A stability detection method, device and equipment of a multi-conversion station system and a medium

Abstract

The application discloses a kind of stability detection method, device, equipment and medium of multi-conversion station system, it is related to power system technical field, method includes: obtaining the impedance matrix of multi-conversion station system;Obtain the port admittance matrix of converter in multi-conversion station system;According to impedance matrix and port admittance matrix, construct the return difference matrix of multi-conversion station system;Generalized radius coefficient of return difference matrix is defined;If generalized radius coefficient is less than preset threshold in research frequency band, then stability criterion is simplified based on generalized diagonal dominance, whether multi-conversion station system is stable according to the stability criterion after simplification is detected.The application constructs the return difference matrix of multi-conversion station system, and the coupling relationship between converter is quantified according to generalized radius coefficient of return difference matrix, if generalized radius coefficient is less than preset threshold, then it can be determined as weak coupling relationship, and then stability criterion is simplified based on generalized diagonal dominance, can reduce the complexity of detecting the stability of multi-conversion station system and improve detection efficiency.

Description

Technical Field

[0001] This application relates to the field of power system technology, and in particular to a method, apparatus, equipment and medium for stability testing of a multi-converter station system. Background Technology

[0002] To address the resonant stability problem of high-proportion power electronic systems, existing analysis methods include impedance analysis, complex torque coefficient method, and mode analysis. Impedance analysis detects system stability by analyzing the impedance-frequency characteristics of components within the system. It has advantages such as clear physical concepts, easy impedance measurement, and simple calculation, and has been widely used in renewable energy grid-connected systems. Depending on the system type, the analysis method can be divided into methods applicable to single-input single-output (SISO) systems and multiple-input multiple-output (MIMO) systems. The impedance model for MIMO systems can be established using the dq-axis impedance model and the sequence impedance model; these two impedance models are interchangeable and have no difference in stability analysis. The complex torque coefficient method divides the electrical and mechanical parts of the system into two subsystems and uses two complex torque coefficients to determine system stability. While the complex torque coefficient method can analyze a specific component, although it has clear physical meaning, this empirical criterion lacks a rigorous mathematical theoretical basis, and the derived oscillation frequency may be misidentified; its effectiveness needs further verification. Model analysis linearizes all dynamic components of a multi-converter power station system at the equilibrium point, obtaining a full-order linear state space in the time domain. By calculating the eigenvalues ​​of the state space matrix, the oscillation mode at the equilibrium point can be obtained, intuitively reflecting the system's stability and stability margin. However, model analysis is based on a full-order detailed model of the system, and real-world systems rarely provide complete parameters, and it suffers from the "curse of dimensionality." Model analysis is typically used for small systems. Summary of the Invention

[0003] The main objective of this application is to provide a method, apparatus, equipment, and medium for stability testing of multi-converter station systems, so as to reduce the complexity of testing the stability of multi-converter station systems and improve the testing efficiency.

[0004] To achieve the above objectives, one aspect of this application proposes a stability detection method for a multi-converter station system, the method comprising the following steps: Find the impedance matrix of the multi-converter station system; Calculate the port admittance matrix of the converter in the multi-converter station system; Construct the hysteresis matrix of the multi-converter station system based on the impedance matrix and the port admittance matrix; Define the generalized radius coefficient of the backlash matrix; If the generalized radius coefficient is less than a preset threshold within the study frequency band, the stability criterion is simplified based on the generalized diagonal dominance, and the stability of the multi-converter station system is detected based on the simplified stability criterion.

[0005] In some embodiments, obtaining the impedance matrix of a multi-converter station system includes the following steps: An equivalent model of the multi-converter station system is established; wherein, the equivalent model includes converters, multi-port passive networks, and ideal voltage sources; The output of the equivalent model is defined as the current at the grid connection point of the converter, and the input of the equivalent model is defined as the voltage at the grid connection point of the converter. The equivalent model is transformed from the time domain to the frequency domain, and the state matrix, input matrix and output moments are transformed by Topelitz transformation to obtain the state space equation. Take the steady-state value of the state-space equation, and determine the impedance matrix of the multi-converter station system based on the state-space equation at the steady-state value.

[0006] In some embodiments, establishing an equivalent model of the multi-converter station system includes the following steps: Establish an equivalent model for any one of the following: an AC power transmission system, a flexible DC power transmission system, or a reactive power compensation device.

[0007] In some embodiments, constructing the hysteresis matrix of the multi-converter station system based on the impedance matrix and the port admittance matrix includes the following steps: The recurrence matrix is ​​constructed as follows: ; in, Let be the backlash matrix. It is the identity matrix. The impedance matrix is... Let be the port admittance matrix. s For Laplace variables; ; ; Where g represents the impedance on the network side and the converter side, The values ​​represent the admittance on the network side and the converter side, where p represents positive sequence, n represents negative sequence, cp represents the coupling relationship from positive sequence to negative sequence, and cn represents the coupling relationship from negative sequence to positive sequence. =s-j2ω1, where ω1 is the fundamental angular frequency.

[0008] In some embodiments, defining the generalized radius coefficient of the backlash matrix includes the following steps: Construct the diagonal matrix of the backlash matrix; Construct a nonnegative matrix associated with the back difference matrix and the diagonal matrix; Calculate the Perron-Frobenius eigenvalues ​​of the nonnegative matrix; The spectral radius of the non-negative matrix is ​​obtained based on the Perron-Frobenius eigenvalues ​​and used as the generalized radius coefficient.

