A method for energy harvesting from a cascaded current transformer bank with resonant compensation

Abstract

The application discloses a kind of resonant compensation cascaded mutual inductor group power taking methods, first obtain the power taking system of following structure, including tuning loop, power taking loop and energy collection loop;Tuning loop includes tuning mutual inductor and tuning capacitor C1, the secondary side of tuning mutual inductor is connected with tuning capacitor C1;Power taking loop includes power taking mutual inductor and multiple power taking capacitors C2, power taking mutual inductor includes multiple power taking secondary sides corresponding with power taking capacitor C2;Energy collection loop includes energy collection mutual inductor and energy collection capacitor C3, energy collection mutual inductor includes multiple energy collection primary sides corresponding with power taking capacitor C2;Power taking capacitor C2 is connected with corresponding power taking secondary side and energy collection primary side;The secondary side of energy collection mutual inductor is connected with energy collection capacitor C3 and forms electric energy output end.The application has the advantages that saturation problem of magnetic core when mutual inductor power taking meets large current can be avoided, and the required electric energy for online monitoring terminal can be output under weak current line.

Description

Technical Field

[0001] This invention relates to the field of high-voltage power supply technology, and in particular to a method for energy extraction from a cascaded transformer group with resonant compensation. Background Technology

[0002] With the accelerated implementation of energy internet-related technologies, a large number of smart terminals are being used in the power grid. However, the complex and diverse operating environment of the power grid poses challenges to the power supply of these terminals. Among them, online monitoring terminal equipment plays a key role in the safe operation of the power grid. However, due to the special geographical location and environment of the power grid, designing a power supply system that can supply power to online monitoring terminal equipment in real time is a critical problem that urgently needs to be solved.

[0003] To address this issue, many researchers have proposed a series of power supply solutions, mainly including solar / wind power + battery power supply, laser power supply, and online energy harvesting. Among these, online energy harvesting technology mostly utilizes current transformers (CTs) for energy harvesting, but the complex and diverse grid conditions make it impossible to achieve stable output. The Journal of Power Supply (2020, 18(05):203-209) disclosed an electric field induction energy harvesting method for powering transmission line monitoring equipment, but the output power of this method is only 40mW; the Proceedings of the CSEE (2019, 39(23):6867-6876) disclosed a "Research on Online Energy Harvesting Method for Transmission Lines Based on Impedance Matching" which uses a resonant compensation current transformer to improve the system output power, but this method is for high-voltage busbars to achieve induction energy harvesting, and the transformer is prone to saturation under wide-range line current fluctuations, resulting in unstable energy harvesting power; Automation of Electric Power Systems (20 The "New Design Principle of Power Supply for Transmission Line Condition Monitoring System" published in 08, 32(1): 76-80) and the "Research on Energy Extraction Method of Resonant Compensated Current Transformer" published in Power System Technology (2021, 45(12): 4896-4902) analyzed the anti-saturation of the transformer core under wide-range current fluctuations. The saturation under high current was weakened by adding an air gap to the CT core. Finally, the power output of 0.25~1.82W was achieved when the ground current was 15A. However, as the ground current continued to decrease, the system power output could not meet the power supply requirements for the continuous operation of the online monitoring equipment. Summary of the Invention

[0004] In view of the shortcomings of the prior art, the technical problem to be solved by the present invention is: how to provide a cascaded transformer group energy extraction method that can both avoid the saturation problem of magnetic core encountering large current when the transformer extracts energy and output sufficient power to meet the needs of online monitoring terminals under weak line current.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0006] A method for harvesting energy from a cascaded current transformer group with resonant compensation, characterized in that an energy harvesting system with the following structure is first obtained, including a tuning circuit, an energy harvesting circuit, and an energy collection circuit;

[0007] The tuning circuit includes a tuning transformer and a tuning capacitor C1, with the secondary side of the tuning transformer connected in series with the tuning capacitor C1.

[0008] The energy harvesting circuit includes an energy harvesting transformer and multiple energy harvesting capacitors C2. The energy harvesting transformer includes multiple energy harvesting secondary sides that are arranged corresponding to the energy harvesting capacitors C2.

[0009] The energy collection circuit includes an energy collection transformer and an energy collection capacitor C3. The energy collection transformer includes multiple primary windings corresponding to the energy harvesting capacitor C2. The energy harvesting capacitor C2 is connected in series with the corresponding secondary winding and the primary winding. The secondary winding of the energy collection transformer is connected in series with the energy collection capacitor C3 to form an energy output terminal.

