Multi-frequency coupling M3C impedance modeling method, device, equipment and medium

Abstract

The invention relates to a multi-frequency coupling M3C impedance modeling method, device, equipment and medium, and the method comprises the steps: carrying out the time domain equivalent modeling of the electrical parameter data of a converter bridge arm based on an M3C average value circuit model, and obtaining a bridge arm loop frequency domain model; according to the bridge arm loop frequency domain model, performing multi-dimensional frequency domain characteristic representation on the steady-state characteristics of the power frequency and low frequency components, and establishing a steady-state frequency domain model of the bridge arm voltage and current; performing linear decomposition on variables of the steady-state frequency domain model, deriving small signal models of bridge arm capacitor voltage and bridge arm current, and establishing a small signal model conversion relation between bridge arm electric parameters and power frequency electric parameters; according to the conversion relation, establishing a power frequency control circuit modularized small signal model so as to deduce a bridge arm modulation small signal model considering power frequency side, low frequency side and circulation control influence; and determining the equivalent admittance of the low-frequency current source, and constructing a power frequency impedance model according to the equivalent admittance. The method has the effect of improving the M3C impedance modeling accuracy.

Description

Technical Field

[0001] This invention belongs to the technical field of converter control modeling, and in particular relates to a multi-frequency coupled M3C impedance modeling method, device, equipment and medium. Background Technology

[0002] Currently, the modular multilevel matrix converter (M3C) is widely used in AC / DC conversion, flexible power transmission, and new energy grid connection. Due to its advantages such as high voltage level, low harmonic distortion, and modular structure, the M3C has become one of the important topologies of multi-terminal converter systems.

[0003] Existing M3C impedance modeling methods are mostly based on average value modeling and frequency domain linearization principles. They construct equivalent admittance or impedance expressions by performing small-signal modeling on single-frequency control components. However, under operating conditions with significant multi-frequency coupling characteristics, there is substantial energy interaction and frequency coupling between the power frequency fundamental and low-frequency fundamental frequencies in the converter arm. Single-frequency modeling cannot accurately characterize the dynamic coupling relationships between multiple frequency components. Furthermore, traditional linearization methods often model the control components and electrical submodules separately, neglecting the mutual interference effects between different frequency ports, resulting in insufficient accuracy of the obtained impedance model in cross-frequency domain analysis.

[0004] The existing technical solutions mentioned above have the following drawbacks: the existing M3C impedance modeling method, due to the use of single-frequency approximation and independent linearization, cannot accurately reflect the mutual coupling characteristics between the power frequency port and the low frequency port. The evaluation results of system stability and control parameters under multiple operating conditions have large deviations, so there is room for improvement. Summary of the Invention

[0005] The purpose of this invention is to provide a multi-frequency coupled M3C impedance modeling method, apparatus, device and medium to solve the technical problem that existing M3C impedance modeling methods, due to the use of single-frequency approximation and independent linearization processing, result in large deviations in the evaluation results of system stability and control parameters under multiple operating conditions.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: In a first aspect, the present invention provides a method for impedance modeling of multi-frequency coupled M3C, the method comprising: Based on the M3C average value circuit model, the electrical parameter data of the converter arm are modeled in the time domain to obtain the frequency domain model of the arm circuit. Based on the frequency domain model of the bridge arm circuit, the steady-state characteristics of the power frequency and low frequency components are characterized by multi-dimensional frequency domain features, and a steady-state frequency domain model of the bridge arm voltage and current in the stationary coordinate system is established. The variables of the steady-state frequency domain model are linearized and decomposed to establish a small-signal model of the bridge arm circuit. Based on the small-signal model of the bridge arm circuit, the small-signal models of the bridge arm capacitor voltage and bridge arm current are derived, and the small-signal model conversion relationship between the bridge arm electrical parameters and the power frequency electrical parameters is established based on the small-signal relationship. Based on the transformation relationship, a modular small-signal model of the power frequency control circuit in the stationary coordinate system is established. Based on the modular small-signal model of the power frequency control circuit in the static coordinate system, the bridge arm modulation small-signal model taking into account the influence of the power frequency side, the low frequency side and the circulating current control is derived. Based on the bridge arm modulation small-signal model, the equivalent admittance of the low-frequency current source is determined, and a power frequency impedance model is constructed based on the equivalent admittance.

[0007] By adopting the above technical solutions, and performing time-domain equivalent modeling of the electrical parameters of the converter arm based on the M3C average circuit model, the energy flow and dynamic response characteristics inside the arm can be accurately characterized without relying on the actual high-frequency switching process, thereby improving the computational stability and simulation convergence efficiency of the modeling. By performing multi-dimensional frequency domain feature characterization of the power frequency and low-frequency components based on the arm circuit frequency domain model, accurate differentiation of the power frequency and low-frequency coupling effects can be achieved, thus ensuring the frequency coverage integrity of the impedance model under complex operating conditions. Furthermore, by linearizing the steady-state frequency domain model variables and deriving the arm capacitance... Small-signal models of voltage and arm current can obtain the dynamic response law of the system under perturbation, thereby realizing the quantitative mapping between power frequency and arm-side signals. By constructing a modular model based on the stationary coordinate system and an arm modulation small-signal model, the multi-loop interaction relationship between power frequency control, low-frequency modulation and circulating current control can be comprehensively reflected, thereby improving the accuracy and usability of the overall impedance model. By determining the equivalent admittance of the low-frequency current source based on the arm modulation small-signal model and constructing a power frequency impedance model, the comprehensive quantification of the power frequency side impedance can be achieved, thereby providing a basis for the stability analysis and control strategy optimization of the converter system.

[0008] In one example, the present invention can be further configured as follows: performing time-domain equivalent modeling on the electrical parameter data of the converter arm to obtain a frequency-domain model of the arm loop includes: Collect electrical parameter data of the converter arm, wherein the electrical parameter data includes the arm modulation signal; Based on the electrical parameter data, a time-domain coupling equation is established between the bridge arm voltage, bridge arm current, and capacitor voltage. The switching action of the sub-module in the time-domain coupling equation is equivalent to the average value of the bridge arm modulation signal, and the time-domain equivalent equation is obtained. The time-domain equivalent equation is stabilized by KCL constraints, and the stabilized time-domain equivalent equation is mapped to the frequency domain model of the bridge arm loop by frequency domain transformation.

[0009] By adopting the above technical solution, and by collecting electrical parameter data of the converter arm and establishing time-domain coupling equations for the arm voltage, current and capacitor voltage, the electromagnetic coupling relationship and switching equivalent effect of the arm can be accurately reflected, thus providing an accurate physical basis for subsequent frequency domain modeling. By stabilizing the time-domain equations and mapping them to the frequency domain model, the complex time-domain nonlinear relationship can be transformed into a frequency-domain linear expression, thereby improving the model solution efficiency and providing a feasible approach for multi-frequency characteristic analysis.

[0010] In one example, the present invention can be further configured as follows: the steady-state characteristics of the power frequency and low-frequency components are characterized in a multi-dimensional frequency domain, and a steady-state frequency domain model of the bridge arm voltage and current in a stationary coordinate system is established, including: Based on the frequency domain vector relationship between the bridge arm voltage, bridge arm current and capacitor voltage in the bridge arm circuit frequency domain model, the power frequency component and low frequency component are expanded into frequency sequences respectively, and arranged according to the frequency order and phase relationship to form a two-dimensional frequency sequence representation. The two-dimensional frequency sequence representation is structurally extended in the low-frequency harmonic dimension to obtain the corresponding three-dimensional Toplitz matrix structure. The three-dimensional Toplitz matrix structure is coupled to the steady-state vector relationship in the frequency domain model of the bridge arm loop, and coordinate unification is performed in the stationary coordinate system to obtain the steady-state frequency domain model of the bridge arm voltage and current in the stationary coordinate system.

[0011] By adopting the above technical solutions, frequency sequence expansion of the power frequency and low frequency components can be performed by expanding the voltage, current and capacitor voltage vector relationships based on the frequency domain model of the bridge arm circuit. This enables the orderly separation and corresponding mapping of multiple frequency components, thereby enhancing the hierarchical clarity of the frequency domain model. By constructing a three-dimensional Toplitz matrix structure in the low-frequency harmonic dimension and coupling it with the steady-state vector relationship in a matrix manner, the cross-coupling characteristics between frequencies can be captured, thereby ensuring that the model still has high accuracy and consistency under low-frequency dynamic changes. By completing the coordinate unification process in the static coordinate system, the reference benchmark of each frequency component can be unified, thereby realizing a unified analysis framework among different frequency components.

