Model-free predictive control method and system for grid-connected converter

By introducing a hybrid cascaded parallel extended state observer (CP-ESO) for model-free predictive control of grid-connected converters, the problem of dynamic performance degradation under high-frequency noise is solved, efficient noise suppression and interference suppression are achieved, and the grid current quality and system robustness are improved.

CN115425642BActive Publication Date: 2025-10-10SHANDONG UNIV
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Patent Information

Application Number
CN202210961193.1
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-08-11
Publication Date
2025-10-10
Estimated Expiration
2042-08-11

AI Technical Summary

Technical Problem

The dynamic performance of traditional grid-connected converters degrades in the presence of high-frequency measurement noise. The existing technology has insufficient noise suppression and interference suppression capabilities, which affects the control effect.

Method used

A hybrid cascaded parallel extended state observer (CP-ESO) is adopted to achieve high-frequency noise suppression and interference suppression by predicting current and voltage in the dq coordinate system and minimizing the cost function to optimize switch control.

Benefits of technology

It improves the dynamic performance of the grid-connected converter, reduces noise interference, improves the quality of grid current, reduces total harmonic distortion, and enhances the robustness of the system.

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Abstract

The application discloses a model-free predictive control method and system of a grid-connected converter, comprising: acquiring grid current and grid voltage data and converting to dq coordinate system; inputting the current in the dq coordinate system into a hybrid cascade parallel extended state observer to obtain a current prediction value and an estimated total disturbance; calculating and selecting a voltage vector based on the voltage in the dq coordinate system; performing two-step grid current prediction based on the current prediction value, the estimated total disturbance and the selected voltage vector; and obtaining an optimal voltage vector based on the two-step grid current prediction result, taking minimization of a cost function as a control target, and performing switching control of the grid-connected converter. The model-free predictive control of the grid-connected converter is realized by using a newly designed CP-ESO, and improved noise suppression is provided while maintaining high interference suppression of the power converter.
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Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of grid-connected converter control, and particularly relates to a model-free predictive control method and system for a grid-connected converter. BACKGROUND

[0002] The statements in this section merely provide background information related to the present application and do not necessarily constitute the prior art.

[0003] Model predictive control (MPC) is an optimization-based control technique. It utilizes dynamic equations to predict the evolution of future system state variables and output variables. The control objective of a grid-connected converter is formulated in terms of grid current optimization variables. At each control period, an optimization problem is solved over a prediction horizon. The final inverter control input sequence that optimizes the problem is found. Finally, only the first input of the sequence is applied to the system. One major challenge of MPC is that its dynamic performance is degraded when model uncertainties occur. Therefore, to overcome this challenge, it is necessary to use model-free predictive control.

[0004] In model-free predictive control of a grid-connected converter, a conventional extended state observer operates at a certain bandwidth. A high gain calculated at the certain bandwidth frequency is used to estimate grid current and total disturbance.

[0005] The conventional extended state observer for model-free predictive control has a high bandwidth gain, which leads to poor performance when high-frequency measurement noise exists.

[0006] The prior art uses a low-pass filter and a resonant filter to separate noise from a measurement signal, but these slow down the fast dynamic performance of the predictive control of the grid-connected converter; the prior art also uses a low-power extended state observer and a cascaded extended state observer for grid-connected converter control, but the noise filtering capability of the low-power extended state observer is very low; the cascaded extended state observer has poor disturbance rejection.

[0007] Therefore, the above scheme can suppress noise to some extent, but significantly reduces the suppression of observer disturbance. SUMMARY

[0008] To solve the above problems, the present application proposes a model-free predictive control method and system for a grid-connected converter, which introduces a new hybrid cascaded parallel extended state observer (CP-ESO) to provide improved noise suppression while maintaining high disturbance rejection of the power converter.

