A method and device for resonant analysis of a multi-frequency coupled system taking into account the frequency coupling characteristics of a converter

Abstract

The application provides a kind of multi-frequency coupling system resonance analysis method considering the frequency coupling characteristics of converter, comprising, based on the coupling relationship between voltage and current of primary harmonic and secondary harmonic at converter node, establishing node multi-frequency coupling self-impedance relationship matrix and mutual-impedance relationship matrix;Frequency coupling impedance matrix between primary harmonic voltage / current and coupled secondary harmonic current / voltage of the system is constructed;According to the frequency coupling impedance matrix, modal analysis operation is carried out;And change the primary harmonic resonance frequency, calculate the eigenvalue of the frequency coupling impedance matrix corresponding to each primary harmonic resonance frequency;Draw the frequency coupling resonance curve;The resonance frequency point of primary harmonic frequency and coupled harmonic frequency is obtained, and the coupled resonance participation factor of each bus of resonance frequency is calculated, to obtain the coupled resonance key bus.The application also discloses corresponding equipment.Implementation of the present application has the characteristics of high efficiency and low cost, which can provide basis for prevention and treatment of multi-frequency coupling resonance.

Description

Technical Field

[0001] This invention relates to the field of harmonic resonance analysis technology in new energy power systems, and in particular to a method and equipment for resonant analysis of multi-frequency coupled systems that takes into account the frequency coupling characteristics of converters. Background Technology

[0002] With the rapid development of new power systems with a high proportion of new energy sources and high proportion of power electronic equipment, the number of nonlinear components in power systems is gradually increasing. These nonlinear components may work together with reactive power compensation devices in the system to cause harmonic resonance in the power system. Furthermore, primary disturbances may generate secondary harmonics again after passing through nonlinear components. Frequency coupling may occur between harmonics of different frequencies, thereby inducing frequency-coupled harmonic resonance in the system.

[0003] In existing technologies, resonance problems can be analyzed using frequency scanning or modal analysis. However, the resonance information obtained by frequency scanning is too limited. Therefore, the industry has gradually begun to study multi-frequency harmonic coupling resonance of primary and secondary disturbances in the system based on modal analysis. With the increasing number of loads and devices generating harmonics in power systems, how to quickly obtain the coupling resonance characteristics of the power grid and effectively prevent coupling resonance has become a very necessary and urgent problem. However, no solution with both high efficiency and low cost has yet emerged in the current technology. Summary of the Invention

[0004] The technical problem to be solved by this invention is to propose a multi-frequency coupled system resonance analysis method and equipment that takes into account the frequency coupling characteristics of converters. It has the characteristics of high efficiency and low cost, and can provide a basis for the prevention and control of multi-frequency coupled resonance.

[0005] The technical solution adopted in this invention is to provide a resonance analysis method for a multi-frequency coupled system that takes into account the frequency coupling characteristics of the converter, which includes at least the following steps:

[0006] Step S10: Based on the coupling relationship between the voltage and current of the primary harmonics and secondary harmonics at the converter nodes, establish the node multi-frequency coupling self-admittance relationship matrix and the inter-node multi-frequency coupling mutual admittance relationship matrix.

[0007] Step S11: Based on the multi-frequency coupling self-admittance relation matrix, the multi-frequency coupling mutual admittance relation matrix, and the admittance matrix formed by the system's primary harmonic voltage and primary harmonic current, construct the frequency coupling admittance matrix between the system's primary harmonic voltage / current and the coupled secondary harmonic current / voltage.

[0008] Step S12: Perform modal analysis calculations based on the frequency coupling admittance matrix; and change the original harmonic resonant frequency so that it varies within a certain range by a certain step size, and calculate the eigenvalues ​​of the frequency coupling admittance matrix corresponding to each original resonant frequency.

[0009] Step S13: Calculate the frequency-coupled mode impedance based on the eigenvalues ​​of the frequency-coupled admittance matrix, and plot the frequency-coupled resonance curve with the original resonant frequency as the abscissa and the frequency-coupled mode impedance as the ordinate.

