M3C double-fundamental-frequency coupling characterization method, device, equipment and medium

Abstract

The invention relates to an M3C double-fundamental-frequency coupling characterization method, device, equipment and medium, and the method comprises the steps: building a basic dynamic equation of bridge arm electrical parameters based on an M3C average value model; based on the basic dynamic equation, performing frequency domain decomposition and matrix representation on the electrical parameters under power frequency and low frequency conditions to generate a two-dimensional frequency domain matrix; performing linear equivalent modeling on the frequency domain operation relation of the two-dimensional frequency domain matrix to obtain a structured matrix; dimensionality reduction processing is carried out on the structured matrix, and steady-state frequency representation of the bridge arm electrical parameters is obtained; and based on the steady-state frequency representation, deducing to obtain a steady-state frequency domain harmonic model of the bridge arm loop. The method has the effect of improving the accuracy of analyzing the steady-state frequency characteristics of the electrical parameters of the bridge arm by the M3C.

Description

Technical Field

[0001] This invention belongs to the technical field of high voltage direct current transmission impedance modeling, and in particular relates to an M3C dual fundamental frequency coupling characterization method, device, equipment and medium. Background Technology

[0002] Currently, multilevel matrix converters (M3Cs) are widely used in high-voltage, high-power energy conversion. An M3C consists of multiple bridge arm modules, and its operation is influenced by capacitor voltage balance, modulation signal waveform, and power coupling at both the mains frequency and low frequency. To accurately describe its dynamic operating characteristics, researchers typically use an average value model to perform time-domain modeling of the bridge arm current and capacitor voltage, and derive the relationship between bridge arm voltage and current under steady-state conditions, thereby analyzing the output characteristics and steady-state performance of the M3C system.

[0003] Existing M3C characterization and modeling methods commonly employ a technique of deriving impedance or voltage equations based on a single-frequency or simplified equivalent-frequency model. This involves time-domain averaging or single-frequency component linearization of the bridge arm electrical parameters to obtain a steady-state small-signal model. However, due to the significant dual-fundamental-frequency coupling between the bridge arm current and capacitor voltage in M3C, single-frequency models have limitations in describing the interaction effects between power frequency and low frequencies, easily leading to issues such as frequency component overlap and harmonic response deviations. Furthermore, traditional models often neglect the coupling structure of electrical parameters at different frequency combinations during convolution operations and matrix modeling, resulting in models that cannot accurately reflect the electrical balance of the bridge arm circuits in the steady-state frequency domain.

[0004] The existing technical solutions mentioned above have the following drawbacks: the existing M3C electrical parameter modeling method only deals with a single frequency or processes frequency interaction in an approximate form, which makes it impossible to accurately characterize the dual fundamental frequency coupling behavior between the power frequency and the low frequency. As a result, there are problems of harmonic distortion and calculation error accumulation when analyzing the steady-state frequency characteristics of the bridge arm electrical parameters, so there is room for improvement. Summary of the Invention

[0005] The purpose of this invention is to provide a method, apparatus, device, and medium for characterizing dual fundamental frequency coupling in M3C, in order to solve the technical problem that existing M3C electrical parameter modeling methods, which only deal with a single frequency or process frequency interaction in an approximate form, cannot accurately characterize the dual fundamental frequency coupling behavior between the power frequency and low frequency, thus resulting in harmonic distortion and accumulation of calculation errors when analyzing the steady-state frequency characteristics of bridge arm electrical parameters.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: In a first aspect, the present invention provides an M3C dual-fundamental-frequency coupling characterization method, the method comprising: Based on the M3C average value model, the basic dynamic equations of the bridge arm electrical parameters are established; Based on the aforementioned fundamental dynamic equations, the electrical parameters are decomposed and matrixed under power frequency and low frequency conditions to generate a two-dimensional frequency domain matrix. Linear equivalence modeling is performed on the frequency domain operation relationships of the two-dimensional frequency domain matrix to obtain a structured matrix; The structured matrix is ​​solved in the frequency domain to obtain the steady-state frequency domain harmonic model of the bridge arm circuit.

[0007] By adopting the above technical solutions, and establishing the basic dynamic equations of the bridge arm electrical parameters based on the M3C average value model, the time-domain constraint relationship between bridge arm voltage, current, and capacitor voltage can be reflected analytically, thus providing a stable mathematical foundation for subsequent frequency domain modeling. By performing frequency domain decomposition and matrix representation of electrical parameters under power frequency and low frequency conditions, the dual fundamental frequency components and their coupling characteristics can be effectively separated, thereby accurately representing the steady-state characteristics of the bridge arm under multi-frequency interaction conditions. By performing linear equivalent modeling of the frequency domain operation relationship of the two-dimensional frequency domain matrix, a matrix description of complex frequency domain convolution relationships can be achieved, thereby reducing modeling complexity and improving numerical solution efficiency. By solving the structured matrix in the frequency domain to obtain the steady-state frequency domain harmonic model of the bridge arm circuit, accurate modeling of the bridge arm harmonic distribution characteristics can be achieved, thus providing theoretical support for the steady-state performance analysis and optimized control of the M3C converter.

[0008] In one example, the present invention can be further configured such that the establishment of the fundamental dynamic equations for the bridge arm electrical parameters includes: Based on the M3C average value model, the equivalent capacitance parameters of each bridge arm submodule are determined, and a dynamic constraint relationship between the time change rate of the bridge arm capacitor voltage and the bridge arm current and modulation signal is established according to the equivalent capacitance parameters. Based on the dynamic constraint relationship, the time-domain expression of the bridge arm voltage is derived, and the bridge arm inductance and resistance parameters are introduced to generate the dynamic equation of the bridge arm voltage. Based on the aforementioned bridge arm voltage dynamic equation, a coupling balance relationship between the power frequency side valve-side voltage and the low frequency side valve-side voltage is established. The potential difference between the neutral points of the power frequency AC side and the low frequency AC side is introduced into the coupling balance relationship, and the potential difference is expressed in a weighted form according to the voltage of each bridge arm to obtain the basic dynamic equation.

[0009] By adopting the above technical solutions, the equivalent capacitance parameters of each bridge arm submodule are determined based on the M3C average value model, and a dynamic constraint relationship is established between the time change rate of the bridge arm capacitor voltage and the bridge arm current and modulation signal. This allows for accurate characterization of energy exchange patterns in the time domain, ensuring the physical consistency and computational stability of the basic dynamic equations. By deriving the time-domain expression of the bridge arm voltage based on the dynamic constraint relationship and introducing bridge arm inductance and resistance parameters, the influence of electrical parameters on the dynamic response of the bridge arm can be considered, thereby improving the model's matching degree to actual electrical behavior. By establishing the coupling balance relationship between the power frequency side valve voltage and the low frequency side valve voltage, the energy transfer path between the two AC sides can be clarified, providing a basis for steady-state characteristic modeling under dual fundamental frequency coupling conditions. By introducing the potential difference between the neutral points of the power frequency AC side and the low frequency AC side into the coupling balance relationship and expressing it with weights, the influence of neutral point potential fluctuations on model stability can be eliminated, thus ensuring the uniformity and accuracy of the bridge arm dynamic equations.

