[0129]

[0130] Problem of choosing the initial critical coupling coefficient

[0131] The PTs-WPT system has strong robustness in the PT symmetric region. However, when the coupling coefficient of the system is less than the critical coupling coefficient, that is, when the system operates in the broken region, the output power and efficiency of the system are very sensitive to the change of the coupling coefficient. Therefore, it is necessary to expand the interval of PT symmetry to expand the distance of constant and effective transmission.

[0132] Reduce kC , it can improve the performance of the PTs-WPT system. That is, it can broaden the PT symmetry range, extend the distance of constant power and constant efficiency, and improve the anti-alignment ability. However, as can be seen from the efficiency expressions listed above, reducing k C is a contradiction to improving efficiency. Reducing k C makes it difficult to obtain high efficiency at the same time. Therefore, this method needs to be comprehensively considered when determining the initial critical coupling coefficient, and according to the application background, whether to prefer a wider PT symmetry range, higher efficiency, or a wider load range.

[0133] Technical effect verification:

[0134] When performing simulations using Application Example 3, based on the adaptive characteristics of the PTs-WPT system and the self-excitation oscillation conditions of the amplifier circuit, the resistance values of the P-P structure negative resistance circuit should satisfy:

[0135]

[0136] Therefore, except that the resistance values of the three resistors in the negative resistance structure are different from those in Example 2, R f1 = 5.5 kΩ, R f2 = 4.5 kΩ, R t1 = 5 kΩ. The structural parameters of other transmitting and receiving circuits are the same as those set in Examples 1 and 2.

[0137] For the simulation results, see Figure 3c , the simulation waveform diagram of the voltage of the transmitting end and the receiving circuit of the P-P type circuit. After entering the PT symmetry state, the voltage amplitude of the receiving circuit is almost the same as that of the transmitting circuit. The relationship diagram of the coupling coefficient with the transmission efficiency and output power is the same as the result obtained in Example 1, as Figure 4 shown.

[0138] Example 4

[0139] An optimization method for a wireless power transmission system based on the parity-time symmetry principle. In this example, an S-P type PTs-WPT wireless power transmission system is constructed. The transmitting circuit is of S type structure, and the receiving circuit is of P type structure. The negative resistance structure is selected as the CNIC type. The circuit schematic diagram is as Figure 1d shown.

[0140] The construction of the S-P type PTs-WPT system and its impedance transformation method are the same as those of the P-P type in Example 3 above, except for the transmitting circuit.

[0141] Technical effect verification:

[0142] In this embodiment, the negative resistance structure is the same as that in Embodiment 1, adopting the CNIC type negative resistance structure. When performing simulation using Embodiment 4, the resistance values of the three resistors in the negative resistance structure are set the same as those in Embodiment 1, and the other transmission and reception circuit structure parameters are also set the same as those in Embodiment 1.

[0143] See the simulation results in Figure 3d , the simulation waveform diagram of the voltage of the transmitting end and the receiving circuit of the S-P type circuit. After entering the PT symmetric state, the voltage amplitude of the receiving circuit is almost the same as that of the transmitting circuit. The relationship diagram of the coupling coefficient with the transmission efficiency and output power is the same as the result obtained in Embodiment 1, as shown in Figure 4 shown.

[0144] In addition, the other impedance transformation methods in this embodiment are the same as those in Embodiment 3, and will not be elaborated here.

[0145] It should be understood that the specific examples and embodiments described in the present invention are non-limiting. When the technology is feasible, different coil parameters and loads can achieve the effects of the claims, and corresponding modifications can be made to the above-mentioned structures, steps, and sequences without departing from the protection scope of the present invention.

Claims

1. An optimization method for a wireless power transfer system based on the principle of parity-time symmetry, characterized in that: It includes the following steps: Step 1: Construct an optimized wireless power transfer system; the optimized wireless power transfer system includes a transmitting circuit and a receiving circuit; the transmitting circuit includes a negative resistance structure and a first LC resonance circuit connected in a closed loop; the first LC resonance circuit includes a resonance capacitor C1 and a transmitting coil L1; the receiving circuit includes a load RL and a second LC resonance circuit connected in a closed loop; the second LC resonance circuit in the receiving circuit includes a resonance capacitor C2 and a receiving coil L2; The wireless power transfer system adopts any one of four topological structures; the four topological structures are S-S type, P-S type, P-P type, and S-P type structures; in the S-S type structure, the first LC resonance circuit adopts a capacitor series structure, and the second LC resonance circuit adopts a capacitor series structure; In the P-S type structure, the first LC resonance circuit adopts a capacitor parallel structure, and the second LC resonance circuit adopts a capacitor series structure; in the P-P type structure, the first LC resonance circuit adopts a capacitor parallel structure, and the second LC resonance circuit adopts a capacitor parallel structure; in the S-P type structure, the first LC resonance circuit adopts a capacitor series structure, and the second LC resonance circuit adopts a capacitor parallel structure; Step 2: Set the inductance value L2 of the receiving coil L2, its parasitic resistance R2, the load size R L and the critical coupling coefficient k C ; Step 3: Determine the capacitance value C2 of the resonance capacitor C2; the capacitance value C2 can transform the load to the optimal load. When the wireless power transfer system adopts the S-S type or P-S type structure, set the capacitance value C2 of the resonance capacitor C2 as shown in Equation (1): where k C is the critical coupling coefficient; L2 is the inductance value of the receiving coil L2; R2 is the parasitic resistance value of the receiving coil L2; R L is the load size; When the wireless power transfer system adopts the P-P type or S-P type structure, set the capacitance value C2 of the resonance capacitor C2 to satisfy the relational expression shown in Equation (2): Step 3: Adjust the negative resistance structure in the transmitting circuit so that the equivalent resistance value of the negative resistance structure is equal to the equivalent load resistance value of the receiving circuit, and obtain the optimized wireless power transfer system.

