MMC impedance modeling method for DC measurement device transmission characteristics

Abstract

The present application relates to a method for modeling the transfer characteristics of a DC measurement device using MMC impedance. The method comprises: constructing a differential and common-mode time-domain small-signal model of the MMC main circuit based on Kirchhoff's voltage law; deriving a coupling law based on the frequency coupling characteristics and phase sequence coupling mechanism of the differential and common-mode time-domain small-signal model; converting the differential and common-mode time-domain small-signal model into an HSS-MMC main circuit model based on the coupling law; establishing various control HSS models based on the MMC control loop structure; deriving a transfer function model of the DC voltage measurement device to update the DC voltage control HSS model; combining the various control HSS models with a modulation wave expression to obtain an MMC control system HSS model; jointly combining the HSS-MMC main circuit model and the MMC control system HSS model to obtain a MIMO admittance model; obtaining a SISO equivalent impedance model of the MMC based on the grid impedance expression and the MIMO admittance model; and solving an impedance analytical value using the MMC SISO impedance model based on MMC system parameters and control gains for different frequency disturbances. The method accurately describes the high-frequency impedance characteristics of the MMC.

Description

Technical Field

[0001] The present application relates to the technical field of high-voltage direct current transmission, and in particular to a method for modeling the MMC impedance of a DC measurement device with respect to transmission characteristics. Background Art

[0002] Modular multilevel converters (MMCs), with their modularity, high output quality, and high redundancy, have become a research hotspot in the field of high-voltage direct current (HVDC) transmission. They are widely used in large-capacity, long-distance power transmission systems. Compared with two-level and three-level converters, MMCs have more complex internal dynamic characteristics, which poses more stability issues for HVDC transmission projects.

[0003] Eigenvalue analysis and impedance analysis are two typical methods for MMC stability analysis. However, eigenvalue analysis has three limitations: first, it is highly model-dependent, limiting its applicability due to system complexity; second, its high-frequency analysis capabilities are limited; and third, the converter control parameters in actual systems are difficult to obtain, making it equivalent to a "black / gray box" model, making it difficult to establish its state-space equations. In comparison, impedance analysis is applicable to complex power system scenarios and has the advantage of being able to be measured on-site (black box modeling), and has therefore been widely studied in recent years.

[0004] Impedance modeling, the foundation of impedance analysis, is commonly employed using methods such as multiharmonic linearization and the harmonic state space (HSS) method. The HSS method, which utilizes the matrix form of the state space expression, offers numerous advantages, including simplicity, intuitiveness, and ease of computer programming. Existing studies, when modeling the impedance of multi-layered circuits (MMCs), primarily consider the impact of various control elements (such as the phase-locked loop, inner current loop, and circulating current suppression loop) and control link delays on impedance characteristics. However, the dynamic transmission characteristics of the DC voltage measurement device are generally not incorporated into the modeling framework. When an MMC utilizes a DC voltage outer loop, the transmission characteristics of the measurement device are indirectly introduced into the modulation wave generation process through the voltage control element, resulting in unintended resonance of the system port impedance at high frequencies and even harmonic oscillation. Summary of the Invention

[0005] Based on this, it is necessary to provide a DC measurement device transmission characteristic MMC impedance modeling method based on the above technical problems, which can accurately analyze the system stability problem in the high frequency band.

[0006] The present invention provides a method for modeling the MMC impedance of a DC measurement device transmission characteristic, the method comprising:

[0007] Based on Kirchhoff's voltage law, a differential and common mode time domain small signal model of the MMC main circuit is constructed;

[0008] According to the frequency coupling characteristics and phase sequence coupling mechanism in the differential common mode time domain small signal model, the frequency coupling law and phase sequence coupling law are derived;

[0009] According to the frequency coupling law and the phase sequence coupling law, the differential common mode time domain small signal model is converted into an HSS-MMC main circuit model;

[0010] According to the MMC control loop structure, establish the phase-locked loop control HSS model, AC current control HSS model, DC voltage control HSS model, and circulating current control HSS model;

[0011] deriving a transfer function model of the DC voltage measuring device, and updating the DC voltage control HSS model using the transfer function model to obtain an updated DC voltage control HSS model;

[0012] Combining the phase-locked loop control HSS model, the AC current control HSS model, the updated DC voltage control HSS model, the circulating current control HSS model and the modulation wave expression, the MMC control system HSS model is obtained;

[0013] The HSS-MMC main circuit model and the MMC control system HSS model are combined to obtain a MIMO admittance model;

[0014] According to the grid impedance expression and the MIMO admittance model, the SISO equivalent impedance model of the MMC is obtained;

[0015] According to the MMC system parameters and the control gains of disturbances at different frequencies, the impedance analytical value is solved using the SISO impedance model of the MMC.

[0016] In one embodiment, constructing a differential common mode time domain small signal model of the MMC main circuit based on Kirchhoff's voltage law includes:

[0017] Based on Kirchhoff's voltage law, the MMC three-phase time domain model is established:

[0018] ;(1)

[0019] ;(2)

[0020] ;(3)

[0021] in, , 、 、 express 、 、 Three-phase, represents the bridge arm resistance, represents the bridge arm inductance, represents the transformer inductance, express Phase upper arm current, express Phase lower arm current, express Phase AC current, express x The current of the bridge arm submodule on the phase, express The current of the lower bridge arm submodule, is the DC side voltage, express The sum of the capacitor voltages of the bridge arm submodules on each phase, express The sum of the capacitor voltages of the bridge arm submodules under the phase, express Phase common coupling point voltage, Indicates DC neutral point To AC neutral point The zero sequence voltage between express Phase upper bridge arm submodule capacitor voltage, express Phase lower bridge arm submodule capacitor voltage, is the submodule capacitance;

[0022] Where:

[0023] ;(4)

[0024] ;(5)

[0025] ;(6)

[0026] ;(7)

[0027] in, for The modulation wave of the upper bridge arm, for The modulation wave of the lower bridge arm, is the DC current, express The sum of the capacitor voltages of the bridge arm submodules on each phase, express The sum of the capacitor voltages of the bridge arm submodules under the phase, express The sum of the capacitor voltages of the bridge arm submodules on each phase, express The sum of the capacitor voltages of the bridge arm submodules under the phase, express The sum of the capacitor voltages of the bridge arm submodules on each phase, express The sum of the capacitor voltages of the bridge arm submodules under the phase, Indicates the number of bridge arm submodules;

[0028] Define the differential mode component and common mode component of any variable in the MMC three-phase time domain model:

[0029] ;

[0030] in, is any variable in formulas (1)-(7), represents the differential mode component, represents the common mode component, is any variable of the upper bridge arm of phase x, is any component of the lower bridge arm of phase x;

[0031] The differential and common mode time domain expressions are obtained according to the differential mode component and the common mode component:

[0032] ;

[0033] ;

[0034] ;

[0035] ;

[0036] in, express The common-mode component of the sum of the phase submodule capacitor voltages, express The differential mode component of the sum of the phase submodule capacitor voltages, express Phase circulating current common mode component, express The common mode component of the phase submodule capacitor voltage, express The differential mode component of the phase submodule capacitor voltage, express The common mode component of the phase modulated wave, express The differential mode component of the phase modulated wave;

[0037] Where:

[0038] ;

[0039] ;

[0040] ;

[0041] ;

[0042] in, for The differential mode component of the phase bridge arm current, express The differential mode component of the sum of the phase submodule capacitor voltages, express The differential mode component of the sum of the phase submodule capacitor voltages, express The differential mode component of the sum of the phase submodule capacitor voltages;

[0043] According to the operating characteristics of MMC, the single-phase equivalent model of MMC in differential and common mode is obtained:

[0044] ;

[0045] ;

[0046] ;

[0047] ;

[0048] in, represents the common mode component of the sum of the submodule capacitor voltages, Represents the differential mode component of the sum of the submodule capacitor voltages, represents the common mode component of the circulating current, represents the voltage at the point of common coupling, represents the common mode component of the submodule capacitor voltage, represents the differential mode component of the submodule capacitor voltage, represents the common mode component of the modulated wave, represents the differential mode component of the modulated wave, Indicates positive and negative sequence AC current;

[0049] Where:

[0050] ;

[0051] ;

[0052] ;

[0053] in, Indicates zero-sequence circulating current;

[0054] The differential and common mode time domain expressions and the MMC single-phase equivalent model are linearized using the perturbation linearization method to construct the differential and common mode time domain small signal model of the MMC main circuit:

[0055] ;

[0056] ;

[0057] ;

[0058] ;

[0059] in, Indicates the small signal disturbance of DC side voltage, It represents the small signal disturbance of the common mode component of the sum of the submodule capacitor voltage, represents the small signal disturbance of the circulating current common mode component, represents the small signal disturbance of the common coupling point voltage, It represents the small signal disturbance of the differential mode component of the sum of the submodule capacitor voltage, Indicates the positive and negative sequence AC current small signal disturbance, Represents the small signal disturbance of the common mode component of the submodule capacitor voltage, represents the small signal disturbance of the common-mode modulation wave, Indicates the small signal disturbance of the differential mode modulation wave, Represents the small signal disturbance of the differential mode component of the submodule capacitor voltage;

[0060] Where:

[0061] ;

[0062] ;

[0063] ;

[0064] in, is the DC current small signal disturbance, Indicates the small signal disturbance of zero-sequence circulating current.