[0010] In one example, the present invention can be further configured as follows: the step of performing frequency domain decomposition and matrix representation of electrical parameters under power frequency and low frequency conditions to generate a two-dimensional frequency domain matrix includes: Based on the time-domain relationship of the electrical parameters in the basic dynamic equation, the electrical parameters are decomposed into frequencies to extract the power frequency component, low frequency component, and multiple sets of frequency components formed by their interaction. Based on the frequency components, a set of steady-state harmonic components under dual fundamental frequency coupling is established, and a corresponding two-dimensional frequency domain matrix structure is constructed using the combination order of each frequency component as an index.

[0011] By adopting the above technical solution, frequency decomposition can be performed based on the time-domain relationship of electrical parameters in the basic dynamic equation, thereby extracting the power frequency, low frequency and their interaction to form composite frequency components, thus providing basic data for harmonic distribution modeling under dual fundamental frequency characteristics. By establishing a set of steady-state harmonic components under dual fundamental frequency coupling and constructing a two-dimensional frequency domain matrix structure with the frequency combination order as the index, a matrix representation of frequency domain energy distribution can be achieved, thereby enhancing the observability and modeling flexibility of the multi-frequency response characteristics of the M3C system.

[0012] In one example, the present invention can be further configured such that the two-dimensional frequency domain matrix structure further includes: The steady-state components of the bridge arm current, bridge arm voltage, capacitor voltage, and modulation signal are characterized in terms of amplitude and phase, respectively, and a conjugate correspondence between the positive frequency components and the negative frequency components is established. In the three-phase structure of the bridge arm, the phase shift relationship of each phase bridge arm at different combined frequencies is defined according to the phase sequence characteristics of the three-phase bridge arm.

[0013] By adopting the above technical solutions, and by characterizing the steady-state components of the bridge arm current, bridge arm voltage, capacitor voltage, and modulation signal in terms of amplitude and phase respectively, and establishing the conjugate correspondence between positive and negative frequency components, the symmetry and physical reversibility of the spectrum modeling can be ensured, thereby improving the accuracy of the steady-state matrix description. By defining the phase shift relationship under different combination frequencies in the three-phase bridge arm structure according to the phase sequence characteristics, the phase coupling law of the three-phase system can be accurately characterized, thereby ensuring the uniformity and electrical consistency of the frequency domain model of the multiphase M3C system.

[0014] In one example, the present invention can be further configured as follows: the linear equivalent modeling of the frequency domain operation relations of the two-dimensional frequency domain matrix to obtain a structured matrix includes: Based on the aforementioned two-dimensional frequency domain matrix structure, the convolution operation relationship between bridge arm voltage, bridge arm current, and capacitor voltage under frequency domain conditions is established. By using a three-dimensional Toplitz matrix expansion strategy, the convolution operation relationship is stacked along the combination direction of the power frequency component, low frequency component and their coupled components to construct a multi-layer matrix structure; The multi-layer matrix structure is linearly renormalized, and the frequency domain convolution operation is equivalently converted into a matrix multiplication operation to obtain the structured matrix.

[0015] By adopting the above technical solutions, and establishing the convolution relationship of bridge arm voltage, bridge arm current, and capacitor voltage under frequency domain conditions based on a two-dimensional frequency domain matrix structure, the nonlinear frequency domain coupling problem can be transformed into a matrix-based convolution form, thus providing a clear algebraic foundation for subsequent equivalent modeling. Through the three-dimensional Toplitz matrix extension strategy, the convolution relationship is stacked along the power frequency component, low frequency component, and their coupling direction to construct a multi-layer matrix structure, which can realize multi-dimensional frequency mapping of dual fundamental frequencies and their cross components, thereby ensuring the ability to finely characterize complex coupled harmonics. By linearly renormalizing the multi-layer matrix structure, the frequency domain convolution operation is equivalently transformed into a matrix multiplication operation, which can effectively reduce the dimensionality of frequency domain calculation and achieve analytical solution, thereby significantly improving the efficiency and stability of steady-state characteristic calculation of the M3C system.

[0016] In one example, the present invention can be further configured as follows: the step of solving the structured matrix in the frequency domain to obtain the steady-state frequency domain harmonic model of the bridge arm circuit includes: The structured matrix is ​​reduced in dimensionality to obtain the steady-state frequency characterization of the bridge arm electrical parameters; Based on the steady-state frequency characterization, the parameter components of the bridge arm voltage, bridge arm current, and bridge arm capacitor voltage under frequency domain conditions are extracted, and the frequency domain correspondence of each parameter component is established in combination with the structured matrix. Based on the frequency domain correspondence and combined with the frequency factor of the power frequency component and the low frequency component, the equivalent impedance matrix and equivalent conductance matrix of the bridge arm circuit are constructed. Substituting the equivalent impedance matrix and the equivalent conductance matrix into the steady-state frequency characterization, the balance relationship between the bridge arm voltage, current and capacitor voltage is obtained. Then, based on the balance relationship, the steady-state harmonic components of the bridge arm current and capacitor voltage are derived, and the steady-state frequency domain harmonic model is generated.

[0017] By adopting the above technical solution, the frequency domain parameter components of bridge arm voltage, bridge arm current, and capacitor voltage are extracted based on steady-state frequency characterization, and a frequency domain correspondence is established by combining a structured matrix. This enables frequency coupling mapping between bridge arm electrical quantities, thereby enhancing the model's accuracy in describing multi-frequency interaction characteristics. By constructing equivalent impedance and equivalent conductance matrices based on the frequency domain correspondence and combining power frequency and low-frequency combination frequency factors, the frequency domain impedance characteristics of the bridge arm circuit can be accurately characterized, thus supporting subsequent quantitative harmonic analysis. By substituting the equivalent impedance and equivalent conductance matrices into the steady-state frequency characterization and solving the balance relationship, the steady-state harmonic components of the bridge arm current and capacitor voltage can be obtained, thereby generating a steady-state frequency domain harmonic model of the M3C bridge arm circuit, achieving a comprehensive characterization of the system's harmonic distribution and stability.

[0018] In one example, the present invention can be further configured as follows: the dimensionality reduction processing of the structured matrix to obtain the steady-state frequency characterization of the bridge arm electrical parameters includes: Based on the structured matrix, the steady-state frequency components of the bridge arm electrical parameters under power frequency and low frequency conditions are extracted, and each frequency component is expanded into a two-dimensional matrix vector according to the dual fundamental frequency combination relationship. Based on the two-dimensional matrix vector, the low-frequency component direction remains unchanged, and the number of row vectors of the matrix is ​​gradually increased with the power frequency component as the cyclic variable to obtain the frequency extension sequence expanded along the power frequency direction. By rearranging the frequency extension sequence into a row vector structure, a dimension-reduced matrix structure is obtained, and the steady-state frequency representation is established based on the dimension-reduced matrix structure.

[0019] By adopting the above technical solution, the steady-state frequency components of the bridge arm electrical parameters under power frequency and low frequency conditions are extracted based on the structured matrix, and expanded into a two-dimensional matrix vector according to the dual fundamental frequency combination relationship. This enables the orderly organization of different frequency components, thereby ensuring the consistency of steady-state frequency characteristics in the matrix space. By keeping the direction of the low-frequency components unchanged and gradually increasing the number of matrix row vectors with the power frequency components as the cyclic variable, the dimension of frequency information can be dynamically expanded, thereby achieving continuous expression and complete preservation of frequency domain samples. By rearranging the frequency expansion sequence into a row vector structure and establishing a dimension-reduced matrix structure, the data dimension can be compressed without losing key information, thereby improving the compactness and computational speed of steady-state frequency representation.