[0009] In some embodiments, the following technical solutions are adopted:

[0010] A model-free predictive control method for a grid-connected converter, comprising:

[0011] Obtain grid current and grid voltage data and convert them into the dq coordinate system;

[0012] The current in the dq coordinate system is input into the hybrid cascade parallel extended state observer to obtain the current current prediction value and the estimated total disturbance;

[0013] Select the voltage vector based on the voltage calculation in the dq coordinate system;

[0014] Two-step grid current forecasting based on the current forecast value, the estimated total disturbance and the selected voltage vector;

[0015] Based on the two-step grid current prediction results, the cost function is minimized as the control objective to obtain the optimal voltage vector and perform switching control of the grid-connected converter.

[0016] As a further solution, the hybrid cascade parallel extended state observer is specifically:

[0017]

[0018]

[0019]

[0020]

[0021] in, represents a pair of parallel extended state observers ESO, γ 1i and γ 2i It's ESO 0i The observer gain is is the estimated current prediction CP-ESO state variables; j∈ξ1,2,3,...,M}; y(t) represents the output, α is the constant control input gain, and M is the total number of sub-frequency levels; yes The first derivative of is the estimated current prediction The CP-ESO state variable is u(t), and u(t) is the controller input.

[0022] As a further solution, the hybrid cascade parallel extended state observer is designed based on the following four rules:

[0023] ① Better noise suppression is achieved when a minimum number of sub-frequency levels receive the measured noise signal y;

[0024] ② When only one sub-frequency level receives the measured noise signal y, the noise suppression is increased by making the number of cascaded sub-frequency levels as large as possible;

[0025] ③ As the number of parallel sub-frequency levels increases, the suppression of interference will also increase;

[0026] ④ As the total number of serially connected sub-frequency levels increases, noise suppression increases, but interference suppression decreases.

[0027] As a further solution, the voltage vector is selected based on the voltage calculation in the dq coordinate system, specifically:

[0028] Based on the voltage in the dq coordinate system, the phase-locked loop is used to calculate the grid voltage phase angle, and the grid voltage phase angle is used to select the voltage vector u dq .

[0029] As a further solution, a two-step grid current prediction is performed based on the current predicted value, the estimated total disturbance and the selected voltage vector, specifically:

[0030]

[0031] Among them, k is the sampling moment, Ts is the sampling time, γ 12 =2ω 02 , γ 13 =2ω 03 , ω 03 =ω0; M is the total number of sub-frequency levels, and ω0 represents the bandwidth of the entire ESO system; is the estimated value of the grid current at the next sampling moment (k+1), is the estimated current of the current discrete sample (k), α is the constant control input gain, and u(k) is the switch state S abc (k) induced converter voltage, i dq (k) is the measured current at the current sampling moment, is the disturbance estimated at the current ESO bandwidth.

[0032] As a further solution, the optimal voltage vector is obtained by minimizing the cost function as the control objective. The cost function is:

[0033]

[0034] in, is the estimated value of the grid current at sampling time (k+2), is the grid current reference value at sampling time (k+2).

[0035] As a further solution, the voltage of each switching state of the three-phase two-level grid-connected converter is evaluated in the cost function, and the voltage u of the minimum value of the cost function is applied. dq The corresponding switching state is used as the switching state S of the grid-connected converter abc .

[0036] In other embodiments, the following technical solutions are adopted:

[0037] A model-free predictive control system for a grid-connected converter, comprising:

[0038] The data acquisition module is used to obtain grid current and grid voltage data and convert them into the dq coordinate system;

[0039] The state observation module is used to input the current in the dq coordinate system into the hybrid cascade parallel extended state observer to obtain the current current prediction value and the estimated total disturbance;

[0040] A voltage selection module is used to select a voltage vector based on voltage calculation in a dq coordinate system;

[0041] A two-step prediction module for performing two-step grid current prediction based on the current prediction value, the estimated total disturbance and the selected voltage vector;

[0042] The grid-connected converter control module is used to obtain the optimal voltage vector based on the two-step grid current prediction results, with minimizing the cost function as the control objective, and perform switching control of the grid-connected converter.

[0043] In other embodiments, the following technical solutions are adopted:

[0044] A terminal device includes a processor and a memory, wherein the processor is used to implement various instructions; the memory is used to store multiple instructions, and the instructions are suitable for being loaded by the processor and executing the above-mentioned model-free predictive control method for a grid-connected converter.