[0065] In one embodiment, converting the differential common mode time domain small signal model into an HSS-MMC main circuit model according to the frequency coupling law and the phase sequence coupling law includes:

[0066] Based on the HSS theory, the differential common mode time domain small signal model is converted into an HSS model:

[0067] ;

[0068] ;

[0069] ;

[0070] ;

[0071] in, is the Toeplitz matrix formed by the steady-state value of the common-mode component of the modulation wave, is the Toeplitz matrix formed by the steady-state value of the differential mode component of the modulated wave, is the Toeplitz matrix of the steady-state value of the circulation, is the Toeplitz matrix composed of the steady-state values ​​of the positive and negative sequence components of the AC side output current;

[0072] Where:

[0073] ;

[0074] ;

[0075] ;

[0076] ;

[0077] in, is the Toeplitz matrix formed by the steady-state value of the common-mode component of the submodule capacitor voltage, is the Toeplitz matrix formed by the steady-state value of the differential mode component of the submodule capacitor voltage, is the imaginary number symbol;

[0078] Where:

[0079] ;

[0080] in, is the angular frequency of the disturbance signal, is the fundamental angular frequency;

[0081] According to the phase sequence coupling law, the phase sequence selection matrix is ​​obtained:

[0082] ;

[0083] in, Denotes a diagonal matrix, the superscript Indicates the positive sequence disturbance injected from the AC side, subscript 、 、 Respectively represent the extraction of negative sequence, zero sequence, and positive sequence currents, To extract the matrix of the negative sequence response component after the MMC injects the positive sequence disturbance from the AC side, To extract the matrix of the zero-sequence response component after the MMC injects positive-sequence disturbance from the AC side, It is the matrix for extracting the positive sequence response component after the MMC injects positive sequence disturbance from the AC side;

[0084] According to the phase sequence selection matrix, the zero-sequence circulating current and AC current expressions in the HSS model are obtained:

[0085] ;

[0086] ;

[0087] in, To extract the matrix of positive and negative sequence response components after the MMC injects positive sequence disturbance from the AC side, HSS vector representing the AC current disturbance;

[0088] Substituting the zero-sequence circulating current and AC current expressions into the HSS model, the HSS-MMC main circuit model is obtained:

[0089] ;

[0090] Where, and The variables are defined as follows:

[0091] ;

[0092] ;

[0093] in, is the voltage disturbance vector, is the current disturbance vector, is the modulation wave disturbance vector, for The coefficient matrix of for The coefficient matrix of for Inverse matrix.

[0094] In one embodiment, establishing a phase-locked loop control HSS model, an AC current control HSS model, a DC voltage control HSS model, and a circulating current control HSS model according to the MMC control loop structure includes:

[0095] According to the MMC phase-locked loop structure, the phase-locked loop control HSS model is established:

[0096] ;

[0097] in, is the HSS vector of phase angle perturbation, is a diagonal matrix whose matrix elements are composed of the gains of the phase-locked loop PI controller at different disturbance frequencies. is the steady-state voltage of the grid The amplitude of the fundamental frequency component, is the HSS model of PLL;

[0098] Where: ;

[0099] Among them, the frequency reduction matrix and upscaling matrix They are:

[0100] ;

[0101] According to the MMC AC current control structure, the AC current control HSS model is established:

[0102] ;

[0103] Where:

[0104] ;

[0105] ;

[0106] ;

[0107] ;

[0108] in, is the fundamental modulation voltage The HSS vector of the phase disturbance, For AC current HSS signal of the axis reference signal disturbance, For AC current HSS signal of the axis reference signal disturbance, is the equivalent inductance, 、 They are middle 、 The Toeplitz matrix of the axis steady-state signal, 、 for middle 、 The Toeplitz matrix of the axis steady-state signal, for The Toeplitz matrix of the steady-state signal of phase A, is the Park inverse transformation matrix, is the current after Park inverse transformation, is the voltage at the point of common coupling after Park inverse transformation, is the modulated wave after Park inverse transform, is the HSS gain matrix formed by the delay link transfer function, is the HSS gain matrix formed by the AC current PI controller transfer function, is the rated voltage of the submodule capacitor;

[0109] According to the MMC DC voltage control structure, the DC voltage control HSS model is established:

[0110] ;

[0111] in, is the HSS gain matrix formed by the DC voltage PI controller transfer function, is the HSS vector of the DC voltage reference signal disturbance, is the HSS signal disturbed by the AC current d-axis reference signal;

[0112] According to the MMC circulation control structure, the circulation control HSS model is established:

[0113] ;

[0114] in, is the HSS vector of the double frequency modulated voltage disturbance, is the HSS gain matrix formed by the circulating PR controller transfer function, HSS vector of circulating current reference signal perturbation.

[0115] In one embodiment, deriving a transfer function model of the DC voltage measurement device and updating the DC voltage control HSS model using the transfer function model to obtain an updated DC voltage control HSS model includes:

[0116] According to the DC voltage measurement device, the transfer function of the DC voltage divider body, the transfer function of the DC voltage divider secondary voltage divider plate, and the transfer function of the electronic isolation device are obtained:

[0117] ;

[0118] ;

[0119] ;

[0120] in, 、 are the equivalent capacitance and equivalent resistance of the high voltage bridge arm of the DC voltage divider body, 、 are the equivalent capacitance and equivalent resistance of the low-voltage bridge arm of the DC voltage divider body, 、 are the equivalent capacitance and equivalent resistance of the high voltage bridge arm of the secondary voltage divider plate of the DC voltage divider, is the equivalent resistance of the low-voltage bridge arm of the secondary voltage divider of the DC voltage divider, s is the Laplace variable, is the damping coefficient, is the cutoff frequency;

[0121] According to the transfer function of the DC voltage divider body, the transfer function of the DC voltage divider secondary voltage divider plate, and the transfer function of the electronic isolation device, a transfer function model of the DC voltage measuring device is obtained:

[0122] ;

[0123] in, ,in, is the calibrated volume transformation ratio of the DC voltage divider, is the standard transformation ratio of the secondary voltage divider;

[0124] The DC voltage measurement device transfer function model is embedded into the DC voltage control HSS model to obtain an updated DC voltage control HSS model:

[0125] .

[0126] In one embodiment, the HSS model of the MMC control system is obtained by combining the phase-locked loop control HSS model, the AC current control HSS model, the updated DC voltage control HSS model, the circulating current control HSS model and the modulation wave expression, including:

[0127] Establish the upper bridge arm modulation wave expression and the lower bridge arm modulation wave expression:

[0128] ;

[0129] ;

[0130] in, is the upper arm modulation wave, is the lower arm modulation wave, is the upper arm modulation voltage, is the lower arm modulation voltage, is the fundamental modulation voltage, is the double frequency modulation voltage;

[0131] According to the upper bridge arm modulation wave expression and the lower bridge arm modulation wave expression, the differential mode modulation wave expression and the common mode modulation wave expression are obtained:

[0132] ;

[0133] ;

[0134] in, is a differential mode modulated wave, is a common mode modulated wave;

[0135] According to the differential-mode modulation wave expression, common-mode modulation wave expression and the phase-locked loop control HSS model, AC current control HSS model, updated DC voltage control HSS model, and circulating current control HSS model, the differential-mode modulation wave small-signal disturbance expression and the common-mode modulation wave small-signal disturbance expression are obtained:

[0136] ;

[0137] ;

[0138] According to the differential mode modulation wave small signal disturbance expression and the common mode modulation wave small signal disturbance expression, the HSS model of the MMC control system is obtained:

[0139] ;

[0140] in, and Represent the control matrices of current and voltage respectively;

[0141] Where:

[0142] ;

[0143] ;

[0144] ;

[0145] .

