Topological Parameter Design Method for Zero-Voltage Switching or Zero-Phase Angle Input in a Wireless Charging System

Abstract

The present invention belongs to the field of wireless charging, and particularly relates to a method for designing topological parameters of zero-voltage switching or zero-phase-angle input in a wireless charging system. Based on the minimum unit of the constant-current and constant-voltage mode conversion, that is, the conversion from the constant-current mode to the constant-voltage mode or from the constant-voltage mode to the constant-current mode, the addition principle of additional compensation devices is proposed; the additional compensation devices are connected in series in the constant-current branch or the additional compensation devices are connected in parallel in the constant-voltage branch; the compensated topological structure is topologically split, and the impedance conversion is carried out with the resonant T-network as the basic unit, and the additional compensation parameters can be directly calculated, and the additional compensation parameters are the topological parameters of zero-voltage switching or zero-phase-angle input. Based on the addition principle of the compensation devices proposed by this invention, all the compensation positions of the topological structure can be obtained; the calculation method of the additional compensation parameters proposed by this invention is simpler. Compared with the traditional method of obtaining the parameter values according to the simulation results, this method greatly shortens the parameter design cycle and is more conducive to the parameter design of the system.

Description

Technical Field

[0001] The present invention belongs to the field of wireless charging, and particularly relates to a method for designing topological parameters of zero-voltage switching or zero-phase-angle input in a wireless charging system. Background Art

[0002] The input impedance of a wireless power transmission system directly reflects the working state of the system. When the input impedance angle is equal to 0°, the system resonates at the operating frequency, meeting the zero-phase-angle input; when the input impedance angle is greater than 0°, the system is weakly inductive, and the inverter operates in the zero-voltage switching state, at which time the switching loss of the inverter is minimized. In practical applications, to improve the efficiency of the inverter, the system usually operates in the zero-voltage switching state. The existing methods for achieving zero-voltage switching in research can be divided into two categories.

[0003] Method 1: Achieve zero-voltage switching by using a control method. Frequency-variable phase-shift control is one of the commonly used control methods. By changing the operating frequency of the system, the system operates in the zero-voltage switching state, and phase-shift control is used to ensure the output power of the system. However, when the mutual inductance or load resistance changes greatly, it may cause the operating frequency to deviate significantly from the resonance frequency and the phase-shift angle to be large, even exceeding the adjustment range of the system. In addition, by designing the inverter to achieve zero-voltage switching, this method will not only increase the system volume but also improve the control complexity of the system.

[0004] Method 2: Achieve zero-voltage switching through topological parameter design. Compared with Method 1, this method has simple control and does not increase the system complexity. Zero-voltage switching can be achieved only through reasonable design of topological parameters. However, in existing research, the parameter design depends on simulation results. By listing the Kirchhoff voltage equations of the system, the expressions of the input impedance angle and output voltage / current are calculated. Since the obtained expressions are too complex, the system parameters cannot be directly designed. Therefore, in existing research, the method of floating all compensation parameters within a certain range is adopted, and the influence of the compensation parameters on the input impedance angle and output current / voltage is observed through simulation results. However, the conclusions obtained based on simulation results are not universal. For the same topological structure, when the parameter settings are different, the obtained conclusions may be different, and the parameter design period of this method is relatively long. Summary of the Invention

[0005] The present invention provides a method for designing topological parameters of zero-voltage switching or zero-phase-angle input in a wireless charging system. Based on this method, all additional compensation positions of the topology can be obtained, and the output current / voltage will not be affected while the input impedance angle of the system is adjusted. In addition, the new method for calculating additional compensation parameters proposed by this invention is simpler. Compared with the traditional method of obtaining parameter values based on simulation results, this method greatly shortens the parameter design period and is more conducive to system design.

[0006] The present invention is achieved through the following technical solutions:

[0007] A method for designing topological parameters of zero-voltage switching or zero-phase-angle input in a wireless charging system, the topological parameter design method including the adding position of an additional compensation device and the parameter calculation method, specifically:

[0008] Based on the minimum unit of the constant-current and constant-voltage mode conversion, that is, the constant-current mode is converted to the constant-voltage mode or the constant-voltage mode is converted to the constant-current mode, the adding principle of the compensation device is proposed;

[0009] The adding principle of the compensation device is: connecting the additional compensation device in series in the constant-current branch or connecting the additional compensation device in parallel in the constant-voltage branch;

[0010] Decompose the topological structure with the compensation device into multiple T networks. If the decomposed T network is not resonant, then construct a resonant T network by introducing a virtual reactance to assist in calculating the compensation parameters;

[0011] Taking the impedance transformation of the resonant T network as the basic unit, the input impedance expression of the compensated topology can be directly obtained. According to the requirements of zero-voltage switching or zero-phase-angle input, the corresponding compensation parameters can be calculated.

