A new energy grid-connected system subsynchronous oscillation tracing method and system

Abstract

The present application relates to the technical field of new energy power system oscillation analysis, and specifically discloses a new energy grid-connected system subsynchronous oscillation tracing method and system. The method obtains wide-area measurement data and topological connection relationship of multiple monitoring nodes in the new energy grid-connected system, performs adaptive variational modal decomposition on the node response sequence after preprocessing, and screens the dominant oscillation characteristic sequence in the subsynchronous frequency band; a variable time delay kernel density estimation transfer entropy model is constructed, the optimal propagation time delay between nodes is dynamically searched, the bidirectional transfer entropy and causal correlation coefficient are calculated; a directed causal graph is constructed with the monitoring nodes as the vertices and the significant directional causal relationship as the directed edges, the oscillation source is located according to the weighted in-degree of the nodes, and the dominant propagation path is extracted step by step from the oscillation source as the starting point, and the positioning and path identification results are output. The present application does not need to rely on the detailed model of the system, can adapt to the nonlinear, non-Gaussian and non-stationary oscillation scene, and improves the subsynchronous oscillation tracing accuracy and causal explainability.

Description

Technical Field

[0001] This invention relates to the field of oscillation analysis technology in new energy power systems, and more specifically to a method and system for tracing the source of subsynchronous oscillations in new energy grid-connected systems. Background Technology

[0002] Currently, with the increasing proportion of wind power, photovoltaics, energy storage, flexible AC transmission, flexible DC transmission, and high-power power electronic loads in power systems, new power systems exhibit characteristics such as low inertia, strong nonlinear coupling, and wideband dynamic interaction. Complex couplings may form between the power electronic converter control loop, synchronous generator excitation and speed regulation system, network impedance, and grid-connected control parameters. Under conditions of weak grids, series compensation, control parameter mismatch, or external disturbances, subsynchronous oscillations are easily induced.

[0003] After a secondary synchronous oscillation occurs, the oscillation component typically propagates outward through electrical networks and equipment control coupling links, exhibiting oscillation characteristics of the same or similar frequencies in the voltage, current, and power responses of multiple buses, converter grid connection points, wind farms, photovoltaic power stations, synchronous generators, and transmission branches. Since both the actual oscillation source and the passive response nodes will exhibit oscillation waveforms, it is difficult to accurately determine the location of the oscillation source or identify the dominant propagation path simply by relying on local amplitude exceeding limits, spectral peak values, or single-point protection actions.

[0004] Existing subsynchronous oscillation analysis methods mainly include model-based methods and data-driven methods. Model-based methods require relatively complete network topology, equipment parameters, and converter control parameters. When the model is accurate, they have strong physical interpretation capabilities. However, in large-scale renewable energy grid-connected systems, equipment control parameters are difficult to obtain completely, operating modes change frequently, and high-dimensional models have high computational complexity, resulting in limited online applicability.

[0005] With the continuous development of intelligent technologies, data-driven methods can utilize measurement data from phasor measurement units, wide-area measurement systems, fault recorders, and field monitoring systems for oscillation identification. Machine learning and deep learning methods can directly extract nonlinear features from measurement data. However, these methods typically rely on sufficient labeled samples, leading to problems such as strong model retraining requirements, insufficient interpretability, and decreased generalization performance. From the perspective of subsynchronous oscillation propagation, there is a natural directional information transfer relationship between the dynamic changes of the oscillation source and the responses observed by other nodes. Transfer entropy, as a nonlinear and asymmetric information theory metric, can quantify the directional dependencies between time series and has been increasingly used for causal relationship inference in complex dynamic systems.

[0006] However, current research on applying causal analysis methods to the problem of locating subsynchronous oscillation sources in novel power systems is limited, and applying statistically based causal analysis methods to practical oscillation analysis still faces several challenges. First, raw wide-area measurement signals typically contain fundamental frequency components, noise components, non-target oscillation modes, and differences in scale. Direct causal analysis can easily lead to misjudgments of propagation direction or false causality. Second, the fixed-delay propagation entropy method struggles to characterize the differences in propagation delays between different nodes caused by network topology, equipment control, and dynamic responses. Third, probability estimation methods based on predefined distributions are also ill-suited for nonlinear, non-Gaussian, and non-stationary oscillation data.

[0007] Therefore, how to provide a subsynchronous oscillation tracing method and system that does not rely on detailed system models and control parameters, can adapt to the nonlinear and non-stationary oscillation characteristics of new energy grid-connected systems, has good causal interpretability and strong engineering applicability is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0008] In view of the above problems, the present invention is proposed to provide a method and system for tracing the subsynchronous oscillation of a new energy grid-connected system to overcome or at least partially solve the above problems.

[0009] To achieve the above objectives, the present invention adopts the following technical solution:

[0010] In a first aspect, the present invention relates to a method for tracing the source of subsynchronous oscillations in a new energy grid-connected system, comprising the following steps: S1. Obtain wide-area measurement data of multiple monitoring nodes in the new energy grid-connected system and the topological connection relationship between each monitoring node.