[0010] Step S14: Obtain the resonant frequency points of the original harmonic frequency and the coupled harmonic frequency based on the peak value of the frequency coupling resonance curve, calculate the coupling resonance participation factor of each bus at the resonant frequency, and obtain the key bus of coupling resonance.

[0011] Preferably, step S10 further includes: determining the coupling relationship between primary and secondary harmonic voltage and current at the converter node according to the following calculation formula:

[0012]

[0013] Among them, f s Represents the primary harmonic frequencies (Hz); f1,…,f h Represents h types of secondary harmonic frequencies (Hz); I i Y represents the vector of primary harmonic frequency current and secondary harmonic current at system node i; ii U represents the self-admittance matrix representing the coupling between the primary and secondary harmonic voltages and currents at node i; i This represents the primary harmonic frequency voltage and secondary harmonic voltage vector at system node i; The frequency at node i is f. s Harmonic currents; similarly, This represents the harmonic current with frequency f1 at node i; The frequency at node i is f. s Harmonic voltages; similarly, This represents the harmonic voltage with frequency f1 at node i; The frequency at node i is f. s voltage The frequency at node i is f s current The self-admittance relationship; similarly, This represents the voltage at node i with frequency f1. The frequency at node i is f s current The coupling self-admittance relationship is determined, and the original harmonic is set as the initial frequency, i.e., f. s =f minAt the same time, set the upper limit frequency f max .

[0014] Preferably, step S10 further includes:

[0015] The coupling relationship between primary and secondary harmonic voltages and currents between system nodes is determined using the following formula:

[0016]

[0017] Among them, I i Y represents the vector of primary harmonic frequency current and secondary harmonic current at system node i; ij U represents the mutual admittance matrix of primary and secondary harmonic voltage-current coupling between node i and node j; j This represents the primary harmonic frequency voltage and secondary harmonic voltage vector at system node j; The frequency at node j is f. s voltage The frequency at node i is f s current The mutual admittance relationship; similarly, This represents the voltage at node j with frequency f1. The frequency at node i is f s current The coupling mutual admittance relationship.

[0018] Preferably, step S11 further includes:

[0019] Construct the frequency coupling admittance matrix of primary harmonic voltage / current and coupled secondary harmonic current / voltage according to the following formula:

[0020]

[0021] Where n represents the number of system nodes; The frequency at n nodes of the system is f s The current vector; This represents the voltage vector with frequency f1 at n nodes of the system; The node voltage at frequency f1 and f s The frequency coupling admittance matrix of the current at the frequency node, the elements of which come from the primary and secondary harmonic voltage-current coupling self / mutual admittance relationship matrix Y. ii / Y ij ; This indicates that the frequency at node 1 is f. s The current value; This represents the current value at node 1 with frequency f1; This represents the voltage at node 1 with frequency f1. The frequency at node 1 is f s current The coupling self-admittance relationship; This represents the voltage at node 2 with frequency f1. The frequency at node 1 is f s current The coupling mutual admittance relationship.

[0022] Preferably, step S12 further includes:

[0023] The frequency coupling matrix of harmonic voltage and harmonic current is decomposed into eigenvalues ​​according to the following formula:

[0024]

[0025] in, Represents the voltage at frequency f1 and the frequency f s The eigenvalue matrix of the current-frequency coupling admittance matrix; Represents the voltage at frequency f1 and the frequency f s The eigenvector matrix of the current-frequency coupling admittance matrix; Represents the voltage at frequency f1 and the frequency f s The first eigenvalue of the eigenvalue matrix of the current-frequency coupling admittance matrix; similarly, Represents the voltage at frequency f1 and the frequency f s The nth eigenvalue of the eigenvalue matrix of the current-frequency coupling admittance matrix.

