Parallel system circulating current suppression method based on energy-information integrated converter

CN123019369APending Publication Date: 2026-10-30SOUTHEAST UNIV
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Patent Information

Application Number
CN202610861884.2
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2026-06-15
Publication Date
2026-10-30

AI Technical Summary

Technical Problem

但目前对于交流微网系统的EIT技术研究较少,在多电力电子变换器并联的交流系统中使用PSDM技术,由于叠加的信号载波的频率幅值的不同,势必会产生瞬时电压差,因而会导致系统内部产生高频通信环流,可能影响交流系统的通信质量和功率均分性能,因此,提出一种基于虚拟阻抗的交流EIT系统高频环流抑制方法具有重要意义

Benefits of technology

[0020](1)本发明在逆变器控制反馈回路中同时设置基频虚拟阻抗和高频虚拟阻抗,能够针对线路阻抗不一致引起的基频环流和信息载波调制引起的高频环流分别形成抑制作用,实现分频段协同抑制。

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Abstract

The application discloses a parallel system circulating current suppression method based on an energy-information integrated converter, and relates to power line communication technology, power electronic parallel system control technology and high-frequency circulating current suppression technology. The application firstly establishes an equivalent output model of a parallel inverter system adopting information carrier modulation; then, a frequency division extraction is performed on inverter output current to obtain a fundamental frequency current component and a high-frequency current component corresponding to a communication carrier; further, a fundamental frequency virtual impedance and a high-frequency virtual impedance are respectively set according to system impedance characteristics, and are introduced into a control feedback loop to realize collaborative suppression of the fundamental frequency circulating current and the high-frequency circulating current. The method does not need to additionally set an independent circulating current suppression device, can reduce the circulating current of the parallel system while guaranteeing the energy-information integrated communication function, improves power sharing performance, and improves system operation stability and communication reliability.
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Description

Technical Field

[0001] This invention relates to the fields of power line communication technology and power electronic parallel system control technology, and in particular to a method for suppressing circulating current in parallel systems based on an integrated energy-information converter. Background Technology

[0002] With the widespread application of distributed clean energy sources such as photovoltaics and wind power, new loads such as energy storage devices and electric vehicles are also being connected to the power grid in large numbers. The rapid development of these new energy source and load devices has not only changed the direction of energy flow in the distribution network but also affected its spatiotemporal distribution. With the advancement of power semiconductor technology, AC / DC hybrid distribution systems based on power electronic devices are gradually becoming an effective solution for controlling multi-directional and multi-energy flow in active distribution networks. As a key hub in the energy internet, power electronic converters, with their bidirectional energy flow, flexible power flow regulation, and fault isolation capabilities, have received increasing attention in recent years. Simultaneously, since the optimized operation of the distribution network typically involves the coordinated control of multiple converters, external communication and data transmission capabilities are required between these converters.

[0003] Currently, coordination between multiple converters typically relies on dedicated communication equipment and links, or on droop control methods that use frequency and voltage changes to achieve simple power distribution. Power electronic devices not only possess power modulation capabilities but also information modulation capabilities, thus enabling them to transmit information while simultaneously performing power conversion and control. Through energy-information integrated transmission (EIT) technology, "software replacing hardware" can be achieved, effectively reducing the cost of power system communication equipment while improving communication reliability.

[0004] Power signal dual-carrier modulation (PSDM) technology has been widely studied in DC microgrids, enabling efficient point-to-point signal transmission at low cost without the need for additional devices. However, research on EIT technology for AC microgrid systems is currently limited. In AC systems with multiple power electronic converters connected in parallel, the use of PSDM technology inevitably leads to instantaneous voltage differences due to the different frequency amplitudes of the superimposed signal carriers. This can result in high-frequency circulating currents within the system, potentially affecting the communication quality and power sharing performance of the AC system. Therefore, proposing a high-frequency circulating current suppression method for AC EIT systems based on virtual impedance is of great significance. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide a method for suppressing circulating current in parallel systems based on an integrated energy-information converter, so as to reduce system circulating current, improve power sharing performance, and enhance system communication reliability and operational stability.