[0012] In one example, the present invention can be further configured as follows: linearizing the variables of the steady-state frequency domain model to establish a small-signal model of the bridge arm loop; deriving small-signal models of the bridge arm capacitor voltage and bridge arm current based on the small-signal model of the bridge arm loop; and establishing a small-signal model conversion relationship between the bridge arm electrical parameters and the power frequency electrical parameters based on the small-signal relationship, including: Based on the steady-state frequency domain model, under steady-state operating conditions, disturbance signals of preset amplitude are introduced to the power frequency side and the low frequency side respectively, and then the voltage and current components under the action of the disturbance signals are expanded into multi-dimensional frequency sequence representations, so as to establish the small-signal model of the bridge arm circuit according to the multi-dimensional frequency sequence representations. Based on the small-signal model of the bridge arm circuit, the small-signal vectors of the bridge arm capacitor voltage and bridge arm current are derived by matrix transformation, and the amplitude frequency characteristics and phase frequency characteristics in the frequency sequence are determined respectively, thus forming the small-signal model of the bridge arm capacitor voltage and bridge arm current. Based on the small-signal model of the bridge arm capacitor voltage and bridge arm current, the coupling matrix relationship between each frequency component is determined. According to the coupling matrix relationship, the phase sequence decomposition of the three-phase bridge arm current components is performed to determine the phase coefficient matrix corresponding to the positive sequence component, negative sequence component and zero sequence component. Based on the phase coefficient matrix, the bridge arm electrical parameters are mapped to power frequency electrical parameters, thus obtaining the small-signal model conversion relationship between the bridge arm electrical parameters and the power frequency electrical parameters.

[0013] By adopting the above technical solutions, and by introducing disturbance signals to the power frequency side and low frequency side under steady-state conditions and expanding them into multi-dimensional frequency sequence representations, the system's sensitive response characteristics to small-signal disturbances can be characterized, thus providing a foundation for establishing a small-signal model of the bridge arm. By matrix-deriving the small-signal vectors of the bridge arm capacitor voltage and current, the amplitude-frequency and phase-frequency characteristics of each frequency component can be obtained, thereby quantitatively describing the dynamic transfer characteristics of the system. By determining the coupling matrix between frequency components and performing phase sequence decomposition on the three-phase current components, positive-sequence, negative-sequence, and zero-sequence components can be separated, thus facilitating the analysis of impedance behavior under unbalanced operating conditions. By mapping the bridge arm electrical parameters to power frequency electrical parameters, a unified representation between the bridge arm side and the power frequency side signals can be achieved, thereby establishing a standardized interface for subsequent control and impedance modeling.

[0014] In one example, the present invention can be further configured as follows: establishing a modular small-signal model of the power frequency control circuit in a stationary coordinate system based on the transformation relationship includes: Based on the small-signal model conversion relationship between the bridge arm electrical parameters and the power frequency electrical parameters, the power frequency three-phase voltage and current variables are transformed in the stationary coordinate system to obtain the small-signal components of the d-axis and q-axis. Based on the small-signal components of the d-axis and q-axis, a linearized transmission relationship of voltage control, current control and phase-locked loop control in the power frequency control loop is established, forming a small-signal description model for each loop. Based on the input-output correlation of each small-signal description model, the power frequency control link is modularly modeled to obtain a modular small-signal model of the power frequency control circuit in the stationary coordinate system.

[0015] By adopting the above technical solutions, the three-phase voltage, current, and capacitor voltage variables at power frequency can be transformed into steady-state d-axis and q-axis components in a stationary coordinate system, thereby simplifying the model structure and the derivation of control equations. By establishing linearized transfer relationships between voltage control, current control, and phase-locked loop control, the impact of each control element on the system dynamics can be quantitatively described, thereby improving the model's accuracy in characterizing control response characteristics. By modularizing the model based on the input-output correlation of small-signal descriptions, overall collaborative modeling can be achieved while ensuring that each module can be analyzed independently, thereby improving the model's reusability and parameter adjustment flexibility.

[0016] In one example, the present invention can be further configured as follows: the derivation of the bridge arm modulation small-signal model, which takes into account the influence of the power frequency side, the low frequency side, and the circulating current control, based on the modular small-signal model of the power frequency control circuit in the stationary coordinate system, includes: Based on the modular small-signal model of the power frequency control circuit, a low-frequency side voltage control loop and a circulating current suppression loop are introduced into the low-frequency control and circulating current control loops, respectively. Based on the linearized characteristic equations of the low-frequency side voltage control loop and the circulating current suppression loop, a transfer matrix expression between the low-frequency side modulation signal and the bridge arm AC voltage is constructed to obtain the low-frequency side modulation small-signal equation. Based on the delay characteristics and phase compensation function of the circulating current suppression circuit, the small-signal component of the circulating current is mapped to the bridge arm side by coordinate transformation, forming the circulating current modulation small-signal equation. The low-frequency side modulation small-signal equation and the circulating current modulation small-signal equation are merged and normalized to obtain the bridge arm modulation small-signal model.

[0017] By adopting the above technical solutions, and introducing low-frequency voltage control and circulating current suppression loops into the low-frequency control and circulating current control loops respectively, the frequency response characteristics of each control loop can be reflected at the modulation level, thereby realizing the synergistic modeling of multiple control channels. By establishing the transfer matrix of the modulation signal and the bridge arm voltage based on the linearized characteristic equations of the low-frequency side voltage control and circulating current suppression loops, the low-frequency side modulation small-signal equation can be constructed, thereby quantifying the influence of low-frequency side modulation on the bridge arm voltage. By mapping the circulating current small signal to the bridge arm side based on the delay characteristics and phase compensation function of the circulating current control, the dynamic phase deviation of the circulating current channel can be corrected, thereby improving the time-domain consistency of the modulation equation. By merging and normalizing the low-frequency side and circulating current modulation equations, a unified bridge arm modulation small-signal model can be formed, thereby ensuring the linearization expression of each control loop is coordinated and consistent.

[0018] In one example, the present invention can be further configured as follows: determining the equivalent admittance of the low-frequency current source and establishing the power frequency impedance model based on the bridge arm modulation small-signal model includes: The correspondence between the low-frequency modulation component and the power frequency voltage small signal is obtained from the bridge arm modulation small signal model. The ratio of the low-frequency current small signal to the power frequency voltage small signal is calculated, and the equivalent admittance matrix of the low-frequency current source is determined. Based on the mapping relationship of each coupling coefficient matrix in the equivalent admittance matrix, a multi-layer admittance solution structure including the power frequency side control link, the low frequency side control link and the circulating current control link is constructed to obtain the comprehensive admittance model. Based on the comprehensive admittance model, the equivalent admittance components of the positive-sequence channel and the negative-sequence channel are extracted respectively, and the corresponding positive-sequence impedance and negative-sequence coupling impedance are calculated. The power frequency impedance model is obtained based on the mutual mapping relationship between the positive sequence impedance and the negative sequence coupling impedance.

[0019] By adopting the above technical solutions, the correspondence between the low-frequency side modulation component and the power frequency side voltage small signal can be obtained from the bridge arm modulation small signal model, thereby establishing the equivalent admittance matrix of the low-frequency current source and realizing cross-frequency domain energy transfer modeling. By constructing a multi-layer admittance solution structure based on each coupling coefficient matrix in the equivalent admittance matrix, the coupling effect of the power frequency, low frequency and circulating current control links can be comprehensively reflected, thereby obtaining the overall comprehensive admittance model of the system. By extracting the positive sequence and negative sequence admittance components from the comprehensive admittance model and calculating the corresponding impedances, the power coupling characteristics of different sequence components can be separated, thereby supporting impedance assessment under asymmetrical operating conditions. By establishing a power frequency impedance model based on the mapping relationship between positive sequence and negative sequence impedances, the impedance distribution characteristics of the converter under different frequency excitations can be quantitatively reflected, thereby providing a theoretical basis for system stability criteria and control compensation design.

[0020] In a second aspect, the present invention provides a multi-frequency coupled M3C impedance modeling apparatus, the apparatus comprising: The modeling initialization module is used to perform time-domain equivalent modeling of the electrical parameter data of the converter arm based on the M3C average value circuit model, so as to obtain the frequency domain model of the arm loop. The frequency domain modeling module is used to characterize the steady-state characteristics of the power frequency and low frequency components in a multi-dimensional frequency domain based on the frequency domain model of the bridge arm circuit, and to establish a steady-state frequency domain model of the bridge arm voltage and current in a stationary coordinate system. The small-signal modeling module is used to linearize the variables of the steady-state frequency domain model to establish a small-signal model of the bridge arm circuit. Based on the small-signal model of the bridge arm circuit, the small-signal models of the bridge arm capacitor voltage and bridge arm current are derived, and the small-signal model conversion relationship between the bridge arm electrical parameters and the power frequency electrical parameters is established based on the small-signal relationship. The control modeling module is used to establish a modular small-signal model of the power frequency control circuit in the stationary coordinate system based on the transformation relationship. The modulation modeling module is used to derive the bridge arm modulation small-signal model that takes into account the influence of the power frequency side, the low frequency side and the circulating current control based on the modular small-signal model of the power frequency control circuit in the stationary coordinate system. The admittance impedance module is used to determine the equivalent admittance of the low-frequency current source based on the bridge arm modulation small-signal model, and to construct the power frequency impedance model based on the equivalent admittance.

[0021] By adopting the above technical solutions, and performing time-domain equivalent modeling of the electrical parameters of the converter arm based on the M3C average circuit model, the energy flow and dynamic response characteristics inside the arm can be accurately characterized without relying on the actual high-frequency switching process, thereby improving the computational stability and simulation convergence efficiency of the modeling. By performing multi-dimensional frequency domain feature characterization of the power frequency and low-frequency components based on the arm circuit frequency domain model, accurate differentiation of the power frequency and low-frequency coupling effects can be achieved, thus ensuring the frequency coverage integrity of the impedance model under complex operating conditions. Furthermore, by linearizing the steady-state frequency domain model variables and deriving the arm capacitance... Small-signal models of voltage and arm current can obtain the dynamic response law of the system under perturbation, thereby realizing the quantitative mapping between power frequency and arm-side signals. By constructing a modular model based on the stationary coordinate system and an arm modulation small-signal model, the multi-loop interaction relationship between power frequency control, low-frequency modulation and circulating current control can be comprehensively reflected, thereby improving the accuracy and usability of the overall impedance model. By determining the equivalent admittance of the low-frequency current source based on the arm modulation small-signal model and constructing a power frequency impedance model, the comprehensive quantification of the power frequency side impedance can be achieved, thereby providing a basis for the stability analysis and control strategy optimization of the converter system.