[0010] The Kirchhoff equations for the tuning circuit, energy harvesting circuit, and energy sinking circuit are as follows:

[0011]

[0012] Where ω is the system input frequency, u1 and i1 are the induced potential and induced current of the ground wire, respectively; R1 is the equivalent resistance of the ground wire, L1 and L 21 For the self-inductance of the primary and secondary coils of the current transformer, L 2t L 3t M t These are the self-inductance of the secondary coil and the mutual inductance of the primary and secondary coils of the tuning circuit, respectively. 31 L4 represents the self-inductance of the primary and secondary coils in the energy collection circuit; M1, M2, and M3 represent the mutual inductance of the primary and secondary coils in the energy extraction circuit, the mutual inductance between the primary coils in the energy collection circuit, and the mutual inductance of the primary and secondary coils in the energy collection circuit, respectively; C1, C2, and C3 represent the compensation capacitors for the tuning circuit, the energy extraction circuit, and the energy collection circuit, respectively; R represents the load resistance; i 21 ~i 25 For the energy extraction loop current, i 2t i 3t The current in the tuning circuit is u0, and the current in i0 is the output voltage and current, respectively.

[0013] When extracting energy, the primary side of the tuned transformer and the energy extraction transformer is set on the live power line to extract energy.

[0014] Furthermore, the self-inductance L of the secondary winding of the energy harvesting transformer 21 =L 31 The self-inductance L of the primary winding of the energy transformer 31The currents in the tuning circuit, energy extraction circuit, and energy collection circuit are equal; the currents in these circuits satisfy the following equation:

[0015]

[0016] in,

[0017]

[0018]

[0019] In the formula, N1 and N2 are the mutual inductance ratios.

[0020] Furthermore, the tuning capacitor C1, the energy extraction capacitor C2, and the energy collection capacitor C satisfy the following equation:

[0021]

[0022] The currents in the tuning circuit, energy harvesting circuit, and energy collecting circuit satisfy the following equation:

[0023]

[0024] Furthermore, the output power P of the energy harvesting system out And the transmission efficiency n is:

[0025]

[0026] In summary, the present invention has the advantages of avoiding the saturation problem of the magnetic core when the current transformer encounters a large current, and being able to output the required power for the online monitoring terminal under weak current conditions on the line. Attached Figure Description

[0027] Figure 1 This is a block diagram of an induction-based energy harvesting system.

[0028] Figure 2 This is the equivalent circuit diagram of the energy extraction transformer.

[0029] Figure 3 This is a cross-sectional view of the energy harvesting transformer.

[0030] Figure 4 This is a simulation model diagram of the magnetic field of the mutual inductor group.

[0031] Figure 5 The figure shows the simulation results of the effect of the number of turns of the current transformer on the system parameters.

[0032] Figure 6 The figure shows the simulation results of the effect of the transformer permeability on the system parameters.

[0033] Figure 7 A circuit model diagram of a multi-stage current transformer group for resonant compensation.

[0034] Figure 8 The waveform diagram shows the system input current and voltage.

[0035] Figure 9 The diagram shows the current waveforms of each circuit in the energy harvesting system.

[0036] Figure 10 The output waveform diagram is for the conventional current transformer induction energy harvesting method.

[0037] Figure 11 The waveforms of the system input current and voltage under uncompensated conditions are shown.

[0038] Figure 12 The waveform diagram of the input current and voltage of the system under compensation.

[0039] Figure 13 The output current and voltage waveforms are shown in the traditional CT energy harvesting method.

[0040] Figure 14 The output current and voltage waveforms are shown in the CT energy harvesting method of this embodiment.

[0041] Figure 15 This is a physical diagram of the energy extraction experimental platform for the multi-stage mutual inductor group with resonant compensation in this embodiment.

[0042] Figure 16 This is a comparison chart of the maximum output power curves of the energy harvesting method in this embodiment and the conventional energy removal method. Detailed Implementation

[0043] The present invention will be further described in detail below with reference to the embodiments.

[0044] This embodiment proposes a resonant compensation cascaded transformer group energy extraction method. It utilizes the electromagnetic field generated in space by the live line to design a multi-stage energy extraction transformer group for extraction and matching with a resonant capacitor to achieve reactive power compensation of the system. This not only avoids the saturation problem of the magnetic core when the transformer extracts energy when it encounters a large current, but also meets the power requirements of the online monitoring terminal when the live line has a weak current.