[0146] In one embodiment, the HSS-MMC main circuit model and the MMC control system HSS model are combined to obtain a MIMO admittance model, including:

[0147] Combining the HSS-MMC main circuit model and the MMC control system HSS model, a complete HSS-MMC model under closed-loop operation is obtained:

[0148] ;

[0149] in, Indicates that the MMC contains the admittance matrix of all frequencies;

[0150] According to the frequency coupling law, the MIMO admittance model is obtained:

[0151] ;

[0152] Where:

[0153] .

[0154] In one embodiment, the MIMO admittance model The detailed expression is:

[0155] ;

[0156] in, , , superscript Indicates MMC, Indicates that the frequency injected into the voltage is The frequency generated by the zero-sequence disturbance is Zero-sequence current disturbance; Indicates that the frequency injected into the voltage is The frequency generated after the negative sequence disturbance is Zero-sequence current disturbance; Indicates that the frequency injected into the voltage is The frequency generated after the positive sequence disturbance is Zero-sequence current disturbance; Indicates that the frequency injected into the voltage is The frequency generated after the zero-sequence disturbance is Negative sequence current disturbance; Indicates that the frequency injected into the voltage is The frequency generated after the negative sequence disturbance is Negative sequence current disturbance; Indicates that the frequency injected into the voltage is The frequency generated after the positive sequence disturbance is Negative sequence current disturbance; Indicates that the frequency injected into the voltage is The frequency generated after the zero-sequence disturbance is Positive sequence current disturbance; Indicates that the frequency injected into the voltage is The frequency generated after the negative sequence disturbance is Positive sequence current disturbance; Indicates that the frequency injected into the voltage is The frequency generated after the positive sequence disturbance is Positive sequence current disturbance.

[0157] In one embodiment, obtaining the SISO equivalent impedance model of the MMC according to the grid impedance expression and the MIMO admittance model includes:

[0158] Building grid impedance The detailed expression of:

[0159] ;

[0160] Among them, the superscript Indicates the power grid, subscript 、 and Represent zero sequence, negative sequence and positive sequence respectively, Indicates the zero-sequence impedance of the DC side of the power grid, Indicates the AC negative sequence impedance of the power grid. Indicates the AC positive sequence impedance of the power grid;

[0161] According to the grid impedance expression and the MIMO admittance model, the SISO equivalent admittance model of the MMC and the SISO equivalent impedance model of the grid are obtained by identifying the dominant frequency coupling path:

[0162] ;

[0163] ;

[0164] Where, and are the SISO equivalent admittance of MMC and the SISO equivalent impedance of the power grid respectively;

[0165] According to the SISO equivalent admittance model of the MMC and the SISO equivalent impedance model of the power grid, the SISO equivalent impedance model of the MMC is obtained:

[0166] .

[0167] In one embodiment, the method of solving the impedance analytical value based on the MMC system parameters and the different frequency disturbance control gains using the SISO impedance model of the MMC includes:

[0168] Bring the MMC system parameters and the control gains of different frequency disturbances into the MIMO admittance model to solve the admittance value;

[0169] The admittance value is substituted into the SISO equivalent impedance model of the MMC to obtain the impedance analytical value.

[0170] The above-mentioned MMC impedance modeling method of the DC measurement device transfer characteristics fully considers the influence of the MMC phase-locked loop, AC current control, DC voltage control and circulating current control structure, and incorporates the DC voltage measurement device into the modeling framework through the DC voltage measurement device transfer function model, which can accurately describe the impedance characteristics of the MMC in the high frequency band and achieve a more complete characterization of the MMC impedance characteristics.

[0171] The details of one or more embodiments of the present application are set forth in the following drawings and description to make other features, objects, and advantages of the present application more readily apparent. BRIEF DESCRIPTION OF THE DRAWINGS

[0172] The drawings described herein are used to provide a further understanding of the present application and constitute a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0173] Figure 1 A schematic diagram of the topological structure of an MMC main circuit provided in an embodiment of the present application;

[0174] Figure 2 This is a flow chart of a method for modeling the MMC impedance of a DC measurement device transmission characteristics provided in an embodiment of the present application;

[0175] Figure 3 This is a flow chart of a method for constructing a differential common mode time domain small signal model of an MMC main circuit provided in an embodiment of the present application;

[0176] Figure 4 This is a flow chart of a method for constructing an HSS-MMC main circuit model provided in an embodiment of the present application;

[0177] Figure 5 This is a schematic diagram of an MMC control loop structure provided in an embodiment of the present application;

[0178] Figure 6 This is a flowchart of a method for constructing an MMC phase-locked loop control HSS model, an MMC AC current control HSS model, an MMC DC voltage control HSS model, and an MMC circulating current control HSS model provided in an embodiment of the present application;

[0179] Figure 7 Schematic diagram of the structure of the DC voltage measuring device provided in the embodiment of the present application;

[0180] Figure 8 This is a flow chart of a method for constructing an updated DC voltage control HSS model provided in an embodiment of the present application;

[0181] Figure 9This is a flow chart of a method for constructing an HSS model of an MMC control system provided in an embodiment of the present application;

[0182] Figure 10 This is a flow chart of a method for constructing a MIMO admittance model provided in an embodiment of the present application;

[0183] Figure 11 This is a flow chart of a method for constructing a SISO equivalent impedance model of an MMC provided in an embodiment of the present application;

[0184] Figure 12 Flowchart of a method for solving an impedance value using the SISO impedance model of the MMC provided in an embodiment of the present application;

[0185] Figure 13 1. This is a schematic diagram showing the comparison between the SISO impedance analytical value and the simulated frequency sweep value of the MMC AC side positive sequence provided in an embodiment of the present application;

[0186] Figure 14 : is a SISO impedance Bode diagram of the positive sequence on the AC side of the MMC grid-connected system provided in an embodiment of the present application;

[0187] Figure 15 Schematic diagram of the simulation results of the MMC grid-connected system provided in the embodiment of the present application;

[0188] Figure 16 This is a schematic diagram of the corresponding harmonic analysis results when the simulation experiment of the MMC grid-connected system provided in the embodiment of the present application adopts a DC voltage control strategy that takes into account the DC voltage measurement link.

[0189] Figure 7 Among them, 1. DC voltage divider body; 2. DC voltage divider secondary voltage divider board. DETAILED DESCRIPTION

[0190] In order to make the purpose, technical solutions and advantages of this application more clearly understood, the present application is described and illustrated below in conjunction with the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely used to explain this application and are not intended to limit this application. Based on the embodiments provided in this application, all other embodiments obtained by those of ordinary skill in the art without creative work are within the scope of protection of this application.

[0191] Obviously, the drawings described below are merely examples or embodiments of the present application. Those skilled in the art can, without inventive effort, apply the present application to other similar scenarios based on these drawings. Furthermore, it is also understood that, although the effort involved in such a development process may be complex and lengthy, for those skilled in the art related to the content disclosed in this application, changes in design, manufacturing, or production based on the technical content disclosed in this application are merely conventional technical means and should not be construed as an insufficiency of the content disclosed in this application.

[0192] References to "embodiments" in this application mean that a particular feature, structure, or characteristic described in connection with the embodiment may be included in at least one embodiment of the application. The appearance of this phrase in various places in the specification does not necessarily refer to the same embodiment, nor does it refer to independent or alternative embodiments that are mutually exclusive of other embodiments. It is understood, both explicitly and implicitly, by those skilled in the art that the embodiments described in this application may be combined with other embodiments unless there is a conflict.