[0020] In a second aspect, the present invention provides an apparatus for an M3C dual-fundamental-frequency coupling characterization method, the apparatus comprising: The basic modeling module is used to establish the basic dynamic equations of the bridge arm electrical parameters based on the M3C average value model; The frequency domain decomposition module is used to decompose and matrix-represent electrical parameters under power frequency and low frequency conditions based on the basic dynamic equations, and generate a two-dimensional frequency domain matrix. The linear modeling module is used to perform linear equivalent modeling on the frequency domain operation relationships of the two-dimensional frequency domain matrix to obtain a structured matrix; The harmonic solving module is used to solve the structured matrix in the frequency domain to obtain the steady-state frequency domain harmonic model of the bridge arm circuit.

[0021] By adopting the above technical solutions, and establishing the basic dynamic equations of the bridge arm electrical parameters based on the M3C average value model, the time-domain constraint relationship between bridge arm voltage, current, and capacitor voltage can be reflected analytically, thus providing a stable mathematical foundation for subsequent frequency domain modeling. By performing frequency domain decomposition and matrix representation of electrical parameters under power frequency and low frequency conditions, the dual fundamental frequency components and their coupling characteristics can be effectively separated, thereby accurately representing the steady-state characteristics of the bridge arm under multi-frequency interaction conditions. By performing linear equivalent modeling of the frequency domain operation relationship of the two-dimensional frequency domain matrix, a matrix description of complex frequency domain convolution relationships can be achieved, thereby reducing modeling complexity and improving numerical solution efficiency. By solving the structured matrix in the frequency domain to obtain the steady-state frequency domain harmonic model of the bridge arm circuit, accurate modeling of the bridge arm harmonic distribution characteristics can be achieved, thus providing theoretical support for the steady-state performance analysis and optimized control of the M3C converter.

[0022] In one example, the present invention can be further configured as follows: the basic modeling module is specifically used for: Based on the M3C average value model, the equivalent capacitance parameters of each bridge arm submodule are determined, and a dynamic constraint relationship between the time change rate of the bridge arm capacitor voltage and the bridge arm current and modulation signal is established according to the equivalent capacitance parameters. Based on the dynamic constraint relationship, the time-domain expression of the bridge arm voltage is derived, and the bridge arm inductance and resistance parameters are introduced to generate the dynamic equation of the bridge arm voltage. Based on the aforementioned bridge arm voltage dynamic equation, a coupling balance relationship between the power frequency side valve-side voltage and the low frequency side valve-side voltage is established. The potential difference between the neutral points of the power frequency AC side and the low frequency AC side is introduced into the coupling balance relationship, and the potential difference is expressed in a weighted form according to the voltage of each bridge arm to obtain the basic dynamic equation.

[0023] In one example, the present invention can be further configured such that the frequency domain decomposition module is specifically used for: Based on the time-domain relationship of the electrical parameters in the basic dynamic equation, the electrical parameters are decomposed by frequency, and multiple sets of frequency components formed by the interaction of the power frequency component, low frequency component, and the power frequency component are extracted. Based on the frequency components, a set of steady-state harmonic components under dual fundamental frequency coupling is established, and a corresponding two-dimensional frequency domain matrix structure is constructed using the combination order of each frequency component as an index.

[0024] In one example, the present invention can be further configured such that the two-dimensional frequency domain matrix structure further includes: The steady-state components of the bridge arm current, bridge arm voltage, capacitor voltage, and modulation signal are characterized in terms of amplitude and phase, respectively, and a conjugate correspondence between the positive frequency components and the negative frequency components is established. In the three-phase structure of the bridge arm, the phase shift relationship of each phase bridge arm at different combined frequencies is defined according to the phase sequence characteristics of the three-phase bridge arm.

[0025] In one example, the present invention can be further configured such that the harmonic solving module is specifically used for: The structured matrix is ​​reduced in dimensionality to obtain the steady-state frequency characterization of the bridge arm electrical parameters; Based on the steady-state frequency characterization, the parameter components of the bridge arm voltage, bridge arm current, and bridge arm capacitor voltage under frequency domain conditions are extracted, and the frequency domain correspondence of each parameter component is established in combination with the structured matrix. Based on the frequency domain correspondence, and combined with the frequency factor of the power frequency component and the low frequency component, the equivalent impedance matrix and equivalent conductance matrix of the bridge arm circuit are constructed. Substituting the equivalent impedance matrix and the equivalent conductance matrix into the steady-state frequency characterization, the balance relationship between the bridge arm voltage, current and capacitor voltage is obtained. Then, based on the balance relationship, the steady-state harmonic components of the bridge arm current and capacitor voltage are derived, and the steady-state frequency domain harmonic model is generated.

[0026] In a third aspect, the present invention provides an electronic device including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the M3C dual-baseband coupling characterization method.

[0027] 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 M3C dual-baseband coupling characterization method described above.

[0028] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. By extracting the frequency domain parameter components of bridge arm voltage, bridge arm current, and capacitor voltage based on steady-state frequency characterization, and establishing frequency domain correspondences with structured matrices, frequency coupling mapping between bridge arm electrical quantities can be achieved, thereby enhancing the model's accuracy in describing multi-frequency interaction characteristics. By constructing equivalent impedance and equivalent conductance matrices based on frequency domain correspondences and combined power frequency and low-frequency frequency factors, the frequency domain impedance characteristics of the bridge arm circuit can be accurately characterized, thus supporting subsequent quantitative harmonic analysis. By substituting the equivalent impedance and equivalent conductance matrices into the steady-state frequency characterization and solving the balance relationship, the steady-state harmonic components of bridge arm current and capacitor voltage can be obtained, thereby generating a steady-state frequency domain harmonic model of the M3C bridge arm circuit, achieving a comprehensive characterization of system harmonic distribution and stability. 2. By extracting the steady-state frequency components of the bridge arm electrical parameters under power frequency and low-frequency conditions based on structured matrices, and expanding them into a two-dimensional matrix vector according to the dual fundamental frequency combination relationship, the orderly organization of different frequency components can be achieved, thereby ensuring the consistency of steady-state frequency characteristics in the matrix space. By keeping the direction of the low-frequency components unchanged and gradually increasing the number of matrix row vectors with the power frequency components as the cyclic variable, the dimension of frequency information can be dynamically expanded, thereby achieving continuous expression and complete preservation of frequency domain samples. By rearranging the frequency expansion sequence into a row vector structure and establishing a dimension-reduced matrix structure, the data dimension can be compressed without losing key information, thereby improving the compactness and computational speed of steady-state frequency representation. 3. By establishing the convolution relationship of bridge arm voltage, bridge arm current, and capacitor voltage under frequency domain conditions based on a two-dimensional frequency domain matrix structure, the nonlinear frequency domain coupling problem can be transformed into a matrix-based convolution form, thus providing a clear algebraic foundation for subsequent equivalent modeling. Through the three-dimensional Toplitz matrix extension strategy, the convolution relationship is stacked along the power frequency component, low frequency component, and their coupling direction to construct a multi-layer matrix structure, which can realize multi-dimensional frequency mapping of dual fundamental frequencies and their cross components, thereby ensuring the ability to finely characterize complex coupled harmonics. By linearly renormalizing the multi-layer matrix structure, the frequency domain convolution operation is equivalently transformed into a matrix multiplication operation, which can effectively reduce the dimensionality of frequency domain calculation and achieve analytical solution, thereby significantly improving the efficiency and stability of steady-state characteristic calculation of the M3C system. Attached Figure Description

[0029] The accompanying drawings, which form part of this specification, 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 the M3C dual-fundamental-frequency coupling characterization method in an embodiment of the present invention; Figure 2 This is a structural block diagram of the M3C dual-fundamental-frequency coupling characterization method device according to an embodiment of the present invention; Figure 3 This is a structural block diagram of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0030] 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 herein can be combined with each other.