[0022] In a third aspect, the present invention provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, characterized in that the processor executes the computer program to implement the steps of the multi-frequency coupled M3C impedance modeling method described above.

[0023] In a fourth aspect, the present invention provides a storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the multi-frequency coupled M3C impedance modeling method described above.

[0024] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. By expanding the frequency sequence of power frequency and low frequency components based on the voltage, current, and capacitor voltage vector relationships in the frequency domain model of the bridge arm circuit, the orderly separation and corresponding mapping of multiple frequency components can be achieved, thereby enhancing the hierarchical clarity of the frequency domain model; by constructing a three-dimensional Toplitz matrix structure in the low-frequency harmonic dimension and coupling it with the steady-state vector relationship in a matrix manner, the cross-coupling characteristics between frequencies can be captured, thereby ensuring that the model still has high accuracy and consistency under low-frequency dynamic changes; by completing the coordinate unification process in the static coordinate system, the reference benchmark of each frequency component can be unified, thereby realizing a unified analysis framework among different frequency components. 2. By introducing low-frequency voltage control and circulating current suppression loops into the low-frequency control and circulating current control loops respectively, the frequency response characteristics of each control loop can be reflected at the modulation level, thereby realizing the synergistic modeling of multiple control channels. By establishing the transfer matrix of the modulation signal and the bridge arm voltage based on the linearized characteristic equations of the low-frequency side voltage control and circulating current suppression loops, the low-frequency side modulation small-signal equation can be constructed, thereby quantifying the influence of low-frequency side modulation on the bridge arm voltage. By mapping the circulating current small signal to the bridge arm side based on the delay characteristics and phase compensation function of the circulating current control, the dynamic phase deviation of the circulating current channel can be corrected, thereby improving the time-domain consistency of the modulation equation. By merging and normalizing the low-frequency side and circulating current modulation equations, a unified bridge arm modulation small-signal model can be formed, thereby ensuring the linearization expression of each control loop is coordinated and consistent. 3. By obtaining the correspondence between the low-frequency modulation component and the power frequency voltage small signal from the bridge arm modulation small-signal model, the equivalent admittance matrix of the low-frequency current source can be established, thereby realizing cross-frequency domain energy transfer modeling; by constructing a multi-layer admittance solution structure based on each coupling coefficient matrix in the equivalent admittance matrix, the coupling effect of the power frequency, low frequency and circulating current control links can be comprehensively reflected, thereby obtaining the overall comprehensive admittance model of the system; by extracting the positive sequence and negative sequence admittance components from the comprehensive admittance model and calculating the corresponding impedances, the power coupling characteristics of different sequence components can be separated, thereby supporting impedance assessment under asymmetrical operating conditions; by establishing a power frequency impedance model based on the mapping relationship between positive sequence and negative sequence impedances, the impedance distribution characteristics of the converter under different frequency excitations can be quantitatively reflected, thereby providing a theoretical basis for system stability criteria and control compensation design. Attached Figure Description

[0025] The accompanying drawings, which form part of this application, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a flowchart of a multi-frequency coupled M3C impedance modeling method in an embodiment of the present invention; Figure 2This is a schematic diagram of the M3C topology; Figure 3 For M3C average value model; Figure 4 For the power frequency side control loop of a modular multilevel matrix converter; Figure 5 This is a structural block diagram of the multi-frequency coupled M3C impedance modeling device according to an embodiment of the present invention; Figure 6 This is a structural block diagram of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0026] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other.

[0027] The following detailed description is exemplary and intended to provide further detailed explanation of the invention. Unless otherwise specified, all technical terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. The terminology used in this invention is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention.

[0028] Example 1 S10: Based on the M3C average value circuit model, the electrical parameter data of the converter arm are modeled in the time domain to obtain the frequency domain model of the arm circuit.

[0029] Specifically, based on the M3C average circuit model, each bridge arm is equivalent to an average branch containing bridge arm inductance, resistance, capacitance, and the corresponding modulation signal. By describing the dynamic coupling relationship between bridge arm voltage, bridge arm current, and bridge arm capacitor voltage in the time domain, the high-frequency switching effect of the sub-module is eliminated in the average value manner, while retaining the main electrical characteristics at power frequency and low frequency. This yields the bridge arm loop time-domain equivalent equation that satisfies steady-state KCL and KVL constraints. The equation is then mapped from the time domain to the frequency domain under steady-state conditions to obtain a bridge arm loop frequency domain model that can be used for frequency domain analysis and modeling.

[0030] S20: Based on the frequency domain model of the bridge arm circuit, the steady-state characteristics of the power frequency and low frequency components are characterized by multi-dimensional frequency domain features, and a steady-state frequency domain model of the bridge arm voltage and current in the stationary coordinate system is established.

[0031] Specifically, the voltage, current, and capacitor voltage components in the frequency domain model of the bridge arm circuit are decomposed into frequencies. The power frequency component and the low frequency component are extracted as independent steady-state signal branches. By uniformly representing their frequency order and phase relationship, the frequency components are arranged in sequence in the stationary coordinate system to form a two-dimensional frequency sequence structure. By introducing the low frequency harmonic dimension, the two-dimensional frequency sequence is expanded and reconstructed to uniformly express the correlation between frequency, phase, and harmonics. This yields a multi-dimensional frequency domain feature description that includes the coupling of power frequency and low frequency characteristics. Then, through coordinate unification transformation, the vector relationship in the frequency domain is converted into a steady-state frequency domain model of the bridge arm voltage and current in the stationary coordinate system to reflect the steady-state response characteristics of the M3C bridge arm under multi-frequency coupling conditions.

[0032] S30: Linearize the variables of the steady-state frequency domain model to establish the small-signal model of the bridge arm circuit. Based on the small-signal model of the bridge arm circuit, derive the small-signal models of the bridge arm capacitor voltage and bridge arm current, and establish the small-signal model conversion relationship between the bridge arm electrical parameters and the power frequency electrical parameters based on the small-signal relationship.

[0033] Specifically, based on the steady-state frequency domain model, a small disturbance signal with controllable amplitude is introduced under the steady-state operation condition of power frequency to perform micro-amplitude disturbance analysis on the voltage and current components of the bridge arm. By linearizing the difference between variables before and after the disturbance, small-signal relationships of voltage, current and capacitor voltage under each frequency component are established to extract the dynamic sensitivity characteristics of the bridge arm under multi-frequency disturbances. Then, the small-signal equations are matrix-organized so that the small-signal characteristics of the bridge arm capacitor voltage and bridge arm current are uniformly described in the frequency domain. Thus, a small-signal model of the bridge arm circuit is established, and based on the small-signal response relationship between the bridge arm capacitor voltage and current, a small-signal conversion relationship between the bridge arm electrical parameters and the power frequency electrical parameters is formed, providing a foundation for subsequent power frequency control circuit modeling.

[0034] S40: Based on the transformation relationship, establish a modular small-signal model of the power frequency control circuit in the stationary coordinate system.

[0035] Specifically, based on the small-signal conversion relationship between the bridge arm electrical parameters and the power frequency electrical parameters, the power frequency three-phase voltage and current signals are subjected to Park transformation and synchronous rotation transformation in a stationary coordinate system to extract the power frequency components of the d-axis and q-axis. Linearized expressions for the main control links such as voltage control, current control, and phase-locked loop control are introduced in this coordinate system. By modularly defining the input-output relationship of these control links in the form of transfer functions, a modular small-signal model of the power frequency control circuit that can be solved separately is constructed. The control links are connected through a small-signal coupling matrix, which can characterize the comprehensive influence of power frequency control on bridge arm modulation and current links.

[0036] S50: Based on the modular small-signal model of the power frequency control circuit in the stationary coordinate system, the bridge arm modulation small-signal model taking into account the influence of the power frequency side, the low frequency side and the circulating current control is derived.

[0037] Specifically, by introducing low-frequency control and circulating current control loops into the modular small-signal model of the power frequency control circuit, a low-frequency voltage control loop is added to the low-frequency side, and a circulating current suppression loop is added to the circulating current loop. The two control loops are linearized to obtain the transmission relationship between the corresponding low-frequency modulation signal and the bridge arm AC voltage. A phase compensation factor and a delay correction function are then introduced into the circulating current suppression loop to describe its dynamic response characteristics. The obtained low-frequency side modulation small-signal equation and circulating current modulation small-signal equation are subjected to unified matrix normalization, thereby forming a bridge arm modulation small-signal model that simultaneously considers the coupling effects of power frequency control, low-frequency control, and circulating current control, which is used to describe the dynamic transmission characteristics of the bridge arm modulation signal under multi-loop control.

[0038] S60: Based on the bridge arm modulation small-signal model, determine the equivalent admittance of the low-frequency current source, and construct the power frequency impedance model based on the equivalent admittance.