[0011] S2. Preprocess the wide-area measurement data to obtain the node response sequence of each monitoring node.

[0012] S3. Perform adaptive variational mode decomposition on the node response sequence to extract the dominant oscillation characteristic sequence of each monitoring node in the subsynchronous frequency band.

[0013] S4. Based on the topological connection relationship, construct the variable time delay kernel density estimation transfer entropy model corresponding to the monitoring nodes with electrical connections.

[0014] S5. Based on the variable delay kernel density estimation model, search for the optimal propagation delay between each monitoring node, and calculate the bidirectional propagation entropy between each monitoring node according to the optimal propagation delay.

[0015] S6. Determine the causal driving direction between each monitoring node based on the bidirectional transfer entropy, calculate the causal correlation coefficient as the edge weight, and construct a subsynchronous oscillation directed causal graph.

[0016] S7. Determine the oscillation source node based on each monitoring node in the directed causal graph, and extract the dominant propagation path step by step based on the edge weight, starting from the oscillation source node.

[0017] S8. Output the identification results corresponding to the dominant oscillation characteristic sequence, the directed causal graph, the weighted in-degree sorting of each monitoring node, the oscillation source node, and the dominant propagation path.

[0018] Preferably, the wide-area measurement data in S1 includes at least one of the following: voltage, current, active power, reactive power, and phase angle information of each monitoring node.

[0019] The monitoring nodes include wind farm grid connection points, photovoltaic power station grid connection points, synchronous generator endpoints, flexible AC transmission device access points, flexible DC transmission device access points, converter grid connection equipment access points, and combinations thereof.

[0020] Preferably, the preprocessing in S2 includes: S21. Perform time alignment and outlier removal processing on the wide-area measurement data of each monitoring node to obtain the oscillation response sequence of each monitoring node.

[0021] S22. Normalize the oscillation response sequence. The normalization process includes at least one of the following: per-unit normalization, mean-variance normalization, maximum-minimum normalization, or conversion to rated capacity and rated voltage.

[0022] S23. The normalized oscillation response sequence is used as the node response sequence to reduce the influence of different voltage levels of each monitoring node on the subsequent analysis results.

[0023] Preferably, the adaptive variational mode decomposition in S3 includes: S31. Perform adaptive variational mode decomposition on the node response sequence. Calculate the energy loss coefficient based on the energy difference between the node response sequence and the reconstructed sequence of each intrinsic mode component. Increase the number of candidate mode decompositions in turn. When the energy loss coefficient is less than the preset energy loss threshold, determine the current number of candidate mode decompositions as the final number of mode decompositions. Decompose the node response sequence into several intrinsic mode components.

[0024] S32. Calculate the center frequency, modal energy, and correlation between each intrinsic modal component and the original node response sequence. Determine the intrinsic modal components whose center frequency is located in the subsynchronous frequency band and whose modal energy or correlation meets the preset threshold conditions as the dominant oscillation modes, and extract each intrinsic modal component as the dominant oscillation feature sequence.

[0025] Preferably, the construction of the S4 time-delay kernel density estimation transfer entropy model includes: S41. Construct a source variable history embedding vector for the source node corresponding to the monitoring node with electrical association, and construct a target variable history embedding vector for the target node corresponding to the monitoring node with electrical association.

[0026] S42. Change the lag time of the target variable or the lag time of the source variable to construct a variable delay transfer entropy expression.

[0027] S43. Using the multivariate kernel density estimation method, nonparametric estimation of the joint probability density and conditional probability density in the variable time delay transfer entropy expression is performed to obtain the variable time delay kernel density estimation transfer entropy model.

[0028] Preferably, S5 includes: S51. For monitoring nodes with electrical connections, calculate the propagation entropy value corresponding to each candidate delay in the candidate delay set, and determine the candidate delay when the propagation entropy reaches the maximum value as the optimal propagation delay.

[0029] S52. Based on the optimal propagation delay, calculate the first propagation entropy in the direction from the first node to the second node and the second propagation entropy in the direction from the second node to the first node, respectively, to obtain the bidirectional propagation entropy.

[0030] Preferably, the construction of the directed causal graph in S6 includes: S61. For monitoring nodes with electrical connections, compare the magnitudes of bidirectional transmission entropy. If the transmission entropy from the first node to the second node is greater than the transmission entropy from the second node to the first node, then determine that the first node is the driving node and the second node is the responding node, with the causal driving direction pointing from the first node to the second node.

[0031] S62. Calculate the causal correlation coefficient based on the difference in bidirectional transfer entropy, the normalized difference in bidirectional transfer entropy, the maximum transfer entropy value, or the significance test result.

[0032] S63. Using each monitoring node as a vertex, the causal driving direction as a directed edge, and the causal correlation coefficient as the edge weight, construct an initial directed causal graph. Remove the directed edges between node pairs that do not meet the preset significance threshold to obtain the subsynchronous oscillation directed causal graph.