[0012] Further, the conversion of the constant-voltage mode to the constant-current mode is specifically that one end of the input voltage U1 is connected to one end of the reactance X CC_1 and the other end of the reactance X CC_1 is respectively connected to one end of the reactance X CC_2 and one end of the load resistor R e ; the other end of the reactance X CC_2 and the other end of the load resistor R e are connected to the other end of the input voltage U1, and the current flowing through the load is I1;

[0013] When the reactance satisfies X CC_1 +X CC_2 =0, the topological module can be converted from the constant-voltage mode to the constant-current mode.

[0014] Further, the conversion of the constant-current mode to the constant-voltage mode further includes that one end of the input current I2 is respectively connected to one end of the reactance X CV_1 and one end of the reactance X CV_2 ; the other end of the reactance X CV_2 is connected to one end of the load resistor R e ; the other end of the reactance X CV_1 and the other end of the load resistor R e are both connected to the other end of the input current I2, and the voltage across the load is U2;

[0015] When the reactance satisfies XCV_1 +X CV_2 When = 0, the topology module can switch from the constant - current mode to the constant - voltage mode.

[0016] Furthermore, in the addition principle of the said additional compensation device, there are two compensation methods for the topology module that switches from the constant - voltage mode to the constant - current mode and two compensation methods for the topology module that switches from the constant - current mode to the constant - voltage mode.

[0017] Furthermore, the two additional compensation methods for the topology module that switches from the constant - voltage mode to the constant - current mode are respectively: One end of the additional compensation device X1 is connected to one end of the input voltage U1 and one end of the reactance X CC_1 respectively, and the other end of the additional compensation device X1 is connected to the other end of the input voltage U1 and the other end of the reactance X CC_2 respectively; One end of the additional compensation device X2 is connected to one end of the reactance X CC_1 and one end of the reactance X CC_2 respectively, and the other end of the additional compensation device X2 is connected to one end of the load resistor R e respectively.

[0018] Furthermore, the two additional compensation methods for the topology module that switches from the constant - current mode to the constant - voltage mode are respectively: One end of the additional compensation device X3 is connected to one end of the reactance X CV_2 and one end of the load resistor R e respectively, and the other end of the additional compensation device X3 is connected to one end of the reactance X CV_1 and the other end of the load resistor R e respectively; One end of the additional compensation device X4 is connected to one end of the input current I2, and the other end of the additional compensation device X4 is connected to one end of the reactance X CV_1 and one end of the reactance X CV_2 respectively.

[0019] Furthermore, X5, X6 and X7 represent reactances, and Z in and Z are the input impedance and impedance respectively. When the reactances satisfy X5 + X6 = 0 and X6 + X7 = 0, it is a resonant T - network; The impedance transformation of the resonant T - network can be expressed as:

[0020]

[0021] All topologies can be decomposed into multiple T - networks.

[0022] Furthermore, when the decomposed T - network is not resonant, a virtual reactance can be introduced to construct a resonant T - network to assist in the calculation, thereby simplifying the calculation;

[0023] The constant-voltage mode to constant-current mode topology module with an additional compensation device X1 is composed of a T-network, but this T-network does not resonate. To simplify the calculation, virtual reactances X8 and X9 are introduced. One end of reactance X8 is connected to one end of reactance X CC_1 and one end of reactance X CC_2 respectively. The other end of reactance X8 is connected to one end of reactance X9; the other end of reactance X9 is connected to one end of load resistor R e .

[0024] The T-network formed by reactance X CC_1 , reactance X CC_2 and reactance X8 is a resonant T-network. The impedance transformation of the resonant T-network can directly obtain the expression of the additional compensation parameters of this topology module

[0025]

[0026] where: θ1 is the input impedance angle of the constant-voltage mode to constant-current mode topology module;

[0027] Similarly, the additional compensation reactances of the other three compensation methods are expressed as:

[0028]

[0029] where: θ2 is the input impedance angle of the constant-current mode to constant-voltage mode topology module.

