Method for attributing low-frequency voltage response mode of new energy weak sending end multi-active support equipment

Abstract

The application discloses a new energy weak sending end multi-active support equipment low-frequency voltage response mode attribution method and belongs to the technical field of new energy grid-connected power generation systems. The application aims to provide a new energy weak sending end multi-active support equipment low-frequency voltage response mode attribution method which can identify a low-frequency voltage response dominant mode under the same operating point and the same low-frequency frequency band caliber and further identify the equipment state source of the dominant mode. The application firstly constructs an equivalent explicit small disturbance state space model considering a power balance constraint of a common coupling point and an equivalent relationship of an external power grid, screens a voltage observation dominant mode set according to a normalized contribution weight and a cumulative contribution threshold value, determines the main equipment state source of each dominant mode, and finally obtains an auxiliary dynamic response strength after the available support capacity is corrected. The application provides a quantitative basis for key dynamic source identification, support equipment parameter setting and voltage support operation evaluation.

Description

Technical Field

[0001] This invention belongs to the technical field of new energy grid-connected power generation systems. Background Technology

[0002] The high proportion of centralized transmission of renewable energy results in a low short-circuit ratio, weak inertia support, and dense integration of power electronic equipment into the sending-end system. In scenarios with weak sending-end characteristics, the voltage at the point of common coupling is more sensitive to the strength of the external power grid, grid connection control, and the dynamic adjustment process of supporting equipment. As the performance requirements for renewable energy grid connection increase, active support equipment such as grid-connected renewable energy power generation equipment, grid-mounted renewable energy power generation equipment, grid-mounted static var generators, and synchronous condensers need to provide dynamic support capabilities under voltage and frequency disturbances.

[0003] When multiple active support devices operate in parallel near a common coupling point, the synchronization methods, outer loop control, droop characteristics, and energy buffering links of different devices differ. Voltage disturbances at the common coupling point will form a low-frequency voltage dynamic correlation between the dynamic support responses of multiple devices, making it difficult to directly identify the dominant mode of the low-frequency voltage response and the source of the device state of the dominant mode.

[0004] Existing system strength indices, impedance modeling methods, sensitivity methods, and traditional modal analysis methods can characterize the operating characteristics of weak networks from different perspectives, but they still have shortcomings. System strength indices mainly reflect the strength evaluation at the system level, making it difficult to identify the dominant equipment states related to voltage observation responses; traditional modal analysis can obtain eigenvalues, damping ratios, and oscillation frequencies, but if modes are selected solely based on frequency or damping, it is difficult to accurately identify the dominant dynamics directly related to the voltage observation target; traditional participation factors mainly characterize the algebraic relationship between state variables and modes, and when comparing across equipment, they may be affected by the state dimensions and eigenvector normalization methods, making it difficult to directly reflect the equipment state contributions related to the voltage observation target. Summary of the Invention

[0005] The purpose of this invention is to propose a method for attributing the low-frequency voltage response mode of multiple active support equipment at the weak transmission end of new energy sources, which can identify the dominant low-frequency voltage response mode at the same operating point and the same low-frequency band, and further identify the source of the dominant mode equipment status.

[0006] The steps of this invention are: S1. For a parallel system of multiple active support equipment at the weak-sending end, including grid-connected wind turbines, grid-connected wind turbines, grid-connected static var generators, and synchronous condensers, a linearized differential-algebraic small perturbation model is established, which includes the low-frequency dynamic equations of the equipment, the power balance constraint at the common coupling point, and the system observation equations. When the operating point satisfies the invertibility condition of the algebraic Jacobian matrix, the voltage phase angle and amplitude algebraic variables at the common coupling point are eliminated by Schur complement, resulting in an explicit small perturbation state-space model that takes into account the power balance constraint at the common coupling point and the equivalent relationship of the external power grid. The explicit small perturbation state-space model is as follows: (5) In the formula, This is a stack of state disturbance vectors for each active support device. State perturbation vector The derivative with respect to time, For system observations, For the system matrix, For the input matrix, For the output matrix, It is a direct feedthrough matrix. The equivalent reactive power support input disturbance vector. For equipment Reactive power support input disturbance; S2. Based on the explicit small disturbance state space model obtained in step S1, the equivalent support input disturbance of each active support device is used as the input quantity. The voltage amplitude of the common coupling point and the voltage-related state inside the device are extracted from the system observations to form a generalized voltage observation. The dynamic transfer function matrix from the equivalent support input to the generalized voltage observation is established to characterize the dynamic relationship between the equivalent support input and the low-frequency voltage observation response, and to provide a basis for modal contribution decomposition. S3, perform eigenvalue decomposition on the system matrix of the explicit small perturbation state-space model obtained in step S1, and expand the dynamic transfer function matrix obtained in step S2 into direct feedthrough terms and frequency domain contribution terms of each mode; merge complex conjugate mode pairs into the same representative mode, calculate the frequency band contribution intensity of each candidate representative mode to the generalized voltage observation response within the preset low frequency band, and screen the set of dominant voltage observation modes according to the normalized contribution weight and cumulative contribution threshold; The aforementioned voltage observation dominant mode set for: (twenty two) In the formula, For candidate set a subset of This is a set of low-frequency candidate modes. For modality The relative proportion of the contribution index of all candidate mode frequency bands. The preset threshold; S4. Based on the state output matrix corresponding to the generalized voltage observation, construct the voltage observation energy matrix. Under the condition that the explicit small perturbation state space model is stable, obtain the voltage observation consistent energy metric matrix by solving the Lyapunov equation, and use the energy metric matrix to transform the left and right eigenvectors of the dominant mode to obtain the enhancement participation factors of each state variable on the dominant mode. The enhancement factors of each state variable on the dominant mode refer to the first... In the mode, the th Enhanced participation factors for each state variable , represented as: (29) In the formula, , These are the components of the right and left eigenvectors after energy metric transformation at the i-th state variable with respect to the k-th dominant mode. , The right and left eigenvectors after transformation are respectively at the th... scalar components of each state position For summing the state variables, index For summing the state variables, index Indicates complex conjugation; S5. For each voltage observation dominant mode obtained in step S3, calculate the relative participation degree of each state variable based on the enhanced participation factor obtained in step S4, and aggregate them according to the active support equipment to which the state variables belong, to obtain the equipment aggregation participation degree of each active support equipment to the corresponding dominant mode, and determine the main equipment state source of each dominant mode accordingly. The main sources of equipment status are as follows: Step S4 yields the enhanced participation factor at the state variable level. To transform the state participation result into an engineering interpretation at the device level, the aggregated participation degree of the same active support device m for the k-th mode is: (30) In the formula, For each active support device m, there is a set of indexes for the state variables; Calculate the corresponding values ​​for grid-type wind turbines (GFL), grid-type wind turbines (GFM), grid-type static var generators (SVG), and synchronous condensers (SC). And sort the devices by their participation rate from largest to smallest. S6, select the support response of each active support device as an auxiliary observation, construct an auxiliary transfer function matrix of equivalent support input to device support response, and calculate the auxiliary dynamic response intensity of unit disturbance between devices; further, based on the available support capacity of the source device at the current operating point, correct the corresponding source column of the auxiliary dynamic response intensity of unit disturbance to obtain the auxiliary dynamic response intensity after the available support capacity correction, which is used to provide auxiliary explanation of the device state attribution results obtained in step S5 from the input-output response direction between devices.