[0045] I. Energy Extraction Principle of Cascaded Current Transformer Groups with Resonance Compensation

[0046] Taking a 220kV overhead transmission line as an example, the current in its optical fiber composite ground wire (OPGW) typically fluctuates within the range of 2A to 15A. Therefore, to ensure stable and reliable power output across a wide range of current conditions in the energized line, a design is required... Figure 1 The energy harvesting system shown.

[0047] Tuning circuit 1 includes a ground wire, a tuning transformer 11 (i.e., a tuning CT), and a tuning capacitor C112. Furthermore, the live line is considered as the primary side of the tuning CT, with the secondary side connected in series with the tuning capacitor C1. By utilizing the series resonance between the tuning capacitor and the self-inductance of the primary line of the transformer, the system input current and voltage are made to be in phase.

[0048] The structure of energy extraction circuit 2 is as follows: Figure 1 As shown in the upper left part, the compensated electrical energy is induced into the energy harvesting CT21 through the live line, and resonates in series with the secondary self-inductance of the energy harvesting CT and the primary self-inductance of the energy collecting CT through the matching energy harvesting capacitor C222, thereby compensating for the reactive power loss in the energy harvesting circuit and improving the energy harvesting output power.

[0049] The energy collection circuit 3 serves to collect electrical energy. It uses the energy collection CT31 to collect the induced electrical energy from multiple energy collection CTs and output it. It is designed to match the energy collection capacitor C332 and make it resonate in series with the secondary side of the energy collection CT, so that it is also purely resistive.

[0050] By converting the series-parallel connection of the circuit into a series-parallel connection of the magnetic circuit, the design difficulty of the back-end circuit is reduced, and the magnetic flux of the energy-gathering transformer can be increased many times over. Finally, the collected electrical energy is processed by the back-end processing circuit to convert the induced alternating current into the direct current required by the monitoring equipment.

[0051] Using the mutual inductance model, the energy harvesting transformer group is equivalent to a circuit model, such as... Figure 2 As shown.

[0052] Where u1 and i1 are the induced potential and induced current of the ground wire, R1 is the equivalent resistance of the energized line, and L1 and L2 are the induced potential and induced current of the ground wire, respectively. 21 For the self-inductance of the primary and secondary coils of the current transformer, L 2t L 3t M t These are the self-inductance of the secondary coil and the mutual inductance of the primary and secondary coils of the tuning circuit, respectively. 31 L4 represents the self-inductance of the primary and secondary coils in the energy collection circuit; M1, M2, and M3 represent the mutual inductance of the primary and secondary coils in the energy extraction circuit, the mutual inductance between the primary coils in the energy collection circuit, and the mutual inductance of the primary and secondary coils in the energy collection circuit, respectively; C1, C2, and C3 represent the compensation capacitors for the tuning circuit, the energy extraction circuit, and the energy collection circuit, respectively; R represents the load resistance; i 21 ~i 25 For the energy extraction loop current, i 2t i 3t U0 represents the tuning circuit current, and i0 represents the output voltage and current.

[0053] Let the system input frequency be ω, where the self-inductance of the secondary winding of the first-stage energy harvesting circuit is the same as that of the primary winding of the second-stage energy collecting circuit, i.e., L. 21 =L 31Based on the above circuit, the Kirchhoff equations for each loop can be written as shown in equation (1).

[0054]

[0055] Solving the system of equations yields the current expressions for each loop:

[0056]

[0057] in

[0058]

[0059] In the formula, N1 and N2 are the mutual inductance ratios, and their specific expressions are as follows:

[0060]

[0061] In addition, the self-inductance of the secondary winding of the first-stage energy harvesting circuit and the primary winding of the second-stage energy collecting circuit are the same, i.e., L 21 =L 31 To enable the energy harvesting system to resonate and achieve maximum power output, the inductive reactance in the circuit should be resonantly compensated. At the same time, N1 needs to be a real number. Therefore, the tuning capacitor C1, the energy harvesting circuit capacitor C2, and the energy collection circuit capacitor C3 need to satisfy the functional relationship of equation (5).

[0062]

[0063] Therefore, the above equation can be further simplified to obtain:

[0064]

[0065] Therefore, equation (5) provides a theoretical basis for matching the resonant capacitor and designing the number of coil turns.

[0066] In addition, the system's output power can also be theoretically referenced by equation (6), and the system's output power P can be further solved to obtain the output power P. out And the expression for the transmission efficiency n:

[0067]

[0068] Equation (7) also provides a theoretical basis for subsequent system optimization.