[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0007] According to the present invention, a circulating current suppression method for parallel systems based on an integrated energy-information converter is applied to a parallel inverter system consisting of at least two parallel-operating single-phase H-bridge inverters. The single-phase H-bridge inverters superimpose modulated information carriers in the control loop to achieve integrated energy and information communication; the method includes the following steps:

[0008] Step S1: Establish the equivalent output model of the parallel inverter system using information carrier modulation, obtain the equivalent output voltage and equivalent output impedance of each single-phase H-bridge inverter, and analyze the base frequency circulating current caused by inconsistent line parameters and the high frequency circulating current caused by information carrier modulation in the parallel inverter system based on the differences between the equivalent output voltage and equivalent output impedance of different single-phase H-bridge inverters.

[0009] Step S2: Determine the baseband virtual impedance based on the transmission line impedance difference from each parallel-operating single-phase H-bridge inverter to the load, the equivalent output impedance, and the communication carrier frequency. and high-frequency virtual impedance ;

[0010] Step S3: Sample the output current of each single-phase H-bridge inverter and extract the output current of the i-th single-phase H-bridge inverter using a digital bandpass filter. Fundamental frequency current component and communication carrier The corresponding high-frequency current component;

[0011] Step S4: Multiply the base frequency current component with the base frequency virtual impedance to form the base frequency virtual voltage drop feedback quantity, multiply the high frequency current component with the high frequency virtual impedance to form the high frequency virtual voltage drop feedback quantity, and introduce the base frequency virtual voltage drop feedback quantity and the high frequency virtual voltage drop feedback quantity into the control feedback loop of the single-phase H-bridge inverter respectively to achieve coordinated suppression of base frequency circulating current and high frequency circulating current.

[0012] As a further optimization scheme for the circulating current suppression method of parallel system based on energy-information integrated converter described in this invention, the single-phase H-bridge inverter adopts a dual closed-loop control strategy of voltage outer loop and current inner loop, and uses SPWM modulation.

[0013] As a further optimization of the circulating current suppression method for parallel systems based on an integrated energy-information converter described in this invention, the information carrier modulation adopts power data dual carrier modulation (PSDM) technology, which modulates the binary data signal into a high-frequency sine wave and superimposes it onto the power frequency reference waveform, and then transmits it through PWM modulation.

[0014] As a further optimization of the circulating current suppression method for parallel systems based on an integrated energy-information converter described in this invention, the center frequency of the digital bandpass filter in step S3 is determined according to the order parameter q. The order parameter q of the digital bandpass filter represents the normalized frequency of the current component to be extracted relative to the fundamental frequency. When q=1, the fundamental frequency current component is extracted through the digital filter; when q=k, the high-frequency current component is extracted through the digital filter. k is the ratio of the communication carrier frequency to the baseband frequency. For communication carrier frequency, This is the fundamental frequency of the AC system.

[0015] As a further optimization scheme of the circulating current suppression method for parallel systems based on an integrated energy-information converter described in this invention, both the fundamental frequency virtual impedance and the high frequency virtual impedance include resistive and inductive components; wherein, the resistive component is used to compensate for the line impedance difference between the parallel-operated single-phase H-bridge inverters, and the inductive component is used to compensate for the inductive component in the equivalent output impedance of the single-phase H-bridge inverter.

[0016] As a further optimization scheme for the circulating current suppression method of a parallel system based on an integrated energy-information converter described in this invention, high-frequency virtual impedance... With fundamental frequency virtual impedance satisfy ,and ,in This is the high-frequency virtual impedance adjustment coefficient.

[0017] As a further optimization scheme for the circulating current suppression method of a parallel system based on an integrated energy-information converter described in this invention, a high-frequency virtual impedance adjustment coefficient is used. The settings are based on the communication carrier frequency and satisfy the following:

[0018] in, This is a preset proportional coefficient. This is the ratio of the communication carrier frequency to the baseband frequency. For communication carrier frequency, This is the fundamental frequency of the AC system.

[0019] Compared with the prior art, the present invention, employing the above technical solution, has the following technical effects:

[0020] (1) The present invention sets both the base frequency virtual impedance and the high frequency virtual impedance in the inverter control feedback loop, which can suppress the base frequency circulating current caused by the inconsistency of line impedance and the high frequency circulating current caused by information carrier modulation, respectively, and realize the frequency band coordinated suppression.