[0007] The process of establishing the explicit small perturbation state-space model in step S1 of this invention is as follows: Define the set of active support devices as: (1) For any device Linearizing its low-frequency dynamic equations near a given operating point yields: (2) In the formula, For equipment The state vector, for The derivative with respect to time, For equipment The internal low-frequency state matrix; This represents the feedback effect of algebraic variables at the common coupling point on the device state. This indicates the driving effect of reactive power support input on the device state. The phase angle and magnitude of the voltage at the common coupling point are algebraic variables. and Do not include voltage phase angle disturbances and voltage amplitude disturbances at the common coupling point; By stacking the state vectors of each device and simultaneously solving the device dynamic equations, the power balance equation at the common coupling point, and the system observation equations, a linearized differential-algebraic small perturbation model is obtained: (3) In the formula, It is a differential state matrix used to characterize the dynamic interaction relationships between the state variables of each device; It is the coupling matrix from algebraic variables to differential states, used to characterize the influence of algebraic variables at common coupling points on the dynamic state of the equipment; This is the equivalent support input matrix in the differential equation; This is the coupling matrix from differential states to algebraic constraints, used to characterize the impact of device states on the power balance at the common coupling point and the network algebraic constraints; It is an algebraic Jacobian matrix used to characterize the linearization constraint relationship between algebraic variables; This is the equivalent support input matrix in the algebraic constraint equation; The output matrix is ​​the differential state matrix; Output matrices for algebraic variables; The direct feedthrough matrix is ​​used to support the input to the system observations; in equation (3), the first row is the dynamic state of the equipment, the second row is the power balance and network constraints of the common coupling point, and the third row is the system observation relationship; When the run point satisfies the algebraic Jacobian regularity condition: Then, the algebraic equation of equation (3) is obtained: (4) In the formula, For algebraic Jacobian matrix inverse matrix Substituting equation (4) into the differential equation and observation equation of equation (3), we obtain the explicit small perturbation state-space model.

[0008] The system matrix in the explicit small perturbation state-space model described in step S1 of this invention Input matrix Output matrix and direct feedthrough matrix It is obtained by the following transformation: (6) Common coupling point power balance constraint through Equivalent incorporation , , and Therefore, the external power grid strength and the voltage constraints at the common coupling point are still fully preserved in the explicit model.

[0009] In step S2 of this invention, the generalized voltage observation includes both the system common voltage and the dynamic states directly related to voltage support within different types of support equipment. A dynamic transfer function matrix is ​​defined for the equivalent support input to the generalized voltage observation. for: (13) In the formula, This is the state output matrix corresponding to the generalized voltage observation. For Laplace variables, It is the identity matrix. This is the direct feedthrough matrix corresponding to the generalized voltage observation.

[0010] The calculation process of the voltage observation consistency energy metric matrix and the enhanced participation factor in step S4 of this invention includes: 1) Construct the voltage observation weighting matrix: (twenty three) In the formula: The voltage observation weight matrix is... This is the weighted voltage observation matrix; according to Construct the normalized voltage observation energy matrix: (twenty four) In the formula, for The transpose of the matrix, For trace operators; Introducing the minimum regularization term: (25) In the formula, For the smallest regular term, This is the regularized voltage observation energy matrix; when Solving the Lyapunov equations when the matrix is ​​Herwitz: (26) In the formula, For voltage observation consistent energy metric matrix, For the system matrix The transpose of the matrix; when When, it is decomposed into: (27) In the formula, for The Choreski decomposition factor or the equivalent matrix factor that satisfies the decomposition relation. It is the transpose of the Choreski decomposition factor or the equivalent matrix factor that satisfies the decomposition relation; use For the Energy metric transformation is performed on the right and left eigenvectors of the dominant modes: (28) In the formula, φ k ψ k These are the right and left eigenvectors corresponding to the k-th mode, respectively. This transformation maps the original state coordinates to energy coordinates consistent with voltage observations, while maintaining the biorthogonal correspondence between the left and right eigenvectors. The enhanced participation factor can be obtained in the energy coordinates.

[0011] The low-frequency voltage response mode attribution system for new energy weak-end multi-active support equipment includes: The model building module is used to establish a linearized differential-algebraic small perturbation model for a parallel system of multiple active support devices at the weak sending end. Under the condition that the algebraic Jacobian matrix is ​​invertible, the explicit small perturbation state space model is obtained by eliminating the algebraic variables of voltage phase angle and amplitude at the common coupling point through Schur compensation. The voltage observation mapping module is used to extract the voltage amplitude at the common coupling point and the voltage-related state inside the equipment from the system observations to form a generalized voltage observation. Based on the explicit small perturbation state space model, it constructs an equivalent dynamic transfer function matrix that supports the input to the generalized voltage observation. The dominant mode selection module is used to perform eigenvalue decomposition on the system matrix of the explicit small perturbation state space model, expand the dynamic transfer function matrix into direct feedthrough terms and frequency domain contribution terms of each mode, merge complex conjugate mode pairs into representative modes, calculate the frequency band contribution intensity of each candidate representative mode in a preset low frequency band, and select the voltage observation dominant mode set according to the normalized contribution weight and cumulative contribution threshold. The energy metric and enhancement participation factor calculation module is used to construct a voltage observation energy matrix based on the state output matrix corresponding to the generalized voltage observation, obtain the voltage observation consistent energy metric matrix by solving the Lyapunov equation, transform the right and left eigenvectors of the dominant mode using the energy metric matrix, and calculate the enhancement participation factor of each state variable on the dominant mode. The equipment state attribution module is used to aggregate the enhanced participation factors according to the active support equipment to which the state variable belongs, to obtain the equipment aggregation participation degree of each active support equipment to the corresponding dominant mode, and to determine the main equipment state source of each dominant mode accordingly. The auxiliary dynamic response analysis module is used to select the support response of each active support device as an auxiliary observation, construct an auxiliary transfer function matrix of equivalent support input to the support response of the device, calculate the auxiliary dynamic response intensity of unit disturbance between devices, and correct the corresponding source end column according to the available support capacity of the source end device at the current operating point to obtain the auxiliary dynamic response intensity after correction of available support capacity. The results output module is used to output one or more of the following: dominant mode set of voltage observation, state enhancement participation factor, equipment aggregation participation degree, main equipment state source and auxiliary dynamic response intensity between equipment. The analysis results of the auxiliary dynamic response analysis module are used to provide auxiliary explanations of the equipment state attribution results from the input-output response direction between equipment, and are not used as a substitute for the screening of voltage observation dominant modes or the determination of the main equipment state sources. Each module is implemented by at least one processor executing a computer program stored in memory.

[0012] The present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by at least one processor, causes the processor to perform the following operations: A linearized differential-algebraic small perturbation model is established for a parallel system of multiple active support devices at the weak delivery end. The algebraic variables at the common coupling point are eliminated by Schur compensation to obtain an explicit small perturbation state-space model. Based on the explicit small perturbation state-space model, an equivalent dynamic transfer function matrix supporting the input to the generalized voltage observation is constructed. Modal expansion is performed on the dynamic transfer function matrix to calculate the frequency band contribution intensity of each candidate representative mode in the preset low frequency band, and the set of dominant voltage observation modes is screened according to the normalized contribution weight and the cumulative contribution threshold. Construct a voltage observation consistent energy metric matrix, and calculate the enhancement participation factor of each state variable to the dominant mode under the energy metric matrix; Aggregate the enhanced participation factors according to the active support equipment to which the state variables belong to obtain the equipment aggregation participation degree of the dominant mode and the main equipment state source; Construct the auxiliary transfer function matrix from the equivalent support input to the equipment support response, and calculate the auxiliary dynamic response intensity between the equipment; This invention aims to achieve the low-frequency voltage response mode attribution method for multiple active support equipment at the weak transmission end of new energy sources.