[0030] The beneficial effects of the present invention are:

[0031] The present invention provides a parameter design method to achieve zero-voltage switching or zero-phase-angle input of a wireless charging system. This parameter design method is applicable to all topological structures, and the beneficial effects include:

[0032] (1) Propose the addition principle of additional compensation parameters. Based on the proposed compensation parameter addition principle, all compensation positions of the topological structure can be obtained, and adding an additional compensation device at any compensation position can adjust the input impedance angle without affecting the output power of the system. The compensation parameters of some compensation positions can be combined with the existing compensation parameters of the topological branch, and the number of topological devices will not be increased; while the addition of some compensation positions will increase the number of branches of the topology, and thus new topological structures derived from the existing topology can be obtained.

[0033] (2) A new method for calculating additional compensation parameters is proposed. By decomposing the topology into multiple T-networks and constructing all T-networks into resonant T-networks by introducing virtual reactance, then, taking the resonant T-network as a unit, the expression of additional compensation parameters can be easily calculated according to the impedance transformation of the resonant T-network. Compared with the existing method of obtaining compensation parameters based on a large number of simulation results, the calculation method proposed in this invention can greatly shorten the design cycle of compensation parameters and is more conducive to the parameter design of the system. Description of the Drawings

[0034] Figure 1 This is the minimum unit for the constant current and constant voltage mode conversion of the present invention. (a) Case 1: Constant voltage mode to constant current mode, (b) Case 2: Constant current mode to constant voltage mode.

[0035] Figure 2 This is the compensation method for the minimum unit of the constant current and constant voltage mode conversion of the present invention. (a) Case 1.1, (b) Case 1.2, (c) Case 2.1, (d) Case 2.2.

[0036] Figure 3 This is the equivalent circuit of the standard T-network of the present invention.

[0037] Figure 4 This is the equivalent circuit for calculating the additional compensation parameters in Case 1.1 of the present invention.

[0038] Figure 5 This is the bilateral LCC equivalent circuit provided by the implementation of the present invention.

[0039] Figure 6 This is the topological analysis of the bilateral LCC provided by the implementation of the present invention.

[0040] Figure 7 This is the equivalent circuit for calculating the parameter of Compensation Position 1 of the bilateral LCC provided by the implementation of the present invention.

[0041] Figure 8 This is the experimental result provided by the implementation of the present invention. (a) Inverter output voltage and current, (b) Measured transmission efficiency. Detailed Implementation Manner

[0042] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0043] A method for designing topological parameters of zero-voltage switching or zero-phase-angle input in a wireless charging system, the topological parameter design method including the addition position and parameter calculation of an additional compensation device, specifically:

[0044] Based on the minimum unit of constant-current and constant-voltage mode conversion, that is, the conversion from constant-current mode to constant-voltage mode or from constant-voltage mode to constant-current mode, the addition principle of the compensation device is proposed;

[0045] The addition principle of the compensation device is: connecting the additional compensation device in series in the constant-current branch or connecting the additional compensation device in parallel in the constant-voltage branch;

[0046] Decompose the topological structure with the compensation device into multiple T networks. If the decomposed T network is not resonant, construct a resonant T network by introducing virtual reactance to assist in calculating the compensation parameters;

[0047] Taking the impedance transformation of the resonant T network as the basic unit, the input impedance expression of the compensated topology can be directly obtained. According to the requirements of zero-voltage switching or zero-phase-angle input, the corresponding compensation parameters can be calculated.

[0048] The addition principle of the above-mentioned additional compensation device is related to the constant-current and constant-voltage branches of the topology. Since all topologies can be decomposed into multiple mode conversion units, and all constant-current and constant-voltage branches of the topology are included in the constant-current and constant-voltage mode conversion units. Therefore, based on the above compensation principle, all compensation positions of the topology can be obtained. In addition, the compensation parameters at some positions can be combined with the existing compensation parameters of the topological branch into one, without increasing the number of compensation devices; while when some compensation devices are added to the system, the number of branches of the topology will increase, and then a new topological structure derived from the existing topology can be obtained.