[0009] In some embodiments, the simplification of the stability criterion based on generalized diagonal dominance includes the following steps: Based on the Nyquist curve of the hysteresis matrix simplified by the generalized diagonal dominance, the simplified stability criterion is obtained. The simplified Nyquist curve is: ; Among them, enc W ( s ) represents the simplified Nyquist curve. w ii For the elements in the backlash matrix, i For element index, n For the number of elements, s For Laplace variables; The step of detecting whether the multi-converter station system is stable based on the simplified stability criterion includes the following steps: If the simplified Nyquist curve encircles the origin 0 times, the multi-converter system is determined to be stable; otherwise, the multi-converter system is determined to be unstable.

[0010] In some embodiments, the method further includes the following steps: If the multi-converter station system is determined to be unstable, the oscillation frequency is determined based on the passive network impedance of each node in the multi-converter station system, and the node at the converter where the negative damping characteristic causes the system to oscillate is located as the oscillation node.

[0011] To achieve the above objectives, another aspect of this application provides a stability testing device for a multi-converter station system, the device comprising: Impedance matrix retrieval unit, used to retrieve the impedance matrix of a multi-converter station system; The admittance matrix calculation unit is used to calculate the port admittance matrix of the converter in the multi-converter station system. A hysteresis matrix construction unit is used to construct the hysteresis matrix of the multi-converter station system based on the impedance matrix and the port admittance matrix. A radius coefficient definition unit is used to define the generalized radius coefficient of the backlash matrix; The stability detection unit is used to simplify the stability criterion based on the generalized diagonal dominance if the generalized radius coefficient is less than a preset threshold in the study frequency band, and to detect whether the multi-converter station system is stable according to the simplified stability criterion.

[0012] To achieve the above objectives, another aspect of this application provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the above-described method.

[0013] To achieve the above objectives, another aspect of the embodiments of this application proposes a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method.

[0014] To achieve the above objectives, another aspect of this application provides a computer program product, including a computer program that, when executed by a processor, implements the above-described method.

[0015] The embodiments of this application include at least the following beneficial effects: This application provides a stability testing method and related equipment for a multi-converter station system. The method involves: obtaining the impedance matrix of the multi-converter station system; obtaining the port admittance matrix of the converters in the system; constructing the hysteresis matrix of the system based on the impedance and port admittance matrices; defining the generalized radius coefficient of the hysteresis matrix; and simplifying the stability criterion based on the generalized diagonal dominance if the generalized radius coefficient is less than a preset threshold within the study frequency band. The simplified stability criterion is then used to detect the stability of the multi-converter station system. By constructing the hysteresis matrix of the multi-converter station system and quantifying the coupling relationship between converters based on the generalized radius coefficient, if the generalized radius coefficient is less than a preset threshold, the converters can be determined to have a weak coupling relationship. This simplifies the stability criterion based on the generalized diagonal dominance, reducing the complexity of detecting the stability of the multi-converter station system and improving detection efficiency. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 A flowchart illustrating a stability testing method for a multi-converter station system provided in this application embodiment; Figure 2An example flowchart of a stability testing method for a multi-converter station system provided in this application embodiment; Figure 3 This is a schematic diagram of a network containing m converters provided in an embodiment of this application; Figure 4 The wind turbine topology and its control block diagram provided in the embodiments of this application; Figure 5 This is a diagram of the MMC main circuit topology provided in the embodiments of this application; Figure 6 This is a diagram of the MMC control structure provided in the embodiments of this application; Figure 7 This application provides an SVG main loop topology diagram for embodiments of the present application. Figure 8 This is a diagram of the SVG control structure provided in the embodiments of this application; Figure 9 This is a structural diagram of a microgrid negative feedback system provided in an embodiment of this application; Figure 10 Example diagram of an AC / DC combined transmission project for offshore wind power transmission provided in this application embodiment; Figure 11 Example diagram of an AC transmission project for offshore wind power transmission provided in this application embodiment; Figure 12 Example diagram of the generalized radius coefficients of rational function matrices provided in embodiments of this application; Figure 13 Example diagram of the working condition-FFT analysis results provided in the embodiments of this application; Figure 14 Z-axis impedance of the offshore wind power transmission system provided in the embodiments of this application xx(11) and Z WF The Bird diagram; Figure 15 Z-axis impedance of the offshore wind power transmission system provided in the embodiments of this application xx(22) and Z SVG The Bird diagram; Figure 16 Z-axis impedance of the offshore wind power transmission system provided in the embodiments of this application xx(33) and Z MMC The Bird diagram; Figure 17 This is a schematic diagram of the structure of a stability testing device for a multi-converter station system provided in an embodiment of this application; Figure 18 This is a schematic diagram of the hardware structure of an electronic device provided in an embodiment of this application. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of this application and are not intended to limit it. In the following description, when referring to the accompanying drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with those of this application; they are merely examples of apparatuses and methods consistent with some aspects of the embodiments of this application as detailed in the summary of the invention.

[0019] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit this application.

[0020] Before providing a detailed description of the embodiments of this application, some related technologies involved in the embodiments of this application will be described first, as follows: The relevant technical solution proposes a frequency domain impedance stability criterion for multi-converter systems, which determines system stability through the port impedance matrices of the converter and the power network. This is achieved by forming a unity negative feedback system with the converter impedance and the passive network impedance, under the following two basic assumptions: 1. The converter is known to be stable when connected to an ideal voltage source. 2. The network is stable before the converter is connected. The system is stable when both conditions are met, and its positive and negative sequence hysteresis matrices, when varying along a D-shaped contour, do not encircle or circle the origin. This approach is applicable to power systems of varying sizes and complexities.

[0021] However, the relevant technology has the following drawbacks: (1) Impedance modeling of converter stations is complex in system modeling. Frequency domain modeling is difficult to handle converters with complex control, the mathematical derivation is complex and the workload is large, and the frequency coupling phenomenon caused by positive and negative sequence coupling increases the model order. Time domain modeling is difficult to characterize high-frequency characteristics, such as the time delay in the control, and for rigid systems, numerical integration may encounter numerical stability problems. The embodiments of this application can effectively reduce the complexity of impedance modeling.

