A power system wide frequency oscillation risk assessment method based on multi-level participation factors

Abstract

The present application relates to a kind of power system broadband oscillation risk assessment method based on multi-level participation factor, belong to power system stability assessment technical field.The method constructs the s-domain node admittance matrix of power system, extracts broadband oscillation mode according to its singular condition and obtains corresponding left, right eigenvector;Based on left, right eigenvector, system level, equipment level non-normalized participation factor is constructed, and oscillation weak area and key equipment are identified;The sensitivity of key equipment admittance to internal parameter is obtained, and parameter level non-normalized participation factor is constructed to identify dominant parameter;Based on the partial derivative of node admittance matrix to complex frequency, mode sensitivity common normalization factor is calculated, and strict mode sensitivity is obtained;According to strict mode sensitivity, the mode shift caused by equipment admittance disturbance or parameter disturbance is calculated, and the influence direction of its to oscillation mode damping and frequency is determined.The method can realize the progressive positioning of broadband oscillation risk and parameter adjustment direction evaluation.

Description

Technical Field

[0001] This invention belongs to the field of power system stability assessment technology, specifically relating to a method for assessing the risk of broadband oscillations in power systems based on multi-level participation factors, and particularly to a method based on... A method for assessing broadband oscillation risk in power systems based on domain node admittance matrix, modal eigenvectors, multi-level participation factors, and gray box admittance sensitivity analysis. Background Technology

[0002] Photovoltaic, wind power, and other new energy power generation equipment are typically connected to the power grid via power electronic converters. Complex couplings exist between multiple dynamic components across various time scales, including phase-locked loops, current loops, voltage loops, DC-side control, and filtering circuits. When these new energy devices are connected to a weak power grid, or interact with transmission lines, reactive power compensation equipment, and conventional generator sets, they can easily trigger broadband oscillations covering subsynchronous, low-frequency, mid-frequency, and high-frequency ranges.

[0003] Such broadband oscillations are characterized by wide frequency bands, complex propagation paths, numerous participating devices, and strong coupling of control parameters, seriously threatening the safe and stable operation of power systems. Accurately assessing the risks of broadband oscillations and identifying vulnerable areas, key participating devices, and the dominant control parameters within those devices are prerequisites for developing effective suppression strategies.

[0004] Existing oscillation analysis methods mainly include eigenvalue analysis, impedance analysis, and traditional participation factor analysis. Eigenvalue analysis requires establishing a global state-space model, which can easily lead to problems such as complex modeling, high model order, and the curse of dimensionality in large-scale power electronic systems. Existing impedance analysis methods often focus on single-port, single-device, or local equivalent models, making it difficult to directly characterize the spatial distribution and propagation characteristics of oscillations throughout the entire network. Traditional participation factor analysis mainly reflects the participation strength of state variables in oscillation modes. In conventional applications, it is usually difficult to further delve from system nodes to specific devices and their internal control parameters, and it is also difficult to directly give the independent influence direction of device or parameter adjustments on modal damping and frequency.

[0005] Therefore, there is an urgent need for a broadband oscillation risk assessment method that can take into account the influence of network topology, device dynamic characteristics and internal parameters, and realize a progressive risk quantification assessment from oscillation mode identification, weak area location, key equipment identification to the source of dominant parameters. Summary of the Invention

[0006] To address the shortcomings and deficiencies of existing technologies, this invention provides a method for assessing the risk of broadband oscillations in power systems based on multi-level participation factors. This method uses the s-domain node admittance matrix of the power system as a unified modeling object. It extracts broadband oscillation modes through the singular conditions of the node admittance matrix and obtains the corresponding left and right eigenvectors. Furthermore, it utilizes the left and right eigenvectors under the same oscillation mode to construct system-level and equipment-level unnormalized participation factors to identify weak oscillation regions and key participating equipment. After identifying key equipment, it obtains the sensitivity of equipment admittance to internal parameters and combines it with equipment-level unnormalized participation factors to form parameter-level unnormalized participation factors, thereby achieving progressive tracing of the dominant parameters. To avoid the problem of being unable to quantitatively determine the direction of parameter adjustment by relying solely on the intensity ranking of participation factors, this invention further introduces a common normalized modal sensitivity factor, converting the unnormalized participation factors into strict modal sensitivities. Based on the strict modal sensitivity, it calculates the oscillation mode shift caused by equipment admittance disturbances or internal parameter disturbances. By analyzing the real and imaginary parts of the modal offset, the direction of the disturbance's influence on the oscillation mode damping and oscillation frequency is determined, respectively. Thus, this invention establishes a complete broadband oscillation risk assessment process, from mode extraction, weak area location, key equipment identification, dominant parameter tracing to parameter tuning direction determination, and is adaptable to different engineering scenarios, including those with known equipment models, partially known equipment, or perturbable parameter measurements.

[0007] The specific technical solution adopted by this invention to solve its technical problem is as follows:

[0008] Addressing the challenges of complex broadband oscillation propagation paths, numerous participating devices, strong coupling of internal control parameters within devices, and the difficulty of progressively locating internal device parameters at the system level using traditional methods in new energy grid-connected systems, this invention utilizes the s-domain node admittance matrix of the power system to characterize the network topology and admittance characteristics of connected devices. Broadband oscillation modes are extracted through the singular conditions of the node admittance matrix. Based on the left and right eigenvectors corresponding to these oscillation modes, a multi-level participation factor system at the system, device, and parameter levels is constructed, enabling progressive identification of weak oscillation regions, key devices, and dominant parameters. Simultaneously, by introducing a common normalization factor for modal sensitivity, the unnormalized participation factor used for intensity ranking is converted into a strict modal sensitivity used for quantitative calculation of modal shift and directionality determination. This determines the direction of influence of device admittance disturbances or internal device parameter disturbances on oscillation mode damping and oscillation frequency.

[0009] Specifically, the power system broadband oscillation risk assessment method provided by the present invention includes the following steps.

[0010] First, an s-domain node admittance matrix of the power system is constructed. Based on the singular conditions of this node admittance matrix, broadband oscillation modes are extracted, yielding the left and right eigenvectors corresponding to each broadband oscillation mode. The node admittance matrix describes the electrical connections between network nodes and the equivalent admittance characteristics of connected devices. The singular conditions include either a zero determinant of the node admittance matrix or a target eigenvalue approaching zero. The resulting broadband oscillation modes reflect the oscillation characteristics of the power system within the corresponding frequency band, while the left and right eigenvectors reflect the distribution characteristics of these oscillation modes among network nodes and connected devices.