[0026] Preferably, step S12 further includes:

[0027] The frequency coupling mode impedance matrix of harmonic voltage and harmonic current is determined using the following formula:

[0028]

[0029] in, Represents the voltage at frequency f1 and the frequency f s Current-frequency coupled mode impedance matrix; Represents the voltage at frequency f1 and the frequency f s Frequency-coupled mode impedance of the current.

[0030] Preferably, in step S13, the coupling resonance curve is plotted according to the following steps:

[0031] Record the native harmonic frequency f at this time. s The corresponding n frequency-coupled mode impedance values;

[0032] Set the native harmonic frequency fs According to step size Δf s Growth, i.e. f s =f s +Δf s Repeat the above process until the upper limit value f is reached. s =f max ;

[0033] Each calculation yields n frequency-coupled mode impedance values, with frequency f s The horizontal axis represents the frequency-coupled mode impedance value. Plot n lines of voltage at frequency f1 and frequency f, with f as the vertical axis. s The coupling resonance curve of the current is used to obtain the coupling resonance frequency point;

[0034] The resonant frequency corresponding to the peak of the curve is the frequency f1, which is the voltage frequency f. s The frequency f of the current that causes coupling resonance s The corresponding vertical axis represents the voltage at frequency f1 and the voltage at frequency f. s Key modes of current coupling

[0035]

[0036] Preferably, in step S14, the frequency f1 voltage and frequency f are determined according to the following calculation formula. s Key busbar for coupled resonance of current:

[0037] Based on the obtained coupled resonance frequency points, the key mode of coupled resonance at the coupled resonance frequency points is selected. The corresponding eigenvector matrix and its inverse matrix Calculate the sensitivity matrix for the corresponding mode:

[0038]

[0039] Where PF represents the sensitivity matrix of the coupled resonance; Representation matrix The m-th column vector; Representation matrix The m-th row vector;

[0040] Define PFim = limtmi as the coupling resonance participation factor, where i is the bus number and m is the mode number. The larger the participation factor, the more likely the bus is to become the frequency f. s The coupled resonant center with frequency f1;

[0041] Obtain the original harmonic f s and different secondary harmonics (f1,…,f h Between each generation of harmonics (f1,…,f),h ) and other different secondary harmonics (f1,…,f h The coupling resonance point between the two and the key resonant busbar.

[0042] Accordingly, another aspect of the present invention also provides a computer device including a memory and a processor, the memory storing a computer program, the processor executing the computer program to implement the steps of the method as described above.

[0043] Implementing the embodiments of the present invention has the following beneficial effects:

[0044] This invention proposes a multi-frequency coupled system resonance analysis method and device that considers the frequency coupling characteristics of converters. By sampling the converter, the voltage-current relationship of the primary harmonics, the voltage-current relationship of the secondary harmonics, and the voltage-current coupling relationship (coupling self-admittance matrix) at the converter's grid connection point can be obtained. A system admittance matrix reflecting the voltage-current relationship at each node of the system is also obtained. Then, based on the obtained voltage-current coupling relationship of the primary and secondary harmonics at the nodes and the voltage-current relationship at each node of the system, a system frequency coupling admittance matrix reflecting the relationship between the voltage / current at the target resonant frequency and the current / voltage at the coupled resonant frequency is constructed. Next, based on the system's frequency coupling admittance matrix, eigenvalue decomposition can be further performed to calculate the key modes of coupled resonance and plot the frequency-mode impedance curves. This allows for convenient acquisition of coupled resonant frequency information and determination of the key resonant bus.

[0045] Implementing this invention provides an efficient and low-cost method for analyzing coupled frequency resonances, which can provide a basis for the prevention and mitigation of multi-frequency coupled resonances. Attached Figure Description

[0046] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0047] Figure 1 This is a schematic diagram of the main flow of an embodiment of a multi-frequency coupled system resonance analysis method that takes into account the frequency coupling characteristics of a converter, provided by the present invention.

[0048] Figure 2 A more detailed flowchart is shown in one embodiment of a resonant analysis method for a multi-frequency coupled system that takes into account the frequency coupling characteristics of a converter. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without inventive effort are within the scope of protection of this invention.