[0022] (2) No accurate threshold is given for the coupling strength between converter stations in a large system, and no simplification is proposed for the stability criterion in a multi-converter grid-connected system below the threshold. The embodiments of this application give a threshold for the coupling strength of multiple converter stations, and propose a new simplified criterion for weakly coupled systems.

[0023] (3) The oscillation location was not clearly determined. In this embodiment, the oscillation source was traced by reducing the high-dimensional matrix to a one-dimensional matrix that is decoupled from each other. At the same time, it can show whether the oscillation is caused by the strong coupling relationship between the converter stations or the oscillation caused by the interaction between the converter station and the passive network, thus clarifying the source of the oscillation.

[0024] Considering that related technologies perform stability testing by detecting the number of times the hysteresis matrix encircles the origin, i.e., using traditional impedance analysis, and that diagonal dominance theory proposes a radius coefficient to measure the relative magnitude between diagonal and off-diagonal elements in the matrix, and to detect whether the system exhibits diagonal dominance. If the system's transfer function exhibits diagonal dominance, the influence of off-diagonal elements can be ignored when testing system stability. In existing research, diagonal dominance theory has been used for converter model order reduction, converter controller design, and simplifying converter grid connection criteria. It has also been used to analyze the stability of single-converter grid-connected systems with diagonal dominance. Simultaneously, the radius coefficient has been used to quantify the intensity of oscillation interaction between different regions in AC / DC hybrid power grids dominated by power electronics. However, the threshold for the radius coefficient has not been studied, nor has the simplification of stability criteria in multi-converter grid-connected systems below the threshold been discussed. Below this threshold, internal oscillations become the dominant factor, while the influence of external regions becomes negligible. Furthermore, there is currently no research on generalized diagonal dominance in the field of power system stability analysis. Compared to narrow diagonal dominance, generalized diagonal dominance has more relaxed conditions and wider applicability.

[0025] Therefore, this application takes offshore wind power transmission systems as inter-site examples and AC transmission projects as intra-site examples as research objects, and proposes a simplified criterion for multi-converter systems based on the generalized diagonal dominance theory. At the same time, it gives an accurate threshold for defining the strong and weak coupling relationship of converters, which provides greater convenience for actual engineering design.

[0026] Reference Figure 1 This application provides a stability testing method for a multi-converter station system. This method may include, but is not limited to, steps S100 to S140, as detailed below: S100: Obtain the impedance matrix of the multi-converter station system; S110: Calculate the port admittance matrix of the converter in the multi-converter station system; S120: Construct the hysteresis matrix of the multi-converter station system based on the impedance matrix and the port admittance matrix; S130: Define the generalized radius coefficient of the backlash matrix; S140: If the generalized radius coefficient is less than a preset threshold in the study frequency band, the stability criterion is simplified based on the generalized diagonal dominance, and the stability of the multi-converter station system is detected according to the simplified stability criterion.

[0027] Optionally, obtaining the impedance matrix of the multi-converter station system includes the following steps: An equivalent model of the multi-converter station system is established; wherein, the equivalent model includes converters, multi-port passive networks, and ideal voltage sources; The output of the equivalent model is defined as the current at the grid connection point of the converter, and the input of the equivalent model is defined as the voltage at the grid connection point of the converter. The equivalent model is transformed from the time domain to the frequency domain, and the state matrix, input matrix and output moments are transformed by Topelitz transformation to obtain the state space equation. Take the steady-state value of the state-space equation, and determine the impedance matrix of the multi-converter station system based on the state-space equation at the steady-state value.

[0028] Optionally, establishing an equivalent model of the multi-converter station system includes the following steps: Establish an equivalent model for any one of the following: an AC power transmission system, a flexible DC power transmission system, or a reactive power compensation device.

[0029] Optionally, constructing the hysteresis matrix of the multi-converter station system based on the impedance matrix and the port admittance matrix includes the following steps: The recurrence matrix is ​​constructed as follows: ; in, Let be the backlash matrix. It is the identity matrix. The impedance matrix is... Let be the port admittance matrix. s For Laplace variables; ; ; Where g represents the impedance on the network side and the converter side, The values ​​represent the admittance on the network side and the converter side, where p represents positive sequence, n represents negative sequence, cp represents the coupling relationship from positive sequence to negative sequence, and cn represents the coupling relationship from negative sequence to positive sequence. =s-j2ω1, where ω1 is the fundamental angular frequency.

[0030] Optionally, defining the generalized radius coefficient of the backlash matrix includes the following steps: Construct the diagonal matrix of the backlash matrix; Construct a nonnegative matrix associated with the back difference matrix and the diagonal matrix; Calculate the Perron-Frobenius eigenvalues ​​of the nonnegative matrix; The spectral radius of the non-negative matrix is ​​obtained based on the Perron-Frobenius eigenvalues ​​and used as the generalized radius coefficient.

[0031] Optionally, the simplification of the stability criterion based on generalized diagonal dominance includes the following steps: Based on the Nyquist curve of the hysteresis matrix simplified by the generalized diagonal dominance, the simplified stability criterion is obtained. The simplified Nyquist curve is: ; Among them, enc W ( s ) represents the simplified Nyquist curve. w ii For the elements in the backlash matrix, i For element index, n For the number of elements, s For Laplace variables; The step of detecting whether the multi-converter station system is stable based on the simplified stability criterion includes the following steps: If the simplified Nyquist curve encircles the origin 0 times, the multi-converter system is determined to be stable; otherwise, the multi-converter system is determined to be unstable.