[0011] In the process of determining broadband oscillation modes, discrete frequency points can be selected within the target broadband band. The minimum eigenvalue trajectory or minimum singular value trajectory of the nodal admittance matrix at each frequency point can be calculated to determine the initial frequency range where the oscillation mode may exist. Then, using the midpoint of this initial frequency range or the valley point of the trajectory as the initial value for iteration, the complex Newton iteration method, the trust region method, or the nonlinear eigenvalue solver can be used to search for complex modes that satisfy the singular conditions of the nodal admittance matrix. By first sweeping the frequency to locate the mode and then solving iteratively, the computational complexity caused by solving the determinant zeros analytically can be avoided, and the feasibility of mode search within a broadband range can be improved.

[0012] Secondly, based on the left and right eigenvectors, system-level unnormalized participation factors and device-level unnormalized participation factors are constructed, respectively. The system-level unnormalized participation factor characterizes the relative participation strength of network nodes in the oscillation mode, and it can be determined by the product of the left and right eigenvector elements of the corresponding node. The device-level unnormalized participation factor characterizes the relative participation strength of power equipment admittance changes in the oscillation mode, and it is determined according to the connection method of the equipment in the network. For power equipment connected in parallel to a single node, its device-level unnormalized participation factor can be determined by the left and right eigenvector elements corresponding to that node; for power equipment connected in series between two nodes, its device-level unnormalized participation factor can be determined by the product of the difference between the left and right eigenvector elements corresponding to the two nodes. This setting allows devices with different access methods to be included in the same modal participation analysis framework.

[0013] Then, weak oscillation regions are identified based on the magnitudes of the system-level unnormalized participation factors, and key equipment is identified from these weak oscillation regions based on the magnitudes of the equipment-level unnormalized participation factors. The magnitudes are used for sorting because participation factors are typically complex numbers, and directly comparing their algebraic magnitudes lacks a unified physical meaning; however, the magnitudes characterize their relative influence on the oscillation modes. The screening of weak oscillation regions, key equipment, or dominant parameters can employ empirical threshold methods, cumulative contribution rate methods, or statistical threshold methods. Screening parameters can be set according to system size, modal density, and engineering safety margin, rather than being limited to a fixed ratio.

[0014] After identifying key equipment, the sensitivity of the equipment admittance to the equipment's internal parameters is obtained. Based on the equipment-level unnormalized participation factor and the sensitivity of the equipment admittance to the equipment's internal parameters, a parameter-level unnormalized participation factor is constructed. The equipment's internal parameters include physical parameters, control parameters, or equivalent admittance model parameters. The parameter-level unnormalized participation factor characterizes the relative participation strength of changes in the equipment's internal parameters on the oscillation mode, thereby further advancing the risk assessment focus from key equipment to the dominant internal parameters of the equipment.

[0015] When different equipment internal parameters have different dimensions or different adjustable ranges, the unnormalized participation factors at the parameter level can be normalized before sorting. This normalization process includes relative parameter normalization based on the current value of the equipment's internal parameters, or normalization based on the allowable disturbance range of the equipment's internal parameters. This process avoids distortion in the comparison of participation strength caused by differences in parameter dimensions or engineering adjustable ranges.

[0016] Furthermore, based on the partial derivative of the node admittance matrix with respect to the complex frequency s, the left eigenvector, and the right eigenvector, a common normalization factor for modal sensitivity is calculated. The negative ratio of the unnormalized participation factor to the common normalization factor for modal sensitivity is taken as the strict modal sensitivity of the corresponding object. The unnormalized participation factor is mainly used for ranking the relative influence intensity between different nodes, devices, or parameters; the strict modal sensitivity is used to quantitatively calculate the oscillation mode shift caused by changes in device admittance or internal device parameters, and to determine the direction of influence of corresponding adjustments on oscillation mode damping and oscillation frequency.

[0017] The distinction between the unnormalized participation factor and the strict modal sensitivity is a key technical design feature of this invention. The unnormalized participation factor can be used to quickly compare the relative participation levels of different objects within the same oscillation mode; while the strict modal sensitivity introduces a common normalized factor related to the mode, reflecting the actual shift trend of the mode to parameter changes. Since this common normalized factor is usually a complex number, it affects not only the shift amplitude but also the phase of the mode shift. Therefore, when determining damping and frequency directivity, the strict modal sensitivity should be used, rather than directly replacing it with the unnormalized participation factor.

[0018] Subsequently, based on the strict modal sensitivity calculation, the oscillation mode shift caused by device admittance disturbances or internal parameter disturbances is calculated. The direction of the disturbance's influence on oscillation mode damping and oscillation frequency is determined according to the real and imaginary parts of the oscillation mode shift. Specifically, the negative of the real part of the oscillation mode shift corresponds to the change in the attenuation factor. When the real part of the oscillation mode shift is less than zero, the attenuation factor increases, and the system damping is enhanced; when the real part of the oscillation mode shift is greater than zero, the attenuation factor decreases, and the system damping is weakened. The imaginary part of the oscillation mode shift corresponds to the change in the oscillation angular frequency. When the imaginary part of the oscillation mode shift is greater than zero, the oscillation frequency increases; when the imaginary part of the oscillation mode shift is less than zero, the oscillation frequency decreases. Therefore, this invention can not only identify which nodes, devices, or parameters participate in the oscillation, but also further determine the direction of the effect of device or parameter adjustments on oscillation stability.

[0019] Under small disturbance conditions, the change in damping ratio can also be calculated based on the real and imaginary parts of the oscillation mode shift. The small disturbance condition refers to a condition where the equipment admittance disturbance or the disturbance of internal equipment parameters is sufficiently small, such that the system operating point does not substantially change, the nodal admittance matrix before and after the disturbance can be considered as a linearized model near the same operating point, and the first-order sensitivity approximation can reflect the main trend of mode shift change. In engineering, the small disturbance condition can be determined by checking whether the steady-state operating point, voltage and current amplitudes, frequency response curves, or mode shift prediction results before and after the disturbance remain within a preset error range. This condition is not limited to a fixed disturbance value but is determined jointly by the effective range of system linearization and engineering accuracy requirements.

[0020] The sensitivity of the device admittance to the internal parameters of the device can be obtained by at least one of the following methods: white-box analysis, gray-box equivalent model fitting, or finite difference measurement.