[0031] 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. The terminology used in this invention is for describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention.

[0032] Example 1 like Figure 1 As shown, this invention discloses an M3C dual-fundamental-frequency coupling characterization method, which specifically includes the following steps: S10: Based on the M3C average value model, establish the basic dynamic equations for the electrical parameters of the bridge arm.

[0033] Specifically, based on the average value model of the multilevel matrix converter, the three-phase arms of the converter are first uniformly modeled. The equivalent capacitance, inductance, and resistance characteristics of each arm submodule are parameterized and the dynamic changes of current, voltage, and capacitor voltage of each arm are represented in the form of average values. On this basis, the basic constraint equations between the electrical parameters of the arms are established, including the time variation relationship between the arm capacitor voltage and the arm current, the modulation relationship of the modulation signal on the arm voltage output, and the coupling voltage balance equation between the power frequency side and the low frequency side, so as to form a dynamic description equation set of the arm electrical parameters, providing an analytical basis for subsequent frequency domain characterization.

[0034] S20: Based on the fundamental dynamic equations, electrical parameters are decomposed and matrixed under power frequency and low frequency conditions to generate a two-dimensional frequency domain matrix.

[0035] Specifically, after obtaining the dynamic equations of the bridge arm electrical parameters, the time-domain signals in the equations are processed by frequency domain transformation to extract the power frequency components, low-frequency components, and their combined components of current, voltage, and capacitor voltage. These frequency components are then arranged in order to form a spectrum set under dual-fundamental-frequency coupling. Based on this, a corresponding matrix representation is established using the frequency components as indices, so that each bridge arm electrical parameter can be characterized in the form of amplitude and phase coupling on the two-dimensional frequency plane, thereby generating a two-dimensional frequency domain matrix containing power frequency and low-frequency dual-dimensional features, providing a unified matrix structure for subsequent linear modeling.

[0036] S30: Perform linear equivalent modeling on the frequency domain operation relationships of the two-dimensional frequency domain matrix to obtain a structured matrix.

[0037] Specifically, based on the two-dimensional frequency domain matrix, the frequency domain operation relationship between the bridge arm electrical parameters is linearized, and the coupling convolution relationship between each frequency component is represented as a linear matrix operation. Through frequency expansion and matrix extension, the complex convolution superposition relationship is equivalently transformed into a matrix multiplication structure in the frequency dimension. A linear equivalent model is established according to the arrangement order of each frequency combination, thereby obtaining a structured matrix that reflects the steady-state response relationship between the bridge arm electrical parameters, so as to solve and analyze the frequency domain components under steady-state conditions.

[0038] S40: Solve the structured matrix in the frequency domain to obtain the steady-state frequency domain harmonic model of the bridge arm circuit.

[0039] Specifically, after obtaining the structured matrix, the multidimensional frequency components contained in the matrix are rearranged and dimensionality reduced according to the frequency coupling relationship. The response data under different frequency combinations are re-expressed in low-dimensional matrix form to obtain the steady-state frequency characterization of the bridge arm electrical parameters. The interaction relationship of each frequency component is introduced into the bridge arm circuit modeling. Based on the correspondence between voltage, current and capacitor voltage in the steady-state frequency domain, the frequency domain electrical equation of the bridge arm circuit is derived. Combining the mutual coupling characteristics of power frequency and low frequency components, the steady-state frequency domain expression of the bridge arm circuit is constructed and harmonic analysis is performed on it. Finally, a harmonic model characterizing the steady-state response characteristics of the bridge arm electrical parameters is obtained, thereby realizing the steady-state characterization of the dual fundamental frequency coupling characteristics of the M3C system.

[0040] In one embodiment, step S10, namely establishing the basic dynamic equations of the bridge arm electrical parameters, includes: S11: Based on the M3C average value model, determine the equivalent capacitance parameters of each bridge arm submodule, and establish a dynamic constraint relationship between the time change rate of the bridge arm capacitor voltage and the bridge arm current and modulation signal based on the equivalent capacitance parameters.

[0041] Specifically, based on the M3C average value model, the time-domain relationship between bridge arm voltage, bridge arm current, and bridge arm capacitor voltage can be obtained. At the same time, the bridge arm voltage and the bridge arm capacitor voltage satisfy the modulation signal relationship. ,in, C eq This is the equivalent capacitance of the bridge arm submodule. v Cxl For bridge arm x Phase, low frequency l The capacitor voltage corresponding to the submodule, m xl For bridge arm x Phase, low frequency l The modulation signal corresponding to the submodule, i xl For bridge arm x Phase, low frequency l Corresponding to the bridge arm current of the submodule, v xl For bridge arm x Phase, low frequency l The phase arm voltages are used to obtain the basic dynamic constraint relationship between the arm current, capacitor voltage, and modulation signal through the above relationship.

[0042] S12: Based on the dynamic constraint relationship, derive the time-domain expression of the bridge arm voltage, and introduce the bridge arm inductance and resistance parameters to generate the dynamic equation of the bridge arm voltage.

[0043] Specifically, after establishing dynamic constraints on the arm current and capacitor voltage, equivalent inductance and resistance parameters of the arm are introduced to characterize the dynamic behavior of the arm circuit. Considering the voltage drop across the arm inductance and resistance based on the M3C average value model, the coupling relationship between the power frequency side valve-side voltage and the low frequency side valve-side voltage can be obtained. ,in, v hx ( x =u, v, w) represents the three-phase AC voltage on the power frequency side. R arm and L arm The equivalent resistance and inductance of the bridge arms are respectively. i xa ( x =u,v,w) represents the bridge arm currents. v xa ( x =u,v,w) represents the bridge arm voltages. v 1a This represents the phase voltage component on the low-frequency side. v go This represents the potential difference between the neutral points of the power frequency AC side and the low frequency AC side, thus reflecting the dynamic mapping relationship between the bridge arm voltage and the bridge arm current in the time domain.

[0044] S13: Based on the dynamic equation of the bridge arm voltage, establish the coupling balance relationship between the power frequency side valve voltage and the low frequency side valve voltage.

[0045] Specifically, based on the dynamic equation of the bridge arm voltage, and considering the symmetry of the lower bridge arm current and voltage components, the relationship between the low-frequency side valve voltage can be expressed as follows: ,in, v lb The b-phase component of the low-frequency side valve voltage is represented by the bridge arm voltage, current, and low-frequency component of the upper and lower bridge arms, which correspond to each other and form a bidirectional coupled voltage balance structure between the power frequency and low frequency to characterize the energy complementarity between the power frequency side valve voltage and the low-frequency side valve voltage.