[0069] Inductive reactance analysis of current transformers: Unlike the solenoid structure of traditional transformer windings, energy extraction using current transformers requires the live line to be used as the primary winding of the current transformer (CT). However, the self-inductance of the live line cannot be directly calculated. Therefore, it is necessary to solve the expression for the magnetizing inductance of the current transformer, and then derive the expressions for the self-inductance and mutual inductance of the primary and secondary windings of the current transformer. The geometry of the current transformer core is as follows: Figure 3As shown, r and R represent the inner and outer diameters of the magnetic core, h is the thickness of the magnetic core, and δ is the air gap height.

[0070] Assume the equivalent permeability of the magnetic core with an air gap is μ. e Its expression is:

[0071]

[0072] In equation (8), l is the average magnetic path length, μ r Let be the relative permeability of the magnetic core. According to Ampere's circuital law, if the current flowing through the ground wire is I, then the magnetic flux produced on a cross-section of width dρ at a distance ρ from the center of the conductor is:

[0073]

[0074] Integrating the above equation yields the total magnetic flux passing through the magnetic core:

[0075]

[0076] Based on the definition of magnetizing inductance, its expression can be derived:

[0077]

[0078] Finally, based on the relationship between the excitation inductance and the self-inductance and mutual inductance of the primary and secondary sides of the transformer, we can obtain:

[0079]

[0080] In the above formula, L Tl and L Rl Let be the leakage impedances of the primary and secondary windings, respectively, and n be the ratio of the number of turns in the primary and secondary windings. Since the leakage impedance of the transformer winding is much smaller than its own impedance, its influence can be ignored. Further simplification of the above equation yields:

[0081]

[0082] Equation (13) has important guiding significance for the parameter design of energy extraction cores. It can be seen from the equation that the self-inductance of the primary side of the current transformer is directly proportional to the permeability of the core; while the self-inductance of the secondary side of the current transformer and the mutual inductance of the primary and secondary sides are inversely proportional to the number of turns and directly proportional to the permeability of the core.

[0083] II. Simulation Analysis of Energy Harvesting Method for Multi-stage Instrument Transformer Banks with Resonance Compensation

[0084] Magnetic circuit simulation analysis: To optimize the parameters of the energy harvesting transformer group, this embodiment uses Ansys-Maxwell finite element simulation software to build a simulation model as follows: Figure 4 As shown, the effects of changes in core permeability and number of turns on system parameters are analyzed.

[0085] The physical dimensions of the energy harvesting transformer cores are designed based on relevant actual engineering projects. The inner and outer diameters and height of the energy harvesting transformer (CT) are 40mm, 50mm, and 30mm, respectively, while the inner and outer diameters and height of the energy collecting transformer (CT) are 60mm, 80mm, and 30mm, respectively. The energy harvesting transformer has a gap of 0.1mm. Simulations were performed on several commonly used core materials and the number of turns in current transformers, and the results are as follows: Figure 5 and Figure 6 As shown.

[0086] As shown in the figure, the self-inductance and mutual inductance of the current transformer are directly proportional to the number of turns and the permeability, verifying the correctness of the aforementioned theoretical derivation. In addition, to consider the volume and withstand voltage issues when matching capacitors in practice, nanocrystalline material was ultimately chosen as the magnetic core, with a permeability of 20,000. The secondary windings of the energy-harvesting CT and the energy-collecting CT are 40 turns and 50 turns, respectively.

[0087] Resonant compensation circuit simulation analysis: In this embodiment, the aforementioned theoretical analysis was simulated and verified using Simulink circuit simulation software. Since the line current is determined by the system load, the line current is equivalent to an AC current source, and its input current is assumed to be 10A. Based on the analysis results of the electromagnetic field simulation software, the parameters of the energy harvesting transformer group were designed. Substituting them into equation (2), the required capacitance of each circuit can be calculated separately, and the energy harvesting system parameters are obtained as shown in Table 1.

[0088] Table 1 System Parameters

[0089]

[0090] Based on the aforementioned theoretical analysis, this paper uses the Simulink simulation platform to build a model for simulation verification, replacing the energy-harvesting CT and energy-collecting CT with equivalent mutual inductance models. Based on the above parameters, a circuit simulation model is built as follows: Figure 7 As shown.

[0091] The system input current and voltage waveforms are as follows: Figure 8 As shown, it can be clearly observed that the current and voltage waveforms of the system input are in phase, meaning that the line impedance characteristics of the energized line are purely resistive. This is because the matching capacitor of the tuning circuit is mapped to the primary side of the energy harvesting transformer, causing series resonance with the inductive impedance of the line, thus compensating the primary side of the energy harvesting CT.