[0021] When using the white-box analytical method, given the internal topology and control logic of the equipment, an analytical model of the equipment port admittance is established. The derivative of this analytical model is then directly calculated to obtain the sensitivity of the equipment admittance to internal parameters. This method is suitable for scenarios where the equipment control structure and parameter relationships are relatively clear.

[0022] When using the gray-box equivalent model fitting method, given that the equipment topology or control structure is partially known, the frequency domain response of the equipment ports is measured, an equivalent admittance model is fitted, and the sensitivity of the equivalent admittance model parameters is analytically calculated based on the equivalent admittance model. If it is necessary to map the equivalent admittance model parameters to the actual equipment control parameters, a correspondence between the equivalent admittance model parameters and the equipment control parameters can be established by combining the internal structure or control loop of the equipment, thereby obtaining the sensitivity of the equipment admittance to the equipment control parameters. This method allows for parameter-level participation analysis through port admittance characteristics even when some internal parameters of the equipment are unknown or inconvenient to disclose.

[0023] When using the finite difference measurement method, under the condition that the internal parameters of the target equipment are accessible, configurable, or can be perturbed through the equipment interface, the port admittance of the equipment is measured before and after the parameter perturbation, and the sensitivity of the equipment admittance to the internal parameters of the target equipment is obtained by using a differential approximation. This method does not require a complete internal model of the equipment, but it requires that the target parameters be perturbable, and that the port admittance measurements before and after the perturbation are performed at the same or equivalent operating points to ensure that the obtained sensitivity can reflect the local influence of the target parameters on the equipment admittance.

[0024] When only the admittance sensitivity at the imaginary axis frequency point is obtained, the admittance sensitivity can be fitted to a rational function model and extended to the complex frequency point corresponding to the broadband oscillation mode; or, when the damping of the broadband oscillation mode meets a preset approximation condition, the admittance sensitivity at the imaginary axis frequency point can be used to approximate the admittance sensitivity at the complex frequency point. The preset approximation condition may include the real part of the broadband oscillation mode being smaller than its imaginary part, or, after engineering verification, the error introduced by substituting the admittance sensitivity at the imaginary axis frequency point for the admittance sensitivity at the complex frequency point being within an acceptable range. Through this process, the admittance sensitivity obtained from frequency domain response measurement can be integrated with complex frequency mode analysis.

[0025] Equipment-level involvement analysis can also include a high-risk equipment screening process. Specifically, by combining the magnitude of the equipment-level strict modal sensitivity and the magnitude of the equipment admittance change, the upper bound of the maximum amplitude shift of the oscillation mode that may be caused by the equipment admittance change can be estimated. Equipment is then ranked according to this upper bound of the maximum amplitude shift to screen for high-risk equipment. This approach allows for further evaluation of the potential impact of equipment admittance changes on the oscillation mode, provided the variable range of equipment admittance is known or estimable.

[0026] This invention can also be adapted to different modeling forms of the node admittance matrix. When the node admittance matrix satisfies the symmetric modeling condition that the left and right eigenvectors are transposes of each other, the unnormalized participation factor can be represented by the square of the corresponding element of the right eigenvector, and sorted by its magnitude. When the node admittance matrix is ​​an asymmetric matrix or the node corresponds to multidimensional port variables, the participation factor is calculated using the general form of the left and right eigenvectors; for multidimensional port variables, the participation strength of the node can be characterized by the product of the corresponding subvectors or the matrix norm. Therefore, this invention is applicable to conventional networks modeled using scalar admittance, as well as scenarios involving cross-coupled control, multi-input multi-output admittance models, or asymmetric network modeling.

[0027] The present invention also provides a power system broadband oscillation risk assessment device. The device includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the aforementioned power system broadband oscillation risk assessment method.

[0028] Compared to existing technologies, this invention and its preferred scheme utilize the s-domain node admittance matrix to uniformly characterize the topology and equipment admittance characteristics of power networks. It can conduct broadband oscillation mode analysis without relying on large-scale global state-space models, which helps to depict the spatial distribution and propagation characteristics of oscillations in complex networks. This invention uses the left and right eigenvectors corresponding to the same oscillation mode as the basis for calculation, constructing multi-level participation factors at the system, equipment, and parameter levels, achieving progressive risk localization from weak oscillation regions to key equipment and then to internal equipment parameters. Furthermore, this invention distinguishes between unnormalized participation factors and strict modal sensitivity, allowing participation intensity ranking and mode shift quantitative calculation to perform different functions, avoiding the problem of inaccurate direction judgment caused by directly equating influence intensity indicators with modal change. This invention also incorporates white-box analysis, gray-box equivalent model fitting, and finite-difference measurement into the parameter-level analysis process through the equipment admittance sensitivity acquisition mechanism, improving the applicability of the method to actual engineering equipment. By analyzing the directional effects of strict modal sensitivity, this invention can determine the direction of the influence of device admittance or internal parameter adjustments on oscillation damping and frequency, providing a basis for subsequent oscillation suppression and parameter optimization. Attached Figure Description

[0029] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0030] Figure 1 This is a topology diagram of a photovoltaic grid-connected system according to an embodiment of the present invention.

[0031] Figure 2 This is a schematic diagram illustrating the relationship between multi-level participation factors and strict modal sensitivity in an embodiment of the present invention.

[0032] Figure 3 The embodiments of the present invention are based on Overall flowchart for broadband oscillation risk assessment of domain node admittance matrix.

[0033] Figure 4 This is a flowchart of device-level participation analysis and directional influence analysis in an embodiment of the present invention.

[0034] Figure 5 This is a flowchart of parameter-level participation analysis and gray box sensitivity acquisition in an embodiment of the present invention.