[0193] Unless otherwise defined, technical or scientific terms used herein shall have the ordinary meaning as understood by persons of ordinary skill in the art to which this application belongs. The terms "a," "an," "an," "the," and similar expressions used herein do not denote quantitative limitations and may refer to either the singular or the plural. The terms "comprise," "include," "have," and any variations thereof, used herein, are intended to cover non-exclusive inclusions. For example, a process, method, system, product, or apparatus comprising a series of steps or modules (units) is not limited to the listed steps or units but may also include steps or units not listed, or may include other steps or units inherent to the process, method, product, or apparatus. The terms "connected," "connected," "coupled," and similar expressions used herein are not limited to physical or mechanical connections but may include electrical connections, whether direct or indirect. As used herein, "plurality" means two or more. "And / or" describes an association between associated objects, indicating that three possible relationships exist. For example, "A and / or B" may mean: A exists alone; A and B exist simultaneously; or B exists alone. The character " / " generally indicates that the objects before and after are in an "or" relationship. The terms "first", "second", "third", etc. involved in this application are only used to distinguish similar objects and do not represent a specific order for the objects.

[0194] The MMC impedance modeling method for the transmission characteristics of a DC measurement device provided in an embodiment of the present application is applied in an MMC converter station as shown in FIG1 .

[0195] The MMC converter station consists of three phases, each phase consists of two upper and lower bridge arms, a total of six bridge arms, each bridge arm has the same structure, and is composed of a bridge arm inductor. , bridge arm resistance and Half-bridge submodules SM1…SM with the same structure N Each half-bridge module contains two power switches and a capacitor. . PCC is the point of common coupling.

[0196] This embodiment provides a method for modeling the MMC impedance of a DC measurement device, as shown in FIG2 , including the following steps:

[0197] Step S101 : constructing a differential common mode time domain small signal model of the MMC main circuit based on Kirchhoff's voltage law.

[0198] Step S102 : deriving a frequency coupling law and a phase sequence coupling law according to the frequency coupling characteristics and phase sequence coupling mechanism in the differential common mode time domain small signal model.

[0199] Specifically, by observing the differential common mode time domain small signal model of the MMC main circuit, it can be seen that when the disturbance signal is multiplied by the variable containing each harmonic, a new frequency coupling component will be generated. The frequency coupling law is obtained through analysis: when the injection frequency on the MMC AC side is After the disturbance voltage, the common mode small signal response 、 will with The odd-multiple frequencies are coupled, while the differential mode small signal response 、 Then Even-harmonic frequency coupling.

[0200] The phase sequence coupling law is obtained through analysis: when the positive sequence disturbance is injected from the AC side, the positive, negative and zero sequence components of the MMC differential mode small signal response and common mode small signal response correspond to n +1=3 k +1, n +1=3 k -1 and n +1=3 k , where n is the steady-state harmonic order, .

[0201] For example, based on the above rules, when the frequency injected into the MMC AC side is After the positive sequence disturbance, the phase sequence and frequency correspondence between the differential mode small signal response and the common mode small signal response generated inside is obtained. The common mode small signal response is: the positive sequence corresponds to etc., negative sequence corresponds to 、 、 etc., zero sequence corresponds to 、 、 etc.; differential mode small signal response is: positive sequence corresponds to etc., negative sequence corresponds to 、 etc., zero sequence corresponding 、 wait.

[0202] It should be noted that the AC current of the MMC only has differential-mode non-zero-sequence components, while the DC current only has common-mode zero-sequence components.

[0203] Step S103 : converting the differential common mode time domain small signal model into an HSS-MMC main circuit model according to the frequency coupling law and the phase sequence coupling law.

[0204] Step S104: establishing a phase-locked loop control HSS model, an AC current control HSS model, a DC voltage control HSS model, and a circulating current control HSS model according to the MMC control loop structure.

[0205] Step S105 , deriving a transfer function model of the DC voltage measurement device, and updating the DC voltage control HSS model using the transfer function model to obtain an updated DC voltage control HSS model.

[0206] Step S106 , combining the phase-locked loop control HSS model, the AC current control HSS model, the updated DC voltage control HSS model, the circulating current control HSS model and the modulation wave expression to obtain the MMC control system HSS model.

[0207] Step S107 , combining the HSS-MMC main circuit model and the MMC control system HSS model to obtain a MIMO admittance model.

[0208] Step S108: Obtain the SISO equivalent impedance model of the MMC according to the grid impedance expression and the MIMO admittance model.

[0209] Step S109 : according to the MMC system parameters and the different frequency disturbance control gains, the impedance analytical value is solved by using the SISO impedance model of the MMC.

[0210] Based on the above embodiment, the embodiment of the present application explains the above embodiment S101 in detail. Specifically, the embodiment of the present application relates to constructing a differential common mode time domain small signal model of the MMC main circuit based on Kirchhoff's voltage law, such as Figure 3 As shown, the specific steps include:

[0211] Step S201: Based on Kirchhoff's voltage law, establish an MMC three-phase time domain model:

[0212] ;(1)

[0213] ;(2)

[0214] ;(3)

[0215] in, , 、 、 express 、 、 Three-phase, represents the equivalent resistance of the bridge arm, represents the equivalent inductance of the bridge arm, represents the transformer equivalent inductance, express Phase upper arm current, express Phase lower arm current, express Phase AC current, express x The current of the bridge arm submodule on the phase, express The current of the lower bridge arm submodule, is the DC side voltage, express The sum of the capacitor voltages of the bridge arm submodules on each phase, express The sum of the capacitor voltages of the bridge arm submodules under the phase, express Phase common coupling point voltage, Indicates DC neutral point To AC neutral point The zero sequence voltage between express Phase upper bridge arm submodule capacitor voltage, express Phase lower bridge arm submodule capacitor voltage, is the submodule capacitance;

[0216] Where:

[0217] ;(4)

[0218] ;(5)

[0219] ;(6)

[0220] ;(7)

[0221] in, for The modulation wave of the upper bridge arm, for The modulation wave of the lower bridge arm, is the DC current, express The sum of the capacitor voltages of the bridge arm submodules on each phase, express The sum of the capacitor voltages of the bridge arm submodules under the phase, express The sum of the capacitor voltages of the bridge arm submodules on each phase, express The sum of the capacitor voltages of the bridge arm submodules under the phase, express The sum of the capacitor voltages of the bridge arm submodules on each phase, express The sum of the capacitor voltages of the bridge arm submodules under the phase, Indicates the number of bridge arm submodules.

[0222] Step S202: define the differential mode component and common mode component of any variable in the MMC three-phase time domain model:

[0223] ;

[0224] in, is any variable in formulas (1)-(7), represents the differential mode component, represents the common mode component, is any variable of the upper bridge arm of phase x, is any component of the lower bridge arm of phase x.

[0225] Step S203, obtaining the differential and common mode time domain expressions according to the differential mode component and the common mode component:

[0226] ;

[0227] ;

[0228] ;

[0229] ;

[0230] in, express The common-mode component of the sum of the phase submodule capacitor voltages, express The differential mode component of the sum of the phase submodule capacitor voltages, express Phase circulating current common mode component, express The common mode component of the phase submodule capacitor voltage, express The differential mode component of the phase submodule capacitor voltage, express The common mode component of the phase modulated wave, express The differential mode component of the phase modulated wave;

[0231] Where:

[0232] ;

[0233] ;

[0234] ;

[0235] ;

[0236] in, for The differential mode component of the phase bridge arm current, express The differential mode component of the sum of the phase submodule capacitor voltages, express The differential mode component of the sum of the phase submodule capacitor voltages, express The differential mode component of the sum of the phase submodule capacitor voltages.

[0237] Step S204: Obtain an MMC single-phase equivalent model in differential common mode according to the MMC operating characteristics:

[0238] ;

[0239] ;

[0240] ;

[0241] ;

[0242] in, represents the common mode component of the sum of the submodule capacitor voltages, Represents the differential mode component of the sum of the submodule capacitor voltages, represents the common mode component of the circulating current, represents the voltage at the point of common coupling, represents the common mode component of the submodule capacitor voltage, represents the differential mode component of the submodule capacitor voltage, represents the common mode component of the modulated wave, represents the differential mode component of the modulated wave, Indicates positive and negative sequence AC current;

[0243] Where:

[0244] ;

[0245] ;

[0246] ;

[0247] in, Indicates the zero-sequence circulating current.