[0033] Preferably, the location of the oscillation source node and the extraction of the dominant propagation path in S7 include: S71. Calculate the weighted in-degree of each node in the directed causal graph, and determine the oscillation source node based on the minimum weighted in-degree.

[0034] S72. Starting from the oscillation source node, select the directed edge with the largest causal correlation coefficient from the downstream candidate causal edges of the current starting point as the next propagation branch.

[0035] S73. Repeat S72 until there are no candidate causal edges that satisfy the causal strength threshold, the path non-loop constraint, or the propagation hierarchy constraint, thus forming the dominant propagation path.

[0036] Preferably, S8 further includes: based on the dominant oscillation characteristic sequence, the directed causal graph, the weighted in-degree sorting of each monitoring node, the identification results corresponding to the oscillation source node and the dominant propagation path, outputting the identification results through at least one of the following forms: graphical interface, data file, monitoring platform interface or scheduling side online analysis platform.

[0037] On the other hand, the present invention also relates to a subsynchronous oscillation tracing system for a new energy grid-connected system, comprising: a data acquisition module for acquiring wide-area measurement data of multiple monitoring nodes in the new energy grid-connected system and the topological connection relationship between each monitoring node.

[0038] The data preprocessing module is used to preprocess the wide-area measurement data to obtain the node response sequence of each monitoring node.

[0039] The adaptive mode decomposition module is used to perform adaptive variational mode decomposition on the node response sequence and extract the dominant oscillation feature sequence of each monitoring node in the subsynchronous frequency band.

[0040] The dynamic causal analysis module is used to construct a variable delay kernel density estimation model for the transfer entropy of monitoring nodes with electrical connections based on the topological connection relationship, search for the optimal propagation delay between each monitoring node, and calculate the bidirectional transfer entropy between each monitoring node based on the optimal propagation delay.

[0041] The directed causal graph construction module is used to determine the causal driving direction between each monitoring node based on the bidirectional transfer entropy, calculate the causal correlation coefficient as the edge weight, and construct a subsynchronous oscillation directed causal graph.

[0042] The oscillation source localization module is used to determine the oscillation source node based on each monitoring node in the directed causal graph.

[0043] The main propagation path extraction module is used to extract the dominant propagation path step by step based on the edge weight, starting from the oscillation source node.

[0044] The results output module is used to output the identification results corresponding to the dominant oscillation feature sequence, the directed causal graph, the weighted in-degree sorting of each monitoring node, the oscillation source node, and the dominant propagation path.

[0045] As can be seen from the above technical solutions, compared with the prior art, the beneficial effects of the present invention include at least the following: ① Using wide-area measurement data as the core input, there is no need to obtain detailed system models and equipment control parameters, which greatly reduces the threshold for engineering deployment and adapts to new energy grid-connected systems with frequent changes in operating modes.

[0046] ② By extracting the dominant oscillation features of the target frequency band through adaptive variational mode decomposition, the interference of fundamental frequency components, noise and redundant modes can be effectively filtered out, the influence of multi-scale differences on causal analysis can be weakened, and false causality and misjudgment of direction can be avoided.

[0047] ③ By adopting a variable delay kernel density estimation model for propagation entropy, the optimal propagation delay between monitoring nodes can be dynamically searched, adapting to the differences in propagation delay caused by different topologies and equipment characteristics. At the same time, the probability distribution is estimated in a non-parametric manner, without the need to preset the data distribution form, and it has stronger adaptability to nonlinear, non-Gaussian, and non-stationary oscillating data.

[0048] ④ By using a directed causal graph to uniformly realize the location of oscillation sources and the identification of propagation paths, and by combining the node in-degree and causal edge weight to quantify the oscillation propagation characteristics, it has clear causal interpretability and can provide data support for the configuration of oscillation suppression devices, protection of key nodes and optimization of control parameters. Attached Figure Description

[0049] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0050] Figure 1 This is a flowchart of the subsynchronous oscillation tracing method for a new energy grid-connected system provided in this embodiment of the invention; Figure 2 This is a schematic diagram of the subsynchronous oscillation tracing system architecture of the new energy grid-connected system provided in this embodiment of the invention; Figure 3 This is a schematic diagram illustrating the subsynchronous oscillation of the current in a new energy grid-connected system provided in an embodiment of the present invention; Figure 4 This is a partially enlarged view of the subsynchronous oscillation of the current in the new energy grid-connected system provided in an embodiment of the present invention. Figure 5 This is a schematic diagram illustrating the subsynchronous oscillation of active power in a new energy grid-connected system provided in an embodiment of the present invention. Figure 6 This is a schematic diagram of mode decomposition of the oscillation signal in the subsynchronous oscillation tracing system of the new energy grid-connected system provided in the embodiments of the present invention; Figure 7 This is a schematic diagram of the oscillation transfer entropy calculation results of the subsynchronous oscillation tracing system of the new energy grid-connected system provided in this embodiment of the invention; Figure 8This is a schematic diagram of the dominant propagation path and oscillation source location of the new energy grid-connected system provided in this embodiment of the invention; Figure 9 This is a comparison chart of the oscillation source analysis results of the new energy grid-connected system provided in the embodiments of the present invention. Detailed Implementation

[0051] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0052] like Figure 1 As shown in the figure, this invention discloses a method for tracing the source of subsynchronous oscillations in a new energy grid-connected system, including the following steps: S1. Obtain wide-area measurement data of multiple monitoring nodes in the new energy grid-connected system and the topological connection relationship between each monitoring node.