[0039] Specifically, by extracting the correlation between the low-frequency side modulation signal component and the power frequency voltage small signal in the bridge arm modulation small signal model, the ratio between the low-frequency current and the power frequency voltage is used as the basis for admittance calculation. The equivalent admittance matrix of the low-frequency current source is calculated, and the coupled admittance components in this matrix are mapped to the power frequency port. Then, a multi-layer admittance solution model is constructed by combining the admittance description structures of the power frequency control link, the low-frequency control link, and the circulating current control link. On this basis, the admittance matrix of the power frequency AC port is inverted, the impedance components of the positive sequence and negative sequence channels are extracted, and the final power frequency impedance model is obtained through the mutual mapping relationship of positive and negative sequence coupling, which is used to characterize the equivalent impedance characteristics of the M3C system power frequency port under the influence of low-frequency admittance.

[0040] In one embodiment, in step S10, the electrical parameter data of the converter arm are modeled in the time domain to obtain the frequency domain model of the arm loop, including: S11: Collect electrical parameter data of the converter arm, including the arm modulation signal.

[0041] Specifically, electrical parameter data of the converter bridge arms are collected, such as... Figure 2 In the schematic diagram of the M3C topology shown, , , as well as , , These are the three-phase AC voltage on the grid side of the M3C power frequency transformer and the three-phase current on the transformer valve side, respectively. , , as well as , , These are the three-phase AC voltage on the grid side and the three-phase AC current on the valve side of the M3C low-frequency transformer, respectively. and These are the equivalent inductance and resistance of the bridge arm, respectively. and Connecting to power frequency Phase and low frequency The phase arm voltage and the phase arm current, among which ; .

[0042] S12: Based on electrical parameter data, establish the time-domain coupling equation between bridge arm voltage, bridge arm current and capacitor voltage, and obtain the time-domain equivalent equation based on the switching action of the sub-module in the equivalent time-domain coupling equation of the average value of the bridge arm modulation signal.

[0043] Specifically, such as Figure 3 The M3C average value model shown incorporates the equivalent inductance, resistance, and modulation signal of the bridge arm into the time-domain voltage equation. Based on the Kirchhoff-Coefficient of Performance (KCL) relationship, the simultaneous-domain coupling relationship between the power frequency and low-frequency transformer side bridge arm voltages is derived, thus obtaining the power frequency transformer side bridge arm voltage. ,in, R arm The equivalent resistance of the bridge arm. i ua For the bridge arm current, L arm The equivalent inductance of the bridge arm, m ua This is the power frequency bridge arm modulation signal. v Cua This is the voltage across the bridge arm capacitor. v las This indicates the voltage of the low-frequency transformer side bridge arm. v Tgo This represents the circulating current coupling voltage component. Simultaneously, the dynamic process of the bridge arm capacitor can be expressed as: , C eq The equivalent capacitance of the bridge arm is used. Since a frequency domain mapping is established between the power frequency side and the low frequency side voltage through harmonic transformation, a frequency scaling factor is introduced to maintain consistency in the time domain. k hTD , k lTD Analytical representations of the power frequency and low frequency transformer side voltages are obtained. ,in, v hup and v lapThese are the phase voltages on the power frequency side and the low frequency side of the high-frequency transformer, respectively. Then, the time-domain equivalent equation of the bridge arm is constructed together using the above formulas to reflect the time-domain coupling relationship of the bridge arm current, bridge arm voltage, and capacitor voltage under the interaction conditions of power frequency and low frequency.

[0044] S13: The time-domain equivalent equation is stabilized by KCL constraints, and the stabilized time-domain equivalent equation is mapped to the frequency domain model of the bridge arm loop by frequency domain transformation.

[0045] Specifically, under steady-state operating conditions, the power frequency, low frequency, and circulating currents of the three phases must all satisfy the node current conservation condition, i.e., the KCL relationship holds. The three-phase current constraint equations can be expressed as: ,in, ( )and ( These are the valve sides of the power frequency transformer. Phase and low-frequency transformer valve side Phase current, i cirxa , i cirxb and i cirxc These are the corresponding circulating current components of the a, b, and c phases on the power frequency side of the bridge arm. i cirul , i cirvl and i cirwl For the corresponding u, v, w three-phase low-frequency side bridge arm circulating current components, the currents on the power frequency side and the low-frequency side also satisfy the equivalent relationship of frequency scaling: ,in, i hup and i lap These are the phase currents on the power frequency side and the low frequency side of the high-frequency transformer, respectively. The above formula describes the constraint and frequency mapping characteristics of the bridge arm current under steady-state conditions. The dynamic relationship between voltage, current and capacitor voltage can be transformed from the time domain to the frequency domain through Fourier transform, thus obtaining the frequency domain equivalent model of the bridge arm circuit.

[0046] In one embodiment, in step S20, the steady-state characteristics of the power frequency and low-frequency components are characterized by multi-dimensional frequency domain features, and a steady-state frequency domain model of the bridge arm voltage and current in the stationary coordinate system is established, including: S21: Based on the frequency domain vector relationship between bridge arm voltage, bridge arm current and capacitor voltage in the bridge arm circuit frequency domain model, the power frequency component and low frequency component are expanded into frequency sequences respectively, and arranged according to frequency order and phase relationship to form a two-dimensional frequency sequence representation.

[0047] Specifically, to clearly describe the multiple harmonic coupling characteristics of power frequency voltage and current, as well as bridge arm voltage and current, a frequency domain matrix vector method is introduced. The steady-state harmonic components of each order are expanded according to their frequency sequences to form a (2k+1)×(2k+1) dimensional frequency domain matrix vector, whose matrix expression is as follows: ,in, f 1 represents the power frequency component, corresponding to the fundamental frequency of the AC voltage and current on the M3C power frequency side. f 2 represents the low-frequency component frequency, corresponding to the frequency of the signal injected into the secondary side or control side of the low-frequency transformer. g For frequency order index, gf 1. gf 2 represents the order index factor of the frequency component after normalization or weighting on the frequency axis. Through the expansion of the above two-dimensional steady-state frequency matrix, the steady-state distribution of power frequency and low frequency signals under different harmonic orders can be completely characterized, forming a two-dimensional frequency sequence representation.

[0048] S22: The two-dimensional frequency sequence representation is structurally extended in the low-frequency harmonic dimension to obtain the corresponding three-dimensional Toplitz matrix structure.

[0049] Specifically, based on the steady-state vector relationship between the bridge arm current, bridge arm capacitor voltage, and modulation signal, the frequency domain steady-state model of the bridge arm loop can be obtained: , Y Ceq0 Let be the admittance matrix of the bridge arm capacitor. V cua Let be the frequency domain steady-state vector of the capacitor voltage of phase u-bridge arm. M ua The steady-state matrix of the bridge arm modulation signal, I ua Let be the frequency domain steady-state vector of the u-phase bridge arm current. Z arm0 The equivalent impedance matrix of the bridge arm. V hus This represents the voltage frequency domain vector at the three-phase AC terminals on the power frequency side. V las The lower bridge arm voltage frequency domain component, V Tgo To represent the frequency domain vector of the reference voltage for the control system or virtual grounding point, and in order to replace the convolution operation with matrix multiplication, the steady-state vector of the bridge arm modulation signal needs to be expanded into a two-dimensional Toplitz matrix form. Taking the steady-state matrix of the bridge arm modulation signal as an example, its two-dimensional Toplitz expansion is defined as follows: ,in M ua0,nThe amplitude coefficients of the modulation signal at different frequency offsets are represented by 0, indicating that there are no directly coupled components at that frequency order, reflecting the frequency coupling and energy transfer characteristics between different harmonic components. Subsequently, by introducing a low-frequency harmonic dimension, the frequency dimension structure of the bridge arm modulation signal is improved, forming a three-dimensional Toplitz matrix. M ua Its form of expression is: , where the matrix M ua0 , M ua±1 These represent the steady-state component matrices of the bridge arm modulation signal at power frequency, low frequency, and harmonic frequency, respectively.

[0050] S23: The three-dimensional Toplitz matrix structure is coupled with the steady-state vector relationship in the frequency domain model of the bridge arm loop in a matrix form, and the coordinate unification process is completed in the stationary coordinate system to obtain the steady-state frequency domain model of the bridge arm voltage and current in the stationary coordinate system.

[0051] Specifically, based on the three-dimensional Toplitz matrix form, matrix coupling between bridge arm voltage, current and modulation signal can be realized in the stationary coordinate system. The steady-state frequency domain model obtained through matrix coupling operation takes into account the spectral characteristics of power frequency and low frequency, realizes a unified description of the steady-state characteristics of bridge arm voltage and current, and provides a multi-dimensional frequency basis for subsequent linearized small signal modeling.

[0052] In one embodiment, in step S30, the variables of the steady-state frequency domain model are linearized to establish a small-signal model of the bridge arm loop. Based on the small-signal model of the bridge arm loop, the small-signal models of the bridge arm capacitor voltage and bridge arm current are derived. Furthermore, based on the small-signal relationships, a small-signal model conversion relationship between the bridge arm electrical parameters and the power frequency electrical parameters is established, including: S31: Based on the steady-state frequency domain model, under steady-state operating conditions, disturbance signals with preset amplitudes are introduced to the power frequency side and the low frequency side respectively. Then, the voltage and current components under the action of the disturbance signals are expanded into multi-dimensional frequency sequence representations, so as to establish a small-signal model of the bridge arm circuit based on the multi-dimensional frequency sequence representations.