[0050] like Figure 1 The diagram shows a schematic representation of an embodiment of a multi-frequency coupled system resonance analysis method considering the frequency coupling characteristics of a converter, provided by the present invention; in conjunction with... Figure 2 As shown, in this embodiment, the method includes:

[0051] Step S10: Based on the coupling relationship between the voltage and current of the primary harmonics and secondary harmonics at the converter nodes, establish the node multi-frequency coupling self-admittance relationship matrix and the inter-node multi-frequency coupling mutual admittance relationship matrix.

[0052] It is understood that a converter is a power conversion device that converts alternating current (AC) to direct current (DC) or vice versa, and is widely used in power electronic equipment. Since converters contain many power electronic devices, such as transistors and diodes, these devices generate harmonics during switching. Therefore, primary and secondary harmonics are generated at the converter nodes. Harmonic information at the converter nodes can be measured using specialized equipment such as harmonic analyzers, or it can be simulated and analyzed using simulation software. In this embodiment of the invention, the coupling relationship between the voltage and current of primary and secondary harmonics at the converter nodes can be used to establish the node multi-frequency coupling self-admittance matrix and the inter-node multi-frequency coupling mutual admittance matrix.

[0053] In a specific example, step S10 further includes:

[0054] The coupling relationship between primary and secondary harmonic voltages and currents at converter nodes is expressed and determined using the following formula:

[0055]

[0056] Among them, f s Represents the primary harmonic frequencies (Hz); f1,…,f h Represents h types of secondary harmonic frequencies (Hz); I i Y represents the vector of primary harmonic frequency current and secondary harmonic current at system node i; ii U represents the self-admittance matrix representing the coupling between the primary and secondary harmonic voltages and currents at node i; i This represents the primary harmonic frequency voltage and secondary harmonic voltage vector at system node i; The frequency at node i is f. s Harmonic currents; similarly, This represents the harmonic current with frequency f1 at node i; The frequency at node i is f. s Harmonic voltages; similarly, This represents the harmonic voltage with frequency f1 at node i; The frequency at node i is f. s voltage The frequency at node i is f s current The self-admittance relationship; similarly, This represents the voltage at node i with frequency f1. The frequency at node i is f s current The coupling self-admittance relationship is determined, and the original harmonic is set as the initial frequency, i.e., f. s =f min At the same time, set the upper limit frequency f max .

[0057] It is understandable that, due to the certain numerical relationship between primary and secondary harmonics, if the primary harmonic f s Changes occur, and the corresponding secondary harmonics f1,…,f h It will also change to some extent, and the coupling relationship matrix between primary harmonics and secondary harmonic voltage and current will also change.

[0058] Step S10 further includes:

[0059] The coupling relationship between primary and secondary harmonic voltages and currents between system nodes is determined using the following formula:

[0060]

[0061] Among them, I i Y represents the vector of primary harmonic frequency current and secondary harmonic current at system node i; ij U represents the mutual admittance matrix of primary and secondary harmonic voltage-current coupling between node i and node j; j This represents the primary harmonic frequency voltage and secondary harmonic voltage vector at system node j; The frequency at node j is f. s voltage The frequency at node i is f s current The mutual admittance relationship; similarly, This represents the voltage at node j with frequency f1. The frequency at node i is f s current The coupling mutual admittance relationship. Typically, there are no devices connected in series between nodes that could generate secondary harmonics, so this matrix only contains elements on the main diagonal.

[0062] Step S11: Based on the multi-frequency coupling self-admittance relation matrix, the multi-frequency coupling mutual admittance relation matrix, and the admittance matrix formed by the system's primary harmonic voltage and primary harmonic current, construct the frequency coupling admittance matrix between the system's primary harmonic voltage / current and the coupled secondary harmonic current / voltage.