[0053] The wide-area measurement data in S1 includes at least one of the following: voltage, current, active power, reactive power, and phase angle information for each monitoring node.

[0054] The monitoring nodes include wind farm grid connection points, photovoltaic power station grid connection points, synchronous generator endpoints, flexible AC transmission device access points, flexible DC transmission device access points, converter grid connection equipment access points, and combinations thereof.

[0055] S2. Preprocess the wide-area measurement data to obtain the node response sequence of each monitoring node.

[0056] Preprocessing in S2 includes: S21. Perform time alignment and outlier removal processing on the wide-area measurement data of each monitoring node to obtain the oscillation response sequence of each monitoring node.

[0057] S22. Normalize the oscillation response sequence. The normalization process includes at least one of the following: per-unit normalization, mean-variance normalization, maximum-minimum normalization, or conversion to rated capacity and rated voltage.

[0058] S23. The normalized oscillation response sequence is used as the node response sequence to reduce the influence of different voltage levels of each monitoring node on the subsequent analysis results.

[0059] S3. Perform adaptive variational mode decomposition on the node response sequence to extract the dominant oscillation characteristic sequence of each monitoring node in the subsynchronous frequency band.

[0060] The adaptive variational mode decomposition in S3 includes: S31. Perform adaptive variational mode decomposition on the node response sequence. Calculate the energy loss coefficient based on the energy difference between the node response sequence and the reconstructed sequence of each intrinsic mode component. Increase the number of candidate mode decompositions in turn. When the energy loss coefficient is less than the preset energy loss threshold, determine the current number of candidate mode decompositions as the final number of mode decompositions. Decompose the node response sequence into several intrinsic mode components.

[0061] S32. Calculate the center frequency, modal energy, and correlation between each intrinsic modal component and the original node response sequence. Determine the intrinsic modal components whose center frequency is located in the subsynchronous frequency band and whose modal energy or correlation meets the preset threshold conditions as the dominant oscillation modes, and extract each intrinsic modal component as the dominant oscillation feature sequence.

[0062] S4. Based on the topological connection relationship, construct the variable time delay kernel density estimation transfer entropy model corresponding to the monitoring nodes with electrical connections.

[0063] The construction of the S4 medium-variable time-delay kernel density estimation transfer entropy model includes: S41. Construct a source variable history embedding vector for the source node corresponding to the monitoring node with electrical association, and construct a target variable history embedding vector for the target node corresponding to the monitoring node with electrical association.

[0064] S42. Change the lag time of the target variable or the lag time of the source variable to construct a variable delay transfer entropy expression.

[0065] S43. Using the multivariate kernel density estimation method, nonparametric estimation of the joint probability density and conditional probability density in the variable time delay transfer entropy expression is performed to obtain the variable time delay kernel density estimation transfer entropy model.

[0066] S5. Based on the variable delay kernel density estimation model, search for the optimal propagation delay between each monitoring node, and calculate the bidirectional propagation entropy between each monitoring node according to the optimal propagation delay.

[0067] S5 includes: S51. For monitoring nodes with electrical connections, calculate the propagation entropy value corresponding to each candidate delay in the candidate delay set, and determine the candidate delay when the propagation entropy reaches the maximum value as the optimal propagation delay.

[0068] S52. Based on the optimal propagation delay, calculate the first propagation entropy in the direction from the first node to the second node and the second propagation entropy in the direction from the second node to the first node, respectively, to obtain the bidirectional propagation entropy.

[0069] S6. Determine the causal driving direction between each monitoring node based on the bidirectional transfer entropy, calculate the causal correlation coefficient as the edge weight, and construct a subsynchronous oscillation directed causal graph.

[0070] The construction of a directed cause-effect graph in S6 includes: S61. For monitoring nodes with electrical connections, compare the magnitudes of bidirectional transmission entropy. If the transmission entropy from the first node to the second node is greater than the transmission entropy from the second node to the first node, then determine that the first node is the driving node and the second node is the responding node, with the causal driving direction pointing from the first node to the second node.

[0071] S62. Calculate the causal correlation coefficient based on the difference in bidirectional transfer entropy, the normalized difference in bidirectional transfer entropy, the maximum transfer entropy value, or the significance test result.

[0072] S63. Using each monitoring node as a vertex, the causal driving direction as a directed edge, and the causal correlation coefficient as the edge weight, construct an initial directed causal graph. Remove the directed edges between node pairs that do not meet the preset significance threshold to obtain the subsynchronous oscillation directed causal graph.