[0248] Specifically, when the MMC operates in three-phase symmetrical mode and the connected AC grid is a three-phase three-wire system, the DC current It can be simplified to be three times of the zero-sequence circulating current; the AC side current Does not contain zero-sequence component.

[0249] Step S205: Perform small signal linearization on the differential and common mode time domain expressions and the MMC single-phase equivalent model using a perturbation linearization method to construct a differential and common mode time domain small signal model of the MMC main circuit:

[0250] ;

[0251] ;

[0252] ;

[0253] ;

[0254] in, Indicates the small signal disturbance of DC side voltage, It represents the small signal disturbance of the common mode component of the sum of the submodule capacitor voltage, represents the small signal disturbance of the circulating current common mode component, represents the small signal disturbance of the common coupling point voltage, It represents the small signal disturbance of the differential mode component of the sum of the submodule capacitor voltage, Indicates the positive and negative sequence AC current small signal disturbance, Represents the small signal disturbance of the common mode component of the submodule capacitor voltage, represents the small signal disturbance of the common-mode modulation wave, Indicates the small signal disturbance of the differential mode modulation wave, Represents the small signal disturbance of the differential mode component of the submodule capacitor voltage;

[0255] Where:

[0256] ;

[0257] ;

[0258] ;

[0259] in, is the DC current small signal disturbance, Indicates the small signal disturbance of zero-sequence circulating current.

[0260] Based on the above embodiment, the embodiment of the present application explains the above embodiment S103 in detail. Specifically, the embodiment of the present application involves converting the differential common mode time domain small signal model into an HSS-MMC main circuit model according to the frequency coupling law and phase sequence coupling law, such as Figure 4 As shown, the specific steps include:

[0261] Step S301: Based on the HSS theory, the differential common mode time domain small signal model is converted into an HSS model:

[0262] ;

[0263] ;

[0264] ;

[0265] ;

[0266] in, is the Toeplitz matrix formed by the steady-state value of the common-mode component of the modulation wave, is the Toeplitz matrix formed by the steady-state value of the differential mode component of the modulated wave, is the Toeplitz matrix of the steady-state value of the circulation, is the Toeplitz matrix composed of the steady-state values ​​of the positive and negative sequence components of the AC side output current;

[0267] Where:

[0268] ;

[0269] ;

[0270] ;

[0271] ;

[0272] in, is the Toeplitz matrix formed by the steady-state value of the common-mode component of the submodule capacitor voltage, is the Toeplitz matrix formed by the steady-state value of the differential mode component of the submodule capacitor voltage, is the imaginary number symbol;

[0273] Where:

[0274] ;

[0275] in, is the angular frequency of the disturbance signal, is the fundamental angular frequency.

[0276] Step S302: According to the phase sequence coupling rule, a phase sequence selection matrix is ​​obtained:

[0277] ;

[0278] in, Denotes a diagonal matrix, the superscript Indicates the positive sequence disturbance injected from the AC side, subscript 、 、 Respectively represent the extraction of negative sequence, zero sequence, and positive sequence currents, To extract the matrix of the negative sequence response component after the MMC injects the positive sequence disturbance from the AC side, To extract the matrix of the zero-sequence response component after the MMC injects positive-sequence disturbance from the AC side, It is the matrix for extracting the positive sequence response component after the MMC injects positive sequence disturbance from the AC side.

[0279] One possible implementation method is to unify the expressions of various variables under different phase sequences. Based on the phase sequence coupling law obtained above, when a positive sequence disturbance is injected into the AC side, a phase sequence selection matrix is ​​obtained.

[0280] Step S303: Obtain zero-sequence circulating current and AC current expressions in the HSS model according to the phase sequence selection matrix:

[0281] ;

[0282] .

[0283] in, To extract the matrix of positive and negative sequence response components after the MMC injects positive sequence disturbance from the AC side, HSS vector representing the AC current disturbance.

[0284] Step S304: Substitute the zero-sequence circulating current and AC current expressions into the HSS model to obtain the HSS-MMC main circuit model:

[0285] ;

[0286] Where, and The variables are defined as follows:

[0287] ;

[0288] ;

[0289] in, is the voltage disturbance vector, is the current disturbance vector, is the modulation wave disturbance vector, for The coefficient matrix of for The coefficient matrix of for Inverse matrix.

[0290] On the basis of the above embodiments, according to Figure 5 The MMC control loop structure diagram is shown in FIG. 1 . The present embodiment of the present application provides a detailed explanation of the above embodiment S104. Specifically, the present embodiment of the present application relates to establishing a phase-locked loop control HSS model, an AC current control HSS model, a DC voltage control HSS model, and a circulating current control HSS model based on the MMC control loop structure. Figure 6 As shown, the specific steps include:

[0291] Step S401: Establish a phase-locked loop control HSS model based on the MMC phase-locked loop structure:

[0292] ;

[0293] in, is the HSS vector of phase angle perturbation, is a diagonal matrix whose matrix elements are composed of the gains of the phase-locked loop PI controller at different disturbance frequencies. is the steady-state voltage of the grid The amplitude of the fundamental frequency component, is the HSS model of PLL;

[0294] Where: ;

[0295] Among them, the frequency reduction matrix and upscaling matrix They are:

[0296] .

[0297] Step S402: Establish an AC current control HSS model based on the MMC AC current control structure:

[0298] ;

[0299] Where:

[0300] ;

[0301] ;

[0302] ;

[0303] ;

[0304] in, is the fundamental modulation voltage The HSS vector of the phase disturbance, For AC current HSS signal of the axis reference signal disturbance, For AC current HSS signal of the axis reference signal disturbance, is the equivalent inductance, 、 They are middle 、 The Toeplitz matrix of the axis steady-state signal, 、 for middle 、 The Toeplitz matrix of the axis steady-state signal, for The Toeplitz matrix of the steady-state signal of phase A, is the Park inverse transformation matrix, is the current after Park inverse transformation, is the voltage at the point of common coupling after Park inverse transformation, is the modulated wave after Park inverse transform, is the HSS gain matrix formed by the delay link transfer function, is the HSS gain matrix formed by the AC current PI controller transfer function, is the rated voltage of the submodule capacitor.

[0305] Step S403: Establish a DC voltage control HSS model based on the MMC DC voltage control structure:

[0306] ;

[0307] in, is the HSS gain matrix formed by the DC voltage PI controller transfer function, is the HSS vector of the DC voltage reference signal disturbance, is the HSS signal disturbed by the AC current d-axis reference signal.

[0308] It should be noted that the MMC DC voltage control HSS model at this time is an MMC DC voltage control HSS model that does not take into account the transmission characteristics of the DC voltage measuring device.

[0309] Step S404: Establish a circulation control HSS model based on the MMC circulation control structure:

[0310] ;

[0311] in, is the HSS vector of the double frequency modulated voltage disturbance, is the HSS gain matrix formed by the circulating PR controller transfer function, HSS vector of circulating current reference signal perturbation.

[0312] On the basis of the above embodiments, according to Figure 7 The DC voltage measurement device structure diagram is shown in FIG. 1 . The embodiment of the present application explains the above embodiment S105 in detail. Specifically, the embodiment of the present application relates to deriving a transfer function model of the DC voltage measurement device, and updating the DC voltage control HSS model by the transfer function model to obtain an updated DC voltage control HSS model, such as Figure 7 As shown, the specific steps include:

[0313] Step S501: Obtain the transfer function of the DC voltage divider body, the transfer function of the secondary voltage divider plate of the DC voltage divider, and the transfer function of the electronic isolation device according to the DC voltage measurement device:

[0314] ;

[0315] ;

[0316] ;

[0317] in, 、 are the equivalent capacitance and equivalent resistance of the high voltage bridge arm of the DC voltage divider body, 、 are the equivalent capacitance and equivalent resistance of the low-voltage bridge arm of the DC voltage divider body, 、 are the equivalent capacitance and equivalent resistance of the high voltage bridge arm of the secondary voltage divider plate of the DC voltage divider, is the equivalent resistance of the low-voltage bridge arm of the secondary voltage divider of the DC voltage divider, s is the Laplace variable, is the damping coefficient, is the cutoff frequency.

[0318] Specifically, Figure 7 The DC voltage measuring device shown includes three parts: a DC voltage divider body 1, a DC voltage divider secondary voltage dividing plate 2 and an electronic isolation device.