[0035] Figure 6 The figure shows the verification results of time-domain active power oscillation before and after the adjustment of key control parameters. Detailed Implementation

[0036] To make the features and advantages of the present invention more apparent and understandable, specific embodiments are described below in detail:

[0037] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used in this specification have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0038] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0039] The purpose of this invention is to provide a power system broadband oscillation risk assessment method based on multi-level participation factors, aiming to solve the problems in existing technologies that make it difficult to characterize the propagation characteristics of broadband oscillations in complex power networks, difficult to progressively locate the root causes of instability, and difficult to quantitatively determine the direction of parameter adjustment. This method first constructs a system based on... This invention employs a frequency-domain network model of the node admittance matrix to obtain the broadband oscillation modes of a power system by solving for the determinant zeros or minimum eigenvalue zeros of the node admittance matrix. Then, based on the left and right eigenvectors and eigenvalue sensitivity theories corresponding to the oscillation modes, a multi-level participation factor system is constructed at the system, equipment, and parameter levels. A distinction is made between unnormalized participation factors used for ranking participation intensity and rigorous mode sensitivity used for quantitative calculation of mode shifts. Finally, by integrating white-box analysis, gray-box equivalent model fitting, and finite-difference measurement methods, a progressive analysis of the multi-level participation factors is performed to locate weak oscillation regions, key equipment, and dominant parameters. The impact of equipment admittance or internal parameter adjustments on oscillation mode damping, frequency, and damping ratio is quantitatively assessed. This invention can characterize the propagation characteristics of broadband oscillations in complex networks, enabling progressive risk tracing from system nodes to equipment and then to internal parameters, providing a basis for developing targeted oscillation suppression strategies.

[0040] To achieve the above objectives, such as Figure 3 As shown, the implementation process of the solution provided in this embodiment of the invention includes the following steps:

[0041] Step S1: Construct the nodal admittance matrix in the s-domain and extract the broadband oscillation modes.

[0042] Build based on The frequency domain network model of the node admittance matrix obtains the broadband oscillation mode of the power system by solving the determinant zeros or minimum eigenvalue zeros of the node admittance matrix. The broadband oscillation mode includes oscillation frequency, oscillation angular frequency, attenuation factor and stability information.

[0043] In mathematical terms, the oscillation modes of a power system It can be derived from the frequency domain nodal admittance matrix The singular conditions are determined. Let... For the first If there are oscillation modes, then it satisfies:

[0044]

[0045]

[0046] Equivalent to:

[0047]

[0048] in, Oscillating mode The corresponding right feature column vector, Let be the corresponding left feature vector. For a single dominant mode, it is preferable to perform standard normalization on the left and right feature vectors to satisfy:

[0049]

[0050] Oscillation mode attenuation factor and oscillation angular frequency Defined as:

[0051]

[0052]

[0053] The corresponding oscillation frequency is:

[0054]

[0055] in, Let be the real part of the oscillation mode. This represents the imaginary part of the oscillation mode. If... ,but If the oscillation mode is determined to be stable; ,but The oscillation mode was determined to be unstable.

[0056] The numerical solution method for the broadband oscillation mode provided in this embodiment is as follows:

[0057] Oscillation mode The optimal numerical solution process includes the following steps:

[0058] First, in the target broadband band Select several discrete frequency points ,make:

[0059]

[0060] Calculate the nodal admittance matrix at each frequency point. The eigenvalue or singular value trajectory. For non-Hermitian or asymmetric admittance matrices, the minimum modulus eigenvalue or minimum singular value can be used for initial mode search. Based on the valley position of the minimum eigenvalue or minimum singular value, the initial frequency range where oscillating modes may exist is determined.

[0061] Secondly, using the midpoint or valley point of the initial frequency interval as the initial value for complex iteration, the complex Newton iteration method, trust region method, or nonlinear eigenvalue solver is used to search for complex modes that satisfy the singular conditions of the nodal admittance matrix.

[0062] make Let be the target eigenvalues ​​of the nodal admittance matrix near the target mode, then the oscillation mode satisfies:

[0063]

[0064] Solve using Newton's iteration method:

[0065]

[0066] in:

[0067]

[0068] Therefore, the iterative formula can be written as:

[0069]

[0070] The iteration is considered to have converged when any of the following conditions are met:

[0071]

[0072] or:

[0073]

[0074] in, To preset the convergence accuracy, the preferred value is: .

[0075] The node voltage response relationship under the dominant mode is shown below:

[0076] When a certain characteristic value When the eigenvalue approaches zero, the modal variable corresponding to that eigenvalue dominates the system response, while the other modal components can be approximately ignored. The left and right eigenvectors satisfy... Under normalization conditions, the inverse of the nodal admittance matrix in the vicinity of this mode can be approximately expressed as:

[0077]

[0078] Therefore, the relationship between the node voltage vector and the node injected current vector under the dominant mode is as follows:

[0079]

[0080] in, For node voltage vectors, Inject current vectors into the nodes. The above relationship shows that the degree of excitation of the voltage response of each node by the injected current perturbation is related to the product of the left and right eigenvectors, and can thus be used to characterize the relative participation of each network node in this oscillation mode.

[0081] Step S2: Construct a multi-level participation factor system

[0082] Based on the oscillation mode obtained in step S1 Left eigenvector and right eigenvectors Combining eigenvalue sensitivity theory and the derivative chain rule, a multi-level participation factor system is constructed. The multi-level participation factor system includes:

[0083] System-level participation factors are used to identify weak nodes and weak regions in oscillations;

[0084] Equipment-level participation factors are used to identify key participating equipment from vulnerable areas;

[0085] Parameter-level participation factors are used to identify dominant physical parameters, control parameters, or equivalent admittance model parameters from critical equipment.

[0086] Define the modal sensitivity common normalization factor:

[0087]

[0088] in, This is a common complex normalization factor for the sensitivity of all parameters under the same oscillation mode. For ranking the relative influence intensity of different nodes, devices, or parameters within the same oscillation mode, the unnormalized participation factor magnitude can be used. Comparison, at this time common factors It does not affect the sorting results; however, when quantitatively calculating the modal shift amplitude and determining the direction of damping and frequency changes, a strict modal sensitivity that includes this common factor must be used.

[0089] For any parameter Its strict modal sensitivity can be expressed as:

[0090]

[0091] Right now:

[0092]

[0093] in:

[0094]

[0095] For parameters For oscillation modes Unnormalized participating factors.

[0096] 1. System-level participation factors

[0097] System-level unnormalized participation factors are used to quantify network nodes. For oscillation modes The degree of participation. For the scalar nodal admittance model, its general expression is:

[0098]

[0099] in, and Left eigenvectors and right eigenvectors The One element. The modulus of the participating factor:

[0100]

[0101] Used to characterize nodes The intensity of participation in the oscillation mode.