[0013] The advantages of this invention compared to the prior art are: 1. It can screen the dominant voltage observation mode from the perspective of the modal contribution of the voltage observation dynamic transfer function in the target low frequency band, avoiding the judgment of the dominant dynamic based solely on the eigenvalue frequency, damping ratio, or single state participation. 2. By constructing a voltage observation consistent energy metric matrix and defining an enhanced participation factor, the impact of state dimension differences and eigenvector normalization on cross-device participation calculation can be reduced, making state attribution and device attribution more consistent with the low-frequency voltage observation target. 3. It can further correlate the dominant mode identification results of low-frequency voltage response with the source of equipment status, and answer the engineering questions of "which modes dominate the low-frequency voltage response" and "which equipment statuses do these modes mainly originate from" in the weak transmission end system; 4. By using the auxiliary dynamic response intensity between devices, the attribution results of the dominant mode device can be corroborated from the perspective of input-output response between devices, thereby improving the engineering interpretability of the attribution conclusions; 5. Applicable to parallel systems with weak-feeding ends for various types of active support equipment, including grid-connected wind turbines, grid-type wind turbines, grid-type static var generators, and synchronous condensers, it can provide quantitative basis for key dynamic source identification, support equipment parameter setting, and voltage support operation evaluation. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of the parallel system of multiple active support devices at the weak end as described in this invention; Figure 2 This is the normalized contribution intensity map of the candidate modes described in this invention; Figure 3 This is a diagram showing the cumulative contribution weights of candidate modes and the truncation positions of dominant modes as described in this invention. Figure 4 This is a diagram showing the aggregation participation of dominant mode devices under the traditional participation factor described in this invention. Figure 5 This is the aggregation participation diagram of the dominant mode device under the enhanced participation factor described in this invention; Figure 6 The auxiliary dynamic response intensity diagram between devices under the benchmark operating conditions described in this invention. Detailed Implementation

[0015] This invention relates to the field of safety and stability analysis and operation evaluation technology for new energy grid-connected power generation systems after they are connected to AC transmission networks. Specifically, it discloses a method for attributing low-frequency voltage response modes of multiple active support equipment at the weak-sending end of new energy systems. For a parallel system of multiple active support equipment at the weak-sending end, including grid-connected wind turbines, grid-connected wind turbines, grid-connected static var generators, and synchronous condensers, a linearized differential-algebraic small perturbation model is first established, incorporating low-frequency dynamic equations of the equipment, power balance constraints at common coupling points, and network algebraic constraints. An explicit small perturbation state-space model is obtained through Schur elimination. Secondly, a dynamic transfer function matrix is ​​constructed representing the equivalent support input to the generalized voltage observation. Within a preset low-frequency band, the frequency band contribution intensity of each mode to the generalized voltage observation response is calculated, and a set of dominant voltage observation modes is selected. Then, based on the state output matrix corresponding to the generalized voltage observation, a voltage observation consistency energy metric matrix is ​​constructed, and enhancement participation factors are defined to achieve state attribution and equipment attribution of the dominant modes. Furthermore, auxiliary dynamic response intensities between equipment are constructed to provide supplementary explanations of the equipment attribution results from the input-output response direction between equipment. This invention can identify the dominant mode of low-frequency voltage response and the source of equipment status of a multi-active support equipment system at a weak transmission end under a unified operating point and a unified low-frequency band. It can provide a quantitative basis for key dynamic source identification, support equipment parameter tuning, and voltage support operation evaluation.

[0016] The present invention will be further described in detail below: This invention includes the following steps: S1. For a parallel system of multiple active support equipment at the weak-sending end, including grid-connected wind turbines, grid-connected wind turbines, grid-connected static var generators, and synchronous condensers, a linearized differential-algebraic small perturbation model is established, which includes the low-frequency dynamic equations of the equipment, the power balance constraint at the common coupling point, and the system observation equations. When the operating point satisfies the invertibility condition of the algebraic Jacobian matrix, the algebraic variables of the voltage phase angle and amplitude at the common coupling point are eliminated by Schur compensation, resulting in an explicit small perturbation state-space model that is equivalent to the power balance constraint at the common coupling point and the equivalent relationship of the external power grid.

[0017] S2. Based on the explicit small perturbation state-space model obtained in step S1, the equivalent support input perturbation of each active support device is used as the input quantity. The voltage amplitude of the common coupling point and the voltage-related state inside the device are extracted from the system observations to form a generalized voltage observation. A dynamic transfer function matrix from the equivalent support input to the generalized voltage observation is established to characterize the dynamic relationship between the equivalent support input and the low-frequency voltage observation response, and to provide a basis for modal contribution decomposition.

[0018] S3. Perform eigenvalue decomposition on the system matrix of the explicit small perturbation state-space model obtained in step S1, and expand the dynamic transfer function matrix obtained in step S2 into direct feedthrough terms and frequency domain contribution terms of each mode; merge complex conjugate mode pairs into the same representative mode, calculate the frequency band contribution intensity of each candidate representative mode to the generalized voltage observation response within the preset low frequency band, and screen the set of dominant voltage observation modes according to the normalized contribution weight and cumulative contribution threshold.

[0019] S4. Based on the state output matrix corresponding to the generalized voltage observation, construct the voltage observation energy matrix. Under the condition that the explicit small perturbation state space model is stable, obtain the voltage observation consistent energy metric matrix by solving the Lyapunov equation, and use the energy metric matrix to transform the left and right eigenvectors of the dominant mode to obtain the enhancement participation factors of each state variable on the dominant mode.

[0020] S5. For each dominant voltage observation mode obtained in step S3, calculate the relative participation degree of each state variable based on the enhanced participation factor obtained in step S4, and aggregate them according to the active support equipment to which the state variables belong, to obtain the equipment aggregation participation degree of each active support equipment for the corresponding dominant mode, and determine the main equipment state source of each dominant mode accordingly.

[0021] S6, select the support response of each active support device as an auxiliary observation, construct an auxiliary transfer function matrix of equivalent support input to device support response, and calculate the auxiliary dynamic response intensity of unit disturbance between devices; further, based on the available support capacity of the source device at the current operating point, correct the corresponding source column of the auxiliary dynamic response intensity of unit disturbance to obtain the auxiliary dynamic response intensity after the available support capacity correction, which is used to provide auxiliary explanation of the device state attribution results obtained in step S5 from the input-output response direction between devices.

[0022] See Figure 1 This embodiment studies a parallel system with weak-feeding end, including grid-connected wind turbines, grid-type wind turbines, grid-type static var generators, and synchronous condensers. These devices are connected in parallel to a common coupling point and then connected to an external equivalent AC power grid via the sending-end lines. Due to differences in synchronization methods, voltage support mechanisms, excitation mechanisms, and energy buffering mechanisms among the devices, voltage disturbances at the common coupling point are fed back to the internal state of each device through network algebraic constraints, forming a low-frequency dynamic correlation among multiple devices.

[0023] This invention is implemented in the following order: "model construction—voltage observation mapping—dominant mode screening—state participation calculation—equipment state attribution—auxiliary response analysis". Step S1 establishes an explicit small-disturbance state-space model; Step S2 constructs a dynamic transfer function matrix for low-frequency voltage response based on this model; Step S3 screens dominant voltage observation modes through mode expansion and frequency band contribution calculation; Step S4 calculates the state enhancement participation factor of the dominant mode; Step S5 aggregates the state participation results to the equipment level to obtain the equipment state attribution results; Step S6 provides auxiliary explanations of the equipment attribution results from the perspective of inter-equipment input-output response.