[0073] S7. Determine the oscillation source node based on each monitoring node in the directed causal graph, and extract the dominant propagation path step by step based on the edge weight, starting from the oscillation source node.

[0074] The location of the oscillation source node and the extraction of the dominant propagation path in S7 include: S71. Calculate the weighted in-degree of each node in the directed causal graph, and determine the oscillation source node based on the minimum weighted in-degree.

[0075] S72. Starting from the oscillation source node, select the directed edge with the largest causal correlation coefficient from the downstream candidate causal edges of the current starting point as the next propagation branch.

[0076] S73. Repeat S72 until there are no candidate causal edges that satisfy the causal strength threshold, the path non-loop constraint, or the propagation hierarchy constraint, thus forming the dominant propagation path.

[0077] S8. Output the identification results corresponding to the dominant oscillation characteristic sequence, the directed causal graph, the weighted in-degree sorting of each monitoring node, the oscillation source node, and the dominant propagation path.

[0078] S8 also includes: based on the dominant oscillation characteristic sequence, directed causal graph, weighted in-degree sorting of each monitoring node, identification results corresponding to the oscillation source node and the dominant propagation path, outputting the identification results through at least one of the following forms: graphical interface, data file, monitoring platform interface or scheduling side online analysis platform.

[0079] like Figure 2As shown in the figure, this embodiment of the invention also discloses a subsynchronous oscillation tracing system for a new energy grid-connected system, including: a data acquisition module, used to acquire wide-area measurement data of multiple monitoring nodes in the new energy grid-connected system and the topological connection relationship between each monitoring node.

[0080] The data preprocessing module is used to preprocess the wide-area measurement data to obtain the node response sequence of each monitoring node.

[0081] The adaptive mode decomposition module is used to perform adaptive variational mode decomposition on the node response sequence and extract the dominant oscillation feature sequence of each monitoring node in the subsynchronous frequency band.

[0082] The dynamic causal analysis module is used to construct a variable delay kernel density estimation model for the transfer entropy of monitoring nodes with electrical connections based on the topological connection relationship, search for the optimal propagation delay between each monitoring node, and calculate the bidirectional transfer entropy between each monitoring node based on the optimal propagation delay.

[0083] The directed causal graph construction module is used to determine the causal driving direction between each monitoring node based on the bidirectional transfer entropy, calculate the causal correlation coefficient as the edge weight, and construct a subsynchronous oscillation directed causal graph.

[0084] The oscillation source localization module is used to determine the oscillation source node based on each monitoring node in the directed causal graph.

[0085] The main propagation path extraction module is used to extract the dominant propagation path step by step based on the edge weight, starting from the oscillation source node.

[0086] The results output module is used to output the identification results corresponding to the dominant oscillation feature sequence, the directed causal graph, the weighted in-degree sorting of each monitoring node, the oscillation source node, and the dominant propagation path.

[0087] The technical solution of the present invention will be described in detail through specific embodiments.

[0088] This invention discloses a method for tracing the source of subsynchronous oscillations in a new energy grid-connected system, comprising the following steps: S1. Obtain wide-area measurement data and topology connection relationships of multiple monitoring nodes in the new energy grid-connected system.

[0089] S2. Perform time alignment, outlier removal, normalization, and data caching preprocessing on the wide-area measurement data to obtain the node response sequence.

[0090] S3. Perform adaptive variational mode decomposition on the response sequence of each node to obtain multiple intrinsic mode components, and select the dominant oscillation mode in the target subsynchronous frequency band from the intrinsic mode components to obtain the dominant oscillation characteristic sequence of each monitoring node.

[0091] S4. For any two adjacent or electrically related monitoring nodes in the physical topology connection relationship, establish a multivariable variable time delay kernel density estimation transfer entropy model.

[0092] S5. Search for the optimal propagation delay between each monitoring node, and calculate the bidirectional transmission entropy between the monitoring nodes accordingly.

[0093] S6. Determine the causal driving direction based on the magnitude relationship of the bidirectional transmission entropy between monitoring nodes, and construct a subsynchronous oscillation directed causal graph using the causal correlation coefficient as the edge weight.

[0094] S7. Determine the oscillation source node based on the weighted in-degree of each monitoring node in the directed causal graph, and extract the dominant propagation path step by step based on the causal edge weight, starting from the oscillation source node.

[0095] S8. Output the dominant oscillation mode, directed causal graph, node in-degree sorting, oscillation source node and main propagation path identification results.

[0096] In this embodiment, the new energy grid-connected system includes a wind farm, a photovoltaic power station, a synchronous generator, transmission lines, transformers, busbars, and grid connection points. The busbars, wind farm grid connection points, photovoltaic power station grid connection points, synchronous generator endpoints, and other dynamic equipment are equivalently represented as monitoring nodes, and the coupling relationships or equivalent electrical connections between monitoring nodes via transmission lines, transformers, and busbars are considered as edges.