[0021] (2) The present invention extracts the fundamental frequency current component and the high frequency current component by means of a digital bandpass filter, so that the virtual impedance feedback only acts on the corresponding frequency band, thereby reducing the coupling effect of the high frequency feedback branch on the fundamental frequency power control link.

[0022] (3) The present invention sets a high-frequency virtual impedance adjustment coefficient according to the communication carrier frequency, so that the high-frequency virtual impedance can adapt to the circulating current suppression requirements under different communication carrier frequencies, which is conducive to improving the reliability of energy-information integrated communication.

[0023] (4) This invention does not require an additional independent circulating current suppression device. It can be implemented using the existing sampling and control resources of a single-phase H-bridge inverter. It has the characteristics of simple structure and easy embedding into existing control systems.

[0024] (5) The present invention can reduce system circulating current, improve power sharing performance, and enhance system communication reliability and operational stability. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of a single-phase H-bridge inverter circuit;

[0026] Figure 2 This is a schematic diagram of the PSDM communication modulation method;

[0027] Figure 3 This is a block diagram of a dual closed-loop control for a single-phase inverter using PSDM technology;

[0028] Figure 4 This is the equivalent circuit diagram of a single-phase inverter;

[0029] Figure 5 This is a schematic diagram of the EIT system circulation.

[0030] Figure 6 This is a block diagram of a dual closed-loop control for a single-phase inverter that introduces virtual impedance.

[0031] Figure 7 This is the system circulation diagram without the introduction of virtual impedance;

[0032] Figure 8 It is a system circulation diagram that introduces virtual impedance. Detailed Implementation

[0033] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0034] This embodiment focuses on a single-phase AC parallel inverter system, which includes at least two single-phase H-bridge inverters operating in parallel. The main circuit of the single-phase H-bridge inverter is as follows: Figure 1 As shown, where DC side voltage to This is an H-bridge switching device, where L is the filter inductor and C is the filter capacitor. For load impedance, For the bridge arm output voltage, This is the inverter output voltage. For the filter inductor current, This is the filter capacitor current. This is the load current.

[0035] like Figure 2 As shown, the single-phase H-bridge inverter uses Power Data Dual Carrier Modulation (PSDM) technology to achieve integrated energy and information communication. Specifically, the binary data signal is first modulated into a high-frequency sinusoidal data carrier, and then superimposed with the power frequency reference waveform to form a reference signal that simultaneously contains power and information components. This reference signal is modulated by PWM or SPWM onto the inverter's switching devices, enabling the inverter to carry communication information while outputting electrical energy.

[0036] The specific steps of the parallel system circulating current suppression method based on the energy-information integrated converter are as follows:

[0037] Step 1: Establish the equivalent output model of the parallel inverter system using information carrier modulation, and determine the fundamental frequency circulating current caused by inconsistent line parameters and the high-frequency circulating current caused by information carrier modulation in the parallel inverter system. Specifically, construct the equivalent output model of a single-phase H-bridge inverter using PSDM technology based on the voltage and current dual closed-loop control loop. The voltage and current dual closed-loop control block diagram without virtual impedance is shown below. Figure 3 As shown. The transfer function of the voltage-current dual closed-loop control system is:

[0038]

[0039] in Output voltage Relative to reference voltage The transfer function, Output voltage Relative to duty cycle perturbation The transfer function, For the output voltage u o Relative to load current i o The equivalent output impedance, It is a voltage loop control function. It is the current loop control function. For the delayed process, and Let be the inductor-capacitor filtering function, and s be the Laplace operator.

[0040]

[0041]

[0042]

[0043] in, To control the sampling period, L is the value of the filter inductance and C is the value of the filter capacitor.

[0044] The output voltage can be obtained. With reference voltage and load current i o and duty cycle disturbances generated by high-frequency signal carriers The relational expression.