[0049] The minimum unit of the constant-current and constant-voltage mode conversion includes two cases. Case 1: The conversion from constant-current mode to constant-voltage mode; Case 2: The conversion from constant-voltage mode to constant-current mode. The mode conversions of the two cases are as Figure 1 shown, X CC_1 ,X CC_2 ,X CV_1 and X CV_2 are compensation reactances. When the reactances satisfy X CC_1 +X CC_2 =0, the topological module can be converted from constant-voltage mode to constant-current mode; when the reactances satisfy X CV_1 +X CV_2 =0, the topological module can be converted from constant-current mode to constant-voltage mode.

[0050] Based on the addition principle of the compensation parameters proposed by this invention, there are four compensation methods for the minimum unit of the constant-current and constant-voltage mode conversion, namely Case 1.1, Case 1.2, Case 2.1 and Case 2.2, as Figure 2As shown. The X1, X2, X3, and X4 are additional compensating reactances.

[0051] A method for designing topological parameters for zero-voltage switching or zero-phase-angle input in a wireless charging system. The conversion from constant-voltage mode to constant-current mode is as Figure 1 (a) shown. Specifically, one end of the input voltage U1 is connected to one end of the reactance X CC_1 The other end of the reactance X CC_1 is respectively connected to one end of the reactance X CC_2 and one end of the load resistor R e The other end of the reactance X CC_2 and the other end of the load resistor R e are connected to the other end of the input voltage U1. The current flowing through the load is I1;

[0052] When the reactances satisfy X CC_1 + X CC_2 = 0, the topological module can be converted from constant-voltage mode to constant-current mode.

[0053] A method for designing topological parameters for zero-voltage switching or zero-phase-angle input in a wireless charging system. The conversion from constant-current mode to constant-voltage mode is as Figure 1 (b) shown. Specifically, one end of the input current I2 is respectively connected to one end of the reactance X CV_1 and one end of the reactance X CV_2 The other end of the reactance X CV_2 is connected to one end of the load resistor R e The other end of the reactance X CV_1 and the other end of the load resistor R e are both connected to the other end of the input current I2. The voltage across the load is U2;

[0054] When the reactances satisfy X CV_1 + X CV_2 = 0, the topological module can be converted from constant-current mode to constant-voltage mode.

[0055] A method for designing topological parameters for zero-voltage switching or zero-phase-angle input in a wireless charging system. The addition principle of the additional compensating device. There are two compensation methods for the topological module when converting from constant-voltage mode to constant-current mode and for the topological module when converting from constant-current mode to constant-voltage mode, as Figure 2 shown.

[0056] The two additional compensations for the topological module when converting from constant-voltage mode to constant-current mode are as Figure 2 (a) and Figure 2 (b) shown. One end of the additional compensating device X1 is respectively connected to one end of the input voltage U1 and the reactance X CC_1One end is connected, and the other end of the additional compensation device X1 is respectively connected to the other end of the input voltage U1 and the reactance X CC_2 The other end is connected; one end of the additional compensation device X2 is respectively connected to the reactance X CC_1 One end and the reactance X CC_2 One end is connected, and the other end of the additional compensation device X2 is connected to the load resistor R e One end is connected.

[0057] Two additional compensations for the topology module that converts from constant current mode to constant voltage mode are as Figure 2 (c) and Figure 2 (d) shown. One end of the additional compensation device X3 is respectively connected to the reactance X CV_2 One end and the load resistor R e One end is connected, and the other end of the additional compensation device X3 is respectively connected to the reactance X CV_1 One end and the load resistor R e The other end is connected; one end of the additional compensation device X4 is connected to one end of the input current I2, and the other end of the additional compensation device X4 is respectively connected to the reactance X CV_1 One end and the reactance X CV_2 One end is connected.

[0058] A method for designing topological parameters of zero-voltage switching or zero-phase-angle input in a wireless charging system, as Figure 3 Shown, X5, X6 and X7 represent reactances, Z in And Z are the input impedance and impedance respectively. When the reactances satisfy X5 + X6 = 0 and X6 + X7 = 0, it is a resonant T-network; the impedance transformation of the resonant T-network can be expressed as:

[0059]

[0060] All topological structures can be decomposed into multiple T-networks.