[0063] Understandably, the admittance matrix between the native harmonic voltages and currents at each node of the system can generally be constructed using the following formula:

[0064]

[0065] Where n represents the number of system nodes; I1 represents the current value of the primary harmonic at node 1; U1 represents the voltage value of the primary harmonic at node 1; y 11 This represents the self-admittance value at node 1; similarly, y 12 This represents the mutual admittance value between node 1 and node 2.

[0066] Therefore, in a specific example, step S11 further includes:

[0067] Construct the frequency coupling admittance matrix of primary harmonic voltage / current and coupled secondary harmonic current / voltage according to the following formula:

[0068]

[0069] Where n represents the number of system nodes; The frequency at n nodes of the system is f s The current vector; This represents the voltage vector with frequency f1 at n nodes of the system; The node voltage at frequency f1 and f s The frequency coupling admittance matrix of the current at the frequency node, the elements of which come from the primary and secondary harmonic voltage-current coupling self / mutual admittance relationship matrix Y. ii / Y ij ; This indicates that the frequency at node 1 is f. s The current value; This represents the current value at node 1 with frequency f1; This represents the voltage at node 1 with frequency f1. The frequency at node 1 is f s current The coupling self-admittance relationship; This represents the voltage at node 2 with frequency f1. The frequency at node 1 is f s current The coupling mutual admittance relationship.

[0070] This formula uses a voltage with frequency f1 and a current with frequency f1. s Taking the coupled resonance analysis between them as an example, the obtained frequency coupling admittance matrix is ​​the voltage at frequency f1 and the frequency f. s The coupling matrix between currents.

[0071] Step S12: Perform modal analysis calculations based on the frequency coupling admittance matrix; and change the original harmonic resonant frequency so that it varies within a certain range by a certain step size, and calculate the eigenvalues ​​of the frequency coupling admittance matrix corresponding to each original resonant frequency.

[0072] In a specific example, step S12 further includes:

[0073] The frequency coupling matrix of harmonic voltage and harmonic current is decomposed into eigenvalues ​​according to the following formula:

[0074]

[0075] in, Represents the voltage at frequency f1 and the frequency f s The eigenvalue matrix of the current-frequency coupling admittance matrix; Represents the voltage at frequency f1 and the frequency f s The eigenvector matrix of the current-frequency coupling admittance matrix; Represents the voltage at frequency f1 and the frequency f s The first eigenvalue of the eigenvalue matrix of the current-frequency coupling admittance matrix; similarly, Represents the voltage at frequency f1 and the frequency f s The nth eigenvalue of the eigenvalue matrix of the current-frequency coupling admittance matrix.

[0076] Preferably, step S12 further includes:

[0077] The frequency coupling mode impedance matrix of harmonic voltage and harmonic current is determined using the following formula:

[0078]

[0079] in, Represents the voltage at frequency f1 and the frequency f s Current-frequency coupled mode impedance matrix; Represents the voltage at frequency f1 and the frequency f s Frequency-coupled mode impedance of the current.

[0080] Step S13: Calculate the frequency-coupled mode impedance based on the eigenvalues ​​of the frequency-coupled admittance matrix, and plot the frequency-coupled resonance curve with the original resonant frequency as the abscissa and the frequency-coupled mode impedance as the ordinate.

[0081] In a specific example, in step S13, the coupling resonance curve is plotted according to the following steps:

[0082] Record the native harmonic frequency f at this time. s The corresponding n frequency-coupled mode impedance values;

[0083] Set the native harmonic frequency f s According to step size Δf s Growth, i.e. f s =f s +Δf s Repeat the above process until the upper limit value f is reached. s =f max ;

[0084] Each calculation yields n frequency-coupled mode impedance values, with frequency f s The horizontal axis represents the frequency-coupled mode impedance value. Plot n lines of voltage at frequency f1 and frequency f, with f as the vertical axis. s The coupling resonance curve of the current is obtained, thus yielding the coupling resonance frequency point;

[0085] The resonant frequency corresponding to the peak of the curve is the frequency f1, which is the voltage frequency f. s The frequency f of the current that causes coupling resonance s The corresponding vertical axis represents the voltage at frequency f1 and the voltage at frequency f. s Key modes of current coupling

[0086]

[0087] It is understandable that, due to the difference between the secondary harmonic f1 and the primary harmonic f... s There is a certain pattern of change between them, so the generated harmonic f1 will change with the primary harmonic f. s It changes with the changes.