[0092] Simultaneously, substituting the parameters from the simulation model into equation (6), the energy extraction circuit current of 1.572A, the tuning circuit current of 1.395A, and the load current of 1.426A can be theoretically calculated. Figure 9 The current values ​​in each loop can also be seen, and the system transmission efficiency can be calculated to be approximately 24.8% based on the current in each loop. The final results show that the theoretical calculation and simulation results are basically consistent.

[0093] Meanwhile, to compare the output power of the multi-stage current transformer group with resonant compensation and the conventional current transformer resonant compensation method, simulation analysis was conducted using the same current transformer structure and parameters to verify the effectiveness of the proposed energy extraction method in improving energy extraction power. The core parameters, load, etc., are consistent with the aforementioned parameters, and capacitor matching is also performed.

[0094] Simulation results are as follows Figure 10 As shown, the output power of conventional current transformer induction energy harvesting methods is much lower than that of the energy harvesting method proposed in this embodiment, especially under weak current input conditions.

[0095] III. Experimental Verification

[0096] Core Parameter Testing Experiment: To verify the accuracy of the aforementioned theoretical analysis and simulation results, the experiment used nanocrystalline material as the transformer core. While ensuring high initial permeability, an air gap was added to prevent saturation. Its physical dimensions are the same as the aforementioned simulation parameters. First, parameter testing was performed on the harvesting CT and the collecting CT. In this embodiment, an indirect measurement method was used. The secondary impedance of the harvesting CT was first measured to be 195.71 mH using an LCR bridge tester.

[0097] Based on the measured self-inductance of the secondary coil of the energy harvesting CT, the magnetizing inductance can be calculated to be 0.123 mH. Therefore, the self-inductance and mutual inductance of the circuit can be calculated to be 0.123 mH and 0.492 mH, respectively. Comparing the calculated results with the aforementioned theoretical analysis, it is found that the two values ​​are basically consistent. The main reason for the error is that the manufacturing process of the 0.1 mm air gap in the magnetic core cannot be accurately controlled.

[0098] Similarly, the tuned CT and the energy-converting CT were measured in the same way, and the final parameters were obtained by using the relationship between the secondary self-inductance and the magnetizing inductance, the primary self-inductance and the mutual inductance of the transformer coil, as shown in Table 2. Comparing the actual measured parameters in the table with the aforementioned theoretical derivation values, it can be found that the two are basically matched, and the final results further verify the correctness of the theoretical analysis of the core parameters.

[0099] Table 2 Measured Parameters

[0100]

[0101] Energy harvesting method comparison experiment: Based on the parameters of each current transformer in the system measured in the previous section, resonance compensation was performed on the primary and secondary sides of each stage of the current transformer. Substituting these parameters into the formula, the capacitances of the tuning circuit C1, energy harvesting circuit C2, and energy collection circuit C3 were found to be 653uF, 24.6uF, and 193uF, respectively.

[0102] The matching capacitor required for the tuning circuit consists of two 330uF non-polarized electrolytic capacitors connected in parallel. These are connected to the system circuit, and the input current and voltage waveforms are measured. To visually demonstrate the effect of the system after compensation using the tuning capacitor, the system input waveform is compared with that without the tuning capacitor. The system input waveforms for both methods are shown below. Figure 11 and Figure 12 As shown.

[0103] from Figure 12 As can be seen from the data, the ground current and voltage are basically in phase, indicating that the tuning circuit capacitor and the ground self-inductance resonate, realizing reactive power compensation on the input side of the energy harvesting system.

[0104] In addition, to demonstrate the superiority of the energy harvesting model in this embodiment, a traditional instrument transformer with the same parameters as the instrument transformer in this design, except for the number of turns in the secondary winding, was selected. Its secondary winding has 200 turns, and the system input current is the maximum ground wire induced current of a 220kV line, 15A. The measured output waveform was compared with the output waveform designed in this embodiment, and the results are as follows: Figure 13 and 14 As shown.

[0105] from Figure 13 It is evident that core saturation leads to distortion of the output current and voltage waveforms. However, the output waveform of the cascaded energy harvesting transformer group designed in this embodiment does not exhibit distortion under larger line currents, which further verifies that this method can effectively avoid core saturation.