[0024] Step S1: Establish an explicit small perturbation state-space model Define the set of active support devices as: (1) In the formula, GFL is a grid-following wind turbine, GFM is a grid-connected wind turbine, SVG is a grid-connected static var generator, and SC is a synchronous condenser.

[0025] For any device m∈M, linearizing its low-frequency dynamic equations near a given operating point yields: (2) In the formula, Let m be the state vector of device m. For equipment The internal low-frequency state matrix; This represents the feedback effect of algebraic variables at the common coupling point on the device state. This indicates the driving effect of reactive power support input on the device state. The phase angle and magnitude of the voltage at the common coupling point are algebraic variables. and These are the voltage phase angle disturbance and voltage amplitude disturbance at the common coupling point, respectively. The equivalent reactive power support input disturbance vector. ; Indicates device The reactive power support input disturbance. For system observations. Equation (2) describes how the internal state of a single device is simultaneously affected by its own supporting input and the voltage change at the common coupling point. Since all devices are connected through the common coupling point, the devices cannot be analyzed in isolation, but the device dynamic equations should be combined with the power balance constraints at the common coupling point.

[0026] By stacking the state vectors of each device and simultaneously solving the device dynamic equations, the power balance equation at the common coupling point, and the system observation equations, a linearized differential-algebraic small perturbation model is obtained: (3) The state vectors of each active support device are stacked. for The derivative with respect to time, It is a differential state matrix used to characterize the dynamic interaction relationships between the state variables of each device; It is the coupling matrix from algebraic variables to differential states, used to characterize the influence of algebraic variables at common coupling points on the dynamic state of the equipment; This is the equivalent support input matrix in the differential equation; This is the coupling matrix from differential states to algebraic constraints, used to characterize the impact of device states on the power balance at the common coupling point and the network algebraic constraints; It is an algebraic Jacobian matrix used to characterize the linearization constraint relationship between algebraic variables; This is the equivalent support input matrix in the algebraic constraint equation; The output matrix is ​​the differential state matrix; Output matrices for algebraic variables; The direct feedthrough matrix is ​​used to support the inputs to the system observations; in equation (3), the first row represents the device state dynamics, the second row represents the power balance and network constraints at the common coupling point, and the third row represents the system observation relationships. Since the model contains algebraic variables... It is not yet possible to directly perform feature decomposition using the standard state-space form.

[0027] When the run point satisfies the algebraic Jacobian regularity condition: Then, from the algebraic equation of equation (3), we can obtain: (4) In the formula, For algebraic Jacobian matrix The inverse function of .

[0028] Equation (4) shows that the phase angle and amplitude disturbance of the common coupling point voltage near the operating point can be equivalently represented by the equipment state disturbance and the equivalent support input disturbance. This processing does not ignore the common coupling point voltage, but provides a substitution relationship for subsequent Schur complement elimination.

[0029] Substituting equation (4) into the differential equation and observation equation of equation (3), we obtain the explicit small perturbation state-space model: (5) In the formula: In the formula, This is a stack of state disturbance vectors for each active support device. State perturbation vector The derivative with respect to time, For system observations, For the system matrix, For the input matrix, For the output matrix, It is a direct feedthrough matrix.

[0030] System Matrix Input matrix Output matrix and direct feedthrough matrix It is obtained by the following transformation: (6) Equations (5) and (6) form the common model basis for subsequent steps. The power balance constraint at the common coupling point is established through... Equivalent incorporation , , and Therefore, the external power grid strength and the voltage constraints at the common coupling point are still fully preserved in the explicit model.

[0031] Step S2: Construct a dynamic mapping from the equivalent support input to the generalized voltage observation. The model obtained in step S1 describes all system states and observations, but this invention focuses on the low-frequency voltage response. Therefore, the voltage amplitude at the common coupling point and the voltage-related states within the equipment are extracted from the system observations, defining a generalized voltage observation vector: (7) In the formula: For SVG output voltage disturbance; For the q-axis transient potential disturbance of SC; This refers to the disturbance of the excitation voltage or internal potential amplitude of grid-type wind turbines. Generalized voltage observations include both the system common voltage and the dynamic states directly related to voltage support within different types of supporting equipment, used to form a unified low-frequency voltage observation caliber.

[0032] set up From Extract The row selection matrix, then (8).

[0033] Substituting the observation equation from equation (5) into equation (8), and defining equation (9), we obtain the generalized voltage observation equation: (9) In the formula: C r,V D is the state output matrix corresponding to the generalized voltage observation. r,VQ This is the direct feedthrough matrix corresponding to the generalized voltage observation; from this, we obtain: .

[0034] Taking the Laplace transform of the state equation (5), under zero initial conditions, we obtain equations (10) and (11): (10) (11) In the formula, State perturbation vector The Laplace transform of; For the equivalent support input perturbation vector The Laplace transform of; To and Identity matrices of the same order.

[0035] Substituting equation (11) into equation (9), we get: (12) In the formula, Generalized voltage observation disturbance vector The Laplace transform of;

[0036] Therefore, the dynamic transfer function matrix equivalent to the support input to the generalized voltage observation is defined as follows: (13) In the formula, is a Laplace variable. Equation (13) describes the overall dynamic relationship between the equivalent support input disturbance near the operating point and the generalized voltage observation response.

[0037] Step S3: Screening the dominant low-frequency voltage response mode Equation (13) provides the overall input-output mapping of the low-frequency voltage response. This matrix can reflect the low-frequency voltage response at different frequencies, but it cannot distinguish the role of each system mode in the overall response. Therefore, step S3 further expands equation (13) modally, decomposing the overall dynamic response into modal contribution terms, and then screening the modes that truly dominate the observed voltage response within the target low-frequency band. To establish the correspondence between the frequency response and the system modes, the following steps are performed: Perform eigenvalue decomposition: (14) In the formula, , These are the right and left eigenvector matrices, respectively; It is a diagonal matrix of eigenvalues; For the first The eigenvalues ​​of each mode can be obtained from the bioorthogonality relation: H represents the conjugate transpose.

[0038] From the biorthogonality relation of equation (14), the system's preliminary solution can be obtained: (15) In the formula, For the first Left eigenvectors of each modality The conjugate transpose of . Left eigenvector matrix The conjugate transpose of .

[0039] Equation (15) dynamically decomposes the entire system into pole terms corresponding to each mode. Substituting these terms into equation (13), we obtain the modal expansion of the dynamic transfer function matrix: (16) In the formula, For the first The frequency domain contribution matrix of each mode pair to the dynamic mapping of the equivalent support input to the generalized voltage observation; This represents the total number of system state variables, and also the total number of modes counted by individual eigenvalues. It is a modal index, and .

[0040] In equation (16) the first The frequency domain contribution matrix corresponding to each mode is: (17) In the formula, , The first The right and left feature vectors corresponding to each modality.

[0041] Equation (17) describes the first from three aspects: input, mode, and output. The effect of each mode on the low-frequency voltage response. Among them: Indicates the first The degree of projection of each mode into the generalized voltage observation; Represents the equivalent support input for the first The excitation level of each mode; therefore, only modes that can be effectively excited by the equivalent supporting input, significantly reflected in the generalized voltage observation, and have a strong response within the target low-frequency band will contribute significantly to voltage observations. Direct feedthrough matrix It does not contain dynamic poles, so it is retained separately from the contribution terms of each dynamic mode.