[0102] For passive networks that satisfy reciprocity and are modeled using scalar admittance, or under the approximation condition of neglecting cross-coupling terms, the node admittance matrix can be regarded as a symmetric matrix, in which case:

[0103]

[0104] System-level participation factors can be simplified to:

[0105]

[0106] For containing For systems with axis coupling, non-reciprocal control elements, or multi-input multi-output admittance models, the participation factor is calculated using a general form of left and right eigenvectors. If the node... For the corresponding multidimensional port variables, then... and This can be understood as the left and right eigenvectors of a corresponding node, and the participation strength of the node can be characterized by the product of the corresponding eigenvectors or the matrix norm. If node i corresponds to a multidimensional port variable, such as a converter port using a dq-axis coupled admittance model, then the components of the left and right eigenvectors corresponding to node i can constitute the left and right eigenvectors, respectively. In this case, the participation strength of the node in the oscillation mode can be characterized by the product, inner product, or matrix norm of the left and right eigenvectors. As a specific approach, for a dq-axis coupled port, the product of the L2 norm of the left and right eigenvectors can be used as a ranking index for participation strength.

[0107] As a preferred method, the identification of weak areas in the system can be achieved using any of the following screening methods:

[0108] Empirical threshold method: Select nodes whose participating factor moduli are greater than a certain proportion of the maximum moduli, for example, those greater than the maximum value. ;

[0109] Cumulative Contribution Rate Method: Participating factors are sorted from largest to smallest based on their magnitude, and those with a cumulative contribution rate reaching a certain threshold are selected. Nodes;

[0110] Statistical threshold method: using the mean of the participating factor magnitudes plus... The standard deviation was used as the screening threshold.

[0111] The screening threshold can be adjusted based on system size, modal density, and engineering safety margin.

[0112] 2. Equipment-level participation factors

[0113] Based on eigenvalue sensitivity theory and the embedding method of device admittance in the node admittance matrix, a device-level participation factor is constructed.

[0114] For parallel access nodes Electrical equipment, whose admittance is denoted as The change in device admittance only affects the nodes in the node admittance matrix. The self-admittance element, therefore its device-level unnormalized participation factor is:

[0115]

[0116] For the series connection to the node With nodes The admittance of the electrical equipment between them is denoted as... The effect of this series admittance change on the nodal admittance matrix is ​​as follows:

[0117]

[0118] in, and These are the unit column vectors corresponding to nodes i and j, respectively.

[0119] Therefore, its device-level unnormalized participation factor is:

[0120]

[0121] The equivalent can be written as:

[0122]

[0123] For a symmetric matrix and In this case, the above formula can be simplified to:

[0124]

[0125] The modulus of the device-level unnormalized participation factor:

[0126]

[0127] This value is used to characterize the relative influence of device admittance changes on oscillation modes. The larger the value, the stronger the correlation between the device and the oscillation modes, indicating that the device may be a critical path or critical node for the propagation of oscillation energy.

[0128] Equipment-level stringent modal sensitivity is used to quantitatively calculate modal shifts caused by changes in equipment admittance. For parallel equipment:

[0129]

[0130] For series devices:

[0131] .

[0132] 3. Parameter-level participation factors

[0133] For parameters inside power equipment This includes equipment physical parameters, control parameters, and equivalent admittance model parameters, and parameter-level participation factors are constructed based on the chain rule.

[0134] Let the device port admittance be Its internal parameters The sensitivity is:

[0135]

[0136] Then the parameter-level unnormalized participation factor is:

[0137]

[0138] in, This is the device-level unnormalized participation factor for this equipment.

[0139] The parameter-level strict modal sensitivity is:

[0140]

[0141] Right now:

[0142]

[0143] The modulus of unnormalized participation factors at the parameter level This can be used to preliminarily characterize the relative influence of this parameter on the oscillation mode. Rigorous modal sensitivity. This is used to quantitatively calculate the modal shift caused by the change in this parameter.

[0144] When different intrinsic parameters have different dimensions or different adjustable ranges, it is preferable to use normalized parameter-level participation factors for sorting. For example, relative parameter normalization can be used:

[0145]

[0146] Alternatively, a normalized form with permissible disturbance range can be used:

[0147]

[0148] in, This represents the maximum allowable parameter adjustment for the project. The normalized participation factor modulus can be used to compare the dominance of different types of parameters.

[0149] Step S3: Integrate the gray box method to conduct progressive risk analysis and directional impact assessment.

[0150] After constructing a multi-level participation factor system, the system integrates white-box analysis, gray-box equivalent model fitting, and finite difference measurement methods to conduct a progressive analysis of the multi-level participation factors. The system sequentially performs equipment-level participation analysis, directional influence analysis, and parameter-level participation analysis to determine the weak oscillation areas, key equipment, dominant parameters, and parameter adjustment directions.

[0151] 1. Device-level participation analysis

[0152] Equipment-level participation analysis combines the magnitude of the equipment-level strict modal sensitivity with the magnitude of the equipment admittance change to estimate the maximum shift amplitude of the oscillation mode that may be caused by the equipment admittance change, thereby quickly identifying high-risk equipment.

[0153] The disturbance vector formed by multiple device admittance changes The upper bound of the modal shift amplitude can be expressed as:

[0154]

[0155] Right now:

[0156]

[0157] in, For the first The strict modal sensitivity corresponding to the device admittance. For the first The change in device admittance. This upper bound can be used for rapid screening of high-risk objects at the device level.

[0158] Equipment-level screening can employ empirical thresholding, cumulative contribution rate methods, or statistical thresholding. For example, the upper bound of the maximum offset amplitude can be selected. As a threshold for screening high-risk equipment.

[0159] 2. Directional Influence Analysis

[0160] Directional influence analysis is used to quantitatively determine the direction of influence of equipment admittance or parameter adjustments on oscillation mode damping, frequency, and damping ratio.

[0161] For device admittance disturbances, the actual first-order mode shift is:

[0162]

[0163] For the admittance change of a single device, it is:

[0164]

[0165] in, It is a complex number.

[0166] Its relationship with the attenuation factor, oscillation angular frequency, and oscillation frequency is as follows:

[0167]

[0168]

[0169]

[0170] Therefore, we can conclude that:

[0171] like ,but This indicates that the attenuation factor increases, and the system damping is enhanced.

[0172] like ,but This indicates that the attenuation factor decreases and the system damping weakens;

[0173] like This indicates an increase in the oscillation frequency;

[0174] like This indicates that the oscillation frequency has decreased.