[0053] Specifically, the superimposed frequency of the steady-state operating point on the AC side of the secondary winding of the power frequency transformer is... f p A positive-sequence voltage small signal is used to excite the modular multilevel matrix converter system to generate a multi-frequency coupled steady-state response. This causes the dynamic characteristics of the bridge arm inductors and capacitors to form corresponding small-signal components under disturbance. To systematically characterize this disturbance response, all voltage and current small-signal components are expanded according to frequency index. ,in, f 1 represents the power frequency disturbance frequency. f 2 represents the low-frequency side disturbance frequency. m ,n The frequency expansion order index corresponds to the frequency doubling order on the power frequency side and the low frequency side, respectively, and a small-signal vector of AC voltage on the u-phase power frequency side is constructed. and current small signal vector Its vector form is The frequency corresponding to each subscript (m,n) is f p + mf 1+ nf 2. By arranging these frequency components into a matrix, the resulting multidimensional frequency sequence can fully reflect the response characteristics of the disturbance signal in each frequency dimension. Since the voltage and current small signal quantities under power frequency and low frequency disturbances are unified into a matrix vector form in the frequency domain, this matrix is ​​the linearized small signal representation of the bridge arm circuit in the frequency domain, thus obtaining the small signal model of the bridge arm circuit.

[0054] S32: Based on the small-signal model of the bridge arm circuit, the small-signal vectors of the bridge arm capacitor voltage and bridge arm current are derived by matrix transformation, and the amplitude frequency characteristics and phase frequency characteristics in the frequency sequence are determined respectively, thus forming the small-signal model of the bridge arm capacitor voltage and bridge arm current.

[0055] Specifically, based on the small-signal model of the bridge arm loop, the small-signal values ​​of the bridge arm capacitor voltage and bridge arm current are expanded in the frequency domain within a matrixed multi-frequency sequence structure. The amplitude-frequency and phase-frequency characteristics of each frequency component are explicitly represented, establishing the coupling relationship between the bridge arm capacitor voltage and the bridge arm current, forming a matrix-form small-signal equation for the bridge arm. The small-signal values ​​of the bridge arm capacitor voltage and the bridge arm current satisfy the following frequency domain linearization relationship: , ,in, Z Ceq This is the bridge arm capacitance impedance matrix. Y arm For the bridge arm inductor admittance matrix, This is a small-signal vector of the bridge arm current. I ua This represents the steady-state component of the bridge arm current. For the small signal component of the modulated signal, Let be the small-signal vector of the virtual grounding point voltage, and their frequency domain expressions are respectively... and Where, diag[.] is a diagonal matrix function, A pd0 This is a correction diagonal matrix for the bridge arm inductance, used to set the admittance term to zero when mod(m+1,3)=0 and mod(m,3)=0, ensuring correct frequency correction and coupling of the inductor components. R arm , L armThe parameters are the resistance and inductance of the bridge arm, respectively. After the frequency domain derivation described above, the small signals of the bridge arm capacitor voltage and current can be expressed in matrix vector form, forming a small signal model of the bridge arm capacitor voltage and current that includes all frequency components.

[0056] S33: Based on the small-signal model of the bridge arm capacitor voltage and bridge arm current, determine the coupling matrix relationship between each frequency component, and perform phase sequence decomposition on the three-phase bridge arm current components according to the coupling matrix relationship to determine the phase coefficient matrix corresponding to the positive sequence component, negative sequence component and zero sequence component.

[0057] Specifically, the small-signal model of the bridge arm contains frequency coupling terms in the three-phase channels. It is necessary to decouple the small-signal representations of the three-phase voltage and current in the positive, negative, and zero-sequence channels through phase sequence decomposition. First, the transformation relationship of the three-phase voltage and current small-signal vectors in the phase sequence domain is defined: ,in, , The small-signal vector of phase v is obtained by shifting phase u by +120 degrees. , The small signal vector of phase w is obtained by shifting phase u by -120 degrees. , These are the small-signal frequency sequence components of the U-phase AC voltage and current on the power frequency side. D hp This is the phase sequence transformation coefficient matrix for three-phase AC voltage and current small signals, used to realize the phase rotation from the physical three-phase coordinate system to the symmetrical component coordinate system. Based on the frequency index (m,n) of the small signal, when... That is, the modulo operation of the power frequency multiplier can define the judgment conditions for positive sequence, negative sequence and zero sequence components respectively, thereby obtaining the phase sequence component correspondence of the three-phase bridge arm current, so as to transform the coupling between different frequency components from the three-phase form into the phase sequence domain linear relationship matrix, laying the foundation for subsequent port mapping, and clearly obtaining the phase coefficient matrix corresponding to the positive, negative and zero sequence components.

[0058] S34: Based on the phase coefficient matrix, map the bridge arm electrical parameters to power frequency electrical parameters to obtain the small-signal model conversion relationship between the bridge arm electrical parameters and the power frequency electrical parameters.

[0059] Specifically, after the phase sequence domain decomposition is completed, the mapping relationship between the bridge arm current, circulating current, and AC current is established through the phase coupling matrix between each sequence component. At this time, the linearization relationship between the three-phase bridge arm current, capacitor voltage, and modulation signal in the phase sequence domain can be further expressed as: ,in This represents the small-signal vector of the x-phase AC current on the power frequency side. This represents the small-signal vector of the low-frequency side I-phase AC current. This is the small-signal vector of the bridge arm circulation corresponding to the xl channel. Let A be the small-signal vector of the equivalent arm current of the bridge arm xl channel. phd A pld A pcid These are the positive-order component transformation matrix, the negative-order component transformation matrix, and the circulation channel transformation matrix, respectively, defined as: This matrix group filters out the coupling relationship of each sequence component through selection and zeroing operations, so that the bridge arm circulating current and bridge arm current component are consistent with the power frequency port quantity, thereby realizing the small signal mapping relationship from the bridge arm side electrical parameters to the power frequency side electrical parameters, and then obtaining the small signal model conversion relationship between the bridge arm electrical parameters and the power frequency electrical parameters.

[0060] In one embodiment, in step S40, based on the small-signal model transformation relationship between the bridge arm electrical parameters and the power frequency electrical parameters, a modular small-signal model of the power frequency control circuit in the stationary coordinate system is established, including: S41: Based on the small-signal model transformation relationship between bridge arm electrical parameters and power frequency electrical parameters, the power frequency three-phase voltage, current and bridge arm capacitor voltage variables are transformed in the stationary coordinate system to obtain the small-signal components of the d-axis and q-axis.

[0061] Specifically, such as Figure 4 In the power frequency side control loop of the modular multilevel matrix converter shown, the synchronization phase angle θ is output by the phase-locked loop (PLL). hPLL As a reference angle for the rotating coordinates, the three-phase AC voltage at power frequency v hns Perform the Park transform to obtain its d-axis component v. hds and q-axis component v hqs Meanwhile, the average value of the bridge arm capacitor voltage v cave Compared with reference value v Cdref The difference is used as the control loop H of the bridge arm capacitor voltage. Cdc The input signal (s) generates the bridge arm current d-axis component reference command i. hdref Then the bridge arm current i hl According to θ PLL To synchronize the rotation of the reference angle, a Park transformation is performed to obtain the d, q, and 0-axis current components i. da i db i dc Their average values ​​are i dave i qave and control loop H with power frequency current hiac (s) input signal i hdref -i dave The difference is obtained by modulating coefficient K. vCdr And the inverse Park coordinate transformation generates the current modulation signal m on the M3C power frequency side. comx The modulation coefficient K hd m hdm hq The power frequency modulation coefficients corresponding to the d and q axis channels are respectively used. Then, by establishing the transformation relationship between the bridge arm capacitor voltage, bridge arm current and AC current in the synchronous rotating coordinate system, the dq coordinate small signal modeling framework of the power frequency control loop is obtained.

[0062] S42: Based on the small-signal components of the d-axis and q-axis, establish the linearized transmission relationship of voltage control, current control and phase-locked loop control in the power frequency control loop, and form the small-signal description model of each loop.

[0063] Specifically, a small disturbance signal is introduced at the steady-state operating point of the power frequency AC voltage, causing the bridge arm capacitor voltage control loop and the power frequency current control loop to simultaneously produce a small dynamic offset, forming a bridge arm current disturbance component in the dq coordinate system. , The difference corresponds to the small-signal components of the bridge arm current, respectively. , Through the power frequency AC current control loop H hiac (s) After transmission, a small-signal modulated power frequency voltage of the modular multilevel matrix converter is generated. By inversely transforming the current and voltage disturbances using Park coordinates, the small-signal component of the secondary voltage of the modular multilevel matrix converter can be obtained. After correction by the modulation coefficient, the small-signal component of the modulation signal is formed. ,in, D h1 , D h2 , D h3 For the time-delay transfer function, the diagonal matrix, G h1 , G h2 , G h3 For a dimension of (2g+1) 2 ×(2g+1) 2 The coupling matrix is ​​defined as follows: Where mod(.,3) is the phase sequence mapping operator modulo 3. m , n Integer index for a two-dimensional frequency sequence. K hd The d-axis AC current decoupling coefficient is... ,in, mid =[(2 g +1) 2 +1] / 2 is the index of the middle position of the row / column of the three-dimensional Toplitz matrix. T hPLL The small-signal gain from the phase perturbation of the PLL phase-locked loop to the coordinate transformation. Iua It is the identity matrix. M ua For the coefficient block of the u-phase steady-state modulation matrix at the corresponding frequency point, v hns1 This is the power frequency secondary fundamental frequency voltage value. This allows the small-signal components of the power frequency voltage, bridge arm current, and capacitor voltage to be expressed in a matrix in the frequency domain, thus obtaining a power frequency modulation small-signal model for a modular multilevel matrix converter.