2. The optimization method of a wireless power transmission system based on the parity-time symmetry principle according to claim 1, wherein: When the load RL ≤ 500Ω, the wireless power transfer system adopts the S-S type or P-S type structure; when the load RL > 500Ω, the wireless power transfer system adopts the P-P type or S-P type structure.

3. The optimization method of a wireless power transmission system based on the parity-time symmetry principle according to claim 1, characterized in that: When the first LC resonance circuit adopts a capacitor series structure, the resonance capacitor C1 and the transmitting coil L1 are connected in series at both ends of the negative resistance structure; when the first LC resonance circuit adopts a capacitor parallel structure, the resonance capacitor C1 and the transmitting coil L1 are connected in parallel at both ends of the negative resistance structure; when the second LC resonance circuit adopts a capacitor series structure, the resonance capacitor C2 and the receiving coil L2 are connected in series at both ends of the load; when the second LC resonance circuit adopts a capacitor parallel structure, the resonance capacitor C2 and the receiving coil L2 are connected in parallel at both ends of the negative resistance structure.

4. The optimization method of a wireless power transmission system based on the parity-time symmetry principle according to claim 1, characterized in that: The negative resistance structure includes an operational amplifier and three feedback resistors R t1 , R f1 and R f2 ; when the first LC resonance circuit adopts a capacitor series structure, the negative resistance structure adopts a CNIC negative resistance structure; when the first LC resonance circuit adopts a capacitor parallel structure, the negative resistance structure adopts a VNIC negative resistance structure; When the negative resistance structure adopts a CNIC negative resistance structure, the inverting input terminal of the operational amplifier is connected to one end of the resistor Rf1; the output terminal of the operational amplifier is connected to the other end of the resistor Rf1 and one end of the resistor Rf2; the non-inverting input terminal of the operational amplifier is connected to the other end of the resistor Rf2 and one end of the resistor Rt1; the other end of the resistor Rt1 and the inverting input terminal of the operational amplifier are respectively the two connection terminals of the negative resistance structure; When the negative resistance structure adopts the VNIC negative resistance structure, the inverting input terminal of the operational amplifier is connected to one end of resistor Rf1 and resistor Rf2; the output terminal of the operational amplifier is connected to the other end of resistor Rf1 and one end of resistor Rt1; the non-inverting input terminal of the operational amplifier is connected to the other end of resistor Rt1; the other end of resistor Rf2 and the non-inverting input terminal of the operational amplifier are respectively the two connection terminals of the negative resistance structure.

5. The optimization method of a wireless power transmission system based on the parity-time symmetry principle according to claim 1, wherein: When the optimized wireless power transmission system adopts the S-S type or S-P type structure, the following relational expressions are satisfied: Among them, R f1 is the resistance value of resistor Rf1; R f2 is the resistance value of resistor Rf2; R t1 is the resistance value of resistor Rt1.

6. The optimization method of a wireless power transmission system based on the parity-time symmetry principle according to claim 1, wherein: When the optimized wireless power transmission system adopts the P-S type structure, the following relational expressions are satisfied: Among them, R f1 is the resistance value of resistor Rf1; R f2 is the resistance value of resistor Rf2; R t1 is the resistance value of resistor Rt1.

7. The optimization method of a wireless power transmission system based on the parity-time symmetry principle according to claim 1, characterized in that: When the optimized wireless power transmission system adopts the P-P type, the following relational expressions are satisfied: Among them, R f1 is the resistance value of resistor Rf1; R f2 is the resistance value of resistor Rf2; R t1 is the resistance value of resistor Rt1.

8. The optimization method of a wireless power transmission system based on the parity-time symmetry principle according to claim 1, characterized in that: When the wireless power transmission system adopts the P-P type or S-P type structure, the capacitance value C2 of the resonant capacitor C2 is obtained by solving the relational expression (2) using the Shengjin formula.

9. The optimization method of a wireless power transmission system based on the parity-time symmetry principle according to claim 1, wherein: The expression of the equivalent load resistance value of the receiving circuit described in step three is as follows:

10. The optimization method of a wireless power transmission system based on the parity-time symmetry principle according to claim 1, characterized in that: The parameters of the resonant capacitor C1 are the same as those of the resonant capacitor C2.

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