[0175] The damping ratio of the oscillation mode is defined as:

[0176]

[0177] Under small disturbance conditions, the change in damping ratio can be approximated as:

[0178]

[0179] Substitution and We can obtain:

[0180]

[0181] This formula can be used to quantitatively assess the direction and magnitude of the influence of equipment admittance or control parameter adjustments on the modal damping ratio.

[0182] 3. Parameter-level participation in analysis

[0183] Parameter-level participation analysis is used to identify the dominant parameters within key equipment that significantly affect oscillation modes and to indicate the direction of parameter adjustment to improve system damping characteristics.

[0184] For parameter perturbation The modal shift can be approximated as:

[0185]

[0186] in, It is a parameter-level strict modal sensitivity.

[0187] When the parameter increases positively (i.e.) )hour, The real and imaginary parts indicate the directions of the effect of increasing the parameter on the real part and frequency of the mode, respectively; when the parameter decreases (i.e., ), modal shift direction and The direction indicated is opposite.

[0188] Parameter-level dominant objects can be compared , Alternatively, normalized parameter levels can be used for factor modulus selection. Preferably, for comparisons between parameters of different dimensions, a method is employed... or Sort them.

[0189] 4. Parameter sensitivity acquisition under the gray box method

[0190] In this invention, the sensitivity of device admittance to internal parameters It can be obtained through white-box analysis, gray-box equivalent model fitting, or finite difference measurement.

[0191] 4.1 White Box Analysis Method

[0192] When the internal topology and control logic of the power equipment are fully known, an analytical model of the equipment port admittance can be established:

[0193]

[0194] in, These are the internal physical or control parameters of the equipment. In this case, direct analytical differentiation is possible.

[0195]

[0196] And substitute them into the parameter-level participation factor and strict modal sensitivity formulas.

[0197] 4.2 Gray Box Equivalent Model Fitting Method

[0198] When the equipment topology and main control elements are known, but some parameters are unknown or confidential, the equipment admittance model can be obtained through port frequency domain response measurement and equivalent circuit fitting.

[0199] The measured admittance is obtained by measuring the voltage disturbance and current response at the device port within the target frequency band.

[0200]

[0201] in, , For the first One measurement frequency point.

[0202] Select several discrete frequency points within the target frequency band and inject small signal voltage disturbances into the device port. The disturbance amplitude can be set to not exceed a certain proportion of the device's rated voltage, such as not exceeding 10% of the rated voltage, to ensure linearized measurement conditions.

[0203] Selecting an equivalent admittance model:

[0204]

[0205] The equivalent parameters were determined by least squares fitting. For example, for a second-order equivalent circuit model:

[0206]

[0207] when This is used to fit the frequency response data. The parameter vector to be identified is:

[0208]

[0209] Define the fitting error function:

[0210]

[0211] Where N is the total number of frequency sampling points.

[0212] The Levenberg-Marquardt optimization algorithm or other nonlinear least squares algorithms can be used to solve this problem.

[0213]

[0214] Fitting accuracy can be checked by the maximum relative error, preferably requiring the maximum relative error to be less than 1. .

[0215] After obtaining the equivalent parameters, the sensitivity of the admittance to the equivalent parameters can be analytically calculated. Let:

[0216]

[0217] but:

[0218]

[0219] Its sensitivity includes:

[0220]

[0221]

[0222]

[0223]

[0224]

[0225] When the analytical admittance model is obtained by fitting the equivalent circuit... At that time, it can be Substitute into the model and calculate:

[0226]

[0227] in, For the parameter vector of the equivalent admittance model, is any parameter in the equivalent parameter vector.

[0228] When only obtain When the shaft frequency response data is available but an explicit analytical model is not obtained, a method can be used when the modal damping is relatively small. Approximation, in Calculate the admittance sensitivity; or first fit the frequency response data with a rational function, and then extend the fitted analytical model to the complex plane modal points. .

[0229] If it is necessary to map equivalent circuit parameters to the actual control parameters of the equipment, an analytical mapping relationship can be established based on the internal structure of the equipment. When an analytical mapping relationship cannot be established, the equivalent parameters can be directly optimized and adjusted.

[0230] Assume that the equivalent parameters and control parameters satisfy the following:

[0231]

[0232] but:

[0233]

[0234] This allows the equivalent parameter sensitivity to be converted into the actual control parameter sensitivity.

[0235] 4.3 Finite Difference Measurement Method

[0236] When the target control parameters are accessible, configurable, or can be subject to small disturbances via the manufacturer's interface, the finite difference measurement method can be used to obtain the sensitivity of the equipment admittance to the actual control parameters. This method does not require knowledge of the complete internal control structure of the equipment, but it does require the ability to subject the target parameters to small disturbances and measure the port admittance before and after the disturbance at the same operating point.

[0237] For parameters Its admittance sensitivity can be approximated using the central difference method:

[0238]

[0239] in, To minimize disturbances that do not change the operating point of the equipment.

[0240] If only unidirectional perturbation is allowed, one-sided difference can also be used:

[0241]

[0242] When it is necessary to use complex modal points When calculating sensitivity, the frequency response sensitivity obtained by finite difference can be extended to a rational function by fitting the rational function. Or, in cases where modal damping is small, adopt Approximate to .

[0243] The implementation of the present invention will be further illustrated below with reference to the accompanying drawings and a more specific simulation example. It should be understood that the following embodiments are only for illustrating the technical solution of the present invention and are not intended to limit the scope of protection of the present invention.

[0244] This embodiment uses a modified IEEE 9-node standard test system, the topology of which is as follows: Figure 1 As shown. The total installed capacity of the photovoltaic power station is 150 MW, consisting of 12 12.5 MW photovoltaic inverters operating in parallel, connected to node 6 via a step-up transformer. The system includes conventional generator sets, transmission lines, loads, and the grid-connected photovoltaic power station.

[0245] First, construct units that include new energy sources. Domain node admittance matrix:

[0246]

[0247] in, for Domain node admittance matrix, For the number of nodes, For nodes Self-guided absorber element, For nodes With nodes The mutual admittance elements between them The equivalent admittance for new energy units.

[0248] 1. Oscillation mode extraction

[0249] Within the target frequency band A frequency sweep is performed to calculate the trajectory of the minimum eigenvalue or minimum singular value, determining the frequency range of the suspected oscillating mode. Then, the complex Newton-Raphson iteration method is used to precisely search for the mode and solve for the condition that satisfies... or Complex modes .