[0046] S14: Introduce the potential difference between the neutral points of the power frequency AC side and the low frequency AC side in the coupling equilibrium relationship, and express the potential difference in the weighted form of the voltage of each bridge arm to obtain the basic dynamic equation.

[0047] Specifically, based on the coupling balance relationship, the potential difference between the neutral points of the power frequency AC side and the low frequency AC side can be defined. ,in, v g and v o These are the voltages at the power frequency AC neutral point and the low frequency AC neutral point, respectively. v goThis represents the weighted distribution of the potential difference among the voltages of each bridge arm. Substituting it back into the coupling balance relationship yields the comprehensive constraint relationship between the bridge arm current, voltage, and capacitor voltage, thus forming the basic dynamic equations of the bridge arm electrical parameters that include characteristics of the power frequency and low frequency sides.

[0048] In one embodiment, step S20 involves performing frequency domain decomposition and matrix representation of electrical parameters under power frequency and low frequency conditions to generate a two-dimensional frequency domain matrix, including: S21: Based on the time-domain relationship of electrical parameters in the basic dynamic equation, frequency decomposition is performed on the electrical parameters to extract the power frequency component, low frequency component and multiple sets of frequency components formed by their interaction.

[0049] Specifically, after establishing the time-domain relationship between the bridge arm voltage, bridge arm current, capacitor voltage, and modulation signal, frequency decomposition is performed on the electrical parameters. Theoretically, the interaction between the bridge arm current, bridge arm capacitor voltage, and modulation signal can generate any harmonic. Without loss of generality, the power frequency components contained in the bridge arm current, equivalent submodule capacitor voltage, and modulation signal are considered. mf 1 and low-frequency components nf 2, of which m and n For integers, these frequency components can be combined to form multiple sets of interactive frequency components. To clearly describe the steady-state distribution under different frequency conditions, a two-dimensional frequency domain matrix-vector method is introduced to arrange the steady-state harmonic components of the bridge arm in order of frequency sequence, thereby constructing a set containing (2 g +1)×(2 g A frequency domain matrix vector with (+1) elements ,in, f 1 represents the fundamental frequency on the power frequency side. f 2 represents the fundamental frequency on the low-frequency side. g To define the harmonic expansion order, the range of matrix orders is defined to characterize the spectral distribution relationship of bridge arm electrical parameters under power frequency and low frequency conditions.

[0050] S22: Based on the frequency components, establish a set of steady-state harmonic components under dual fundamental frequency coupling, and construct the corresponding two-dimensional frequency domain matrix structure using the combination order of each frequency component as an index.

[0051] Specifically, taking the ua bridge arm as an example, the steady-state vectors of the bridge arm current, bridge arm capacitor voltage, and modulation signal can be constructed in matrix form, where the steady-state matrix of the bridge arm ua current is... , among which, I ua,m,n Indicates the power frequency component mf 1 and low-frequency components nf 2. Current steady-state component at combined frequency, capacitor voltage steady-state matrix ,in, Vcua,m,n Corresponding power frequency mf 1 and low frequency nf The complex voltage component of 2, and the steady-state moment of the modulation signal. , of which M ua,m,n For power frequency mf 1 and low frequency nf The modulated signal components under condition 2, where the first digit in the subscript indicates the frequency. mf 1. The second digit indicates the frequency. nf 2, that is , , The negative frequency component and the positive frequency component are conjugates, that is... , , The superscript * indicates conjugate operation, used to describe the frequency domain distribution characteristics of the bridge arm electrical parameters under dual fundamental frequency coupling.

[0052] Furthermore, to maintain a frequency domain coordinate system consistent with the two-dimensional frequency domain matrix of the bridge arm layer, and to establish a unified steady-state expression for the system port variables, the AC terminals on the power frequency side and the low frequency side are indexed using a two-dimensional index ( mf 1, nf 2) Construct the port steady-state matrix vector: the steady-state matrix vector of the u-phase AC voltage on the power frequency side. With current steady-state matrix vector Non-zero components are taken only at the indices (m=±1, n=0), and the elements at the other frequency indices are zero, to indicate that only the main steady-state component is retained at the power frequency end; the steady-state matrix vector of phase a AC voltage on the low-frequency side. With current steady-state matrix vector Only non-zero components are taken at the index (m=0, n=±1), and the rest are zero. This is used to indicate that only the main steady-state components are retained at the low-frequency end, so as to align the frequency domain indexing system of the port layer and the bridge arm layer.

[0053] In one embodiment, step S22, i.e., the two-dimensional frequency domain matrix structure, further includes: S221: Characterize the arm current, arm voltage, capacitor voltage, and steady-state components of the modulation signal in terms of amplitude and phase, respectively, and establish the conjugate correspondence between the positive frequency components and the negative frequency components.

[0054] Specifically, the complex vector representation of each element in the steady-state matrix can simultaneously characterize the arm current, arm voltage, capacitor voltage, and the amplitude and phase information of the modulation signal, at various frequencies. mf 1+ nf Steady-state components and frequencies at point 2 – mf 1– nf The components at point 2 are conjugates, ensuring the symmetry of the matrix on the frequency axis and the energy conservation relationship.

[0055] S222: In the three-phase structure of the bridge arm, the phase shift relationship of each phase bridge arm at different combination frequencies is defined according to the phase sequence characteristics of the three-phase bridge arm.

[0056] Specifically, based on the three-phase symmetry relation, for frequency mf 1+ nf The steady-state components at points 2 are defined with power frequency axis indices. m and low-frequency axis index n The phase shift angle relationship between two adjacent phases is: , Thus, any combination of frequencies between the three phases {u,v,w} on the power frequency side and the three phases {a,b,c} on the low frequency side. mf 1+ nf In both cases, the phase shift and phase sequence attributes of two adjacent phases can be determined. When the determination result is... The value of 2π / 3 corresponds to positive sequence, 2π / 3 corresponds to negative sequence, and 0 corresponds to zero sequence, thus maintaining the consistency and computability of the phase relationship between the three-phase bridge arm voltage and current in the entire domain of the two-dimensional frequency domain index (m,n).

[0057] In one embodiment, step S30 involves performing linear equivalence modeling on the frequency domain operations of the two-dimensional frequency domain matrix to obtain a structured matrix, including: S31: Based on the two-dimensional frequency domain matrix structure, establish the convolution operation relationship between bridge arm voltage, bridge arm current and capacitor voltage under frequency domain conditions.

[0058] Specifically, based on the steady-state component relationship of the bridge arm represented by a two-dimensional frequency domain matrix, the convolutional form of the bridge arm current, capacitor voltage, and modulation signal under frequency domain conditions is expanded. The steady-state model expression of the bridge arm circuit under frequency domain can be obtained through the convolutional relationship. , , where Y Ceq0 Let be the admittance matrix of the bridge arm capacitor. V Cua Let be the frequency domain vector of the bridge arm capacitor voltage. M ua The frequency domain matrix representation of the modulated signal. I ua Let be the frequency domain vector of the bridge arm current. Z arm0 The equivalent impedance matrix of the bridge arm. V hus For power frequency related items, V las For low-frequency related terms, V Tgo This is a term related to the neutral point potential difference. This convolution relationship can fully describe the frequency domain interaction between the electrical parameters of the bridge arms.

[0059] S32: By using a three-dimensional Toplitz matrix expansion strategy, the convolution operation relationship is stacked along the combination direction of the power frequency component, low frequency component and their coupled components to construct a multi-layer matrix structure.