[0032] Optionally, the method further includes the following steps: If the multi-converter station system is determined to be unstable, the oscillation frequency is determined based on the passive network impedance of each node in the multi-converter station system, and the node at the converter where the negative damping characteristic causes the system to oscillate is located as the oscillation node.

[0033] The following sections will provide a detailed description and explanation of some optional embodiments of this application, using specific application examples.

[0034] The calculation process for the stability criterion based on generalized diagonal dominance is as follows: Figure 2 As shown, firstly, impedance modeling is performed on the passive network and each converter station to obtain the converter station impedance Zg and admittance matrix Y. a0 Next, calculate the system's hysteresis matrices Dp and Dn, and then use the generalized radius coefficients of the hysteresis matrix... θ * To determine whether the system is a generalized diagonally dominant system within the research frequency band, if the conditions are met... θ * If the value is less than 1, the generalized diagonal dominance theory can be applied to simplify the stability criterion, and impedance analysis can be used to individually detect the impedance of each converter station and the network impedance at that port. θ *If the value is greater than 1, then modal analysis is used to detect strong coupling within the regional power station. The simplified criterion fails when there is strong coupling between multiple converter stations.

[0035] In summary, the generalized radius coefficient θ * The impact of the interaction coupling between multiple converters on stability can be measured. θ * The smaller the value, the weaker the coupling between the converters. θ * When <1, the influence of converters on stability testing can be ignored.

[0036] Specifically, this embodiment includes the following technical solutions: 1. Includes network modeling with multiple converter stations.

[0037] Consider a microgrid (multi-converter station system) such as Figure 3 As shown, the converters in the network adopt both grid-connected and grid-structured converters, and are connected with... n An ideal voltage source passes through m + n The ports are interconnected in a passive network. The network nodes are divided into three categories: the first category is nodes connected to the converter, denoted as { x 1, x 2,…, x m The second type is the node connected to an ideal voltage source, denoted as { s 1, s 2,…, s n The remaining nodes in the network are third-class nodes, denoted as { k 1, k 2,…, k t}, where m is the number of nodes connected to the converter, n is the number of nodes connected to the ideal voltage source, and t is the number of the remaining nodes.

[0038] Taking PMSG as an example, the modeling of MMC and SVG is similar. The output is taken as the converter's grid connection point. x The current at point 1 is i 1=[ i ax1 , i bx1 , i cx1 The input is the converter grid connection point. x The voltage at point 1 is u 1=[ u ax1 , u bx1 , ucx1 By transforming the time-domain model of the wind turbine to the frequency-domain model, and simultaneously adjusting the state matrix... A 1. Input matrix B 1 and output matrix C 1. The state-space equation (1) is obtained by performing the Toplitz transformation.

[0039] (1) The subscript 1 indicates that the model corresponds to the first converter port or wind turbine port. This represents the column vector of state variables of the wind turbine after harmonic state-space transformation. express The derivative with respect to time, This represents the harmonic order offset matrix. This represents the input vector after harmonic state-space transformation of the voltage input vector at the grid connection point of the wind turbine. Γ( represents the output vector of the wind turbine grid connection point current output vector after harmonic state-space transformation.) A 1) Γ( B 1) Γ( C 1) Represent the matrices respectively A 1. B 1. C 1. Let the harmonic state-space matrix obtained after performing the Toplitz transformation be... The steady-state value was obtained, and finally the impedance model of the wind turbine was obtained. As shown in equation (2).

[0040] (2) To more accurately characterize the multi-harmonic coupling law of the AC side impedance of the converter, it is necessary to establish a multi-input multi-output transfer function matrix. The harmonic transfer matrix is ​​obtained by transforming the three-phase voltage and current into positive and negative sequence voltage and current through equation (3). Y MIMO .

[0041] (3) Among them, YMIMO is the AC side multi-input multi-output harmonic transfer matrix of the converter, which is used to characterize the frequency domain mapping relationship between three-phase voltage disturbance and positive and negative sequence current response; For voltage disturbance U The positive sequence component of the converter output current under the influence of the action. For voltage disturbance U The negative sequence component of the converter output current under the action. A The rotation factor in the three-phase symmetric component transformation. , j is the imaginary unit; For voltage disturbance U The output current response of phase a of the converter under the action; For voltage disturbance U The output current response of the converter's phase b under the action; For voltage disturbance U The output current response of the c-phase of the converter under the action.

[0042] 1.1 PMSG model.

[0043] A wind turbine generator set includes a wind turbine, a machine-side converter, and a grid-side converter. The dynamic model of a direct-drive wind turbine generator set includes: a DC-side dynamic model, a phase-locked loop (PLL) dynamic model, a main circuit dynamic model, a voltage outer loop dynamic model, a reactive power outer loop dynamic model, a current inner loop dynamic model, and a modulation process dynamic model. Since the grid-connected dynamics of the wind turbine generator set are mainly determined by the characteristics of the grid-side converter, the machine-side converter and the grid-side converter can be decoupled through a DC-side capacitor, and the wind turbine and the machine-side converter can be equivalent to a constant power current source. Wind turbine generator sets at the same wind farm site have basically the same model and parameters; therefore, a single-unit aggregation method is used to represent the wind farm.

[0044] The topology and control block diagram of the wind turbine are as follows: Figure 4 As shown.

[0045] 1.2 MMC Model.

[0046] The MMC employs a grid-based control strategy, primarily focusing on grid-connected characteristics while neglecting switching characteristics. The main circuit uses a bridge-arm averaging model. The control structure employs a capacitor energy-active power droop outer loop, a reactive power outer loop, and a DC voltage-DC current dual closed-loop control strategy. This structure ensures controllable DC link voltage while utilizing the energy stored in the submodule capacitors for grid construction. The MMC uses a bridge-arm averaging model, including a DC-side dynamic model, a phase-locked loop dynamic model, a main circuit dynamic model, a circulating current suppression dynamic model, a current dual closed-loop dynamic model, and voltage and reactive power outer loop dynamic models.