[0045]

[0046] like Figure 4 As shown, a single-phase H-bridge inverter using PSDM technology can be equivalently represented as a controlled voltage source connected in series with an equivalent output impedance. Its equivalent output voltage source is:

[0047]

[0048] in, This is the equivalent output voltage source for a single-phase H-bridge inverter. Because different inverters may have different reference voltages, information carrier disturbances, and equivalent output impedances, circulating currents will form within the parallel system when multiple inverters are connected in parallel. Figure 5 The diagram shows the circulating current of an AC EIT system, taking a dual-machine parallel system as an example. , It is the equivalent output voltage source of the inverter. , It is the sum of the inverter's equivalent impedance and the line impedance. It is the load impedance. , Equivalent voltage sources , The output current, For load current, The reference voltage is 0. and Approximately equal and both are denoted as At that time, the circulating current component between the two inverters can be expressed as:

[0049]

[0050] By separating the power frequency reference component and the high-frequency information carrier component in the equivalent output voltage source, the expressions for the fundamental frequency circulating current and the high-frequency circulating current can be obtained respectively:

[0051] in, For fundamental frequency circulation, It is a high-frequency circulating current; , These are the voltage reference values ​​for two single-phase H-bridge inverters, 1 and 2, respectively. , These are duty cycle disturbances caused by information carrier modulation in two single-phase H-bridge inverters; and Let be the transfer function of the base frequency voltage of inverters 1 and 2. and Let be the high-frequency voltage transfer function for inverters 1 and 2. It can be seen that inconsistencies in line impedance, inverter control parameters, and information carrier disturbances can all lead to circulating current in the parallel system.

[0052] Step 2: To suppress the aforementioned circulating current, this embodiment sets a virtual impedance in the control loop. The virtual impedance consists of resistive and inductive components, and its general form is as follows:

[0053]

[0054] in, For virtual impedance, This is the resistive component of the virtual impedance. This represents the inductive component of the virtual impedance. The resistive component is used to compensate for resistive differences in the impedance of parallel lines, while the inductive component is used to compensate for the inductive component in the equivalent output impedance of the inverter.

[0055]

[0056]

[0057] in, The active power consumed by the local load of the i-th inverter; The reactive power consumed by the local load of the i-th inverter; Let be the effective value of the output voltage of the i-th inverter; This represents the equivalent resistive component of the local load of the first inverter. Let be the equivalent inductive component of the local load of the i-th inverter.

[0058] The formula for calculating the common load consumption is as follows:

[0059]

[0060]

[0061] in, Let be the active power output by the i-th inverter to the common load; Let be the reactive power output by the i-th inverter to the common load; Let be the resistive component of the line impedance between the i-th inverter and the common coupling point; Let be the reactance component of the line impedance between the i-th inverter and the common coupling point; This represents the effective value of the voltage at the common coupling point. Let be the phase angle difference between the output voltage of the i-th inverter and the voltage at the common coupling point.

[0062] The formula for calculating the total output power of the inverter is as follows:

[0063]

[0064]

[0065] in, Let be the total active power output of the i-th inverter; Let be the total reactive power output of the i-th inverter; Let be the equivalent resistance component resulting from the combination of the equivalent output impedance of the i-th inverter and the line impedance. Let be the equivalent reactance component resulting from the combination of the equivalent output impedance of the i-th inverter and the line impedance.

[0066] Based on the transformation of the formula related to the output power of the micro-source:

[0067]

[0068] in, and These are intermediate variables constructed based on the active power, reactive power, and line impedance parameters output by the i-th inverter to the common load, and are used to subsequently solve for the power impedance corresponding to the i-th inverter. The equivalent component representing the voltage difference term weighted by the line impedance. It represents the equivalent component after the phase angle difference term is weighted by the line impedance.

[0069] Therefore, the power impedance can be obtained:

[0070]

[0071] in, The resistive component in the equivalent power impedance calculated based on the active and reactive power output of the i-th inverter. The reactance component in the equivalent power impedance calculated based on the active and reactive power output of the i-th inverter.

[0072] Therefore, the theoretical virtual impedance value can be obtained:

[0073]

[0074] in, This represents the virtual impedance resistive compensation amount that needs to be introduced for the i-th inverter. This represents the virtual impedance inductive compensation amount that needs to be introduced for the i-th inverter. The target equivalent resistance value preset for the parallel inverter system; The target equivalent reactance value preset for the parallel inverter system.