[0064] S43: Based on the input-output correlation of each small-signal description model, modular modeling of the power frequency control link is performed to obtain a modular small-signal model of the power frequency control circuit in the stationary coordinate system.

[0065] Specifically, the dynamic response characteristics of the power frequency AC current control loop, phase-locked loop, and bridge arm capacitor voltage control loop are represented by delay transfer function matrices, and three sets of diagonal matrices are defined: , , ,in, T Hiac , T Hvac , T Cde These are the filtering delays for AC current control, AC voltage control, and DC voltage control loops, respectively. This matrix group characterizes the delay and phase compensation characteristics of each power frequency control loop in the frequency domain. It can couple the small-signal model of the bridge arm with the modular structure of power frequency control, thereby realizing the small-signal modeling of the power frequency control circuit in the stationary coordinate system.

[0066] In one embodiment, in step S50, based on the modular small-signal model of the power frequency control circuit in the stationary coordinate system, a bridge arm modulation small-signal model considering the influence of the power frequency side, the low-frequency side, and the circulating current control is derived, including: S51: Based on the modular small-signal model of the power frequency control circuit, a low-frequency side voltage control loop and a circulating current suppression loop are introduced into the low-frequency control and circulating current control loops, respectively.

[0067] Specifically, a low-frequency voltage outer loop and a current inner loop structure are established in the low-frequency side control channel, and the low-frequency side outer loop adopts a voltage control element. H vac (s) To adjust the steady-state deviation of low-frequency AC voltage, the inner loop employs a current control element. H iac(s) Suppressing current ripple and stabilizing system output, the circulating current control loop establishes a current suppression channel based on the bridge arm current feedback signal. By introducing a proportional resonant controller and a delay compensation function, circulating current feedback regulation is achieved, thereby enabling dual constraints on the voltage and current on the power frequency and low frequency sides in the bridge arm modulation layer. Based on the principle of linearization modeling, the modulation signals on the low frequency side and the circulating current side can be represented as a functional relationship between the bridge arm voltage and current disturbance, forming a parallel modulation channel that includes voltage feedback and current feedback, providing a structural basis for subsequent small-signal matrix expression.

[0068] S52: Based on the linearized characteristic equations of the low-frequency side voltage control loop and the circulating current suppression loop, construct the transfer matrix expression between the low-frequency side modulation signal and the bridge arm AC voltage, and obtain the low-frequency side modulation small-signal equation.

[0069] Specifically, the low-frequency side connects to a current source, a phase-locked loop (PLL), and a frequency control module. Based on the low-frequency AC voltage outer loop control and the low-frequency component inner loop suppression framework of the bridge arm current, a low-frequency output modulation small-signal model can be obtained by establishing a mapping relationship between the low-frequency modulation signal and the low-frequency AC voltage in the low-frequency control branch. ,in, G l1 , G l2 For (2) g +1) 2 ×(2 g +1) 2 The gain matrix, D l1 , D l2 These are the delay transfer function matrices for low-frequency AC current control and AC voltage control, respectively. This is a small-signal column vector of the AC voltage on the primary side of the low-frequency transformer. All elements are 0 except for the elements listed below. Specifically, it is defined as follows: ,in, V cdc The average voltage on the DC side. H liac (s) is the transfer function of the low-frequency AC current control loop. k ld The d-axis decoupling coefficient for low-frequency alternating current. ,in, H vac(s) is the transfer function for the low-frequency AC voltage outer loop control. D l1 , D l2 The expressions are as follows: , ,in T liac , Tvac These represent the filtering delays of low-frequency AC current and AC voltage control, respectively, thereby establishing a precise frequency domain correspondence between the low-frequency side modulation signal and the bridge arm voltage.

[0070] S53: Based on the delay characteristics and phase compensation function of the circulating current suppression circuit, the small-signal component of the circulating current is mapped to the bridge arm side by coordinate transformation, forming the circulating current modulation small-signal equation.

[0071] Specifically, the circulating current control circuit uses a proportional resonant controller PR to regulate small-signal disturbances in the bridge arm current. Let the delay function of the circulating current controller be... D lo1 The small signal component of the circulating current control output is Then the circulating modulation equation can be expressed as: ,in G lo1 (2g+1) 2 ×(2g+1) 2 The coupling matrix of the circulating control element, D lol is the delay transfer function matrix, defined as follows: ,in, H lop1 , H lop2 These are the PR controller transfer functions for the circulating d-axis and q-axis, respectively. ,in, T lo The delay constant of the circulating current control channel is represented. After coordinate transformation and delay correction, the circulating current disturbance is mapped to the bridge arm modulation side, realizing a unified frequency domain coupling expression of the circulating current component and the bridge arm modulation.

[0072] S54: The low-frequency side modulation small-signal equation and the circulating current modulation small-signal equation are merged and normalized to obtain the bridge arm modulation small-signal model.

[0073] Specifically, the low-frequency modulation small-signal equation and the circulating current modulation small-signal equation are matrix-merged in a unified stationary coordinate system. Normalization is then used to eliminate amplitude reference differences between different control elements, ultimately yielding the bridge arm modulation small-signal model. The coupling matrix relationship of each channel is as follows: This small-signal model can characterize the frequency domain interaction relationship between power frequency modulation, low-frequency modulation and circulating current modulation within a unified framework.

[0074] In one embodiment, in step S60, based on the bridge arm modulation small-signal model, the equivalent admittance of the low-frequency current source is determined and the power frequency impedance model is established, including: S61: Obtain the correspondence between the low-frequency side modulation component and the power frequency side voltage small signal from the bridge arm modulation small signal model, calculate the ratio of the power frequency AC current small signal to the power frequency voltage small signal, and determine the equivalent admittance matrix of the low-frequency current source.

[0075] Specifically, based on the bridge arm modulation small-signal model, the current response of the power frequency disturbance signal is extracted under steady-state conditions. The ratio between the power frequency AC current small signal and the power frequency voltage small signal is established through frequency domain linearization. The equivalent admittance matrix of the low-frequency current source is defined as follows: This is used to characterize the response capability of the low-frequency control element to power frequency voltage disturbances.

[0076] S62: Based on the mapping relationship of each coupling coefficient matrix in the equivalent admittance matrix, a multi-layer admittance solution structure including the power frequency side control link, the low frequency side control link and the circulating current control link is constructed to obtain the comprehensive admittance model.

[0077] Specifically, parameters such as the low-frequency current source, bridge arm voltage modulation element, circulating current control, and capacitor voltage control are coupled into a system admittance equation. Through matrix derivation, the M3C system admittance expression is: ,in, This is the coefficient matrix showing the influence of the bridge arm circuit on the M3C's power frequency admittance. This is the steady-state operating point coefficient matrix. This is the coefficient matrix for the power frequency AC current control link. This is the low-frequency AC current control link coefficient matrix. This is the circulating control link coefficient matrix. This is the bridge arm capacitor voltage control coefficient matrix. This is the coupling coefficient matrix of the bridge arm capacitor voltage and current loop. This is the low-frequency voltage control coefficient matrix. This is the impedance coefficient matrix of a low-frequency current source. This is the control coefficient matrix for the power frequency phase-locked loop. This is the coupling coefficient matrix between the bridge arm capacitor voltage control and the low-frequency AC control. Here are the coefficient matrices for the power frequency transformer; all of the above matrices are (2g+1). 2 ×(2g+1) 2 A square matrix of order 1, its specific expansion is as follows: ,in, G 4 represents the equivalent gain matrix of the bridge arm capacitor voltage control link. G 3 represents the auxiliary gain matrix in low-frequency voltage control / power frequency coupling. G 2 represents the equivalent gain matrix from the low-frequency side voltage control link to the bridge arm side. U It is the identity matrix, used for closed-loop equivalent operations. Z LThis is the equivalent impedance of a low-frequency current source. k nTD The normalized coefficients of the power frequency modulation / current loop are used to fully reflect the multidimensional coupling relationship between each control loop and the bridge arm current in the M3C system, thereby obtaining the comprehensive admittance model.

[0078] S63: Based on the integrated admittance model, extract the equivalent admittance components of the positive-sequence channel and the negative-sequence channel respectively, and calculate the corresponding positive-sequence impedance and negative-sequence coupling impedance.

[0079] Specifically, based on the component distribution of the power frequency disturbance frequency, from the admittance matrix... Y M3C Extract the elements in the mid-th row and mid-th column to represent the positive-order admittance component, and simultaneously extract the elements in the mid-th column. The element in row 2, mid-column represents the negative-order coupling admittance component, from which the following definition can be made: ,in Y M3C ( mid , mid Characterizing the system at frequency f p + f The positive-sequence admittance response at 1, Y M3C ( mid 2, mid Characterizing frequency f p 2 f The cross admittance response under condition 1, the former corresponds to the positive sequence impedance, and the latter reflects the coupling effect between the positive and negative sequence channels.