[0060] Specifically, based on the convolution operation relationship established by the two-dimensional frequency domain matrix, in order to describe the convolution translation characteristics of the bridge arm loop under the power frequency component, low frequency component, and their combination frequency, the power frequency component is first considered. f 1 and low-frequency components f The multiple harmonic components of 2 will g times f 1 and f The steady-state harmonic vector of 2 is expanded into a two-dimensional matrix vector according to a fixed frequency sequence. Based on the above two-dimensional matrix vector, take n =– g , m Increment the column vector to obtain a new (2 g +1)×1 row steady-state column vector In order to establish a frequency extension structure in three-dimensional frequency space with power frequency components, low frequency components and their combination frequencies as indices, and then stack them along the third dimension to form a multi-layer Toplitz matrix, so that the convolution translation relationship is continuously mapped in the combination direction of power frequency and low frequency.

[0061] S33: Perform linear renormalization on the multi-layer matrix structure, and convert the frequency domain convolution operation into an equivalent matrix multiplication operation to obtain a structured matrix.

[0062] Specifically, each (2) in the multi-layered Toplitz matrix structure g +1)×1 row vector transpose to form a new column vector, according to the intermediate layer g The position +1 expands to (2) g +1)×(2 g +1) order Toplitz matrix, during the renormalization process, row 1 to row 2 g The row vectors of each row are shifted one unit to the left of the next row and padded with zeros. g +2 lines to the 2nd line g The row vectors of row +1 are shifted one unit to the right in the next row and filled with 0, thus forming an extended matrix with frequency shift characteristics. Then, through frequency index iteration, the above extended matrix is ​​cyclically extended and rearranged along the frequency sequence to (2 g +1) 2 ×(2 g +1) 2 From the 1 / 2-order matrix, we obtain the linearized Topletz matrix vector. This is a structured matrix, which transforms the convolution and translation relationships in the three-dimensional Toplitz matrix into matrix multiplication relationships, achieving linear equivalence between frequency domain convolution operations and matrix multiplication operations.

[0063] In one embodiment, step S40, namely, solving the structured matrix in the frequency domain to obtain the steady-state frequency domain harmonic model of the bridge arm circuit, includes: S41: Dimensionality reduction of the structured matrix yields the steady-state frequency characterization of the bridge arm electrical parameters.

[0064] Specifically, after obtaining the structured matrix, the multidimensional frequency components contained in the matrix are rearranged and dimensionality reduced according to the frequency coupling relationship. The response data under different frequency combinations are re-expressed in the form of a low-dimensional matrix. During the dimensionality reduction process, the integrity of the low-frequency direction is maintained and the power frequency component is used as the expansion direction, so that the dimensionality-reduced matrix can reflect the steady-state frequency distribution characteristics of the electrical parameters of each bridge arm on a two-dimensional plane. The matrix obtained through this dimensionality reduction process can be used as a frequency characterization model of the bridge arm electrical parameters under steady-state conditions for subsequent harmonic characteristic derivation.

[0065] S42: Based on steady-state frequency characterization, extract the parameter components of bridge arm voltage, bridge arm current and bridge arm capacitor voltage under frequency domain conditions, and establish the frequency domain correspondence of each parameter component in combination with the structured matrix.

[0066] Specifically, based on the steady-state frequency characterization of the bridge arm circuit, frequency domain parameter components of the bridge arm voltage, bridge arm current, and capacitor voltage are selected, and their frequency domain convolution correspondence is established in the structured matrix. At this time, the capacitor equivalent admittance matrix Y Ceq0x Modulation signal matrix M uax and bridge arm current vector I uax Satisfies the following frequency domain equations: , where V Cuax Let be the steady-state frequency domain vector of the bridge arm capacitor voltage. Similarly, the balance relationship between the bridge arm voltage and current can be expressed as: Among them, Z arm0x Characterizing the equivalent impedance of the bridge arm, V husx V lasx V Tgo These are the power frequency side voltage, low frequency side voltage, and neutral point voltage components, respectively.

[0067] S43: Based on the frequency domain correspondence and combined with the frequency factor of the power frequency component and the low frequency component, construct the equivalent impedance matrix and equivalent conductance matrix of the bridge arm circuit.

[0068] Specifically, based on the frequency domain parameter components in the frequency domain correspondence, the power frequency component is considered. f 1 and low-frequency components f 2 combined frequency factors, construct (2g +1)2×(2 g +1) Equivalent impedance matrix and equivalent conductance matrix of the second-order bridge arm , Where, diag[] denotes the diagonal matrix construction operation indexed by frequency components, R arm Let U be the bridge arm resistance, U be the identity matrix, and L be the... arm For the bridge arm inductance, C eq The equivalent capacitance of the bridge arm is used to model the multi-frequency equivalent parameters of the bridge arm electrical parameters in the frequency domain.

[0069] S44: Substitute the equivalent impedance matrix and equivalent conductance matrix into the steady-state frequency characterization to solve for the balance relationship between the bridge arm voltage, current and capacitor voltage. Then, based on the balance relationship, derive the steady-state harmonic components of the bridge arm current and capacitor voltage to generate a steady-state frequency domain harmonic model.

[0070] Specifically, the equivalent impedance matrix and equivalent conductance matrix Z of the bridge arm circuit are... arm0x Y Ceq0x Substituting the frequency domain correspondences, the frequency domain electrical equations of the bridge arm circuit under steady-state conditions are obtained. Subsequently, by separating and solving the frequency domain variables, the electrical harmonic model of the bridge arm circuit under steady-state conditions can be derived. , , The expression characterizing the steady-state frequency domain bridge arm capacitor voltage and bridge arm current is given by Z. Ceq0x Y is the equivalent impedance matrix of the bridge arm capacitor branch. arm0x Let be the equivalent admittance matrix of the bridge arm branch.

[0071] In one embodiment, step S41, namely, performing dimensionality reduction on the structured matrix to obtain the steady-state frequency characterization of the bridge arm electrical parameters, includes: S411: Based on the structured matrix, extract the steady-state frequency components of the bridge arm electrical parameters under power frequency and low frequency conditions, and expand each frequency component into a two-dimensional matrix vector according to the dual fundamental frequency combination relationship.

[0072] Specifically, in the set of frequency components of the structured matrix, the components corresponding to the power frequency are selected. f 1 and low-frequency components f The steady-state response components of 2 are used as an index reference to construct a two-dimensional steady-state frequency matrix vector, where the arrangement of each frequency combination term follows a combination expansion rule from low to high order, i.e. This allows for the characterization of the steady-state harmonic distribution characteristics of the bridge arm electrical parameters under power frequency and low frequency conditions on the frequency plane, providing a basic matrix form for dimensionality reduction calculations.

[0073] S412: Based on the two-dimensional matrix vector, keep the direction of the low-frequency component unchanged, and gradually increase the number of row vectors of the matrix with the power frequency component as the cyclic variable to obtain the frequency extension sequence expanded along the power frequency direction.

[0074] Specifically, in the constructed two-dimensional matrix vector, the low-frequency components are fixed. f The frequency indices of 2 will be used to determine the power frequency components. f The frequency multiplication factor m increases sequentially to form a cyclic variable, gradually expanding the number of row vectors in the matrix, thus obtaining the frequency extension sequence expanded along the power frequency direction. This allows for the acquisition of a continuous frequency distribution sequence in the power frequency direction while keeping the low-frequency components unchanged, thereby enabling the directional expansion of the dual-fundamental-frequency coupled components.