[0042] Equation (17) gives the modal contribution corresponding to a single eigenvalue, but complex modes in real coefficient systems usually appear in pairs in conjugate form. The two eigenvalues, positive and negative imaginary parts, jointly describe the same actual oscillation process. If they are sorted separately, the same physical mode will be counted repeatedly. Therefore, for real modes, they are directly treated as independent statistical objects; for complex conjugate mode pairs, the positive imaginary part mode is used as the representative mode, and the corresponding negative imaginary part conjugate mode is merged into the same statistical object. Representative mode The corresponding set of statistical indexes is: (18) In the formula: Represents the set of real numbers. Eigenvalues The imaginary part; To and The corresponding conjugate mode index. It also contains two conjugate modes, one with a positive imaginary part and the other with a negative imaginary part.

[0043] Based on this, the collection The frequency domain contribution matrices of each mode are summed to obtain the representative mode. Actual frequency domain contribution matrix: (19) In the formula, for Modal index in This is the frequency domain contribution matrix corresponding to the r-th mode.

[0044] For a real mode, Equation (19) equals the contribution matrix of that mode itself; for a representative complex mode, Equation (19) equals the sum of the contribution matrices of a pair of complex conjugate modes. Through this process, each statistical object corresponds to an independent actual dynamic mode. Equation (19) is still a matrix that varies with frequency, and the value of a single frequency point cannot be used to directly determine whether a mode dominates the overall low-frequency voltage response. Therefore, it is necessary to uniformly evaluate the contribution of each representative mode within the target low-frequency band.

[0045] Let the target low-frequency band be: , , This corresponds to 0.1–2.0 Hz. Low-frequency candidate mode set. It consists of representative modes that participate in the evaluation of the target frequency band contribution.

[0046] For any candidate representative mode The voltage observation frequency band contribution intensity is defined as: (20) In the formula: Representing modes The voltage observation frequency band contribution intensity; The imaginary unit, Angular frequency, It is the Frobenius norm.

[0047] Equation (20) first uses the Frobenius norm to transform the matrix contribution of the mode to multiple input ports and multiple voltage observations at a certain frequency into a single amplitude index. Then, it integrates this index within the target low-frequency band and divides it by the bandwidth to obtain the average contribution intensity of the mode within the entire target frequency band. Therefore, The larger the value, the more modal it is. The stronger the combined effect on the generalized voltage observation response under equivalent supporting input excitation, the greater the influence. To compare the relative importance of each mode in the same candidate mode set, the frequency band contribution intensity is normalized as follows: (twenty one) In the formula, This is a set of low-frequency candidate modes. for Candidate representative modality index, Representing modes The relative proportion of the contribution index of all candidate mode frequency bands. The voltage observation band contribution intensity represents mode q.

[0048] Calculate the representative modes of all candidates Then, they are sorted in descending order of their values, and the values ​​are accumulated sequentially starting with the mode that contributed the most. The cumulative contribution weight is calculated when it first reaches or exceeds a preset threshold. The selection process is stopped at this point, and all previously included representative modes are determined as the dominant voltage observation mode set: (twenty two) In the formula, The minimum set of modes required to meet the cumulative contribution requirement; For candidate set A subset of. The cumulative contribution threshold is used. The actual screening process of Equation (22) is as follows: First, calculate the frequency band contribution intensity of each candidate representative mode according to Equation (20), then calculate the normalized contribution weight according to Equation (21), and then arrange them in descending order of weight and accumulate them sequentially until the cumulative value reaches or exceeds the threshold for the first time. .

[0049] For example, when the threshold is taken When the normalized contribution weights of the first three modes are 0.53, 0.25, and 0.10 respectively, the cumulative contribution of the first two modes is 0.78, which is below 0.8. After adding the third mode, the cumulative contribution is 0.88, exceeding the threshold for the first time. Therefore, the first three modes should be selected as the dominant modes, and modes with smaller contributions should no longer be included.

[0050] Through the above processing, equations (18) and (19) solve the problem of modal statistical caliber; equation (20) transforms the frequency correlation matrix response into a comprehensive frequency band contribution index; equation (21) forms the relative contribution ranking of each mode; and equation (22) determines the number of dominant modes entering the subsequent attribution analysis. The final result... This is used to answer "which modes dominate the target low-frequency voltage response" and serves as the analysis object for steps S4 and S5; subsequent steps further answer "from which device states do these dominant modes mainly originate".

[0051] Step S4: Construct a voltage observation-consistent energy metric and define an enhancement participation factor. Step S3 identified the dominant modes that contribute most to the low-frequency voltage observation response, but it has not yet been determined which equipment states these modes primarily originate from. Traditional participation factors mainly reflect the algebraic relationship between state variables and modes; however, when there are differences in the dimensions and dynamic scales of various equipment states, direct cross-equipment comparisons are insufficient to fully reflect the low-frequency voltage observation objective. Therefore, step S4 introduces the generalized voltage observation mapping into the state-space energy metric, ensuring that the state participation calculation is consistent with the low-frequency voltage observation objective.

[0052] Construct the voltage observation weighting matrix: (twenty three) In the formula: The voltage observation weight matrix is... This is the weighted voltage observation matrix.

[0053] according to Construct the normalized voltage observation energy matrix: (twenty four) In the formula, for The transpose of the matrix, For trace operators; trace normalization is used to reduce the influence of the overall scale of the observation matrix on the energy metric.

[0054] To ensure the positive definiteness and numerical stability of the right-hand side matrix of the subsequent Lyapunov equations, a minimum regularization term is introduced: (25) In the formula, For the smallest regular term, This is the voltage observation energy matrix after regularization.

[0055] when Solving the Lyapunov equations when the matrix is ​​a Hurwitz matrix: (26) In the formula, Q e The voltage observation energy matrix is ​​represented by the Hurwitz matrix. All eigenvalues ​​have real parts less than zero.

[0056] when When, it is decomposed into: (27) In the formula, for The Cholesky decomposition factor or the equivalent matrix factor that satisfies this decomposition relation. It is the transpose of the Choreski decomposition factor or the equivalent matrix factor that satisfies the decomposition relation.

[0057] use For the Energy metric transformation is performed on the left and right eigenvectors of the dominant modes: (28) This transformation maps the original state coordinates to energy coordinates consistent with voltage observations, while maintaining the biorthogonal correspondence between the left and right eigenvectors.

[0058] In the energy coordinate system, the first In the mode, the th The enhancement participation factors for each state variable are: (29) In the formula: Indicates in Next The state is the first The relative participation of each dominant mode The right and left eigenvectors after energy metric transformation are respectively at the th... Components at each state variable , The right and left eigenvectors after energy metric transformation are respectively at the th... At the state variable, the first The components of the dominant mode, , The right and left eigenvectors after transformation are respectively at the th... scalar components of each state position For summing the state variables, index The total number of system state variables. This indicates complex conjugation. Step S4 no longer re-selects modes, but instead applies the modalities obtained in step S3. The relative participation of each state variable under the voltage observation consistent energy scale is calculated to provide a state-level basis for the equipment state attribution in step S5.

[0059] Step S5: Complete the attribution of the dominant modality's device state. Step S4 yields enhanced participation factors at the state variable level. To transform the state participation results into an engineering interpretation at the device level, factors belonging to the same active support device are considered. For the The aggregation participation of each modality is: (30) In the formula, For active support equipment For the Device aggregation participation in each dominant mode. Calculate the corresponding values ​​for GFL, GFM, SVG and SC respectively. The devices are then ranked by their aggregation participation from largest to smallest. The device with the highest aggregation participation indicates that its associated state is the main source of the dominant mode; other devices with non-zero aggregation participation indicate that their states also participate in the dynamics of the mode.