[0319] It's important to note that the technologies involved in A / D conversion in electronic isolation devices are relatively mature, ensuring accurate signal conversion across all frequency bands. Currently, optocouplers used in engineering applications have nanosecond response times, can transmit frequencies up to 10 MHz, and have a very flat passband, virtually negligible impact on the transfer characteristics of DC voltage measurement devices. When constructing the transfer function for an electronic isolation device, the primary consideration is the impact of the low-pass filter on the overall device. In electronic isolation devices, this low-pass filter is typically a second-order Butterworth filter.

[0320] Step S502: Obtain a transfer function model of a DC voltage measuring device according to the transfer function of the DC voltage divider body, the transfer function of the secondary voltage divider plate of the DC voltage divider, and the transfer function of the electronic isolation device:

[0321] ;

[0322] in, ,in, is the calibrated volume ratio of the DC voltage divider, is the standard transformation ratio of the secondary voltage divider.

[0323] Step S503: embed the DC voltage measurement device transfer function model into the MMC DC voltage control HSS model to obtain an updated DC voltage control HSS model:

[0324] .

[0325] It should be noted that the updated DC voltage control HSS model is an HSS model of MMC DC voltage control that takes into account the transmission characteristics of the DC voltage measuring device.

[0326] Based on the above embodiment, the embodiment of the present application explains the above embodiment S106 in detail. Specifically, the embodiment of the present application relates to obtaining the MMC control system HSS model according to the combination of the phase-locked loop control HSS model, the AC current control HSS model, the updated DC voltage control HSS model, the circulating current control HSS model and the modulation wave expression, such as Figure 8 As shown, the specific steps include:

[0327] Step S601: Establish an upper bridge arm modulation wave expression and a lower bridge arm modulation wave expression:

[0328] ;

[0329] ;

[0330] in, is the upper arm modulation wave, is the lower arm modulation wave, is the upper arm modulation voltage, is the lower arm modulation voltage, is the fundamental modulation voltage, is the double frequency modulation voltage.

[0331] Step S602: Obtain a differential mode modulation wave expression and a common mode modulation wave expression according to the upper bridge arm modulation wave expression and the lower bridge arm modulation wave expression:

[0332] ;

[0333] ;

[0334] in, is a differential mode modulated wave, It is a common mode modulated wave.

[0335] Step S603: Obtain the differential mode modulation wave small signal disturbance expression and the common mode modulation wave small signal disturbance expression according to the differential mode modulation wave expression, the common mode modulation wave expression, the phase-locked loop control HSS model, the AC current control HSS model, the updated DC voltage control HSS model, and the circulating current control HSS model:

[0336] ;

[0337] .

[0338] Step S604: Obtain the HSS model of the MMC control system according to the differential mode modulation wave small signal disturbance expression and the common mode modulation wave small signal disturbance expression:

[0339] ;

[0340] in, and Represent the control matrices of current and voltage respectively;

[0341] Where:

[0342] ;

[0343] ;

[0344] ;

[0345] .

[0346] Based on the above embodiment, the embodiment of the present application explains the above embodiment S107 in detail. Specifically, the embodiment of the present application relates to combining the HSS-MMC main circuit model and the MMC control system HSS model to obtain the MIMO admittance model, such as Figure 10 As shown, the specific steps include:

[0347] Step S701: Combine the HSS-MMC main circuit model and the MMC control system HSS model to obtain a complete HSS-MMC model under closed-loop operation:

[0348] ;

[0349] in, It means that the MMC contains the admittance matrix of all frequencies.

[0350] Step S702: Obtain a MIMO admittance model based on the frequency coupling law:

[0351] ;

[0352] Where:

[0353] .

[0354] Specifically, the MIMO admittance model The detailed expression is:

[0355] ;

[0356] in, , , superscript Indicates MMC, Indicates that the frequency injected into the voltage is The frequency generated after the zero-sequence disturbance is Zero-sequence current disturbance; Indicates that the frequency injected into the voltage is The frequency generated after the negative sequence disturbance is Zero-sequence current disturbance; Indicates that the frequency injected into the voltage is The frequency generated after the positive sequence disturbance is Zero-sequence current disturbance; Indicates that the frequency injected into the voltage is The frequency generated after the zero-sequence disturbance is Negative sequence current disturbance; Indicates that the frequency injected into the voltage is The frequency generated after the negative sequence disturbance is Negative sequence current disturbance; Indicates that the frequency injected into the voltage is The frequency generated after the positive sequence disturbance is Negative sequence current disturbance; Indicates that the frequency injected into the voltage is The frequency generated after the zero-sequence disturbance is Positive sequence current disturbance; Indicates that the frequency injected into the voltage is The frequency generated after the negative sequence disturbance is Positive sequence current disturbance; Indicates that the frequency injected into the voltage is The frequency generated after the positive sequence disturbance is Positive sequence current disturbance.

[0357] Based on the above embodiment, the embodiment of the present application explains the above embodiment S108 in detail. Specifically, the embodiment of the present application relates to obtaining the SISO equivalent impedance model of the MMC based on the grid impedance expression and the MIMO admittance model, such as Figure 11 As shown, the specific steps include:

[0358] Step S801: Build grid impedance The detailed expression of:

[0359] ;

[0360] Among them, the superscript Indicates the power grid, subscript 、 and Represent zero sequence, negative sequence and positive sequence respectively, Indicates the zero-sequence impedance of the DC side of the power grid, Indicates the AC negative sequence impedance of the power grid. Indicates the AC positive sequence impedance of the power grid.

[0361] Step S802: According to the grid impedance expression and the MIMO admittance model, the SISO equivalent admittance model of the MMC and the SISO equivalent impedance model of the grid are obtained by identifying the dominant frequency coupling path:

[0362] ;

[0363] ;

[0364] in, and are the SISO equivalent admittance of MMC and the SISO equivalent impedance of the power grid, respectively.

[0365] Step S803: Obtain the SISO equivalent impedance model of the MMC according to the SISO equivalent admittance model of the MMC and the SISO equivalent impedance model of the power grid:

[0366] .

[0367] Specifically, the SISO equivalent impedance model of MMC is used for stability analysis.

[0368] Based on the above embodiment, the embodiment of the present application explains the above embodiment S109 in detail. Specifically, the embodiment of the present application involves solving the impedance analytical value based on the MMC system parameters and the different frequency disturbance control gains using the SISO impedance model of the MMC, such as Figure 12 As shown, the specific steps include:

[0369] Step S901: Substitute the MMC system parameters and the disturbance control gains at different frequencies into the MIMO admittance model to obtain the admittance value.

[0370] Step S902: Substitute the admittance value into the SISO equivalent impedance model of the MMC to obtain an impedance analytical value.

[0371] To verify the accuracy of the embodiment of the present application, voltage disturbance signals of different frequencies were injected into the MMC simulation system, and the impedance sweep value was obtained by fast Fourier transform analysis of the response characteristics. The impedance sweep value was compared with the SISO impedance analysis value obtained in the embodiment of the present application. The results are as follows: Figure 13 As shown, it can be seen that the amplitude and phase angle of the SISO impedance analysis value are basically consistent with the amplitude and phase angle of the impedance simulation sweep value, verifying the accuracy of the analytical model established in the embodiment of the present application.

[0372] In order to verify the necessity of taking into account the transmission characteristics of the DC voltage measurement device, the SISO impedance of the MMC is obtained using the embodiment of the present application. The magnitude and phase angle of the grid impedance are obtained according to the grid impedance expression. The amplitude and phase angle of Figure 14 As shown, it can be seen that the SISO impedance of MMC Amplitude and grid SISO impedance The amplitudes intersect near 3285.3Hz, and the impedance phase angle difference between the two is ,Exceed , indicating that the system is unstable at this time.

[0373] Furthermore, a simulation experiment was conducted on the MMC grid-connected system. Before the time equals 2s, the system adopts a DC voltage control strategy that does not take into account the DC voltage measurement link. When the time equals 2s, it switches to a DC voltage control strategy that takes into account the DC voltage measurement link. The voltage at the common coupling point of phase a is as follows: Figure 15 As shown in the figure, it can be seen that the voltage at the common coupling point of phase a remains stable before time equal to 2s. After switching to the DC voltage control strategy taking into account the DC voltage measurement link at time equal to 2s, the voltage at the common coupling point of phase a shows obvious oscillation components.