[0075] S413: By rearranging the frequency extension sequence into a row vector structure, a dimension-reduced matrix structure is obtained, and a steady-state frequency representation is established based on the dimension-reduced matrix structure.

[0076] Specifically, after obtaining the frequency extension sequence, the frequency terms are recombined in sequence into a row vector structure, forming a dimension-reduced matrix representation with a single frequency dimension. This allows the three-dimensional mapping of the original dual-fundamental-frequency structure to be linearized in a two-dimensional matrix space. Based on this dimension-reduced matrix structure, the power frequency and low-frequency steady-state responses of the bridge arm electrical parameters can be uniformly described as steady-state frequency characterization vectors, which are used to characterize the steady-state spectral distribution of the M3C under dual-fundamental-frequency action.

[0077] Example 2 like Figure 2 As shown, based on the same inventive concept as the above embodiments, the present invention also provides an M3C dual-fundamental-frequency coupling characterization method apparatus, comprising: The basic modeling module is used to establish the basic dynamic equations of the bridge arm electrical parameters based on the M3C average value model; The frequency domain decomposition module is used to decompose and matrix-represent electrical parameters under power frequency and low frequency conditions based on the basic dynamic equations, and generate a two-dimensional frequency domain matrix. The linear modeling module is used to perform linear equivalent modeling of the frequency domain operation relationships of a two-dimensional frequency domain matrix to obtain a structured matrix; The harmonic solving module is used to solve the structured matrix in the frequency domain to obtain the steady-state frequency domain harmonic model of the bridge arm circuit.

[0078] Optional, the basic modeling module includes: The parameter determination submodule is used to determine the equivalent capacitance parameters of each bridge arm submodule based on the M3C average value model, and to establish a dynamic constraint relationship between the time change rate of the bridge arm capacitor voltage and the bridge arm current and modulation signal based on the equivalent capacitance parameters. The equation derivation submodule is used to derive the time-domain expression of the bridge arm voltage based on the dynamic constraint relationship, and to generate the dynamic equation of the bridge arm voltage by introducing the bridge arm inductance and resistance parameters. The coupling modeling submodule is used to establish the coupling balance relationship between the power frequency side valve-side voltage and the low frequency side valve-side voltage based on the bridge arm voltage dynamic equation; The potential compensation submodule is used to introduce the potential difference between the neutral points of the power frequency AC side and the low frequency AC side in the coupling balance relationship, and express the potential difference in a weighted form according to the voltage of each bridge arm to obtain the basic dynamic equation.

[0079] Optional, the frequency domain decomposition module includes: The frequency extraction submodule is used to perform frequency decomposition on electrical parameters based on the time-domain relationship of electrical parameters in the basic dynamic equation, and extract the power frequency component, low frequency component and multiple sets of frequency components formed by their interaction. The matrix construction submodule is used to establish a set of steady-state harmonic components under dual fundamental frequency coupling based on the frequency components, and to construct the corresponding two-dimensional frequency domain matrix structure using the combination order of each frequency component as an index.

[0080] Optionally, the matrix construction submodule also includes: The steady-state characterization unit is used to characterize the steady-state components of the bridge arm current, bridge arm voltage, capacitor voltage, and modulation signal in terms of amplitude and phase, respectively, and to establish the conjugate correspondence between the positive frequency components and the negative frequency components. The phase sequence definition unit is used to define the phase shift relationship of each phase arm at different combination frequencies in a three-phase structure of a bridge arm, based on the phase sequence characteristics of the three-phase bridge arm.

[0081] Optional, linear modeling modules include: The convolution modeling submodule is used to establish the convolution operation relationship between bridge arm voltage, bridge arm current and capacitor voltage under frequency domain conditions based on a two-dimensional frequency domain matrix structure. The Top extension submodule is used to stack the convolution operation relationship along the combination direction of the power frequency component, low frequency component and their coupled components to construct a multi-layer matrix structure through the three-dimensional Toplitz matrix extension strategy; The linear renormalization submodule is used to perform linear renormalization on multi-layer matrix structures, converting frequency domain convolution operations into matrix multiplication operations to obtain structured matrices.

[0082] Optionally, the harmonic solution module includes: The dimension reduction analysis submodule is used to reduce the dimension of the structured matrix to obtain the steady-state frequency characterization of the bridge arm electrical parameters. The frequency domain extraction submodule is used to extract the parameter components of bridge arm voltage, bridge arm current and bridge arm capacitor voltage under frequency domain conditions based on steady-state frequency characterization, and to establish the frequency domain correspondence of each parameter component in combination with the structured matrix. The impedance construction submodule is used to construct the equivalent impedance matrix and equivalent conductance matrix of the bridge arm circuit based on the frequency domain correspondence and the combined frequency factor of the power frequency component and the low frequency component. The harmonic solution submodule is used to substitute the equivalent impedance matrix and equivalent conductance matrix into the steady-state frequency characterization, solve for the balance relationship between the bridge arm voltage, current and capacitor voltage, and then derive the steady-state harmonic components of the bridge arm current and capacitor voltage based on the balance relationship, generating a steady-state frequency domain harmonic model.

[0083] Optional, the dimensionality reduction analysis submodule includes: The frequency extraction unit is used to extract the steady-state frequency components of the bridge arm electrical parameters under power frequency and low frequency conditions based on the structured matrix, and expand each frequency component into a two-dimensional matrix vector according to the dual fundamental frequency combination relationship. The cyclic expansion unit is used to obtain a frequency expansion sequence along the power frequency direction by keeping the low-frequency component direction unchanged and gradually increasing the number of row vectors of the matrix with the power frequency component as the cyclic variable. The dimension reduction and reconstruction unit is used to obtain a dimension reduction matrix structure by rearranging the frequency extension sequence into a row vector structure, and to establish a steady-state frequency representation based on the dimension reduction matrix structure.

[0084] Example 3 like Figure 3 As shown, the present invention also provides an electronic device 100 for implementing the M3C dual-baseband coupling characterization 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.

[0085] The memory 101 can be used to store the computer program 103. The processor 102 implements the steps of the M3C dual-baseband coupling characterization 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.

[0086] 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.

[0087] 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.

[0088] The memory 101 in the electronic device 100 stores multiple instructions to implement an M3C dual-baseband coupling characterization method, and the processor 102 can execute multiple instructions to achieve the following: Based on the M3C average value model, the basic dynamic equations of the bridge arm electrical parameters are established; Based on the fundamental dynamic equations, electrical parameters are decomposed and matrixed under power frequency and low frequency conditions to generate a two-dimensional frequency domain matrix. Linear equivalence modeling is performed on the frequency domain operation relationships of the two-dimensional frequency domain matrix to obtain a structured matrix; The structured matrix is ​​solved in the frequency domain to obtain the steady-state frequency domain harmonic model of the bridge arm circuit.

[0089] 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).

[0090] 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.

[0091] 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.

[0092] 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.

[0093] 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.

[0094] 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.

[0095] 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 protection scope of the claims of the present invention.