[0060] Thus, step S5 generates two types of attribution results: state-level enhanced participation factor ranking, used to locate specific control states or physical states; and device-level aggregate participation ranking, used to determine which type of active support device each dominant mode mainly originates from.

[0061] Step S6: Provide auxiliary dynamic response evidence between equipment. Steps S3-S5 have completed the screening of the dominant low-frequency voltage response mode and the attribution of equipment status. To further corroborate the attribution results from the input-output response direction between equipment, the support response of each active support device is selected as an auxiliary observation. In this embodiment, the auxiliary observation is the reactive power response of each device: (31) In the formula, Provide auxiliary observations for equipment support response; These represent the reactive power response increments near the operating point for grid-connected wind turbines, grid-type wind turbines, grid-type static var generators, and synchronous condensers; each response component uses a unified per-unit reference, and their arrangement order corresponds to the subsequent auxiliary transfer function matrix. The output order is consistent.

[0062] set up and Let the state output matrix and direct feedthrough matrix corresponding to the equipment support response be respectively. Then, according to equation (5), the auxiliary transfer function matrix from the equivalent support input to the equipment support response is obtained: (32) In the formula, Provide a state output matrix corresponding to the device's support response. This is the equivalent support input matrix in the explicit small perturbation state-space model. Equation (13) and Equation (32) have different uses: the former is used to screen the dominant modes related to the generalized voltage observation response; the latter is used to observe the direction of the influence of the source equipment's equivalent support input on the receiving equipment's support response, and is only used as an auxiliary evidence for the equipment attribution results.

[0063] For source devices and receiving end equipment Define the band-average auxiliary response intensity under unit equivalent support input: (33) In the formula, Indicates source device The unit equivalent reactive power support input to the receiving end equipment The band-average action intensity of reactive response, The lower limit angular frequency of the target low-frequency band. The upper limit angular frequency of the target low-frequency band. Let be the auxiliary transfer function matrix at frequency ω. Let i be the element in the i-th row and j-th column of the matrix; when At this time, this element does not participate in the inter-device channel comparison.

[0064] When it is necessary to further reflect the differences in available support capabilities of different source-end devices at the current operating point, the normalized available support input amplitude of the source-end devices can be used. right The corresponding source-end columns are corrected to obtain the auxiliary effective dynamic response intensity matrix: (34) In the formula, Indicates source device The normalized available values ​​at the current operating point support the input amplitude. This is the dynamic response strength matrix after correction for available support capacity. The auxiliary dynamic response intensity matrix for unit disturbance between equipment; The auxiliary dynamic response strength matrix can be modified based on the available support capacity. Let be the number of devices. Equation (34) uses the form of right-multiplied diagonal matrix because... The column corresponds to the source device. Source device The available support capacity is only scaled by the first The column does not directly change the corresponding column of other source devices.

[0065] Step S6 is only used to verify whether the device state attribution results obtained in step S5 can obtain a consistent auxiliary interpretation in the input-output response direction among devices. This step does not re-select the dominant mode or modify it in reverse. The resulting device attribution results are not used to generate active or reactive power allocation control commands for the devices.

[0066] Examples and simulation results To illustrate the implementation process and results of the method of the present invention in a parallel system of multiple active support devices at the weak-feed end, this embodiment uses MATLAB / Simulink to build a parallel system at the weak-feed end containing grid-following wind turbines, grid-connected wind turbines, grid-connected static var generators, and synchronous condensers. The system structure is as follows: Figure 1 As shown, each device is connected in parallel to a common coupling point and then connected to an external equivalent AC power grid via a sending-end line.

[0067] This embodiment completes the explicit small disturbance model construction, voltage observation dynamic mapping, dominant mode screening, enhanced participation factor calculation, equipment state attribution, and auxiliary dynamic response analysis in sequence according to steps S1-S6.

[0068] 1) Simulation preparation The system baseline capacity is 20 MVA, the short-circuit ratio (SCR) is 2, the baseline frequency is 50 Hz, and the PCC voltage is 1.0965 pu. The rated capacities of the grid-connected and grid-connected wind turbines are 14 MVA and 6 MVA, respectively. The capacity of the grid-connected static var generator (SVM) and the synchronous condenser is 2 Mvar. At the baseline operating point, the active and reactive power outputs of the grid-connected and grid-connected wind turbines are 0.35 / 0.02 pu and 0.25 / 0.02 pu, respectively, while the active and reactive power outputs of the grid-connected SVM and the synchronous condenser are 0 / 0.06 pu and 0 / 0.04 pu, respectively. The baseline for the unified support input port is set to 0.02 pu. The target low-frequency band is set to 0.1–2.0 Hz, and the cumulative contribution threshold is set to 0.8. Table 1 shows the baseline parameters and operating point settings used in this embodiment.

[0069] Table 1. Baseline Parameters and Operating Point Settings

[0070] 2) Voltage observation dominant mode screening First, according to step S1, the low-frequency dynamic equations of each active support device, the power balance equation of the common coupling point, and the external power grid constraints are linearized near the reference operating point to obtain the differential-algebraic small disturbance model; the voltage phase angle and amplitude algebraic variables of the common coupling point are eliminated by Schur compensation to obtain the explicit small disturbance state space model.

[0071] Subsequently, according to step S2, a dynamic transfer function matrix is ​​constructed using the equivalent support input of each active support device as the input quantity and the generalized voltage observation consisting of the voltage amplitude at the common coupling point, the potential amplitude inside the grid-type wind turbine, the output voltage of the grid-type static var generator, and the q-axis transient potential of the synchronous condenser as the output quantity. .

[0072] The This is used to establish a dynamic relationship between the equivalent support input and the generalized voltage observation response, enabling mode selection to simultaneously consider the input excitation level, output projection level, and its own frequency response characteristics, rather than solely relying on eigenvalue frequencies and damping. According to step S3, eigenvalue decomposition is performed on the system matrix, and the contribution intensity and normalized contribution weight of each candidate representative mode in the 0.1–2.0 Hz frequency band are calculated. The results are as follows: Figure 2 and Figure 3 As shown.

[0073] Depend on Figure 2As can be seen, the normalized contribution weights representing modes 17, 12, and 16 are approximately 0.53, 0.25, and 0.10, respectively, significantly higher than the other candidate modes. Figure 3 As can be seen, the cumulative contribution of the first two modes is approximately 0.78, which has not yet reached the threshold of 0.8; after adding the third mode, the cumulative contribution reaches 0.87754, exceeding the preset threshold for the first time. Therefore, the set of dominant voltage observation modes is obtained: Table 2 presents the results of the voltage observation dominant mode screening.

[0074] Table 2. Results of voltage observation dominant mode screening

[0075] The above results indicate that, within the current operating point and the target low-frequency band, the system's low-frequency voltage response is mainly concentrated in a few dynamic modes, rather than being uniformly determined by all system modes. Figure 2 and Figure 3 This is used to answer the question "Which modes dominate the low-frequency voltage response?"

[0076] 3) Dominant mode device state attribution After obtaining the set of dominant voltage observation modes, a voltage observation consistency energy metric matrix is ​​constructed according to step S4, and state enhancement participation factors are calculated for modes 17, 12, and 16. Subsequently, according to step S5, state enhancement participation factors belonging to the same device are aggregated to obtain the device aggregation participation degree of each device for the corresponding dominant mode. The device aggregation results under the traditional participation factor and the enhanced participation factor are as follows: Figure 4 and Figure 5 As shown. Figure 4 It reflects the algebraic participation relationship between state variables and modes under the original state coordinates; Figure 5 This reflects the relative participation of each device state in the dominant mode under the voltage observation consistent energy metric. Table 3 lists the attribution results of the main device states under the enhanced participation factor.