[0097] To further implement the above technical solution, the specific content of acquiring wide-area measurement data and topology connection relationships in S1 includes: S11. New energy grid-connected power systems include wind farms, photovoltaic power stations, flexible AC transmission equipment, flexible DC transmission equipment, synchronous generators, converter grid-connected equipment, or combinations thereof.

[0098] S12. Obtain at least one of the following information from each bus or dynamic equipment node in the new energy grid-connected power system: voltage, branch current, active power, reactive power, and phase angle.

[0099] S13. Obtain the topological connections and node numbers of wind farms, photovoltaic power stations, synchronous generators, and transmission lines.

[0100] S14. At least one of the sampling data from the phasor measurement unit of the new energy grid-connected power system, the wide area measurement system, the station monitoring system, the fault recorder, or the converter local controller.

[0101] S15. Perform unified time-scale calibration on data of multiple time scales and record the sampling frequency, data window length, and event start time.

[0102] like Figure 3The figure shows the oscillation characteristics of the three-phase currents in the wind farm's grid-connected tie line before and after a disturbance. The red, blue, and green curves represent the current signals of phases A, B, and C, respectively. The horizontal axis represents time, and the vertical axis represents the current amplitude. As can be seen from the figure, before 2 seconds, the system is in a stable operating state. The waveforms of the three-phase currents in the wind farm tie line exhibit periodic changes, maintaining good symmetry among the three phases. The amplitudes are basically stable, without significant oscillations or abrupt amplitude changes, indicating that the wind farm's grid-connected system is operating smoothly at this time.

[0103] When a disturbance is applied to the system at approximately 2 seconds, the three-phase current waveforms change rapidly, disrupting the original symmetrical operating state. The current amplitude increases significantly within a short period, accompanied by violent fluctuations. Subsequently, the three-phase current signals continue to exhibit irregular oscillation characteristics, with increased waveform distortion and significant shifts in the amplitude and phase relationship of the interphase currents. This indicates that the disturbance caused a dynamic instability trend in the wind farm grid-connected system.

[0104] like Figure 4 As shown, it demonstrates Figure 3 The magnified area in the block diagram further demonstrates that, after the disturbance, the oscillation amplitude and waveform differences of the three-phase currents significantly increase, and the system transitions from a stable operating state before the disturbance to a strongly oscillating operating state after the disturbance. Therefore, this diagram can intuitively reflect the transient response process and oscillation development characteristics of the tie-line three-phase currents after the wind farm is subjected to external disturbances.

[0105] like Figure 5 The figure shows the dynamic response curve of the active power of the new energy grid-connected system as a function of time under the target operating conditions. The horizontal axis represents time in seconds, and the vertical axis represents active power in MW.

[0106] As shown in the figure, from 1.5s to approximately 2.0s, the system's active power remained relatively stable at around 550MW, with only minor fluctuations, indicating that the system was in a relatively stable operating state before the disturbance. After approximately 2.0s, the system was affected by the disturbance, and the active power waveform began to exhibit obvious periodic oscillations. As time progressed, the oscillation amplitude gradually increased, and the upper and lower envelopes of the power curve continued to expand, indicating that the oscillation energy caused by the disturbance continued to accumulate in the system, disrupting the system's stable operating state. In particular, from approximately 3.2s to 3.7s, the active power oscillation amplitude reached a high level, with the power fluctuating significantly between positive and negative directions, reaching a minimum of nearly -400MW and a maximum of nearly 900MW, indicating that the system entered a relatively violent oscillation state.

[0107] To further implement the above technical solution, the specific content of S2 is as follows: S21. Time-align all measurement data and remove outliers to obtain the oscillation response sequence of each electrical node.

[0108] S22. Perform at least one of the following on all oscillating response sequences: per-unit normalization, mean-variance normalization, maximum-minimum normalization, or conversion to rated capacity and rated voltage.

[0109] S23. Use the pre-processed oscillation response sequence to reduce the impact of different voltage levels at each monitoring node on the causal analysis results.

[0110] To further implement the above technical solution, the specific content of adaptive variational mode decomposition in S3 is as follows: S31. Perform variational mode decomposition on the node response sequence to be analyzed. Calculate the energy loss coefficient based on the energy difference between the node response sequence and the reconstructed sequence of each intrinsic mode component. Increase the number of candidate mode decompositions in turn. When the energy loss coefficient is less than the preset energy loss threshold, determine the current number of candidate mode decompositions as the final number of mode decompositions. Decompose the node response sequence into several intrinsic mode components. In this embodiment, the constrained variational problem of variational mode decomposition is expressed as:

[0111] in, The number of modes to be decomposed (positive integer); Indicates the decomposition of the first... One modal component, Indicates the decomposition of the first... One center frequency; It is the Dirac function; This is the convolution operator; To obtain the partial derivative; To obtain the analytic signal of the original signal; This is represented as shifting the spectrum to the fundamental frequency band; The imaginary unit; This is the input signal.