[0047] MMC topology as follows Figure 5 As shown, the MMC control structure is as follows: Figure 6 As shown.

[0048] 1.3 SVG model.

[0049] The SVG adopts a delta-chain main circuit structure. Its control objective is to maintain a constant reactive power output at the grid connection point. It employs predictive instantaneous reactive power control, utilizing single-phase phase-locked loop (PLL), inter-phase submodule voltage equalization control, voltage feedforward control, and circulating current suppression control. The transformer uses YNd11 connection. The SVG uses a bridge arm averaging model and phase-by-phase control. The SVG can employ constant voltage control and constant reactive power control; to conform to engineering practice, this paper adopts constant reactive power control. The dynamic model of the SVG includes a single-phase PLL dynamic model, a main circuit dynamic model, a circulating current suppression-current inner loop dynamic model, a voltage feedforward dynamic model, an inter-phase voltage equalization outer loop for submodules, and a reactive power outer loop dynamic model.

[0050] SVG topology as Figure 7 As shown, the SVG control structure is as follows: Figure 8 As shown.

[0051] 1.4 Submarine cable model.

[0052] The submarine cable adopts a three-phase single-core structure. Assume the length of the submarine cable is... l 0, the impedance and admittance per unit length are respectively and Then its equivalent impedance Z a0 ( s and equivalent admittance Y b0 ( s As shown in equation (4): (4) in γ It is the line propagation constant. , Z C It is wave impedance. Y cable ( s Y is the equivalent admittance matrix of the submarine cable in the complex frequency domain s. cable ( s The scanned values ​​and the parsed values ​​are shown in the image. Figure 6 The model has a high degree of consistency.

[0053] 2. Stability criteria for multi-converter systems.

[0054] Figure 3 The system shown can be modeled using the nodal admittance method, and equation (5) can be obtained.

[0055] (5) in, This is the positive-sequence voltage disturbance vector at the converter port. This is the negative sequence voltage disturbance vector at the converter port. This is the positive-sequence current disturbance vector at the converter port. This is the negative sequence current disturbance vector at the converter port. I It is the identity matrix. Z g ( s ) is the network impedance matrix. Y a0 ( s ) is the port admittance matrix of the converter.

[0056] in: ; ; Where s is the Laplace variable, =s-j2ω1, where ω1 is the fundamental angular frequency, I is the identity matrix, and the subscripts g and a0 represent the impedance (admittance) on the network side and the converter side, respectively. p and n represent positive sequence and negative sequence, respectively, and cp and cn represent the coupling relationship from positive sequence to negative sequence and from negative sequence to positive sequence, respectively. The submatrices on the main diagonal reflect the relationship between the positive (negative) sequence current and voltage at each node and are called the self-impedance (admittance) matrix; while the submatrices on the secondary diagonal reflect the relationship between positive sequence current and negative sequence voltage, and negative sequence current and positive sequence voltage, and are called the coupling impedance (admittance) matrix.

[0057] As can be seen from equation (5), the microgrid system can be regarded as a closed-loop negative feedback system. The input is the current of a certain type of node, the output is the voltage of a certain type of node, the forward transfer function matrix is ​​the network impedance matrix, and the feedback matrix is ​​the port admittance matrix of the converter. The structure diagram of the microgrid negative feedback system is shown below. Figure 9 As shown.

[0058] The stability of a negative feedback system is related to the hysteresis matrix, which is defined as follows: W ( s As shown in equation (6): (6) 3. Calculate the generalized radius coefficient of the system.

[0059] The interaction between multiple converters has a significant impact on system stability. Passive networks themselves do not suffer from small-disturbance instability. The off-diagonal elements of the hysteresis matrix are the products of the impedances of each converter station and the passive network admittance. These off-diagonal elements reflect the coupling relationships between the converters, and the strength of this coupling can be characterized by the ratio of the magnitude of the diagonal elements to the magnitude of the off-diagonal elements. To accurately assess the degree of coupling between converters, a generalized radius coefficient is introduced as an evaluation metric. The calculation process for the generalized radius coefficient is shown below.

[0060] Define the return matrix W ( sThe generalized radius coefficient of ) is θ * ( s For the sake of simplicity, the complex frequency domain symbol “” will be omitted below. s ". θ * The calculation method is as follows: Step 1: Construct the matrix W diagonal matrix W diag ,have ; diagonal matrix W diag Elements in; Step 2: Construction and Matrix W and W diag Associated nonnegative matrices M ( W -1 diag W )={ m ij}; m ij A nonnegative matrix M Elements in; Step 3: Calculate the matrix M ( W -1 diag W Perron-Frobenius eigenvalues λ p ; Step 4: Find M ( W -1 diag W The generalized radius coefficient can be obtained from the spectral radius. θ * ,Right now .

[0061] 4. For weakly coupled systems, a simplified criterion based on the generalized diagonal dominance theory is used.