[0077] Table 3. Attribution results of dominant modal devices based on enhanced participation factors.

[0078] Depend on Figure 5 It is evident that the primary equipment state sources for modes 17 and 12 are synchronous condensers, with equipment aggregation participation rates of approximately 0.64 and 0.50, respectively; the primary equipment state source for mode 16 is the grid-connected wind turbine, with an equipment aggregation participation rate of approximately 0.62. The related states of grid-connected wind turbines and grid-connected static var generators also participate in some dominant modes, but their aggregation participation rates are lower than those of their corresponding dominant equipment.

[0079] 4) Auxiliary dynamic response analysis between equipment According to step S6, this embodiment constructs the auxiliary transfer function matrix G. QQ (s), and calculate the auxiliary response intensity per unit disturbance and the auxiliary dynamic response intensity after correction for available support capacity at the current operating point. The results are as follows: Figure 6 As shown.

[0080] Depend on Figure 6 It is evident that GFL→SVG is the strongest inter-device response direction at the baseline operating point, while GFM→SVG and SC→SVG also exhibit relatively significant responses. SVG, overall, represents the primary receiving-end device. This result indicates that there are clear dynamic input-output directions among multiple active support devices. The SC and GFM-related states identified in step S5 have high participation in some dominant modes, and the inter-device dynamic responses obtained in step S6 also show significant directions of influence from corresponding devices. These two types of results have complementary explanatory significance regarding the role of key devices, but their indices have different meanings: the former describes the source of device states in the dominant mode, while the latter describes the input-output response direction between devices; therefore, their ranking results are not required to be completely identical.

[0081] comprehensive Figure 2 — Figure 6 , Figure 2 and Figure 3 The dominant mode of low-frequency voltage response was determined by calculating the contribution of frequency band modes. Figure 4 and Figure 5 The source of the dominant mode's device state is determined by state-enhanced participation factors and device aggregation participation. Figure 6 Furthermore, it reveals the direction of dynamic input-output response between devices. Thus, under a unified operating point, a unified low-frequency band, and a unified voltage observation caliber, this invention can sequentially solve the two problems of "which modes dominate the low-frequency voltage response" and "which device states these dominant modes mainly originate from," and improve the engineering interpretability of the attribution results through auxiliary dynamic response analysis between devices.

[0082] Therefore, under the conditions of unified operating point, unified low-frequency band and unified voltage observation caliber, the present invention can solve the two problems of "which modes dominate the low-frequency voltage response" and "which equipment states these modes mainly originate from", and improve the engineering interpretability of the attribution results through the auxiliary dynamic response relationship between equipment.

Claims

1. A method for attributing low-frequency voltage response modes of multi-active support equipment at the weak transmission end of new energy sources, characterized in that: The steps are as follows: S1. Establish a linearized differential-algebraic small perturbation model. Eliminate the voltage phase angle and amplitude algebraic variables at the common coupling point through Schur compensation to obtain an explicit small perturbation state-space model. The linearized differential-algebraic small perturbation model includes the low-frequency dynamic equations of the equipment, the power balance constraints at the common coupling point, and the system observation equations. The explicit small perturbation state-space model is as follows: （5） In the formula, This is a stack of state disturbance vectors for each active support device. State perturbation vector The derivative with respect to time, For system observations, For the system matrix, For the input matrix, For the output matrix, It is a direct feedthrough matrix. The equivalent reactive power support input disturbance vector. For equipment Reactive power support input disturbance; S2 defines the generalized voltage observation and establishes the dynamic transfer function matrix supporting the input to voltage response. The generalized voltage observation is based on the obtained explicit small disturbance state space model, with the equivalent support input disturbance of each active support device as the input quantity, and extracts the voltage amplitude of the common coupling point and the voltage-related state inside the device from the system observation. The transfer function matrix is ​​the dynamic matrix used to establish the equivalent support input to the generalized voltage observation; S3, perform eigenvalue decomposition on the system matrix of the explicit small perturbation state-space model obtained in step S1, and filter the set of voltage dominant modes according to the contribution of the low-frequency band: （22） In the formula, For candidate set a subset of This is a set of low-frequency candidate modes. For modality The relative proportion of the contribution index of all candidate mode frequency bands. The preset threshold; The screening process for the voltage-dominant mode set is as follows: the system matrix of the obtained explicit small-perturbation state-space model is decomposed into eigenvalues, and the obtained dynamic transfer function matrix is ​​expanded into direct feedthrough terms and frequency domain contribution terms of each mode; complex conjugate mode pairs are merged into the same representative mode, and the frequency band contribution intensity of each candidate representative mode to the generalized voltage observation response is calculated within a preset low-frequency band, and the mode is screened according to the normalized contribution weight and the cumulative contribution threshold. S4. Solve the Lyapunov equations to obtain the voltage observation-consistent energy metric matrix, and calculate the enhancement participation factor of each state to the dominant mode. The calculation process for the voltage observation consistency energy metric matrix and the enhanced participation factor includes: 1) Construct the voltage observation weighting matrix: （23） In the formula: The voltage observation weight matrix is... This is the weighted voltage observation matrix; according to Construct the normalized voltage observation energy matrix: （24） In the formula, for The transpose of the matrix, For trace operators; Introducing the minimum regularization term: （25） In the formula, For the smallest regular term, This is the regularized voltage observation energy matrix; when Solving the Lyapunov equations when the matrix is ​​Herwitz: （26） In the formula, For voltage observation consistent energy metric matrix, For the system matrix The transpose of the matrix; when When, it is decomposed into: （27） In the formula, for The Choreski decomposition factor or the equivalent matrix factor that satisfies the decomposition relation. It is the transpose of the Choreski decomposition factor or the equivalent matrix factor that satisfies the decomposition relation; use For the Energy metric transformation is performed on the right and left eigenvectors of the dominant modes: （28） In the formula, φ k ψ k These are the right and left eigenvectors corresponding to the k-th mode, respectively. This transformation maps the original state coordinates to energy coordinates consistent with voltage observations, while maintaining the biorthogonal correspondence between the left and right eigenvectors, thus obtaining the enhanced participation factor in the energy coordinates. The voltage observation consistent energy metric matrix is ​​constructed based on the state output matrix corresponding to the generalized voltage observation. It is obtained by solving the Lyapunov equations under the condition that the explicit small-perturbation state-space model is stable. Then, the left and right eigenvectors of the dominant mode are transformed using the energy metric matrix to obtain the enhancement participation factors of each state variable on the dominant mode. （29） In the formula, For the first In the mode, the th Enhanced participation factors for each state variable , The right and left eigenvectors after energy metric transformation are respectively at the th... At the state variable, the first The components of the dominant mode, , The right and left eigenvectors after transformation are respectively at the th... scalar components of each state position For summing the state variables, index For summing the state variables, index Indicates complex conjugation; S5, aggregate according to the active support equipment to which the state variable belongs, to obtain the equipment aggregation participation degree of each active support equipment in the corresponding dominant mode: （30） In the formula, Let m be the aggregation participation degree of the same active support device for the k-th mode. The set of state variable indices contained in the active support equipment m; the process of obtaining the equipment aggregation participation degree is as follows: for each voltage observation dominant mode, calculate the relative participation degree of each state variable according to the obtained enhanced participation factor, and aggregate according to the active support equipment to which the state variable belongs, to obtain the equipment aggregation participation degree of each active support equipment for the corresponding dominant mode; S6. Construct an auxiliary response transfer function and provide auxiliary explanations for the device state attribution results from the input-output response direction between devices. The auxiliary transfer function matrix is ​​constructed by selecting the support response of each active support device as an auxiliary observation, constructing an equivalent support input to the device support response matrix, and calculating the auxiliary dynamic response intensity per unit disturbance between devices. The device available capacity correction is based on the available support capacity of the source device at the current operating point, and the corresponding source column of the auxiliary dynamic response intensity per unit disturbance is corrected to obtain the auxiliary dynamic response intensity after the available support capacity correction.