[0061] A method for designing topological parameters of zero-voltage switching or zero-phase-angle input in a wireless charging system. When the decomposed T-network is not resonant, a virtual reactance can be introduced to construct a resonant T-network to assist in the calculation, thereby simplifying the calculation.

[0062] The constant voltage mode to constant current mode topological module with the additional compensation device X1 is composed of a T-network, but this T-network is not resonant. To simplify the calculation, virtual reactances X8 and X9 are introduced. One end of the reactance X8 is respectively connected to the reactance X CC_1 One end and the reactance X CC_2 One end is connected, and the other end of the reactance X8 is connected to one end of the reactance X9; the other end of the reactance X9 is connected to the load resistor R e One end is connected, as Figure 4 Shown.

[0063] Reactance X CC_1 and reactance X CC_2 and the T-network composed of reactance X8 is a resonant T-network, and the impedance transformation of the said resonant T-network can directly obtain the expression of the additional compensation parameters of this topological module

[0064]

[0065] Where: θ1 is the input impedance angle of the topological module for the constant voltage mode to constant current mode;

[0066] Similarly, the additional compensation reactances of the other three compensation methods are expressed as:

[0067]

[0068] Where: θ2 is the input impedance angle of the topological module for the constant current mode to constant voltage mode.

[0069] See Figure 5 , this embodiment is a bilateral LCC topology with zero voltage switching, where: U in is the input AC voltage, L p2 , L s2 are the self-inductances of the primary and secondary coils respectively, M is the mutual inductance of the two coils, L p1 and L s1 are the compensation inductances of the primary and secondary sides respectively, C p1 and C p2 are the primary side compensation capacitors, C s1 and C s2 are the secondary side capacitors, R e is the equivalent load value. The topological parameters are set to satisfy:

[0070]

[0071] Where: ω is the operating frequency.

[0072] Figure 6 is the topological analysis circuit of the bilateral LCC. It can be seen from the figure that the mode conversion of the bilateral LCC includes three parts: constant voltage to constant current, constant current to constant voltage, and constant voltage to constant current. According to the additional compensation parameter compensation principle proposed by the present invention, there are three compensation positions (P1, P2, and P3), two series-connected constant current branches and one parallel-connected constant voltage branch. Among them, X c1 , X c2 and X c3 are the additional compensation reactances at positions P1, P2, and P3 respectively.

[0073] Figure 7Equivalent circuit for calculating additional compensation parameters at compensation position P1. As can be seen from the figure, the three T-networks of the bilateral LCC are all resonant. Therefore, there is no need to introduce a virtual reactance to construct a resonant T-network here. Therefore, the impedance transformation of the bilateral LCC is as follows:

[0074]

[0075] According to the above formula, the expression for the additional compensation parameter can be obtained as:

[0076]

[0077] where: θ C is the input impedance angle of the bilateral LCC.

[0078] Similarly, the expressions for the additional compensation parameters at compensation position P2 and compensation position P3 can be calculated

[0079] X c2 =-R e tanθ c

[0080]

[0081] When additional compensation is added to the bilateral LCC at position P1, the additional compensation parameter can be combined with the existing compensation capacitor C p2 without increasing the number of compensation devices of the bilateral LCC. The output voltage and current of the inverter are as shown in Figure 8 (a). As can be seen from the figure, the phase of the inverter output voltage is slightly ahead of the current, and the system is weakly inductive. At this time, the inverter operates in the zero-voltage switching state, and the switching loss of the inverter is minimized. The DC-DC efficiency of the system is 94.85%, as shown in Figure 8 (b).