[0106] Power Output Experiment of Energy Harvesting Method: To verify the effectiveness of the inductive energy harvesting method proposed in this embodiment in power enhancement, the experimental results of this method are compared with those of the conventional current transformer energy harvesting method. The experimental circuit for energy harvesting from a cascaded transformer group under resonant compensation is as follows: Figure 7 The simulation model is consistent, and the experimental platform is built based on the aforementioned relevant system parameters, such as... Figure 15 As shown.

[0107] Figure 15 The following components are provided: ① AC current source, ② energy harvesting transformer, ③ compensation capacitor, ④ energy collecting transformer, ⑤ equivalent load, and ⑥ oscilloscope. A 50Ω sliding rheostat is used as the energy harvesting load to facilitate load adjustment. By comparing the experiments of the two inductive energy harvesting methods, the experimental results show that the output power of the cascaded transformer group energy harvesting method with resonant compensation is much greater than that of the conventional transformer inductive energy harvesting method. To more clearly illustrate the difference in energy harvesting capability between the two methods, the maximum power points of the two methods under the same line current are plotted as follows: Figure 16 The curve.

[0108] from Figure 16As clearly seen, under different line current levels, the output power of the cascaded current transformer group energy harvesting method with resonant compensation is approximately 10 times that of the conventional current transformer energy harvesting method. Especially when the line current is only a weak current of 2-4A, the conventional current transformer induction energy harvesting method is almost unable to harvest energy, while the method proposed in this embodiment can still achieve an output power of 1.46W, meeting the power demand of electrical equipment.

[0109] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method of extracting power from a resonant-compensated cascaded transformer bank, comprising: The power taking system with the following structure is obtained, comprising a tuning loop (1), a power taking loop (2) and a power collecting loop (3); The tuning loop (1) comprises a tuning transformer (11) and a tuning capacitor C1 (12), and the secondary side of the tuning transformer (11) is connected in series with the tuning capacitor C1 (12); The power taking loop (2) comprises a power taking transformer (21) and a plurality of power taking capacitors C2 (22), and the power taking transformer (21) comprises a plurality of power taking secondary sides corresponding to the power taking capacitors C2 (22); The power collecting loop (3) comprises a power collecting transformer (31) and a power collecting capacitor C3 (32), and the power collecting transformer (31) comprises a plurality of power collecting primary sides corresponding to the power taking capacitors C2 (22); the power taking capacitors C2 (22) are connected in series with the corresponding power taking secondary sides and power collecting primary sides; the secondary side of the power collecting transformer (31) is connected in series with the power collecting capacitor C3 (32) and forms an electric energy output end; The Kirchhoff equations of the tuning loop (1), the power taking loop (2) and the power collecting loop (3) are as follows: ； Wherein, ω is the system input frequency, u1, i1 are the line induced voltage and induced current, respectively; R1 is the equivalent resistance of the line, L1, L 21 are the self-inductance of the primary and secondary coils of the energy extraction transformer, L 2t , L 3t , M t are the self-inductance of the secondary coil and the mutual inductance of the primary and secondary coils of the tuning loop, L 31 , L4 are the self-inductance of the primary and secondary coils of the energy collection loop, M1, M2, M3 are the mutual inductance of the primary and secondary coils of the energy extraction loop, the mutual inductance between each primary coil of the energy collection loop, and the mutual inductance of the primary and secondary coils of the energy collection loop, respectively, C1, C2, C3 are the compensation capacitors of the tuning loop, the energy extraction loop, and the energy collection loop, respectively, R is the load resistance, i 21 ~i 25 is the current of the energy extraction loop, i 2t , i 3t is the current of the tuning loop, u0, i0 are the output voltage and current, respectively. When taking power, the primary sides of the tuning transformer (11) and the power taking transformer (21) are arranged on the live line to take power; The self-inductance L of the secondary winding of the power-taking transformer (21) 21 = L 31 The self-inductance L of the primary winding of the power-accumulating transformer (31) 31 The currents of the tuning circuit (1), the power-taking circuit (2) and the power-accumulating circuit (3) satisfy the following equation: ； Wherein, ； ； In the formula, N1 and N2 are mutual inductance ratios.

2. The resonant-compensated cascaded transformer set power deriving method as claimed in claim 1, characterized by, The tuning capacitor C1, the power taking capacitor C2 and the power collecting capacitor C satisfy the following formula: ； The currents of the tuning loop (1), the power taking loop (2) and the power collecting loop (3) satisfy the following formula: 。 3. The resonant-compensated cascaded transformer set power deriving method according to claim 2, wherein, The output power P of the power taking system out And the transmission efficiency n is: 。

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