[0045] In other embodiments, the following technical solutions are adopted:

[0046] A computer-readable storage medium stores a plurality of instructions, wherein the instructions are suitable for being loaded and executed by a processor of a terminal device for the above-mentioned model-free predictive control method for a grid-connected converter.

[0047] Compared with the prior art, the present invention has the following beneficial effects:

[0048] (1) This paper introduces a novel hybrid cascaded parallel extended state observer (CP-ESO) that addresses the problem of conventional extended state observers with high bandwidth gain, which leads to poor performance in the presence of high-frequency measurement noise, by achieving high-frequency noise suppression and maintaining a high level of interference rejection in the observer. Model-free predictive control of a grid-connected converter is implemented using the newly designed CP-ESO and provides improved noise suppression while maintaining high interference rejection in the power converter.

[0049] Other features and advantages of additional aspects of the present invention will be given in part in the following description and in part will become obvious from the following description or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 Schematic diagram of a three-phase grid-connected converter in an embodiment of the present invention;

[0051] Figure 2 Schematic diagram of a model-free predictive control method for a grid-connected converter in an embodiment of the present invention;

[0052] Figure 3 It is a generalized hybrid cascade parallel extended state observer in an embodiment of the present invention;

[0053] Figure 4 Schematic diagram of a hybrid cascaded parallel ESO with M=3 sub-frequency levels in an embodiment of the present invention;

[0054] Figure 5 Schematic diagram of different CP-ESO structures when M=4 sub-frequency levels;

[0055] Figures 6(a)-(b) are schematic diagrams comparing the noise suppression performance of the CP-ESO in this embodiment and the existing ESO observer;

[0056] Figure 7 Schematic diagram of the anti-interference performance of CP-ESO in this embodiment and the existing ESO observer. DETAILED DESCRIPTION

[0057] It should be noted that the following detailed description is illustrative and is intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used in the present invention have the same meaning as commonly understood by those skilled in the art to which the present application belongs.

[0058] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0059] Example 1

[0060] like Figure 1 As shown, the grid-connected converter schematic diagram has the following dynamic model:

[0061]

[0062] Among them, i abc Represents the grid current, e gabc Represents the grid voltage; u abc =f(S abc ) represents the output voltage of the power converter, which is the switching state S abc function of ; L represents the filter inductance and R represents the filter resistance.

[0063] Formula (1) can be transformed into:

[0064]

[0065] Among them, u abc is the converter control input, is the constant control input gain,

[0066] Because traditional extended state observers for model-free predictive control have high bandwidth gain, they can lead to poor performance in the presence of high-frequency measurement noise. Therefore, this embodiment uses a hybrid cascade-parallel extended state observer (CP-ESO) to estimate the total interference components at different frequencies within the bandwidth and sum all of these components to obtain the total interference quantity F. The hybrid cascade-parallel extended state observer is composed of multiple observers arranged in parallel, each tuned to a different sub-frequency smaller than the system bandwidth. The interference rejection capability of the observer (CP-ESO) is significantly improved, and secondly, the noise suppression is better than that of the traditional high-gain extended state observer ESO.

[0067] In one or more embodiments, a model-free predictive control method for a grid-connected converter is disclosed, combining Figure 2 , specifically including the following process:

[0068] (1) Obtaining the grid current i abc and grid voltage e g,abcData is converted to the dq coordinate system to obtain the current in the dq coordinate system and voltage e dq .

[0069] (2) Input the current in the dq coordinate system into the hybrid cascade parallel extended state observer to obtain the current current prediction value and the estimated total disturbance

[0070] In this embodiment, combined with Figure 3 , the hybrid cascade-parallel extended state observer (CP-ESO) is modeled in the time domain as:

[0071]

[0072] in, represents a pair of parallel Extended State Observer (ESO) levels, γ 1i and γ 2i It's ESO 0i The observer gain of the sub-frequency is ESO 0i , ω0 = the entire ESO system bandwidth.