[0062] when θ * <1 For each point on the D-shaped boundary line s When they are all established, W ( s It has a generalized diagonal dominance, and vice versa. W ( sThe system does not possess generalized diagonal dominance and is not suitable for simplified criteria. When the system possesses generalized diagonal dominance, the interaction between converters through the passive network has little impact on stability; it is only necessary to check whether the impedance characteristics between each converter and the passive network satisfy the stability condition. If the hysteresis matrix of the negative feedback system... W ( s It exhibits generalized diagonal dominance; when s changes one full revolution along the D-shaped contour, W ( s The number of revolutions encircling the origin can be converted into W ( s )of m The sum of the number of times each diagonal scalar function encircles the origin. When testing system stability, a multivariable system can be equivalently decoupled into multiple univariate systems for analysis. The specific steps are as follows: Step 1: Detect the generalized radius coefficient θ * The relationship between the value of the threshold 1 and the value of the threshold 1 θ * >1 indicates a strongly coupled system; θ * <1 indicates a weakly coupled system; Step 2: For weakly coupled systems, simplification can be achieved. W ( s The Nyquist curve, i.e. ; enc represents the encirclement number function, used to calculate the number of times a closed curve encircles the origin; enc W(s) represents the number of times the Nyquist curve corresponding to det[W(s)] encircles the origin clockwise when s changes one revolution along the D-shaped contour; enc w ii (s) represents the scalar function w as s changes one revolution along the contour of the D-shape. ii (s) represents the number of times the Nyquist curve corresponding to the origin is clockwise; w ii (s) is the i-th diagonal element of the backlash matrix W(s), where i is the port number.

[0063] Step 3: Check if the number of times the Nyquist curve encircles the origin is 0, i.e. ; Step 4: If step 3 is true, the system is stable; if not, the system is unstable. Step 5: If the system is unstable, observe the passive network impedance of each node and the corresponding node to obtain the oscillation frequency and the negative damping characteristic of the converter at which node caused the system oscillation, thus tracing the source of the oscillation.

[0064] In summary, the embodiments of this application include the following technical solutions: (1) The analysis and modeling objects are AC / DC transmission systems composed of various types of converters, including grid-type MMC, grid-type PMSG, and SVG. This better reflects the complex scenario of multiple types of converters coexisting and different control structures in actual engineering, and breaks through the limitation of traditional research that only focuses on a single type of converter.

[0065] (2) By introducing the generalized radius coefficient θ * It enables a quantitative assessment of the coupling relationship between converters and provides a precise threshold of 1 to define whether the electrical coupling strength between any two or more converter ports through the passive network is a strong coupling relationship or a weak coupling relationship.

[0066] (3) Regarding the generalized radius coefficient θ * For weakly coupled systems with (s) < 1, a simplified stability criterion is proposed. The core of this criterion is that when testing the overall stability of the system, the interaction between converters can be ignored, and only the classical impedance analysis method needs to be applied to the admittance of a single converter station and the equivalent impedance of the passive network at that port.

[0067] (4) After identifying potential risk frequency bands through the generalized radius coefficient, the impedance characteristic curves of each converter port in the frequency band are analyzed to accurately locate the converters exhibiting "negative damping" characteristics and identify them as the main risk sources that cause system resonance, providing a clear direction for subsequent control parameter optimization and mitigation.

[0068] Combining the above four technical solutions can differentiate the coupling strength of converters within the system, simplify stability criteria, improve computational efficiency and speed, and enable oscillation source tracing. This can provide a foundation for stability analysis studies in the early stages of engineering design.

[0069] 3.1 Specific Implementation Examples (Engineering Case Studies).

[0070] Offshore wind power transmission systems include three types of converter stations: AC transmission projects (Wind Farm, WF), flexible DC transmission projects, and SVG (Static Var Compensator). For example... Figure 10 As shown, the AC transmission project of the offshore wind farm transmits power via submarine cables, connects to a reactive power compensation device, and simultaneously connects to the onshore converter station of the offshore wind farm. It then connects to the flexible DC transmission project of the offshore wind farm, and after passing through the onshore grid impedance, they are jointly connected to the grid. This project includes various converter types, and the interaction between the converters may lead to resonant instability. Therefore, it is necessary to study the impact of their coupling degree on system stability. The flexible DC transmission project refers to a flexible DC transmission system that uses a Modular Multilevel Converter (MMC) as the core converter equipment.

[0071] The power transmission lines are connected to the onshore power grid via impedance. This project includes various types of converters, and the interaction between these converters may lead to resonant instability. Therefore, it is necessary to study the impact of their coupling degree on system stability.

[0072] The offshore wind power transmission system in scenario one is an inter-site calculation example, consisting of a wind farm, submarine cable, flexible DC converter station, and onshore control center, such as... Figure 10 As shown. Specific parameters for operating condition one are as follows: 345kV wind farm with 3 circuits, 71km long, and a cross-sectional area of ​​630mm². 2 The submarine cable is transmitted to the onshore control center. The onshore control center is equipped with two three-winding step-up transformers. The 36kV side of the transformers is connected to two sets of 50Mvar reactive power compensation devices, and the 525kV side is connected to the 2000MW flexible DC transmission project, which is connected to the system at a 500kV voltage level. The 36kV and 525kV circuits are converted to the 345kV side. Considering the transformer leakage inductance, the line is modeled using a π-type equivalent circuit. The AC transmission project is an example within the wind farm, consisting of wind turbine units. A wind farm consists of multiple wind turbine units connected to a step-up substation via eighteen collector lines. Wind farms can be aggregated into three sub-wind farms by region, such as... Figure 11 As shown, the three sub-wind farms are aggregated individually, with 10, 12, and 8 turbines respectively. Sub-wind farm A has a diameter of 400mm. 2 Submarine cable transmission, sub-wind farm B with a diameter of 500mm 2 Submarine cable transmission, sub-wind farm C diameter 240mm 2 Submarine cable delivery.

[0073] 3.2 Calculation example verification.

[0074] 3.2.1 Case where coupling between converter stations is weak ( θ * <1).