[0088] Obtain the original resonant frequency f s Then, simultaneously calculate the secondary frequencies f1 and f2 that cause coupled resonance. s f1 and f2 are the primary and secondary coupling resonant frequencies, respectively.

[0089] Step S14: Obtain the resonant frequency points of the original harmonic frequency and the coupled harmonic frequency based on the peak value of the frequency coupling resonance curve, calculate the coupling resonance participation factor of each bus at the resonant frequency, and obtain the key bus of coupling resonance.

[0090] In a specific example, in step S14, the frequency f1 voltage and frequency f are determined according to the following calculation formula. s Key busbar for coupled resonance of current:

[0091] Based on the obtained coupled resonance frequency points, the key mode of coupled resonance at the coupled resonance frequency points is selected. The corresponding eigenvector matrix and its inverse matrix Calculate the sensitivity matrix for the corresponding mode:

[0092]

[0093] Where PF represents the sensitivity matrix of the coupled resonance; Representation matrix The m-th column vector; Representation matrix The m-th row vector;

[0094] Define PFim = limtmi as the coupling resonance participation factor, where i is the bus number and m is the mode number. The larger the participation factor, the more likely the bus is to become the frequency f. s The coupled resonant center with frequency f1;

[0095] The original harmonic f can be calculated using the method described above. s and different secondary harmonics (f1,…,f h Between each generation of harmonics (f1,…,f), h ) and other different secondary harmonics (f1,…,f h The coupling resonance point between the two and the key resonant busbar.

[0096] After identifying the critical resonant bus, a series of measures can be taken to mitigate or eliminate the impact of resonance on the power system, such as increasing the grounding impedance, using filters or resonance suppressors, etc. The methods used for these measures need to be determined based on the specific circumstances and system requirements, and their selection and installation must be considered.

[0097] Specifically, increasing the grounding impedance of the power system can reduce the occurrence of resonance problems. Grounding all equipment and metal components in the system, increasing the grounding resistance, or using grounding inductance can effectively prevent resonance problems from occurring.

[0098] Alternatively, passive or active filters can be used at the critical resonant bus to eliminate or reduce the impact of resonance problems. The selection of the filter should consider factors such as resonant frequency, impedance, and capacitance.

[0099] Resonance suppressors, including active and passive ones, can also be installed to eliminate resonance problems. Passive resonance suppressors, such as feedback and predictive types, can control the occurrence of resonance. Active resonance suppressors, on the other hand, can be externally powered and their output adjusted as needed to effectively suppress resonance.

[0100] In some cases, techniques to reduce resonance problems can be employed during the transformer design phase. For example, using a three-phase transformer and employing shielding or isolation between the high- and low-voltage windings.

[0101] In another aspect, the present invention provides a computer device including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement, as follows: Figure 1 and Figure 2 The steps of the described method. For more details, please refer to and combine with the foregoing explanation. Figure 1 and Figure 2 The description of that will not be repeated here.

[0102] Implementing the embodiments of the present invention has the following beneficial effects:

[0103] This invention proposes a multi-frequency coupled system resonance analysis method that considers the frequency coupling characteristics of converters. By sampling the converter, the voltage-current relationship of primary harmonics, the voltage-current relationship of secondary harmonics, and the voltage-current coupling relationship (coupling self-admittance matrix) at the converter's grid connection point can be obtained. A system admittance matrix reflecting the voltage-current relationship at each node of the system is also obtained. Then, based on the obtained voltage-current coupling relationship of primary and secondary harmonics at the nodes and the voltage-current relationship at each node of the system, a system frequency coupling admittance matrix reflecting the relationship between the voltage / current at the target resonant frequency and the current / voltage at the coupled resonant frequency is constructed. Next, based on the system's frequency coupling admittance matrix, eigenvalue decomposition can be further performed to calculate the key modes of coupled resonance and plot the frequency-mode impedance curves. This allows for convenient acquisition of coupled resonant frequency information and determination of the key resonant bus.