Claims

1. A method for designing topological parameters of zero-voltage switching or zero-phase-angle input in a wireless charging system, characterized in that, The topological parameter design method includes the addition position of additional compensation devices and parameter calculation, specifically as follows: Based on the minimum unit of the constant current and constant voltage mode conversion, that is, the constant current mode is converted to the constant voltage mode or the constant voltage mode is converted to the constant current mode, the addition principle of the compensation device is proposed; The addition principle of the compensation device is: connect the additional compensation device in series in the constant current branch or connect the additional compensation device in parallel in the constant voltage branch; decompose the topological structure with the compensation device into multiple T networks. If the decomposed T network is not resonant, introduce a virtual reactance to construct a resonant T network to assist in calculating the compensation parameters; Taking the impedance transformation of the resonant T network as the basic unit, the input impedance expression of the compensated topology can be directly obtained. According to the requirements of zero voltage switching or zero phase angle input, the corresponding compensation parameters can be calculated; There are two compensation methods for the topological module with the constant voltage mode converted to the constant current mode and two compensation methods for the topological module with the constant current mode converted to the constant voltage mode in the addition principle of the additional compensation device; The two additional compensation methods of the topology module for converting the constant voltage mode to the constant current mode are respectively: one end of the additional compensation device X1 is connected to one end of the input voltage U1 and one end of the reactance X CC_1 respectively, and the other end of the additional compensation device X1 is connected to the other end of the input voltage U1 and the other end of the reactance X C1_2 respectively; one end of the additional compensation device X2 is connected to one end of the reactance X CC_1 and one end of the reactance X CC_2 respectively, and the other end of the additional compensation device X2 is connected to one end of the load resistor R e respectively; The two additional compensation methods of the constant current mode to constant voltage mode topology module are respectively: one end of the additional compensation device X3 is respectively connected to one end of the reactance X CV_2 and one end of the load resistor R e ; the other end of the additional compensation device X3 is respectively connected to one end of the reactance X CV_1 and the other end of the load resistor R e ; one end of the additional compensation device X4 is connected to one end of the input current I2, and the other end of the additional compensation device X4 is respectively connected to one end of the reactance X CV_1 and one end of the reactance X CV_2 .

2. The method for designing topological parameters of zero-voltage switching or zero-phase-angle input in a wireless charging system according to claim 1, characterized in that, Specifically, when the constant voltage mode is switched to the constant current mode, one end of the input voltage U1 is connected to one end of the reactance X CC_1 ; the other end of the reactance X CC_1 is respectively connected to one end of the reactance X CC_2 and one end of the load resistor R e ; the other end of the reactance X CC_2 and the other end of the load resistor R e are connected to the other end of the input voltage U1, and the current flowing through the load is I1. When the reactance satisfies X CC_1 +X CC_2 = 0, the topology module can switch from the constant voltage mode to the constant current mode.

3. The method for designing topological parameters of zero-voltage switching or zero-phase-angle input in a wireless charging system according to claim 1, characterized in that, The conversion from the constant current mode to the constant voltage mode includes that one end of the input current I2 is respectively connected to one end of the reactance X CV_1 and one end of the reactance X CV_2 . The other end of the reactance X CV_2 is connected to one end of the load resistor R e . The other end of the reactance X CV_1 and the other end of the load resistor R e are both connected to the other end of the input current I2, and the voltage across the load is U2; When the reactance satisfies X CV_1 + X CV_2 = 0, the topology module can switch from the constant current mode to the constant voltage mode.

4. The method for designing topological parameters of zero-voltage switching or zero-phase-angle input in a wireless charging system according to claim 1, characterized in that, The specific T network is such that X5, X6, and X7 represent reactances, and Z in and Z are the input impedance and impedance respectively; when the reactances satisfy X5 + X6 = 0 and X6 + X7 = 0, it is a resonant T network; the impedance transformation of the resonant T network can be expressed as: All topological structures can be decomposed into multiple T networks.

5. The method for designing topological parameters of zero-voltage switching or zero-phase-angle input in a wireless charging system according to claim 1, characterized in that, When the decomposed T network is not resonant, a virtual reactance can be introduced to construct a resonant T network to assist in the calculation, thereby simplifying the calculation; The constant-voltage mode to constant-current mode topology module with an additional compensation device X1 is composed of a T-network, but this T-network is not resonant. To simplify the calculation, virtual reactances X8 and X9 are introduced. One end of reactance X8 is connected to one end of reactance X CC_1 and one end of reactance X CC_2 respectively. The other end of reactance X8 is connected to one end of reactance X9. The other end of reactance X9 is connected to one end of load resistor R e . Reactance X CC_1 and reactance X CC_2 The T-network composed of reactance X8 is a resonant T-network. The impedance transformation of the resonant T-network can directly obtain the expression of the additional compensation parameters of this topological module: Where: θ1 is the input impedance angle of the topological module with the constant voltage mode converted to the constant current mode; Similarly, the additional compensation reactances of the other three compensation methods are expressed as: Where: θ2 is the input impedance angle of the topological module with the constant current mode converted to the constant voltage mode.

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