[0075] First, the network output impedance matrix needs to be calculated. Z g With converter admittance matrix Y a0 Next, the rational function matrices are examined respectively. D n ( s )= I + (s) Y an ( s )and D p ( s )= I + (s)[ Yap ( s )+ Y ep Does (s) possess generalized diagonal dominance? Where, D p (s) and D n (s) are the positive-order back difference matrix and the negative-order back difference matrix, respectively; (s) is the negative-order port admittance matrix Y of the network. gn The inverse matrix of (s), Y an ( s Y is the converter port admittance matrix. a0 The negative-order self-admittance matrix in (s) (s) is the network positive-order port admittance matrix Y gp The inverse matrix of (s), Y ap ( s Y is the converter port admittance matrix. a0 The positive-order self-admittance matrix in (s) Y ep (s) is the equivalent additional admittance matrix referred to the positive-sequence channel after considering the effects of positive and negative sequence frequency coupling. The generalized radius coefficients of the rational function matrix are as follows: Figure 12 As shown.

[0076] observe Figure 12 In D p At this point, it can be discovered D p It reaches its peak at 871Hz. From Figure 13 The results show that the system resonates at 871Hz. When the system resonates, the impedance amplitude-frequency characteristic shows a sharp peak, and the peak is concentrated in a narrow frequency band. The system only responds strongly to the frequency band near the peak, while the response to disturbances at slightly higher frequencies decays rapidly. That is, the generalized radius coefficient forms a peak at 871Hz and decays rapidly to below 1 outside of 849Hz to 886Hz. The generalized radius coefficient is less than 1 in all frequencies except this band. Under this condition, the coupling between the converter stations in the system is considered weak. It should be noted that the generalized radius coefficient surges at the peak. In this case, it is necessary to observe whether the generalized radius coefficient is greater than 1 in the frequency bands other than the peak. Only when the generalized radius coefficient is greater than 1 in the frequency bands other than the peak is the system considered to be a strongly coupled system.

[0077] rational function matrix D p (s) If it is a generalized diagonal dominance matrix, then when Z xx(11) / Z WF ,Z xx(22) / Z SVG , Z xx(33) / Z MMC The system is stable when none of the Nyquist curves cross or enclose the point (-1, 0). Plot the impedance of the offshore wind power transmission system. Z xx(11) and Z WF Bird diagram Figure 14 , Z xx(22) and Z SVG Bird diagram Figure 15 , Z xx(33) and Z MMC Bird diagram Figure 16 ,visible Z xx(22) and Z SVG The phase difference at the intersection point at 871 Hz exceeds 180 degrees, and Z xx(11) and Z WF and Z xx(33) and Z MMC The phase at each intersection point does not exceed 180 degrees, which does not satisfy the stable phase margin condition, i.e., it does not satisfy the simplified stability criterion shown in equation (12). The system is unstable, which is consistent with the results of impedance analysis. This indicates that when the multi-converter station system has a weak coupling relationship ( θ * <1), the simplified criterion is consistent with the results of impedance analysis.

[0078] in, Z xx(11) This represents the port self-impedance corresponding to the wind farm access port in the network impedance matrix. Z WF This represents the equivalent output impedance of the wind farm. Z xx(22) This represents the port self-impedance corresponding to the SVG access port in the network impedance matrix. Z SVG This is the equivalent output impedance of the SVG. Z xx(33) This represents the port self-impedance corresponding to the MMC access port in the network impedance matrix. Z MMC This is the equivalent output impedance of the MMC.

[0079] Under this operating condition, the coupling effect between the SVG and the other two converter stations can be ignored. The SVG has negative damping characteristics near the oscillation frequency. Therefore, the interaction between the SVG and the passive network is the key factor leading to the instability of the offshore wind power grid-connected system.

[0080] Reference Figure 17 This application also provides a stability testing device for a multi-converter station system, which can implement the above-described stability testing method for a multi-converter station system. The device includes: Impedance matrix retrieval unit, used to retrieve the impedance matrix of a multi-converter station system; The admittance matrix calculation unit is used to calculate the port admittance matrix of the converter in the multi-converter station system. A hysteresis matrix construction unit is used to construct the hysteresis matrix of the multi-converter station system based on the impedance matrix and the port admittance matrix. A radius coefficient definition unit is used to define the generalized radius coefficient of the backlash matrix; The stability detection unit is used to simplify the stability criterion based on the generalized diagonal dominance if the generalized radius coefficient is less than a preset threshold in the study frequency band, and to detect whether the multi-converter station system is stable according to the simplified stability criterion.

[0081] It is understood that the content of the above method embodiments is applicable to the present device embodiments. The specific functions implemented by the present device embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0082] This application also provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the method of this application. This electronic device can be any smart terminal, including tablet computers, in-vehicle computers, etc.

[0083] It is understood that the content of the above method embodiments is applicable to the device embodiments. The specific functions implemented by the device embodiments are the same as those of the methods of this application, and the beneficial effects achieved are the same as those achieved by the methods of this application.

[0084] Figure 18 The hardware structure of an electronic device according to another embodiment is illustrated. The electronic device includes: The processor 101 can be implemented using a general-purpose CPU (Central Processing Unit), microprocessor, application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of this application. The memory 102 can be implemented as a read-only memory (ROM), static storage device, dynamic storage device, or random access memory (RAM). The memory 102 can store the operating system and other applications. When the technical solutions provided in the embodiments of this specification are implemented through software or firmware, the relevant program code is stored in the memory 102 and is called and executed by the processor 101. Input / output interface 103 is used to implement information input and output; The communication interface 104 is used to enable communication and interaction between this device and other devices. Communication can be achieved through wired means (such as USB, network cable, etc.) or wireless means (such as mobile network, WIFI, Bluetooth, etc.). Bus 105 transmits information between various components of the device (e.g., processor 101, memory 102, input / output interface 103, and communication interface 104); The processor 101, memory 102, input / output interface 103 and communication interface 104 are connected to each other within the device via bus 105.

[0085] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method of this application.

[0086] It is understood that the content of the above method embodiments is applicable to this storage medium embodiment. The specific functions implemented in this storage medium embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0087] This application also provides a computer program product, including a computer program that, when executed by a processor, implements the above-described method.