Claims

1. A dual-fundamental-frequency coupling characterization method for M3C, characterized in that, The method comprises: establishing a basic dynamic equation of the bridge arm electrical parameter based on an M3C average value model; performing frequency domain decomposition and matrix representation of the electrical parameter under a power frequency and a low frequency condition based on the basic dynamic equation, and generating a two-dimensional frequency domain matrix; linearly equivalent modeling a frequency domain operation relationship of the two-dimensional frequency domain matrix to obtain a structured matrix; solving the structured matrix in a frequency domain to obtain a steady-state frequency domain harmonic model of the bridge arm circuit.

2. The M3C dual base frequency coupling characterization method of claim 1, wherein, The establishing of the basic dynamic equation of the bridge arm electrical parameter comprises: determining equivalent capacitance parameters of each bridge arm sub-module based on the M3C average value model, and establishing a dynamic constraint relationship between a time variation rate of a bridge arm capacitor voltage and a bridge arm current and a modulation signal according to the equivalent capacitance parameters; deriving a time domain expression of a bridge arm voltage according to the dynamic constraint relationship, and introducing bridge arm inductance and resistance parameters to generate a bridge arm voltage dynamic equation; establishing a coupling balance relationship between a power frequency side valve side voltage and a low frequency side valve side voltage according to the bridge arm voltage dynamic equation; introducing a potential difference between a power frequency alternating current side and a low frequency alternating current side neutral point in the coupling balance relationship, and expressing the potential difference in a weighted form of each bridge arm voltage to obtain the basic dynamic equation.

3. The M3C dual base frequency coupling characterization method of claim 1, wherein, The performing of the frequency domain decomposition and the matrix representation of the electrical parameter under the power frequency and the low frequency condition to generate the two-dimensional frequency domain matrix comprises: performing frequency decomposition on the electrical parameter according to a time domain relationship of the electrical parameter in the basic dynamic equation, and extracting a plurality of groups of frequency components formed by a power frequency component and a low frequency component and interaction; establishing a steady-state harmonic component set under a double fundamental frequency coupling according to the frequency components, and constructing a corresponding two-dimensional frequency domain matrix structure with a combination order of each frequency component as an index.

4. The M3C dual base frequency coupling characterization method of claim 3, wherein, The two-dimensional frequency domain matrix structure further comprises: respectively representing steady-state components of the bridge arm current, the bridge arm voltage, the capacitor voltage and the modulation signal in an amplitude and a phase form, and establishing a conjugate corresponding relationship between positive frequency components and negative frequency components; in the three-phase structure of the bridge arm, defining a phase shift relationship of each phase bridge arm under different combination frequencies according to a phase sequence characteristic of the three-phase bridge arm.

5. The M3C dual base frequency coupling characterization method of claim 1, wherein, The solving of the structured matrix in the frequency domain to obtain the steady-state frequency domain harmonic model of the bridge arm circuit comprises: performing dimension reduction processing on the structured matrix to obtain a steady-state frequency representation of the bridge arm electrical parameter; extracting parameter components of the bridge arm voltage, the bridge arm current and the bridge arm capacitor voltage under a frequency domain condition based on the steady-state frequency representation, and establishing a frequency domain corresponding relationship of each parameter component in combination with the structured matrix; constructing an equivalent impedance matrix and an equivalent conductance matrix of the bridge arm circuit according to the frequency domain corresponding relationship and a combination frequency factor of the power frequency component and the low frequency component; substituting the equivalent impedance matrix and the equivalent conductance matrix into the steady-state frequency representation to obtain a balance relationship between the bridge arm voltage, the current and the capacitor voltage, and then deriving steady-state harmonic components of the bridge arm current and the capacitor voltage according to the balance relationship to generate the steady-state frequency domain harmonic model.

6. An M3C dual basis frequency coupling characterization apparatus, characterized by, The device comprises: a basic modeling module configured to establish a basic dynamic equation of a bridge arm electrical parameter based on an M3C average value model; The frequency domain decomposition module is configured to perform frequency domain decomposition and matrix representation of electrical parameters under power frequency and low frequency conditions based on the basic dynamic equation, and generate a two-dimensional frequency domain matrix; The linear modeling module is configured to perform linear equivalent modeling on a frequency domain operation relationship of the two-dimensional frequency domain matrix, and obtain a structured matrix; The harmonic solving module is configured to perform frequency domain solving on the structured matrix, and obtain a steady-state frequency domain harmonic model of the bridge arm loop.

7. The M3C dual base frequency coupling characterization apparatus of claim 6, wherein, The basic modeling module is specifically configured to: determine equivalent capacitance parameters of each bridge arm sub-module based on an M3C average value model, and establish a dynamic constraint relationship between a time variation rate of bridge arm capacitor voltage and bridge arm current and modulation signals according to the equivalent capacitance parameters; deduce a time domain expression of bridge arm voltage according to the dynamic constraint relationship, and generate a bridge arm voltage dynamic equation by introducing bridge arm inductance and resistance parameters; establish a coupling balance relationship between power frequency side valve side voltage and low frequency side valve side voltage according to the bridge arm voltage dynamic equation; introduce a potential difference between power frequency alternating current sides and low frequency alternating current sides in the coupling balance relationship, and express the potential difference in a weighted form of each bridge arm voltage to obtain the basic dynamic equation.

8. The M3C dual base frequency coupling characterization apparatus of claim 6, wherein, The frequency domain decomposition module is specifically configured to: perform frequency decomposition on electrical parameters according to a time domain relationship of the electrical parameters in the basic dynamic equation, and extract a plurality of groups of frequency components formed by power frequency components and low frequency components and interactions; establish a steady-state harmonic component set under double base frequency coupling according to the frequency components, and construct a corresponding two-dimensional frequency domain matrix structure with a combination order of each frequency component as an index.

9. The M3C dual base frequency coupling characterization apparatus of claim 8, wherein, The two-dimensional frequency domain matrix structure further includes: steady-state components of bridge arm current, bridge arm voltage, capacitor voltage and modulation signals are represented in amplitude and phase forms respectively, and a conjugate corresponding relationship between positive frequency components and negative frequency components is established; in the three-phase structure of the bridge arm, a phase shift relationship of each phase bridge arm under different combination frequencies is defined according to phase sequence characteristics of the three-phase bridge arm.

10. The M3C dual base frequency coupling characterization apparatus of claim 6, wherein, The harmonic solving module is specifically configured to: perform dimension reduction processing on the structured matrix to obtain a steady-state frequency representation of the bridge arm electrical parameters; extract parameter components of bridge arm voltage, bridge arm current and bridge arm capacitor voltage under frequency domain conditions based on the steady-state frequency representation, and establish a frequency domain corresponding relationship of each parameter component in combination with the structured matrix; construct an equivalent impedance matrix and an equivalent conductance matrix of the bridge arm loop according to the frequency domain corresponding relationship and combination frequency factors of the power frequency components and the low frequency components; substitute the equivalent impedance matrix and the equivalent conductance matrix into the steady-state frequency representation to obtain a balance relationship between bridge arm voltage, current and capacitor voltage, and then deduce steady-state harmonic components of bridge arm current and capacitor voltage according to the balance relationship to generate the steady-state frequency domain harmonic model.

11. An electronic device, comprising: The processor is configured to execute a computer program stored in the memory to implement the steps of the M3C double base frequency coupling representation method according to any one of claims 1 to 5.

12. 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 M3C dual base frequency coupling characterization method in any one of claims 1 to 5.

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