[0250] In this embodiment, two mid-to-high frequency oscillation modes, 171 Hz and 271 Hz, are obtained. The attenuation factor of the 171 Hz mode is negative, so this mode is determined to be an unstable mode.

[0251] For the unstable mode, obtain the corresponding left and right eigenvectors. and and normalization Simultaneously calculate the common normalization factor:

[0252]

[0253] 2. Multi-level participation factor calculation

[0254] Multi-level participation factors and strict modal sensitivity relationships are as follows: Figure 2 As shown.

[0255] First, based on system-level participation factors:

[0256]

[0257] Calculate the participation intensity of each node in the instability mode, and identify weak nodes and weak regions of the system based on the magnitude of the participation factor.

[0258] Then, the device-level participation factor is further calculated within the weak region. For parallel devices, the following is used:

[0259]

[0260] For series-connected devices, the following method is used:

[0261]

[0262] according to The intensity of equipment involvement is ranked to identify key participating equipment.

[0263] In this embodiment, device-level analysis results show that the photovoltaic (PV) power plant has the highest participation in the 171 Hz instability mode, followed by generator set G2, generator set G1, and load L5. Therefore, the PV power plant is identified as a key participating device in this oscillation mode.

[0264] 3. Equipment-level Directional Influence Analysis

[0265] based on Figure 4 The device-level participation analysis and directional influence analysis workflow is shown below. The device-level strict modal sensitivity is calculated as follows:

[0266]

[0267] Assume the admittance of the critical equipment is scaled by 5% in its original direction to simulate capacity change, i.e.:

[0268]

[0269] The modal variation is then:

[0270]

[0271] Further calculations:

[0272]

[0273]

[0274] In this embodiment, based on the rigorous modal sensitivity calculation results, the modal change is determined when the admittance of the PV device is increased. The real part is positive, therefore This indicates that the attenuation factor decreases and the system damping weakens; at the same time This indicates that the oscillation frequency has increased. Therefore, increasing the admittance of the PV device will further deteriorate the stability of this oscillation mode.

[0275] 4. Gray box sensitivity acquisition and parameter-level participation analysis

[0276] The process of parameter-level participation analysis and gray-box sensitivity acquisition is as follows: Figure 5 As shown.

[0277] For critical equipment (PV), if its white-box admittance model is known, the sensitivity of the equipment admittance to control parameters can be directly calculated analytically. If the equipment control structure is known but the parameters are unknown, the equivalent circuit fitting method or finite difference measurement method can be used to obtain the parameter sensitivity.

[0278] In this embodiment, taking a photovoltaic inverter as an example, the phase-locked loop proportional coefficient is obtained using the finite difference measurement method. Sensitivity to device port admittance. Apply a small perturbation, measure the port admittance before and after the perturbation, and use the central difference approximation:

[0279]

[0280] in, This represents a small disturbance in the proportional gain of the phase-locked loop.

[0281] Then based on the modal points or Approximate calculation of unnormalized participation factors at the parameter level:

[0282]

[0283] And strict modal sensitivity:

[0284]

[0285] The modal shift caused by parameter perturbation is:

[0286]

[0287] Calculation results show that when the phase-locked loop proportional coefficient is reduced At that time, modal change The real part is negative, therefore This means that as the attenuation factor increases, the oscillation mode shifts to the left of the complex plane, and the system stability is enhanced.

[0288] 5. Time-domain simulation verification

[0289] To verify the effectiveness of the proposed method, a simulation model of the modified IEEE 9-bus system was built in Matlab / Simulink. The simulation scenario was set as follows: based on the steady-state operation of the system, broadband oscillation modes covering the mid-to-high frequency band were excited by adjusting the control parameters of the renewable energy power plants or changing the operation mode of the local power grid.

[0290] Based on the parameter-level participation analysis results, the proportional gain of the photovoltaic inverter phase-locked loop is... The value has been adjusted from 5 to 3. Figure 6 The time-domain simulation results show that the active power oscillation phenomenon of the adjusted system is significantly attenuated and eventually disappears, verifying the effectiveness of the risk assessment method proposed in this invention for identifying key parameters and determining the direction of parameter optimization.

[0291] The aforementioned method for assessing the broadband oscillation risk of power systems based on multi-level participation factors can be implemented by a computer program. This program can be stored in a computer-readable storage medium and, when executed by a processor, implements the broadband oscillation risk assessment method described above. The storage medium includes, but is not limited to, ROM, RAM, hard disks, optical disks, etc.

[0292] In summary, compared with the prior art, the embodiments of the present invention have the following beneficial effects:

[0293] 1. This invention constructs The domain node admittance matrix integrates network topology, line parameters, load characteristics, and admittance characteristics of new energy equipment into the frequency domain model, which can characterize the spatial distribution and propagation characteristics of broadband oscillation modes in complex power networks without the need to establish a large-scale global state space model.

[0294] 2. Based on the left and right eigenvectors and eigenvalue sensitivity theory corresponding to oscillation modes, this invention constructs a multi-level participation factor system at the system, equipment, and parameter levels, realizing a progressive risk quantification assessment from the weak oscillation region to the key participating equipment and then to the internal dominant parameters.

[0295] 3. This invention distinguishes between unnormalized participation factors and strict modal sensitivity. Unnormalized participation factors are used for ranking influence intensity, while strict modal sensitivity is used for modal shift and directional influence analysis, thereby improving the mathematical rigor and engineering interpretability of risk assessment results.

[0296] 4. This invention is achieved through... The quantitative calculation of the real and imaginary parts of the device or the direction of the influence of parameter adjustment on the attenuation factor, oscillation frequency and damping ratio can provide a clear basis for the parameter-oriented optimization in the oscillation suppression strategy.

[0297] 5. This invention integrates white-box analysis, gray-box equivalent model fitting, and finite difference measurement methods, and can be applied to various engineering scenarios where the equipment model is completely known, partially known, or the parameters can be measured with perturbations, thus improving the applicability of the method to actual new energy equipment.

[0298] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0299] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

[0300] This invention is not limited to the preferred embodiment described above. Anyone inspired by this invention can derive other forms of a power system broadband oscillation risk assessment method based on multi-level participation factors. All equivalent changes and modifications made within the scope of the claims of this invention shall fall within the scope of this invention.