[0088] Memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs and non-transitory computer-executable programs. Furthermore, memory may include high-speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, memory may optionally include memory remotely located relative to the processor, and these remote memories can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0089] The embodiments described in this application are for the purpose of more clearly illustrating the technical solutions of the embodiments of this application, and do not constitute a limitation on the technical solutions provided by the embodiments of this application. As those skilled in the art will know, with the evolution of technology and the emergence of new application scenarios, the technical solutions provided by the embodiments of this application are also applicable to similar technical problems.

[0090] Those skilled in the art will understand that the technical solutions shown in the figures do not constitute a limitation on the embodiments of this application, and may include more or fewer steps than shown, or combine certain steps, or different steps.

[0091] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0092] Those skilled in the art will understand that all or some of the steps in the methods disclosed above, as well as the functional modules / units in the systems and devices, can be implemented as software, firmware, hardware, or suitable combinations thereof.

[0093] The terms “first,” “second,” “third,” “fourth,” etc. (if present) in the specification and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms “comprising” and “having,” and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0094] It should be understood that in this application, "at least one (item)" means one or more, and "more than" means two or more. "And / or" is used to describe the relationship between related objects, indicating that three relationships can exist. For example, "A and / or B" can represent three cases: only A exists, only B exists, and both A and B exist simultaneously, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one (item) of the following" or similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one (item) of a, b, or c can represent: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, and c can be single or multiple.

[0095] In the several embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of the units described above is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.

[0096] The units described above as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0097] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0098] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes multiple instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this application. The aforementioned storage medium includes various media capable of storing programs, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0099] The preferred embodiments of the present application have been described above with reference to the accompanying drawings, but this does not limit the scope of the claims of the present application. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and substance of the embodiments of the present application shall be within the scope of the claims of the present application.

Claims

1. A stability testing method for a multi-converter station system, characterized in that, The method includes the following steps: Find the impedance matrix of the multi-converter station system; Calculate the port admittance matrix of the converter in the multi-converter station system; Construct the hysteresis matrix of the multi-converter station system based on the impedance matrix and the port admittance matrix; Define the generalized radius coefficient of the backlash matrix; If the generalized radius coefficient is less than a preset threshold within the study frequency band, the stability criterion is simplified based on the generalized diagonal dominance, and the stability of the multi-converter station system is detected based on the simplified stability criterion. Defining the generalized radius coefficient of the backlash matrix includes the following steps: Construct the diagonal matrix of the backlash matrix; Construct a nonnegative matrix associated with the back difference matrix and the diagonal matrix; Calculate the Perron-Frobenius eigenvalues ​​of the nonnegative matrix; The spectral radius of the nonnegative matrix is ​​obtained based on the Perron-Frobenius eigenvalues ​​and used as the generalized radius coefficient. The simplification of the stability criterion based on generalized diagonal dominance includes the following steps: Based on the Nyquist curve of the hysteresis matrix simplified by the generalized diagonal dominance, the simplified stability criterion is obtained. The step of detecting whether the multi-converter station system is stable based on the simplified stability criterion includes the following steps: If the simplified Nyquist curve encircles the origin 0 times, the multi-converter system is determined to be stable; otherwise, the multi-converter system is determined to be unstable.

2. The stability testing method for a multi-converter station system according to claim 1, characterized in that, The process of obtaining the impedance matrix of a multi-converter station system includes the following steps: An equivalent model of the multi-converter station system is established; wherein, the equivalent model includes converters, multi-port passive networks, and ideal voltage sources; The output of the equivalent model is defined as the current at the grid connection point of the converter, and the input of the equivalent model is defined as the voltage at the grid connection point of the converter. The equivalent model is transformed from the time domain to the frequency domain, and the state matrix, input matrix and output moments are transformed by Topelitz transformation to obtain the state space equation. Take the steady-state value of the state-space equation, and determine the impedance matrix of the multi-converter station system based on the state-space equation at the steady-state value.

3. The stability testing method for a multi-converter station system according to claim 2, characterized in that, The establishment of the equivalent model of the multi-converter station system includes the following steps: Establish an equivalent model for any one of the following: an AC power transmission system, a flexible DC power transmission system, or a reactive power compensation device.

4. The stability testing method for a multi-converter station system according to claim 1, characterized in that, Constructing the hysteresis matrix of the multi-converter station system based on the impedance matrix and the port admittance matrix includes the following steps: Multiply the impedance matrix on the left by the port admittance matrix to obtain the matrix product. The backlash matrix is ​​obtained by adding the identity matrix to the matrix product.

5. The stability testing method for a multi-converter station system according to claim 1, characterized in that, The method also includes the following steps: If the multi-converter station system is determined to be unstable, the oscillation frequency is determined based on the passive network impedance of each node in the multi-converter station system, and the node at the converter where the negative damping characteristic causes the system to oscillate is located as the oscillation node.

6. A stability testing device for a multi-converter station system, characterized in that, The device is used to implement the stability detection method for a multi-converter station system as described in claim 1, and the device includes: Impedance matrix retrieval unit, used to retrieve the impedance matrix of a multi-converter station system; The admittance matrix calculation unit is used to calculate the port admittance matrix of the converter in the multi-converter station system. A hysteresis matrix construction unit is used to construct the hysteresis matrix of the multi-converter station system based on the impedance matrix and the port admittance matrix. A radius coefficient definition unit is used to define the generalized radius coefficient of the backlash matrix; The stability detection unit is used to simplify the stability criterion based on the generalized diagonal dominance if the generalized radius coefficient is less than a preset threshold in the study frequency band, and to detect whether the multi-converter station system is stable according to the simplified stability criterion.

7. An electronic device, characterized in that, The electronic device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the method as described in any one of claims 1 to 5.

8. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 5.

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