2. The low-frequency voltage response mode attribution method for new energy weak-transmission end multi-active support equipment according to claim 1, characterized in that: The process of establishing the explicit small perturbation state-space model in step S1 is as follows: Define active support equipment set for: （1） In the formula, GFL is a grid-following wind turbine, GFM is a grid-connected wind turbine, SVG is a grid-connected static var generator, and SC is a synchronous condenser; For any device Linearizing its low-frequency dynamic equations near a given operating point yields: （2） In the formula, For equipment The state vector, for The derivative with respect to time, For equipment The internal low-frequency state matrix; This represents the feedback effect of algebraic variables at the common coupling point on the device state. This indicates the driving effect of reactive power support input on the device state. The phase angle and magnitude of the voltage at the common coupling point are algebraic variables. and Do not include voltage phase angle disturbances and voltage amplitude disturbances at the common coupling point; By stacking the state vectors of each device and simultaneously solving the device dynamic equations, the power balance equation at the common coupling point, and the system observation equations, a linearized differential-algebraic small perturbation model is obtained: （3） In the formula, The state vectors of each active support device are stacked. for The derivative with respect to time, It is a differential state matrix used to characterize the dynamic interaction relationships between the state variables of each device; It is the coupling matrix from algebraic variables to differential states, used to characterize the influence of algebraic variables at common coupling points on the dynamic state of the equipment; This is the equivalent support input matrix in the differential equation; This is the coupling matrix from differential states to algebraic constraints, used to characterize the impact of device states on the power balance at the common coupling point and the network algebraic constraints; It is an algebraic Jacobian matrix used to characterize the linearization constraint relationship between algebraic variables; This is the equivalent support input matrix in the algebraic constraint equation; The output matrix is ​​the differential state matrix; Output matrices for algebraic variables; The direct feedthrough matrix is ​​used to support the input to the system observations; in equation (3), the first row is the dynamic state of the equipment, the second row is the power balance and network constraints of the common coupling point, and the third row is the system observation relationship; When the run point satisfies the algebraic Jacobian regularity condition: Then, the algebraic equation of equation (3) is obtained: （4） In the formula, For algebraic Jacobian matrix The inverse function; Substituting equation (4) into the differential equation and observation equation of equation (3), we obtain the explicit small perturbation state-space model.

3. The low-frequency voltage response mode attribution method for new energy weak-transmission end multi-active support equipment according to claim 1, characterized in that: The system matrix in the explicit small perturbation state-space model described in step S1 Input matrix Output matrix and direct feedthrough matrix It is obtained by the following transformation: （6） Common coupling point power balance constraint through Equivalent incorporation , , and Therefore, the external power grid strength and the voltage constraints at the common coupling point are still fully preserved in the explicit model.

4. The low-frequency voltage response mode attribution method for new energy weak-transmission end multi-active support equipment according to claim 1, characterized in that: The generalized voltage observation includes both the system common voltage and the dynamic states of different types of support equipment that are directly related to voltage support. A dynamic transfer function matrix is ​​defined for the equivalent support input to the generalized voltage observation. for: （13） In the formula, This is the state output matrix corresponding to the generalized voltage observation. For Laplace variables, It is the identity matrix. This is the direct feedthrough matrix corresponding to the generalized voltage observation.

5. A low-frequency voltage response mode attribution system for multi-active support equipment at the weak transmission end of new energy sources, used to implement the method of claim 1 or 2, characterized in that: include: The model building module is used to establish a linearized differential-algebraic small perturbation model for a parallel system of multiple active support devices at the weak sending end. Under the condition that the algebraic Jacobian matrix is ​​invertible, the explicit small perturbation state space model is obtained by eliminating the algebraic variables of voltage phase angle and amplitude at the common coupling point through Schur compensation. The voltage observation mapping module is used to extract the voltage amplitude at the common coupling point and the voltage-related state inside the equipment from the system observations to form a generalized voltage observation. Based on the explicit small perturbation state space model, it constructs an equivalent dynamic transfer function matrix that supports the input to the generalized voltage observation. The dominant mode selection module is used to perform eigenvalue decomposition on the system matrix of the explicit small perturbation state space model, expand the dynamic transfer function matrix into direct feedthrough terms and frequency domain contribution terms of each mode, merge complex conjugate mode pairs into representative modes, calculate the frequency band contribution intensity of each candidate representative mode in a preset low frequency band, and select the voltage observation dominant mode set according to the normalized contribution weight and cumulative contribution threshold. The energy metric and enhancement participation factor calculation module is used to construct a voltage observation energy matrix based on the state output matrix corresponding to the generalized voltage observation, obtain the voltage observation consistent energy metric matrix by solving the Lyapunov equation, transform the right and left eigenvectors of the dominant mode using the energy metric matrix, and calculate the enhancement participation factor of each state variable on the dominant mode. The equipment state attribution module is used to aggregate the enhanced participation factors according to the active support equipment to which the state variable belongs, to obtain the equipment aggregation participation degree of each active support equipment to the corresponding dominant mode, and to determine the main equipment state source of each dominant mode accordingly. The auxiliary dynamic response analysis module is used to select the support response of each active support device as an auxiliary observation, construct an auxiliary transfer function matrix of equivalent support input to the support response of the device, calculate the auxiliary dynamic response intensity of unit disturbance between devices, and correct the corresponding source end column according to the available support capacity of the source end device at the current operating point to obtain the auxiliary dynamic response intensity after correction of available support capacity. The results output module is used to output one or more of the following: dominant mode set of voltage observation, state enhancement participation factor, equipment aggregation participation degree, main equipment state source and auxiliary dynamic response intensity between equipment. The analysis results of the auxiliary dynamic response analysis module are used to provide auxiliary explanations of the equipment state attribution results from the input-output response direction between equipment, and are not used as a substitute for the screening of voltage observation dominant modes or the determination of the main equipment state sources. Each module is implemented by at least one processor executing a computer program stored in memory.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by at least one processor, it causes the processor to perform the following operations: A linearized differential-algebraic small perturbation model is established for a parallel system of multiple active support devices at the weak delivery end. The algebraic variables at the common coupling point are eliminated by Schur compensation to obtain an explicit small perturbation state-space model. Based on the explicit small perturbation state-space model, an equivalent dynamic transfer function matrix supporting the input to the generalized voltage observation is constructed. Modal expansion is performed on the dynamic transfer function matrix to calculate the frequency band contribution intensity of each candidate representative mode in the preset low frequency band, and the set of dominant voltage observation modes is screened according to the normalized contribution weight and the cumulative contribution threshold. Construct a voltage observation consistent energy metric matrix, and calculate the enhancement participation factor of each state variable to the dominant mode under the energy metric matrix; Aggregate the enhanced participation factors according to the active support equipment to which the state variables belong to obtain the equipment aggregation participation degree of the dominant mode and the main equipment state source; Construct the auxiliary transfer function matrix from the equivalent support input to the equipment support response, and calculate the auxiliary dynamic response intensity between the equipment; To achieve the low-frequency voltage response mode attribution method for new energy weak-transmission end multi-active support equipment as described in any one of claims 1 to 4.

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