[0075] Step 3: As Figure 6 The diagram shows the introduction of a digital bandpass filter and a frequency-divided virtual impedance branch in the dual closed-loop control block diagram of a single-phase H-bridge inverter. The digital bandpass filter is used to extract current components of different frequency bands from the inverter output current, and its transfer function can be expressed as:

[0076]

[0077] in, This represents the q-th order current component obtained after passing through a digital bandpass filter. Here, h is the damping coefficient, and h is the multiple of the frequency to be extracted relative to the fundamental frequency. Let be the fundamental angular frequency, and q be the order parameter. At that time, a digital bandpass filter is used to extract the fundamental frequency current component. ;when At that time, the digital bandpass filter is used to extract the high-frequency current component corresponding to the communication carrier. ,and , For communication carrier frequency, This is the fundamental frequency of the AC system.

[0078] Step 4: In the control feedback loop, the fundamental frequency current component... With fundamental frequency virtual impedance Multiplication forms a fundamental frequency virtual voltage drop feedback quantity, which incorporates the high-frequency current component. With high-frequency virtual impedance The product of these two factors forms a high-frequency virtual voltage drop feedback quantity. The output voltage after introducing virtual impedance feedback can be expressed as:

[0079]

[0080] in, For the fundamental frequency virtual impedance, This refers to the high-frequency virtual impedance. The fundamental frequency virtual impedance primarily acts on the fundamental frequency current component, suppressing fundamental frequency circulating current caused by inconsistent line parameters; the high-frequency virtual impedance primarily acts on the high-frequency current component corresponding to the communication carrier, suppressing high-frequency communication circulating current caused by information carrier modulation. To reduce the impact of the high-frequency feedback branch on the fundamental frequency power control performance, this embodiment sets the high-frequency virtual impedance as a proportional form of the fundamental frequency virtual impedance:

[0081]

[0082] in, This is the high-frequency virtual impedance adjustment factor. This adjustment factor is set according to the communication carrier frequency and can be expressed as:

[0083]

[0084] Wherein, the parameters The adjustment coefficient is used to correspond to different frequency information carriers. The value of this coefficient should increase as the frequency of the high-frequency communication carrier increases.

[0085] Where m is a preset proportionality coefficient, and k is the ratio of the communication carrier frequency to the baseband frequency. For communication carrier frequency, This is the fundamental frequency of the AC system. In practice, m can be adjusted based on system stability margin, communication carrier amplitude, and circulating current suppression requirements.

[0086] Implementation Case:

[0087] To verify the effectiveness of the method described in this invention, a dual-inverter energy-information integrated parallel operation model was built on the MATLAB / Simulink platform. The system simulation parameters are shown in Table 1.

[0088] Table 1

[0089]

[0090] Time-domain circulating current comparison: Under the same simulation conditions, the first simulation did not introduce virtual impedance control in the control loop, and the resulting system circulating current waveform is as follows. Figure 7As shown, its circulating current amplitude is approximately 2.55A. Subsequently, after introducing fundamental frequency virtual impedance and high-frequency virtual impedance feedback into the control loop, a second simulation was performed, and the resulting system circulating current waveform is shown below. Figure 8 As shown, its circulating current amplitude is approximately 2.44A. The results indicate that after introducing virtual impedance feedback, the total circulating current amplitude of the system decreases by approximately 4.3%, demonstrating that the method proposed in this invention can suppress the circulating current in parallel systems.

[0091] Under the aforementioned simulation parameters, the active power distribution of the two parallel inverters was further compared and analyzed. Since the impedance of line 1 is less than that of line 2, without virtual impedance control, the parallel system exhibits significant power distribution unevenness. Inverter 1 outputs approximately 2.60 kW of active power, while inverter 2 outputs approximately 2.24 kW, with a power distribution error of approximately 14.9%. After introducing virtual impedance feedback into the control loop, the output active power of the two inverters becomes approximately 2.47 kW and 2.37 kW, respectively, reducing the power distribution error to approximately 4.1%. The comparison shows that after introducing virtual impedance control, the output power of the two inverters in the parallel system is much closer. This indicates that the method proposed in this invention can not only suppress circulating current to a certain extent but also effectively improve the power distribution performance of the parallel system, thereby enhancing the operational stability and coordinated control capability of the AC energy-information integrated system. The power distribution comparison results are shown in Table 2.