[0080] S64: Based on the mutual mapping relationship between positive sequence impedance and negative sequence coupling impedance, the power frequency impedance model is obtained.

[0081] Specifically, based on the complex conjugate relation, the negative-sequence impedance and the negative-sequence coupling impedance can be obtained through conjugate mapping, i.e. Based on this, a complete power frequency impedance matrix model including positive and negative sequences and coupling channels can be established to simultaneously characterize the stability and dynamic characteristics of the system under multi-frequency interaction conditions, serving as the final calculation result for the impedance modeling of the M3C converter.

[0082] Example 2 like Figure 5 As shown, based on the same inventive concept as the above embodiments, the present invention also provides a multi-frequency coupled M3C impedance modeling device, comprising: The modeling initialization module is used to perform time-domain equivalent modeling of the electrical parameter data of the converter arm based on the M3C average value circuit model, so as to obtain the frequency domain model of the arm loop. The frequency domain modeling module is used to characterize the steady-state characteristics of the power frequency and low frequency components in a multi-dimensional frequency domain based on the frequency domain model of the bridge arm circuit, and to establish a steady-state frequency domain model of the bridge arm voltage and current in the stationary coordinate system. The small-signal modeling module is used to linearize the variables of the steady-state frequency domain model to establish the small-signal model of the bridge arm circuit. Based on the small-signal model of the bridge arm circuit, the small-signal models of the bridge arm capacitor voltage and bridge arm current are derived, and the small-signal model conversion relationship between the bridge arm electrical parameters and the power frequency electrical parameters is established based on the small-signal relationship. The control modeling module is used to establish a modular small-signal model of the power frequency control circuit in the stationary coordinate system based on the transformation relationship. The modulation modeling module is used to derive the bridge arm modulation small-signal model that takes into account the influence of the power frequency side, low frequency side and circulating current control based on the modular small-signal model of the power frequency control circuit in the stationary coordinate system. The admittance impedance module is used to determine the equivalent admittance of a low-frequency current source based on the bridge arm modulation small-signal model, and to construct a power frequency impedance model based on the equivalent admittance.

[0083] Optionally, the modeling initialization module includes: The data acquisition submodule is used to acquire electrical parameter data of the converter arm, including the arm modulation signal; The equation modeling submodule is used to establish the time-domain coupling equation between the bridge arm voltage, bridge arm current, and capacitor voltage based on electrical parameter data, and to obtain the time-domain equivalent equation based on the switching action of the submodule in the equivalent time-domain coupling equation of the average value of the bridge arm modulation signal. The frequency domain transformation submodule is used to stabilize the time-domain equivalent equations through KCL constraints, and then map the stabilized time-domain equivalent equations to the frequency domain model of the bridge arm loop through frequency domain transformation.

[0084] Optional, the frequency domain modeling module includes: The frequency expansion submodule is used to expand the frequency sequence of the power frequency component and the low frequency component based on the frequency vector relationship between the bridge arm voltage, bridge arm current and capacitor voltage in the bridge arm circuit frequency domain model, and arrange them according to the frequency order and phase relationship to form a two-dimensional frequency sequence representation. The matrix extension submodule is used to structurally extend the two-dimensional frequency sequence representation in the low-frequency harmonic dimension to obtain the corresponding three-dimensional Toplitz matrix structure. The matrix coupling submodule is used to matrix-couple the three-dimensional Toplitz matrix structure with the steady-state vector relationship in the frequency domain model of the bridge arm loop, and to perform coordinate unification processing in the stationary coordinate system to obtain the steady-state frequency domain model of the bridge arm voltage and current in the stationary coordinate system.

[0085] Optional, the small-signal modeling module includes: The disturbance injection submodule is used to introduce disturbance signals of preset amplitude to the power frequency side and the low frequency side under steady-state operating conditions based on the steady-state frequency domain model. Then, the voltage and current components under the action of the disturbance signal are expanded into a multi-dimensional frequency sequence representation, so as to establish a small-signal model of the bridge arm circuit based on the multi-dimensional frequency sequence representation. The signal derivation submodule is used to perform matrix derivation of the small-signal vectors of bridge arm capacitor voltage and bridge arm current based on the small-signal model of the bridge arm circuit, determine the amplitude frequency characteristics and phase frequency characteristics in the frequency sequence respectively, and form the small-signal model of bridge arm capacitor voltage and bridge arm current. The phase sequence decomposition submodule is used to determine the coupling matrix relationship between each frequency component based on the small-signal model of the bridge arm capacitor voltage and bridge arm current. Based on the coupling matrix relationship, the phase sequence decomposition of the three-phase bridge arm current components is performed to determine the phase coefficient matrix corresponding to the positive sequence component, negative sequence component and zero sequence component. The model mapping submodule is used to map the bridge arm electrical parameters to power frequency electrical parameters based on the phase coefficient matrix, thereby obtaining the small-signal model conversion relationship between the bridge arm electrical parameters and the power frequency electrical parameters.

[0086] Optionally, the control modeling module includes: The coordinate transformation submodule is used to transform the power frequency three-phase voltage, current and bridge arm capacitor voltage variables in the stationary coordinate system based on the small-signal model conversion relationship between the bridge arm electrical parameters and the power frequency electrical parameters, and obtain the small-signal components of the d-axis and q-axis. The control linearization submodule is used to establish the linearized transmission relationship of voltage control, current control and phase-locked control in the power frequency control link based on the small signal components of the d-axis and q-axis, and form the small signal description model of each link; The modular modeling submodule is used to perform modular modeling of the power frequency control link according to the input-output correlation of each small signal description model, so as to obtain the modular small signal model of the power frequency control circuit in the stationary coordinate system.

[0087] Optionally, the modulation modeling module includes: The control introduction submodule is used to introduce low-frequency side voltage control and circulating current suppression links into the low-frequency control and circulating current control loops, respectively, based on the modular small-signal model of the power frequency control circuit. The matrix construction submodule is used to construct the transfer matrix expression between the low-frequency side modulation signal and the bridge arm AC voltage based on the linearized characteristic equations of the low-frequency side voltage control loop and the circulating current suppression loop, and obtain the low-frequency side modulation small-signal equation. The phase mapping submodule is used to perform coordinate transformation and mapping of the small-signal component of the circulating current to the bridge arm side based on the delay characteristics and phase compensation function of the circulating current suppression link, thus forming the circulating current modulation small-signal equation. The model normalization submodule is used to merge and normalize the low-frequency side modulation small-signal equation and the circulating current modulation small-signal equation to obtain the bridge arm modulation small-signal model.

[0088] Optional, admittance impedance modules include: The admittance extraction submodule is used to obtain the correspondence between the low-frequency side modulation component and the power frequency side voltage small signal from the bridge arm modulation small signal model, calculate the ratio of the low-frequency current small signal to the power frequency voltage small signal, and determine the equivalent admittance matrix of the low-frequency current source. The admittance coupling submodule is used to construct a multi-layer admittance solution structure that includes the power frequency side control link, the low frequency side control link and the circulating current control link according to the mapping relationship of each coupling coefficient matrix in the equivalent admittance matrix, so as to obtain the comprehensive admittance model. The impedance decomposition submodule is used to extract the equivalent admittance components of the positive-sequence and negative-sequence channels based on the comprehensive admittance model, and calculate the corresponding positive-sequence impedance and negative-sequence coupling impedance. The impedance modeling submodule is used to obtain the power frequency impedance model based on the mapping relationship between positive sequence impedance and negative sequence coupling impedance.

[0089] Example 3 like Figure 6 As shown, the present invention also provides an electronic device 100 for implementing a multi-frequency coupled M3C impedance modeling method; The electronic device 100 includes a memory 101, at least one processor 102, a computer program 103 stored in the memory 101 and executable on at least one processor 102, and at least one communication bus 104.

[0090] The memory 101 can be used to store the computer program 103. The processor 102 implements the steps of the multi-frequency coupled M3C impedance modeling method of Embodiment 1 by running or executing the computer program stored in the memory 101 and calling the data stored in the memory 101.

[0091] The memory 101 may primarily include a program storage area and a data storage area. The program storage area may store the operating system, application programs required for at least one function (such as sound playback function, image playback function, etc.), etc.; the data storage area may store data created based on the use of the electronic device 100 (such as audio data), etc. In addition, the memory 101 may include non-volatile memory, such as hard disk, RAM, plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, at least one disk storage device, flash memory device, or other non-volatile solid-state storage device.

[0092] At least one processor 102 may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. Processor 102 may be a microprocessor or any conventional processor. Processor 102 is the control center of electronic device 100, connecting various parts of electronic device 100 via various interfaces and lines.

[0093] The memory 101 in the electronic device 100 stores multiple instructions to implement a multi-frequency coupled M3C impedance modeling method, and the processor 102 can execute multiple instructions to achieve the following: Based on the M3C average value circuit model, the electrical parameter data of the converter arm are modeled in the time domain to obtain the frequency domain model of the arm circuit. Based on the frequency domain model of the bridge arm circuit, the steady-state characteristics of the power frequency and low frequency components are characterized by multi-dimensional frequency domain features, and a steady-state frequency domain model of the bridge arm voltage and current in the stationary coordinate system is established. The variables of the steady-state frequency domain model are linearized and decomposed to establish a small-signal model of the bridge arm circuit. Based on the small-signal model of the bridge arm circuit, the small-signal models of the bridge arm capacitor voltage and bridge arm current are derived. Based on the small-signal relationship, the small-signal model conversion relationship between the bridge arm electrical parameters and the power frequency electrical parameters is established. Based on the transformation relationship, a modular small-signal model of the power frequency control circuit in the stationary coordinate system is established; Based on the modular small-signal model of the power frequency control circuit in the stationary coordinate system, the bridge arm modulation small-signal model that takes into account the influence of the power frequency side, the low frequency side and the circulating current control is derived. Based on the bridge arm modulation small-signal model, the equivalent admittance of the low-frequency current source is determined, and the power frequency impedance model is constructed based on the equivalent admittance.