[0104] Implementing this invention provides an efficient and low-cost method for analyzing coupled frequency resonances, which can provide a basis for the prevention and mitigation of multi-frequency coupled resonances.

[0105] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, apparatus, 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.

[0106] 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 for specifying modules in one or more boxes.

[0107] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for resonant analysis of a multi-frequency coupled system considering the frequency coupling characteristics of a converter, characterized in that, It should include at least the following steps: Step S10: Based on the coupling relationship between the voltage and current of the primary harmonics and secondary harmonics at the converter nodes, establish the node multi-frequency coupling self-admittance relationship matrix and the inter-node multi-frequency coupling mutual admittance relationship matrix. Step S11: Based on the multi-frequency coupling self-admittance relation matrix, the multi-frequency coupling mutual admittance relation matrix, and the admittance matrix formed by the system's primary harmonic voltage and primary harmonic current, construct the frequency coupling admittance matrix between the system's primary harmonic voltage / current and the coupled secondary harmonic current / voltage. Step S12: Perform modal analysis calculations based on the frequency coupling admittance matrix; and change the original harmonic resonant frequency so that it varies within a certain range by a certain step size, and calculate the eigenvalues ​​of the frequency coupling admittance matrix corresponding to each original resonant frequency. Step S13: Calculate the frequency-coupled mode impedance based on the eigenvalues ​​of the frequency-coupled admittance matrix, and plot the frequency-coupled resonance curve with the original resonant frequency as the abscissa and the frequency-coupled mode impedance as the ordinate. Step S14: Obtain the resonant frequency points of the original harmonic frequency and the coupled harmonic frequency based on the peak value of the frequency coupling resonance curve, calculate the coupling resonance participation factor of each bus at the resonant frequency, and obtain the key bus of coupling resonance.

2. The method as described in claim 1, characterized in that, Step S10 further includes: determining the coupling relationship between primary harmonic and secondary harmonic voltage and current at the converter node according to the following calculation formula: in, f s Indicates the original harmonic frequency (Hz); f 1,…, f h The frequency of h secondary harmonics is represented in Hz. Represents system nodes i The vectors of the primary harmonic frequency current and the secondary harmonic current at the location; Represents a node i The self-admittance relationship matrix of voltage-current coupling between primary and secondary harmonics; Represents system nodes i The primary harmonic frequency voltage and secondary harmonic voltage vector at the location; express i The frequency at the node is f s Harmonic currents; express i The frequency at the node is f The harmonic current of 1; express i The frequency at the node is f s Harmonic voltages; express i The frequency at the node is f The harmonic voltage of 1; Indicates at node i The frequency at that location is f s voltage With nodes i The frequency at that location is f s current The self-admittance relationship; Indicates at node i The frequency at that location is f voltage of 1 With nodes i The frequency at that location is f s current The coupling self-admittance relationship, with the primary harmonic as the initial frequency, i.e. f s = f min At the same time, an upper limit frequency is set. f max .

3. The method as described in claim 2, characterized in that, Step S10 further includes: The coupling relationship between primary and secondary harmonic voltages and currents between system nodes is determined using the following formula: in, Represents system nodes i The vectors of the primary harmonic frequency current and the secondary harmonic current at the location; Represents a node i and nodes j The mutual admittance relationship matrix between primary and secondary harmonic voltage-current coupling; Represents system nodes j The primary harmonic frequency voltage and secondary harmonic voltage vector at the location; Indicates at node j The frequency at that location is f s voltage With nodes i The frequency at that location is f s current The mutual admittance relationship; Indicates at node j The frequency at that location is f voltage of 1 With nodes i The frequency at that location is f s current The coupling mutual admittance relationship.