[0092] Table 2 Comparison of Active Power Distribution in Parallel Inverter Systems

[0093]

[0094] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for suppressing circulating current in a parallel system based on an integrated energy-information converter, characterized in that, This method is applied to parallel inverter systems consisting of at least two single-phase H-bridge inverters operating in parallel. The single-phase H-bridge inverters superimpose a modulated information carrier wave in the control loop to achieve integrated energy and information communication; it includes the following steps: Step S1: Establish the equivalent output model of the parallel inverter system using information carrier modulation, obtain the equivalent output voltage and equivalent output impedance of each single-phase H-bridge inverter, and analyze the base frequency circulating current caused by inconsistent line parameters and the high frequency circulating current caused by information carrier modulation in the parallel inverter system based on the differences between the equivalent output voltage and equivalent output impedance of different single-phase H-bridge inverters. Step S2: Determine the baseband virtual impedance based on the transmission line impedance difference from each parallel-operating single-phase H-bridge inverter to the load, the equivalent output impedance, and the communication carrier frequency. and high-frequency virtual impedance ; Step S3: Sample the output current of each single-phase H-bridge inverter and extract the output current of the i-th single-phase H-bridge inverter using a digital bandpass filter. Fundamental frequency current component and communication carrier The corresponding high-frequency current component; Step S4: Multiply the base frequency current component with the base frequency virtual impedance to form the base frequency virtual voltage drop feedback quantity, multiply the high frequency current component with the high frequency virtual impedance to form the high frequency virtual voltage drop feedback quantity, and introduce the base frequency virtual voltage drop feedback quantity and the high frequency virtual voltage drop feedback quantity into the control feedback loop of the single-phase H-bridge inverter respectively to achieve coordinated suppression of base frequency circulating current and high frequency circulating current.

2. The circulating current suppression method for a parallel system based on an integrated energy-information converter according to claim 1, characterized in that, The single-phase H-bridge inverter adopts a dual closed-loop control strategy with an outer voltage loop and an inner current loop, and uses SPWM modulation.

3. The circulating current suppression method for a parallel system based on an integrated energy-information converter according to claim 1, characterized in that, The information carrier modulation adopts the power data dual carrier modulation (PSDM) technology, which modulates the binary data signal into a high-frequency sine wave and superimposes it onto the power frequency reference waveform, and then transmits it through PWM modulation.

4. The method for suppressing circulating current in a parallel system based on an integrated energy-information converter according to claim 1, characterized in that, In step S3, the center frequency of the digital bandpass filter is determined based on the order parameter q. The order parameter q of the digital bandpass filter represents the normalized frequency of the current component to be extracted relative to the fundamental frequency. When q=1, the fundamental frequency current component is extracted through the digital filter; when q=k, the high-frequency current component is extracted through the digital filter. k is the ratio of the communication carrier frequency to the baseband frequency. For communication carrier frequency, This is the fundamental frequency of the AC system.

5. The method for suppressing circulating current in a parallel system based on an integrated energy-information converter according to claim 1, characterized in that, Both the fundamental frequency virtual impedance and the high frequency virtual impedance include resistive and inductive components. The resistive component is used to compensate for the line impedance difference between single-phase H-bridge inverters operating in parallel, while the inductive component is used to compensate for the inductive component in the equivalent output impedance of a single-phase H-bridge inverter.

6. The method for suppressing circulating current in a parallel system based on an integrated energy-information converter according to claim 5, characterized in that, High-frequency virtual impedance With fundamental frequency virtual impedance satisfy ,and ,in This is the high-frequency virtual impedance adjustment coefficient.

7. The method for suppressing circulating current in a parallel system based on an integrated energy-information converter according to claim 6, characterized in that, High-frequency virtual impedance adjustment coefficient The settings are based on the communication carrier frequency and satisfy the following: ; in, This is a preset proportional coefficient. This is the ratio of the communication carrier frequency to the baseband frequency. For communication carrier frequency, This is the fundamental frequency of the AC system.