[0073] The observer gains are chosen via the gain parameterization to ensure that the two observer poles are located at s = ω0. Therefore, γ 1i =2ω 0i , ω 01 <ω 02 <...<ω 0M =ω0.

[0074] System Status and observer state Related

[0075]

[0076] It should be noted that the number of ESO stages in parallel can be 2 or more. In this patent, 2 parallel ESO stages are shown for clarity of the present invention. situation.

[0077] In this embodiment, combined with Figure 4 , assuming the total number of sub-frequency levels is M = 3, the time domain dynamics is:

[0078]

[0079] The discrete form of equation (4) implemented on a microcontroller is:

[0080]

[0081] where k is the sampling instant, T s is the sampling time γ 11 = 2ω 01 , γ 12 = 2ω 02 , γ 13 = 2ω 03 , ω 03 = ω0; z j : j e {1,2,3} is the estimated current CP-ESO state variable.

[0082] In this embodiment, CP-ESO is a novel ESO structure with two main advantages:

[0083] 1) It has very good measurement noise rejection;

[0084] 2) It has better disturbance rejection than conventional ESO. These two qualities make it superior to the prior art.

[0085] CP-ESO can be designed in different structures depending on the preferred control characteristics.

[0086] The features of the chosen structure of the observer are guided by the following four rules:

[0087] ① Better noise rejection is achieved when the minimum number of sub-frequency stages (preferably one stage) receives the measured noise signal y;

[0088] ② When only one stage receives the measured noise signal y, increase the noise rejection by having as many series sub-frequency stages as possible. Noise rejection increases with the total number of series stages.

[0089] ③ As the number of parallel sub-frequency stages increases, so does the rejection of disturbances.

[0090] ④ As the total number of series sub-frequency stages increases, noise rejection increases, but disturbance rejection decreases.

[0091] Based on the above rules, the following applies to CP-ESO with 4 sub-frequency stages, as shown in (a)-(b) in Figure 5

[0092] i) Figure 5 (a) and (d) in (a) and (d) have the best measurement noise rejection / disturbance rejection characteristics because they only receive one stage of the measured noise signal y.

[0093] ​ii) In all 4 structures, Figure 5 (d) will have the best noise rejection / noise immunity because it has 3 sub-frequency stages in series, unlike all other structures which have only 2 sub-frequency stages in series. However, Figure 5 (d) in (i) will also have the weakest disturbance rejection.

[0094] iii) Figure 5 (a) and (b) in (iii) will yield the best noise immunity because they have the largest number of sub-frequency stages in parallel. Nonetheless, Figure 5 (a) in (iii) will have better noise rejection than (b) because it has only one level to receive the measured noise signal y.

[0095] iv) Figure 5 (a) in (iv) will have the best combination of noise rejection and disturbance rejection capabilities.

[0096] Based on the above rules, the skilled person can choose the CP-ESO structure that best suits the system control objectives as needed.

[0097] (3) Based on the voltage in the dq coordinate system, the grid voltage phase angle is calculated using a phase-locked loop, and the grid voltage phase angle is applied to select the voltage vector u dq .

[0098] (4) Based on the current prediction value, the estimated total disturbance, and the selected voltage vector, a two-step grid current prediction is performed;

[0099] In this embodiment, the method of two-step prediction is as follows:

[0100]

[0101] where k is the sampling time, Ts is the sampling time, γ 12 = 2ω 02 , γ 13 = 2ω 03 , ω 03 = ω0; ω0 represents the entire ESO system bandwidth, is the grid current prediction estimate at the next sampling (k+1) time, is the estimated current of the current discrete sample (k), α = 1 / L, u(k) is the converter voltage caused by the switching state S abc (k) in Table 1, dq (k) is the measured current at the current sampling time, is the disturbance estimated at the current ESO bandwidth.

[0102] (5) Based on the two-step grid current prediction results, the cost function is minimized as the control objective to obtain the optimal voltage vector and perform switching control of the grid-connected converter.

[0103] In this embodiment, the control goal is to track the reference by minimizing the cost function J The minimization cost function is:

[0104]

[0105] in, and k p , k i is the PI controller gain for regulating the DC bus voltage Vdc, i.e. the DC bus voltage, is the DC bus voltage reference.