[0094] Example 4 If the modules / units integrated in the electronic device 100 are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments of the present invention can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, and read-only memory (ROM).

[0095] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0096] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0097] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0098] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0099] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0100] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A multi-frequency coupled (M3C) impedance modeling method, characterized by, The method comprises: Based on the M3C average value circuit model, the electrical parameter data of the converter bridge arm is time-domain equivalent modeling to obtain the bridge arm loop frequency domain model; According to the bridge arm loop frequency domain model, the steady-state characteristics of the power frequency and low frequency components are characterized in multi-dimensional frequency domain, and the steady-state frequency domain model of the bridge arm voltage and current in the static coordinate system is established; The variables of the steady-state frequency domain model are linearly decomposed to establish the bridge arm loop small signal model, according to the bridge arm loop small signal model, the small signal model of the bridge arm capacitor voltage and the bridge arm current is derived, and the small signal model conversion relationship between the bridge arm electrical parameters and the power frequency electrical parameters is established according to the small signal model; According to the small signal model conversion relationship, the modular small signal model of the power frequency control circuit in the static coordinate system is established; Based on the modular small signal model of the power frequency control circuit in the static coordinate system, the bridge arm modulation small signal model considering the influence of the power frequency side, the low frequency side and the circulating current control is derived; Based on the bridge arm modulation small signal model, the equivalent admittance of the low frequency current source is determined, and the power frequency impedance model is constructed according to the equivalent admittance.

2. The multi-frequency coupled (M3C) impedance modeling method of claim 1, wherein, The method comprises: Collecting electrical parameter data of the converter bridge arm, wherein the electrical parameter data comprises bridge arm modulation signals; Based on the electrical parameter data, the time-domain coupling equation between the bridge arm voltage and the bridge arm current and the capacitor voltage is established, and the time-domain equivalent equation is obtained by equivalent switching action of the sub-modules in the time-domain coupling equation according to the average value of the bridge arm modulation signals; Through KCL constraint, the steady-state of the time-domain equivalent equation is processed, and the steady-state of the time-domain equivalent equation is mapped to the bridge arm loop frequency domain model through frequency domain conversion.

3. The multi-frequency coupled (M3C) impedance modeling method of claim 1, wherein, The method comprises: Based on the frequency domain vector relationship of the bridge arm voltage, the bridge arm current and the capacitor voltage in the bridge arm loop frequency domain model, the frequency sequence expansion of the power frequency component and the low frequency component is carried out respectively, and the two-dimensional frequency sequence representation is arranged according to the frequency order and the phase relationship; The two-dimensional frequency sequence representation is structurally expanded in the low frequency multiple frequency dimension to obtain the corresponding three-dimensional toplitz matrix structure; The three-dimensional toplitz matrix structure and the steady-state vector relationship in the bridge arm loop frequency domain model are matrix coupled, and the coordinate consistency processing is completed in the static coordinate system to obtain the steady-state frequency domain model of the bridge arm voltage and current in the static coordinate system.

4. The multi-frequency coupled (M3C) impedance modeling method of claim 1, wherein, The method comprises: The steady-state frequency domain model is used to introduce a preset amplitude disturbance signal to the power frequency side and the low frequency side respectively under a steady-state working condition, and then voltage and current components under the disturbance signal are expanded into a multi-dimensional frequency sequence representation, so as to establish the bridge arm loop small signal model according to the multi-dimensional frequency sequence representation; According to the bridge arm loop small signal model, a matrix is derived for a small signal vector of the bridge arm capacitor voltage and the bridge arm current, and amplitude-frequency characteristics and phase-frequency characteristics in the frequency sequence are determined respectively, so as to form the small signal model of the bridge arm capacitor voltage and the bridge arm current; Based on the small signal model of the bridge arm capacitor voltage and the bridge arm current, a coupling matrix relationship between frequency components is determined, and according to the coupling matrix relationship, three-phase bridge arm current components are phase sequence decomposed to determine phase coefficient matrices corresponding to positive sequence components, negative sequence components and zero sequence components; According to the phase coefficient matrix, the bridge arm electrical parameters are mapped to the power frequency electrical parameters to obtain the small signal model conversion relationship between the bridge arm electrical parameters and the power frequency electrical parameters.

5. The multi-frequency coupled (M3C) impedance modeling method of claim 1, wherein, The small signal model conversion relationship is used to establish a modular small signal model of a power frequency control circuit in a stationary coordinate system, including: Based on the small signal model conversion relationship between the bridge arm electrical parameters and the power frequency electrical parameters, three-phase voltage and current variables are coordinate-transformed in the stationary coordinate system to obtain small signal components of d-axis and q-axis; According to the small signal components of d-axis and q-axis, linearized transfer relationships of voltage control, current control and phase-locked control in the power frequency control link are established to form small signal description models of each link; According to input-output correlation relationships of the small signal description models, the power frequency control link is modeled in a modular manner to obtain a modular small signal model of the power frequency control circuit in the stationary coordinate system.

6. The multi-frequency coupled (M3C) impedance modeling method of claim 1, wherein, Based on the modular small signal model of the power frequency control circuit in the stationary coordinate system, a bridge arm modulation small signal model considering the influences of the power frequency side, the low frequency side and the circulating current control is derived, including: Based on the modular small signal model of the power frequency control circuit, a low frequency side voltage control link and a circulating current suppression link are introduced into the low frequency control and the circulating current control loop respectively; According to linearized characteristic equations of the low frequency side voltage control link and the circulating current suppression link, a transfer matrix expression between the low frequency side modulation signal and the bridge arm alternating voltage is constructed to obtain a low frequency side modulation small signal equation; According to the delay characteristic and the phase compensation function of the circulating current suppression link, small signal components of the circulating current are coordinate-transformed and mapped to the bridge arm side to form a circulating current modulation small signal equation; The low frequency side modulation small signal equation and the circulating current modulation small signal equation are combined and normalized to obtain the bridge arm modulation small signal model.

7. The multi-frequency coupled (M3C) impedance modeling method of claim 1, wherein, Based on the bridge arm modulation small signal model, an equivalent admittance of a low frequency current source is determined and a power frequency impedance model is established, including: A corresponding relationship between the low frequency side modulation component and the power frequency side voltage small signal is obtained from the bridge arm modulation small signal model, a ratio of the low frequency current small signal to the power frequency voltage small signal is calculated, and an equivalent admittance matrix of the low frequency current source is determined. According to the mapping relationship of each coupling coefficient matrix in the equivalent admittance matrix, a multi-layer admittance solving structure including a power frequency side control link, a low frequency side control link and a circulating current control link is constructed, and a comprehensive admittance model is obtained; Based on the comprehensive admittance model, the equivalent admittance components of the positive sequence channel and the negative sequence channel are extracted respectively, and the corresponding positive sequence impedance and negative sequence coupling impedance are calculated; According to the mutual mapping relationship between the positive sequence impedance and the negative sequence coupling impedance, the power frequency impedance model is obtained.

8. A multi-frequency coupled (M3C) impedance modeling apparatus, comprising: The device comprises: A modeling initialization module is configured to perform time domain equivalent modeling on electrical parameter data of a bridge arm of a converter based on an M3C average value circuit model, and obtain a bridge arm loop frequency domain model; A frequency domain modeling module is configured to perform multi-dimensional frequency domain feature characterization on steady state characteristics of power frequency and low frequency components according to the bridge arm loop frequency domain model, and establish a steady state frequency domain model of bridge arm voltage and current in a stationary coordinate system; A small signal modeling module is configured to linearly decompose variables of the steady state frequency domain model to establish a bridge arm loop small signal model, derive a small signal model of bridge arm capacitor voltage and bridge arm current according to the bridge arm loop small signal model, and establish a small signal model conversion relationship between bridge arm electrical parameters and power frequency electrical parameters according to the small signal relationship; A control modeling module is configured to establish a modularized small signal model of a power frequency control circuit in a stationary coordinate system according to the conversion relationship; A modulation modeling module is configured to derive a bridge arm modulation small signal model considering the influence of power frequency side, low frequency side and circulating current control based on the modularized small signal model of the power frequency control circuit in the stationary coordinate system; An admittance impedance module is configured to determine an equivalent admittance of a low frequency current source based on the bridge arm modulation small signal model, and construct a power frequency impedance model according to the equivalent admittance.

9. An electronic device, comprising: The device comprises a processor and a memory, and the processor is configured to execute a computer program stored in the memory to implement the steps of the multi-frequency coupling M3C impedance modeling method according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer readable storage medium stores at least one instruction, and the at least one instruction is executed by the processor to implement the steps of the multi-frequency coupling M3C impedance modeling method according to any one of claims 1 to 7.

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