[0112] By introducing the Lagrange multiplication operator and penalty coefficient, the constrained variational problem described above is transformed into an unconstrained optimization problem, the augmented Lagrange expression of which is:

[0113] in, This is a penalty factor used to constrain the bandwidth of each modal component; For Lagrange multipliers; This indicates the inner product operation.

[0114] The energy loss coefficient is expressed as:

[0115] in, xThis represents the node response sequence obtained after preprocessing.

[0116] The threshold-based adaptive mode decomposition number is expressed as:

[0117] in, This is a preset energy loss threshold.

[0118] S32. Calculate the center frequency, modal energy, and correlation between each intrinsic mode component and the original node response sequence. Determine the intrinsic mode components whose center frequency is located in the target subsynchronous frequency band and whose modal energy or correlation meets the threshold condition as the dominant oscillation mode.

[0119] like Figure 6 As shown, the figure illustrates the decomposition results and reconstruction effect of the nodal response signal after adaptive variational mode decomposition. The first subfigure in the figure compares the preprocessed signal with the variational mode decomposition reconstructed signal, where the black solid line represents the original response signal after preprocessing, and the orange dashed line represents the variational mode decomposition reconstructed signal obtained by superimposing the intrinsic mode components. As can be seen from the figure, the variational mode decomposition reconstructed signal and the preprocessed signal are basically consistent in overall trend, peak and valley positions, and amplitude variations, exhibiting a high degree of overlap. This indicates that the adaptive variational mode decomposition method can extract the main dynamic components of the original signal relatively completely, with small reconstruction errors, and the decomposition results have good accuracy and completeness.

[0120] The second to fourth sub-figures illustrate several intrinsic mode components obtained through variational mode decomposition. The different mode components exhibit significant differences in oscillation frequency, amplitude variation, and waveform characteristics, indicating that the multi-scale oscillation components in the original nodal response signal have been effectively separated. The frequency hierarchy among the mode components is clear, and no obvious mode aliasing occurs, demonstrating that the adaptively determined number of mode decompositions can well adapt to the frequency structure of the nodal response signal. The fifth sub-figure shows the residual components or high-frequency perturbation components after decomposition. These components exhibit strong random fluctuation characteristics with relatively small amplitudes, mainly corresponding to noise, local abrupt changes, or non-dominant dynamic components in the original signal. Separating these non-dominant components from the main oscillation modes helps reduce the impact of noise and irrelevant perturbations on subsequent oscillation feature extraction, transfer entropy calculation, and oscillation source localization results.

[0121] To further implement the above technical solution, the specific content of S4 is as follows: S41. For the source node response sequence and the target node response sequence, construct the source variable historical embedding vector and the target variable historical embedding vector respectively.

[0122] S42. By changing the lag time of the target variable or the lag time of the source variable, a variable delay kernel density estimation transfer entropy model is constructed.

[0123] The variable-delay kernel density estimation transfer entropy model is expressed as:

[0124]

[0125]

[0126] in, The lag time of the source variable; The lag time for the target variable; For joint probability density; For conditional probability density, For source variables To target variable The propagation entropy; , Discrete time series of the source and target variables, respectively; , These are the historical embedding orders of the source and target variables, respectively; The time of the sample is 1000.

[0127] S43. Using the multivariate kernel density estimation method, nonparametric estimation is performed on the joint probability density and conditional probability density in the transitive entropy expression.

[0128] Among them, the multivariate kernel density estimation method is a nonparametric probability density estimation method. It estimates the joint probability density distribution of multivariate random variables by smoothing a finite sample through a kernel function, without having to pre-assume that the data follows a specific parametric distribution form.

[0129] Based on Bayes' theorem, the conditional probability density is transformed into the joint probability density form:

[0130] Based on this, the joint probability density is calculated using the multivariate kernel density estimation method, assuming... , , , , The joint sample vector consists of the current value of the target variable, the historical embedding of the target variable, and the historical embedding of the source variable. The joint sample vector consists of the historical embeddings of the target variable and the historical embeddings of the source variable. The joint sample vector consists of the current value of the target variable and its historical embeddings. Embed the target variable's history.

[0131] We can obtain:

[0132] in, This represents the conditional probability density estimate. The number of valid samples; It is a symmetric positive definite bandwidth matrix; For multivariate kernel functions, the Gaussian kernel function is specifically chosen. This represents the valid sample number in kernel density estimation.

[0133] To further implement the above technical solution, the specific content of S5 is as follows: S51. The candidate delay that obtains the maximum value of the propagation entropy between each monitoring node is determined as the optimal propagation delay, which is used to characterize the difference in oscillation propagation delay caused by network topology and dynamic response characteristics.

[0134] The propagation process of subsynchronous oscillations in large-scale renewable energy grid-connected systems exhibits time-varying characteristics, with propagation delays commonly existing between different measured signals. Therefore, in causal analysis based on kernel density estimation of transfer entropy, the propagation delay between signals is not a constant. If the variable... lag time Then when the variable lag time The true time delay between the two variables At this point, the kernel density estimation of the transfer entropy will reach its peak. At this point, the transfer entropy value can more reliably reflect the causal relationship between variables, and its mathematical expression is:

[0135] S52. Calculate the bidirectional transmission entropy between nodes based on the optimal propagation delay.