[0106] For the values ​​of n={0, 1, ..., 7} in Table 1, each switching state voltage u dq The cost function is evaluated. Among these 8 choices, the voltage u with the minimum value of J is used. dq As the switching state S of the grid-connected converter abc .

[0107] Table 1: Switching states of three-phase two-level grid-connected converter

[0108]

[0109]

[0110] Figures 6(a)-(b) respectively show the results of adding white noise to the measurement output before feedback to the ESO; Figure 6(a) shows the noise suppression performance of the CP-ESO observer in this embodiment, and Figure 6(b) shows the noise suppression performance of the existing ESO observer; in Figures 6(a) and 6(b), the upper figure shows the phase A grid current, and the lower figure shows the spectrum of the phase A grid current.

[0111] It can be seen that the method of this embodiment can filter noise better than the standard ESO. The traditional standard ESO causes a total harmonic distortion (THD) of 4.1110%, while the new invention reduces the THD to 2.7628%.

[0112] Figure 7 Schematic diagram showing the disturbance rejection performance of CP-ESO and existing ESO observers; Figure 7In the figure, the upper plot shows the d-axis grid current, and the lower plot shows the phase A grid current. It can be seen that the DC bus capacitor voltage reference is increased from 140V to 190V, resulting in a corresponding increase in grid current. Compared to the cascaded ESO, the proposed method produces smaller grid current overshoot and ripple, and is more robust.

[0113] Example 2

[0114] In one or more embodiments, a model-free predictive control system for a grid-connected converter is disclosed, comprising:

[0115] The data acquisition module is used to obtain grid current and grid voltage data and convert them into the dq coordinate system;

[0116] The state observation module is used to input the current in the dq coordinate system into the hybrid cascade parallel extended state observer to obtain the current current prediction value and the estimated total disturbance;

[0117] A voltage selection module is used to select a voltage vector based on voltage calculation in a dq coordinate system;

[0118] A two-step prediction module for performing two-step grid current prediction based on the current prediction value, the estimated total disturbance and the selected voltage vector;

[0119] The grid-connected converter control module is used to obtain the optimal voltage vector based on the two-step grid current prediction results, with minimizing the cost function as the control objective, and perform switching control of the grid-connected converter.

[0120] It should be noted that the specific implementation of each of the above modules has been described in Example 1 and will not be described in detail here.

[0121] Example 3

[0122] In one or more embodiments, a terminal device is disclosed, including a server. The server includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the model-free predictive control method for a grid-connected converter according to Example 1 is implemented. For the sake of brevity, this description is omitted here.

[0123] It should be understood that in this embodiment, the processor may be a central processing unit (CPU), or may be other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), off-the-shelf field-programmable gate arrays (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or any conventional processor, etc.

[0124] The memory may include a read-only memory and a random access memory, and provides instructions and data to the processor. A portion of the memory may also include a non-volatile random access memory. For example, the memory may also store information about the device type.

[0125] During implementation, each step of the above method may be completed by an integrated logic circuit of hardware in a processor or by instructions in the form of software.

[0126] Example 4

[0127] In one or more embodiments, a computer-readable storage medium is disclosed, in which a plurality of instructions are stored. The instructions are suitable for being loaded and executed by a processor of a terminal device to implement the model-free predictive control method for a grid-connected converter described in the first embodiment.

[0128] Although the above describes the specific embodiments of the present invention in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without any creative work are still within the scope of protection of the present invention.

Claims

1. A model-free predictive control method for a grid-connected converter, characterized in that: include: Obtain grid current and grid voltage data and convert them into the dq coordinate system; The current in the dq coordinate system is input into the hybrid cascade parallel extended state observer to obtain the current current prediction value and the estimated total disturbance; the hybrid cascade parallel extended state observer is specifically: in, represents a pair of parallel extended state observers ESO, ; and yes The observer gain is is the estimated current prediction CP-ESO state variables; ; y(t) represents the output, is the constant control input gain, M is the total number of sub-frequency levels; yes The first derivative of is the estimated current prediction CP-ESO state variables, is the controller input; Select the voltage vector based on the voltage calculation in the dq coordinate system; Two-step grid current forecasting based on the current forecast value, the estimated total disturbance and the selected voltage vector; Based on the two-step grid current prediction results, the cost function is minimized as the control objective to obtain the optimal voltage vector and perform switching control of the grid-connected converter.