[0374] When the DC voltage control strategy taking into account the DC voltage measurement link is adopted, the corresponding Fourier analysis of the voltage at the common coupling point of phase a is as follows: Figure 16 As shown, it can be seen that the main oscillation frequency is 3286Hz, which is consistent with Figure 14 The SISO impedance of the MMC Amplitude and grid SISO impedance The amplitude intersection value of 3285.3Hz is close to that of 1000 Hz, which proves the necessity of considering the transmission characteristics of DC voltage measurement devices.

[0375] It should be understood that, although the various steps in the flowcharts involved in the various embodiments described above are displayed in sequence according to the instructions of the arrows, these steps are not necessarily executed in sequence in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order restriction on the execution of these steps, and these steps can be executed in other orders. Moreover, at least a portion of the steps in the flowcharts involved in the various embodiments described above can include multiple steps or multiple stages, and these steps or stages are not necessarily executed and completed at the same time, but can be executed at different times, and the execution order of these steps or stages is not necessarily to be carried out in sequence, but can be executed in turn or alternately with other steps or at least a portion of steps or stages in other steps.

[0376] The technical features of the above-mentioned embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the above-mentioned embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0377] The above-described embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art could make various modifications and improvements without departing from the spirit of the present application, all of which fall within the scope of protection of the present application. Therefore, the scope of protection of the present patent application shall be determined by the appended claims.

Claims

1. A DC measurement device transmission characteristic MMC impedance modeling method, characterized in that: The method comprises: Based on Kirchhoff's voltage law, a differential and common mode time domain small signal model of the MMC main circuit is constructed; According to the frequency coupling characteristics and phase sequence coupling mechanism in the differential common mode time domain small signal model, the frequency coupling law and phase sequence coupling law are derived; According to the frequency coupling law and the phase sequence coupling law, the differential common mode time domain small signal model is converted into an HSS-MMC main circuit model; According to the MMC control loop structure, establish the phase-locked loop control HSS model, AC current control HSS model, DC voltage control HSS model, and circulating current control HSS model; deriving a transfer function model of the DC voltage measuring device, and updating the DC voltage control HSS model using the transfer function model to obtain an updated DC voltage control HSS model; Combining the phase-locked loop control HSS model, the AC current control HSS model, the updated DC voltage control HSS model, the circulating current control HSS model and the modulation wave expression, the MMC control system HSS model is obtained; The HSS-MMC main circuit model and the MMC control system HSS model are combined to obtain a MIMO admittance model; According to the grid impedance expression and the MIMO admittance model, the SISO equivalent impedance model of the MMC is obtained; According to the MMC system parameters and the control gains of disturbances at different frequencies, the impedance analytical value is solved using the SISO impedance model of the MMC.

2. The method according to claim 1, characterized in that The differential and common mode time domain small signal model of the MMC main circuit is constructed based on Kirchhoff's voltage law, including: Based on Kirchhoff's voltage law, the MMC three-phase time domain model is established: ;(1) ;(2) ;(3) in, , 、 、 express 、 、 Three-phase, represents the bridge arm resistance, represents the bridge arm inductance, represents the transformer inductance, express Phase upper arm current, express Phase lower arm current, express Phase AC current, express x The current of the bridge arm submodule on the phase, express The current of the lower bridge arm submodule, is the DC side voltage, express The sum of the capacitor voltages of the bridge arm submodules on each phase, express The sum of the capacitor voltages of the bridge arm submodules under the phase, express Phase common coupling point voltage, Indicates DC neutral point To AC neutral point The zero sequence voltage between express Phase upper bridge arm submodule capacitor voltage, express Phase lower bridge arm submodule capacitor voltage, is the submodule capacitance; Where: ;(4) ;(5) ;(6) ;(7) in, for The modulation wave of the upper bridge arm, for The modulation wave of the lower bridge arm, is the DC current, express The sum of the capacitor voltages of the bridge arm submodules on each phase, express The sum of the capacitor voltages of the bridge arm submodules under the phase, express The sum of the capacitor voltages of the bridge arm submodules on each phase, express The sum of the capacitor voltages of the bridge arm submodules under the phase, express The sum of the capacitor voltages of the bridge arm submodules on each phase, express The sum of the capacitor voltages of the bridge arm submodules under the phase, Indicates the number of bridge arm submodules; Define the differential mode component and common mode component of any variable in the MMC three-phase time domain model: ; in, is any variable in formulas (1)-(7), represents the differential mode component, represents the common mode component, is any variable of the upper bridge arm of phase x, is any component of the lower bridge arm of phase x; The differential and common mode time domain expressions are obtained according to the differential mode component and the common mode component: ; ; ; ; in, express The common-mode component of the sum of the phase submodule capacitor voltages, express The differential mode component of the sum of the phase submodule capacitor voltages, express Phase circulating current common mode component, express The common mode component of the phase submodule capacitor voltage, express The differential mode component of the phase submodule capacitor voltage, express The common mode component of the phase modulated wave, express The differential mode component of the phase modulated wave; Where: ; ; ; ; in, for The differential mode component of the phase bridge arm current, express The differential mode component of the sum of the phase submodule capacitor voltages, express The differential mode component of the sum of the phase submodule capacitor voltages, express The differential mode component of the sum of the phase submodule capacitor voltages; According to the operating characteristics of MMC, the single-phase equivalent model of MMC in differential and common mode is obtained: ; ; ; ; in, represents the common mode component of the sum of the submodule capacitor voltages, Represents the differential mode component of the sum of the submodule capacitor voltages, represents the common mode component of the circulating current, represents the voltage at the point of common coupling, represents the common mode component of the submodule capacitor voltage, represents the differential mode component of the submodule capacitor voltage, represents the common-mode modulated wave, represents the differential mode modulated wave, Indicates positive and negative sequence AC current; Where: ; ; ; in, Indicates zero-sequence circulating current; The differential and common mode time domain expressions and the MMC single-phase equivalent model are linearized using the perturbation linearization method to construct the differential and common mode time domain small signal model of the MMC main circuit: ; ; ; ; in, Indicates the small signal disturbance of DC side voltage, It represents the small signal disturbance of the common mode component of the sum of the submodule capacitor voltage, represents the small signal disturbance of the circulating current common mode component, represents the small signal disturbance of the common coupling point voltage, It represents the small signal disturbance of the differential mode component of the sum of the submodule capacitor voltage, Indicates the positive and negative sequence AC current small signal disturbance, Represents the small signal disturbance of the common mode component of the submodule capacitor voltage, represents the small signal disturbance of the common-mode modulation wave, Indicates the small signal disturbance of the differential mode modulation wave, Represents the small signal disturbance of the differential mode component of the submodule capacitor voltage; Where: ; ; ； in, is the DC current small signal disturbance, Indicates the small signal disturbance of zero-sequence circulating current.

3. The method according to claim 2, characterized in that The converting of the differential common mode time domain small signal model into an HSS-MMC main circuit model according to the frequency coupling law and the phase sequence coupling law includes: Based on the HSS theory, the differential common mode time domain small signal model is converted into an HSS model: ; ; ; ; in, is the Toeplitz matrix formed by the steady-state value of the common-mode component of the modulation wave, is the Toeplitz matrix formed by the steady-state value of the differential mode component of the modulated wave, is the Toeplitz matrix of the steady-state value of the circulation, is the Toeplitz matrix composed of the steady-state values ​​of the positive and negative sequence components of the AC side output current; Where: ; ; ; ; in, is the Toeplitz matrix formed by the steady-state value of the common-mode component of the submodule capacitor voltage, is the Toeplitz matrix formed by the steady-state value of the differential mode component of the submodule capacitor voltage, is the imaginary number symbol; Where: ； in, is the angular frequency of the disturbance signal, is the fundamental angular frequency; According to the phase sequence coupling law, the phase sequence selection matrix is ​​obtained: ； in, Denotes a diagonal matrix, the superscript Indicates the positive sequence disturbance injected from the AC side, subscript 、 、 Respectively represent the extraction of negative sequence, zero sequence, and positive sequence currents, To extract the matrix of the negative sequence response component after the MMC injects the positive sequence disturbance from the AC side, To extract the matrix of the zero-sequence response component after the MMC injects positive-sequence disturbance from the AC side, It is the matrix for extracting the positive sequence response component after the MMC injects positive sequence disturbance from the AC side; According to the phase sequence selection matrix, the zero-sequence circulating current and AC current expressions in the HSS model are obtained: ； ； in, To extract the matrix of positive and negative sequence response components after the MMC injects positive sequence disturbance from the AC side, HSS vector representing the AC current disturbance; Substituting the zero-sequence circulating current and AC current expressions into the HSS model, the HSS-MMC main circuit model is obtained: ； Where, and The variables are defined as follows: ； ； in, is the voltage disturbance vector, is the current disturbance vector, is the modulation wave disturbance vector, for The coefficient matrix of for The coefficient matrix of for Inverse matrix.