Claims

1. A method for assessing the risk of broadband oscillations in power systems based on multi-level participation factors, characterized in that, Includes the following steps: Construct the s-domain node admittance matrix of the power system, and extract the broadband oscillation mode and its corresponding left and right eigenvectors based on the singular conditions of the node admittance matrix; Based on the left and right eigenvectors, system-level unnormalized participation factors and device-level unnormalized participation factors are constructed respectively. The oscillation-weak regions are identified based on the magnitude of the system-level unnormalized participation factor, and key equipment is identified from the oscillation-weak regions based on the magnitude of the device-level unnormalized participation factor. The sensitivity of the device admittance of the key equipment to the internal parameters of the equipment is obtained, and a parameter-level unnormalized participation factor is constructed based on the device-level unnormalized participation factor and the sensitivity of the device admittance to the internal parameters of the equipment. The modal sensitivity common normalization factor is calculated based on the partial derivative of the node admittance matrix with respect to the complex frequency s, the left eigenvector, and the right eigenvector. The negative ratio of the unnormalized participation factor to the modal sensitivity common normalization factor is taken as the strict modal sensitivity of the corresponding object. Dominant parameters are identified from the key equipment based on the modulus of the parameter-level unnormalized participation factors; Based on the strict modal sensitivity calculation, the oscillation mode offset caused by the device admittance disturbance or the device internal parameter disturbance is determined, and the direction of the disturbance's influence on the oscillation mode damping and oscillation frequency is determined according to the real part and imaginary part of the oscillation mode offset.

2. The method for assessing the risk of broadband oscillations in power systems based on multi-level participation factors according to claim 1, characterized in that: The extraction of the broadband oscillation mode includes: Within the target wideband, select discrete frequency points, calculate the minimum eigenvalue trajectory or minimum singular value trajectory of the nodal admittance matrix at each frequency point, and determine the initial frequency range of the oscillation mode. Using the midpoint or valley point of the initial frequency interval as the initial value for iteration, the complex modes that satisfy the singular conditions of the nodal admittance matrix are searched using the complex Newton iteration method, the trust region method, or the nonlinear eigenvalue solver.

3. The method for assessing the risk of broadband oscillations in power systems based on multi-level participation factors according to claim 1, characterized in that: The system-level unnormalized participation factor is calculated by multiplying the left and right eigenvector elements of the corresponding node. For power equipment connected in parallel to a single node, its equipment-level unnormalized participation factor is equal to the system-level unnormalized participation factor of that node. For power equipment connected in series between two nodes, its equipment-level unnormalized participation factor is calculated by multiplying the difference between the left and right eigenvector elements corresponding to the two nodes.

4. The method for assessing the risk of broadband oscillations in power systems based on multi-level participation factors according to claim 1, characterized in that: The unnormalized participation factor is used to rank the relative influence intensity among different objects; The strict modal sensitivity is used to quantitatively calculate the modal offset amplitude caused by changes in equipment admittance or internal parameters, and to determine the direction of the influence of equipment admittance adjustment or internal parameter adjustment on oscillation characteristics. When multiple internal parameters of a device have different dimensions or different adjustable ranges, the unnormalized participation factors at the parameter level are normalized, and the dominant parameter is identified based on the normalized parameter participation factor modulus. The normalization process includes relative parameter normalization based on the current value of the internal parameters of the device, or normalization based on the allowable disturbance range of the internal parameters of the device.

5. The method for assessing the risk of broadband oscillations in power systems based on multi-level participation factors according to claim 1, characterized in that: The negative of the real part of the oscillation mode offset corresponds to the change in the damping factor. When the real part of the oscillation mode offset is less than zero, the damping factor increases and the system damping is enhanced; when the real part of the oscillation mode offset is greater than zero, the damping factor decreases and the system damping is weakened. The imaginary part of the oscillation mode offset corresponds to the change in oscillation angular frequency. When the imaginary part of the oscillation mode offset is greater than zero, the oscillation frequency increases; when the imaginary part of the oscillation mode offset is less than zero, the oscillation frequency decreases. Under small disturbance conditions, the change in damping ratio is calculated based on the real and imaginary parts of the oscillation mode offset.

6. The method for assessing the risk of broadband oscillations in power systems based on multi-level participation factors according to claim 1, characterized in that: The sensitivity of the device admittance to the internal parameters of the device is obtained by at least one of the following methods: When using the white-box analytical method, given the internal topology and control logic of the equipment, an analytical model of the equipment port admittance is established and the sensitivity is obtained by direct differentiation. When using the gray box equivalent model fitting method, given that the equipment topology or control structure is partially known, the port frequency domain response is measured, the equivalent admittance model is fitted, and the sensitivity of the equivalent admittance model parameters is analytically calculated. When using the finite difference measurement method, under the condition that the internal parameters of the target device are accessible, configurable, or can be perturbed through the device interface, the port admittance before and after the parameter perturbation is measured, and the sensitivity is obtained by using the differential approximation.

7. The method for assessing the risk of broadband oscillations in power systems based on multi-level participation factors according to claim 6, characterized in that: When only the admittance sensitivity at the imaginary axis frequency point is obtained, the admittance sensitivity is fitted to a rational function model and extended to the complex frequency point corresponding to the broadband oscillation mode. Alternatively, when the damping of the broadband oscillation mode satisfies the preset approximation condition, the admittance sensitivity at the imaginary axis frequency point is used to approximate the admittance sensitivity at the complex frequency point.

8. The method for assessing the risk of broadband oscillations in power systems based on multi-level participation factors according to claim 1, characterized in that: Device-level participation analysis also includes: By combining the magnitude of the device-level strict modal sensitivity and the magnitude of the device admittance change, the upper bound of the maximum offset amplitude of the oscillation mode that may be caused by the device admittance change is estimated. The devices are sorted according to the upper bound of the maximum offset amplitude to filter out high-risk devices.

9. The method for assessing the risk of broadband oscillations in power systems based on multi-level participation factors according to claim 1, characterized in that: When the node admittance matrix satisfies the symmetric modeling condition that the left and right eigenvectors are transposes of each other, the unnormalized participation factor is represented by the square of the corresponding element of the right eigenvector and sorted by its magnitude. When the node admittance matrix is ​​an asymmetric matrix or the node corresponds to a multidimensional port variable, the participation factor is calculated using the general form of the left and right eigenvectors; for multidimensional port variables, the participation strength of the node is characterized by the product of the corresponding subvectors or the matrix norm.

10. A power system broadband oscillation risk assessment device, characterized in that, It includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the method of any one of claims 1 to 9.

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