2. The model-free predictive control method for a grid-connected converter according to claim 1, wherein: The hybrid cascade parallel extended state observer is designed based on the following four rules: Better noise suppression is achieved when a minimum number of sub-frequency levels receive the measured noise signal y; When only one sub-frequency stage receives the measured noise signal y, noise suppression is increased by making the number of cascaded sub-frequency stages as large as possible; As the number of parallel sub-frequency levels increases, the suppression of interference increases; As the total number of serially connected sub-frequency stages increases, noise rejection increases but interference rejection decreases.

3. The model-free predictive control method for a grid-connected converter according to claim 1, wherein: The voltage vector is selected based on the voltage calculation in the dq coordinate system, specifically: Based on the current in the dq coordinate system, the grid voltage phase angle is calculated using a phase-locked loop, and the grid voltage phase angle is used to select the voltage vector .

4. The model-free predictive control method for a grid-connected converter according to claim 1, wherein: Based on the current prediction value, the estimated total disturbance and the selected voltage vector, a two-step grid current prediction is performed as follows: in, The entire ESO system bandwidth; is the estimated value of the grid current at the next sampling time (k+1), is the estimated current of the current discrete sample (k), is a constant control input gain, u(k) is the switching state S abc (k) induced converter voltage, is the measured current at the current sampling moment, is the disturbance estimated at the current ESO bandwidth.

5. The model-free predictive control method for a grid-connected converter according to claim 1, wherein: The optimal voltage vector is obtained by minimizing the cost function as the control objective. The cost function is: in, is the estimated value of the grid current at sampling time (k+2), is the grid current reference value at sampling time (k+2).

6. The model-free predictive control method for a grid-connected converter according to claim 5, wherein: The voltage of each switching state of the three-phase two-level grid-connected converter is evaluated in the cost function, and the voltage of the minimum value of the cost function is applied. The corresponding switching state is used as the switching state S of the grid-connected converter abc .

7. A model-free predictive control system for a grid-connected converter, characterized in that: include: The data acquisition module is used to obtain grid current and grid voltage data and convert them into the dq coordinate system; The state observation module is used to input the current in the dq coordinate system into the hybrid cascade parallel extended state observer to obtain the current current prediction value and the estimated total disturbance; the hybrid cascade parallel extended state observer is specifically: in, represents a pair of parallel extended state observers ESO, ; and yes The observer gain is is the estimated current prediction CP-ESO state variables; ; y(t) represents the output, is the constant control input gain, M is the total number of sub-frequency levels; yes The first derivative of is the estimated current prediction CP-ESO state variables, is the controller input; A voltage selection module is used to select a voltage vector based on voltage calculation in a dq coordinate system; A two-step prediction module for performing two-step grid current prediction based on the current prediction value, the estimated total disturbance and the selected voltage vector; The grid-connected converter control module is used to obtain the optimal voltage vector based on the two-step grid current prediction results, with minimizing the cost function as the control objective, and perform switching control of the grid-connected converter.

8. A terminal device comprising a processor and a memory, wherein the processor is used to implement various instructions; the memory is used to store multiple instructions, characterized in that: The instructions are suitable for being loaded by a processor and executing the model-free predictive control method for a grid-connected converter according to any one of claims 1 to 6.

9. A computer-readable storage medium storing a plurality of instructions, characterized in that: The instructions are suitable for being loaded by a processor of a terminal device and executing the model-free predictive control method for a grid-connected converter according to any one of claims 1 to 6.

Citation Information

Patent Citations

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    CN108762096A

  • Device and method for predictive control of grid-connected inverter without alternating-current voltage sensor

    CN114665512A