4. The method according to claim 3, characterized in that According to the MMC control loop structure, a phase-locked loop control HSS model, an AC current control HSS model, a DC voltage control HSS model, and a circulating current control HSS model are established, including: According to the MMC phase-locked loop structure, the phase-locked loop control HSS model is established: ； in, is the HSS vector of phase angle perturbation, is a diagonal matrix whose matrix elements are composed of the gains of the phase-locked loop PI controller at different disturbance frequencies. is the steady-state voltage of the grid The amplitude of the fundamental frequency component, is the HSS model of PLL; Where: ; Among them, the frequency reduction matrix and upscaling matrix They are: ； According to the MMC AC current control structure, the AC current control HSS model is established: ； Where: ； ； ； ； in, is the fundamental modulation voltage The HSS vector of the phase disturbance, For AC current HSS signal of the axis reference signal disturbance, For AC current HSS signal of the axis reference signal disturbance, is the equivalent inductance, 、 They are middle 、 The Toeplitz matrix of the axis steady-state signal, 、 for middle 、 The Toeplitz matrix of the axis steady-state signal, for The Toeplitz matrix of the steady-state signal of phase A, is the Park inverse transformation matrix, is the current after Park inverse transformation, is the voltage at the point of common coupling after Park inverse transformation, is the modulated wave after Park inverse transform, is the HSS gain matrix formed by the delay link transfer function, is the HSS gain matrix formed by the AC current PI controller transfer function, is the rated voltage of the submodule capacitor; According to the MMC DC voltage control structure, the DC voltage control HSS model is established: ； in, is the HSS gain matrix formed by the DC voltage PI controller transfer function, is the HSS vector of the DC voltage reference signal disturbance; According to the MMC circulation control structure, the circulation control HSS model is established: ； in, is the HSS vector of the double frequency modulated voltage disturbance, is the HSS gain matrix formed by the circulating PR controller transfer function, HSS vector of circulating current reference signal perturbation.

5. The method according to claim 4, characterized in that The method of deriving a transfer function model of the DC voltage measuring device and updating the DC voltage control HSS model using the transfer function model to obtain an updated DC voltage control HSS model includes: According to the DC voltage measurement device, the transfer function of the DC voltage divider body, the transfer function of the DC voltage divider secondary voltage divider plate, and the transfer function of the electronic isolation device are obtained: ； ； ； in, 、 are the equivalent capacitance and equivalent resistance of the high voltage bridge arm of the DC voltage divider body, 、 are the equivalent capacitance and equivalent resistance of the low-voltage bridge arm of the DC voltage divider body, 、 are the equivalent capacitance and equivalent resistance of the high voltage bridge arm of the secondary voltage divider plate of the DC voltage divider, is the equivalent resistance of the low-voltage bridge arm of the secondary voltage divider of the DC voltage divider, s is the Laplace variable, is the damping coefficient, is the cutoff frequency; According to the transfer function of the DC voltage divider body, the transfer function of the DC voltage divider secondary voltage divider plate, and the transfer function of the electronic isolation device, a transfer function model of the DC voltage measuring device is obtained: ； in, , is the calibrated volume transformation ratio of the DC voltage divider, is the standard transformation ratio of the secondary voltage divider; The DC voltage measurement device transfer function model is embedded into the DC voltage control HSS model to obtain an updated DC voltage control HSS model: 。 6. The method according to claim 5, characterized in that The HSS model of the MMC control system is obtained by combining the phase-locked loop control HSS model, the AC current control HSS model, the updated DC voltage control HSS model, the circulating current control HSS model and the modulation wave expression, including: Establish the upper bridge arm modulation wave expression and the lower bridge arm modulation wave expression: ； ； in, is the upper arm modulation wave, is the lower arm modulation wave, is the upper arm modulation voltage, is the lower arm modulation voltage, is the fundamental modulation voltage, is the double frequency modulation voltage; According to the upper bridge arm modulation wave expression and the lower bridge arm modulation wave expression, the differential mode modulation wave expression and the common mode modulation wave expression are obtained: ； ； in, is a differential mode modulated wave, is a common mode modulated wave; According to the differential-mode modulation wave expression, common-mode modulation wave expression and the phase-locked loop control HSS model, AC current control HSS model, updated DC voltage control HSS model, and circulating current control HSS model, the differential-mode modulation wave small-signal disturbance expression and the common-mode modulation wave small-signal disturbance expression are obtained: ； ； According to the differential mode modulation wave small signal disturbance expression and the common mode modulation wave small signal disturbance expression, the HSS model of the MMC control system is obtained: ； in, and Represent the control matrices of current and voltage respectively; Where: ； ； ； 。 7. The method according to claim 6, characterized in that The HSS-MMC main circuit model and the MMC control system HSS model are combined to obtain a MIMO admittance model, including: Combining the HSS-MMC main circuit model and the MMC control system HSS model, a complete HSS-MMC model under closed-loop operation is obtained: ； in, Indicates that the MMC contains the admittance matrix of all frequencies; According to the frequency coupling law, the MIMO admittance model is obtained: ； Where: 。 8. The method according to claim 7, characterized in that include: The MIMO Admittance Model The detailed expression is: ； in, , , superscript Indicates MMC, Indicates that the frequency injected into the voltage is The frequency generated after the zero-sequence disturbance is Zero-sequence current disturbance; Indicates that the frequency injected into the voltage is The frequency generated after the negative sequence disturbance is Zero-sequence current disturbance; Indicates that the frequency injected into the voltage is The frequency generated after the positive sequence disturbance is Zero-sequence current disturbance; Indicates that the frequency injected into the voltage is The frequency generated after the zero-sequence disturbance is Negative sequence current disturbance; Indicates that the frequency injected into the voltage is The frequency generated after the negative sequence disturbance is Negative sequence current disturbance; Indicates that the frequency injected into the voltage is The frequency generated after the positive sequence disturbance is Negative sequence current disturbance; Indicates that the frequency injected into the voltage is The frequency generated after the zero-sequence disturbance is Positive sequence current disturbance; Indicates that the frequency injected into the voltage is The frequency generated after the negative sequence disturbance is Positive sequence current disturbance; Indicates that the frequency injected into the voltage is The frequency generated after the positive sequence disturbance is Positive sequence current disturbance.

9. The method according to claim 8, characterized in that The SISO equivalent impedance model of the MMC is obtained according to the grid impedance expression and the MIMO admittance model, including: Building grid impedance The detailed expression of: ； Among them, the superscript Indicates the power grid, subscript 、 and Represent zero sequence, negative sequence and positive sequence respectively, Indicates the zero-sequence impedance of the DC side of the power grid, Indicates the AC negative sequence impedance of the power grid. Indicates the AC positive sequence impedance of the power grid; According to the grid impedance expression and the MIMO admittance model, the SISO equivalent admittance model of the MMC and the SISO equivalent impedance model of the grid are obtained by identifying the dominant frequency coupling path: ； ； Where, and are the SISO equivalent admittance of MMC and the SISO equivalent impedance of the power grid respectively; According to the SISO equivalent admittance model of the MMC and the SISO equivalent impedance model of the power grid, the SISO equivalent impedance model of the MMC is obtained: 。 10. The method according to claim 9, characterized in that The method of solving the impedance analytical value based on the MMC system parameters and the different frequency disturbance control gains and utilizing the SISO impedance model of the MMC includes: Bring the MMC system parameters and the control gains of different frequency disturbances into the MIMO admittance model to solve the admittance value; The admittance value is substituted into the SISO equivalent impedance model of the MMC to obtain the impedance analytical value.

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