4. The method as claimed in claim 2 or 3, characterized in that, Step S11 further includes: Construct the frequency coupling admittance matrix of primary harmonic voltage / current and coupled secondary harmonic current / voltage according to the following formula: Where n represents the number of system nodes; This indicates that the frequency at n nodes of the system is f s The current vector; This indicates that the frequency at n nodes of the system is f Voltage vector of 1; express f Node voltage at frequency 1 and f s The frequency coupling admittance matrix of the current at the frequency node, the elements of which are derived from the primary and secondary harmonic voltage-current coupling self / mutual admittance relationship matrix. / ; The frequency at node 1 is... f s The current value; The frequency at node 1 is... f The current value of 1; The frequency at node 1 is . f voltage of 1 The frequency at node 1 is f s current The coupling self-admittance relationship; The frequency at node 2 is . f voltage of 1 The frequency at node 1 is f s current The coupling mutual admittance relationship.

5. The method as described in claim 4, characterized in that, Step S12 further includes: The frequency coupling matrix of harmonic voltage and harmonic current is decomposed into eigenvalues ​​according to the following formula: in, Represents frequency f 1. Voltage and frequency f s The eigenvalue matrix of the current-frequency coupling admittance matrix; Represents frequency f 1. Voltage and frequency f s The eigenvector matrix of the current-frequency coupling admittance matrix; ; Represents frequency f 1. Voltage and frequency f s The first eigenvalue of the eigenvalue matrix of the current-frequency coupling admittance matrix; similarly, Represents frequency f 1. Voltage and frequency f s The nth eigenvalue of the eigenvalue matrix of the current-frequency coupling admittance matrix.

6. The method as described in claim 5, characterized in that, Step S12 further includes: The frequency coupling mode impedance matrix of harmonic voltage and harmonic current is determined using the following formula: in, Represents frequency f 1. Voltage and frequency f s Current-frequency coupled mode impedance matrix; Represents frequency f 1. Voltage and frequency f s Frequency-coupled mode impedance of the current.

7. The method as described in claim 6, characterized in that, In step S13, the coupling resonance curve is plotted according to the following steps: Record the native harmonic frequency at this time. f s The corresponding n frequency-coupled mode impedance values; Set the native harmonic frequency f s According to step size Δ f s Growth, that is f s = f s +Δ f s Repeat the above process until the upper limit is reached. f s = f max ; Based on the n frequency-coupled mode impedance values ​​obtained from the calculation, in terms of frequency... f s The horizontal axis represents the frequency-coupled mode impedance value. , i Let the values ​​be 1, 2, ..., n, and let n be the ordinates. Plot n frequencies. f 1. Voltage and Frequency f s The coupling resonance curve of the current is used to obtain the coupling resonance frequency point; The resonant frequency corresponding to the peak of the curve is the frequency. f 1. Voltage and Frequency f s The frequency of the current that causes coupling resonance f s The corresponding vertical axis represents frequency. f 1. Voltage and Frequency f s Key modes of current coupling .

8. The method as described in claim 7, characterized in that, In step S14, the frequency is determined according to the following calculation formula. f 1. Voltage and Frequency f s Key busbar for coupled resonance of current: Based on the obtained coupled resonance frequency points, the key mode of coupled resonance at the coupled resonance frequency points is selected. The corresponding eigenvector matrix and its inverse matrix Calculate the sensitivity matrix for the corresponding mode: in, PF The sensitivity matrix representing the coupled resonance; Representation matrix The m-th column vector; Representation matrix The m Row vectors; definition For coupling resonance participation factors, i For busbar number, m For mode numbers, the bus with the larger the participation factor is, the more likely it is to become a frequency. f s and frequency f The coupled resonance center of 1; Obtaining native harmonics f s and different secondary harmonics f 1,…, f h Between each generation of harmonics f 1,…, f h Other different secondary harmonics f 1,…, f h The coupling resonance point and the key resonant bus between them.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method as described in any one of claims 1 to 8.

Images