[0136] like Figure 7 The diagram illustrates the calculated kernel density estimation transfer entropy of the subsynchronous oscillation signal between adjacent branches of the system. Solid and dashed arrows represent the oscillation information transmission relationship in two opposite directions between adjacent nodes, with the numerical values ​​next to the arrows representing the variable-delay kernel density estimation transfer entropy values ​​in the corresponding directions. By comparing the kernel density estimation transfer entropy values ​​in opposite directions at both ends of the same branch, the dominant propagation direction of the subsynchronous oscillation signal in that branch can be determined. Specifically, when the variable-delay kernel density estimation transfer entropy value in a certain direction is greater than the corresponding value in its opposite direction, it indicates that the oscillation information transmission intensity is higher in that direction, and the oscillation energy mainly propagates along that direction.

[0137] Depend on Figure 7It can be seen that in each adjacent branch, the kernel density estimated transfer entropy value corresponding to the solid arrow is greater than or significantly greater than the kernel density estimated transfer entropy value corresponding to the dashed arrow, indicating that the propagation direction of this synchronous oscillation signal in the system network has a strong unidirectional dominance. The oscillation energy transfer direction of each branch is not randomly distributed, but shows a relatively consistent propagation trend along the system topology, indicating that the oscillation signal of this frequency has a clear propagation path and energy transfer law in the system.

[0138] To further implement the above technical solution, the specific content of S6 is as follows: S61, if node To node The propagation entropy in the direction is greater than that of the node. To node The direction of propagation entropy determines the node. For driving nodes, nodes For the responding node.

[0139] S62. The causal correlation coefficient is calculated based on the bidirectional transmission entropy difference, the bidirectional transmission entropy normalized difference, the maximum transmission entropy value, the significance test result, or a combination thereof, and is used to characterize the intensity of directional information transmission of subsynchronous oscillations between nodes.

[0140] S63. Establish directed causal edges between adjacent nodes or nodes with electrical connections. If the difference between the two does not meet the significance threshold, then remove the valid causal edge between the node pair to form a subsynchronous oscillation directed causal graph.

[0141] To further implement the above technical solution, the specific content of S7 is as follows: S71. Based on the constructed directed causal graph, determine the oscillation source node according to the minimum weighted in-degree.

[0142] A node in the network in-degree Its calculation expression is:

[0143] S72. Starting from the identified oscillation source node, select the directed edge with the largest causal correlation coefficient from the downstream candidate causal edges of the current monitoring node as the next propagation branch; repeat this process until there are no candidate causal edges that satisfy the causal strength threshold, the path non-loop constraint, or the propagation level constraint, thus forming the dominant propagation path.

[0144] like Figure 8The diagram illustrates the dominant propagation path of subsynchronous oscillation energy, extracted based on the numerical comparison of the transfer entropy values ​​obtained from the kernel density estimation of adjacent branches with varying time delays. The red arrows in the diagram indicate the dominant propagation direction of the oscillation energy in the system network, and the values ​​next to the arrows are the kernel density estimation transfer entropy values ​​in the corresponding directions. By comparing the bidirectional transfer entropy values ​​between adjacent nodes, the direction with the larger transfer entropy is selected as the dominant oscillation propagation direction for that branch, thus constructing the dominant propagation path diagram of the subsynchronous oscillation signal in the system. It can be seen that the oscillation signal propagates from node 10 to both sides of the system and adjacent external networks. Specifically, the oscillation signal propagates from node 10 through the intermediate branches to nodes 9, 8, 7, and the left-side network.

[0145] On the other hand, the oscillation signal is transmitted from node 10 to the branches containing nodes 11, 3, and 4, respectively. The arrows of each dominant propagation path all show outward diffusion from node 10, indicating that the oscillation energy output at node 10 is significant and has a strong oscillation driving effect on surrounding nodes. Further analysis of the connectivity of node 10 in the dominant propagation path topology reveals that node 10 only has outward-output dominant propagation edges, and no dominant propagation edges pointing from other nodes to node 10; that is, the in-degree of node 10 is 0. This result indicates that in the extracted dominant oscillation propagation network, node 10 does not receive dominant oscillation input from other nodes, but rather acts as the starting node or root node for the outward propagation of the oscillation signal. Therefore, node 10 can be determined as the source node of this subsynchronous oscillation. Combined with the actual disturbance settings under this operating condition, it can be known that the subsynchronous oscillation source is located at the wind farm connected to bus 10. This demonstrates that the obtained dominant propagation path matches the actual oscillation source location of the system, and the location result accurately reflects the propagation law of the subsynchronous oscillation signal in the power grid.

[0146] like Figure 9 The diagram shows the transfer entropy analysis results between the wind farm and 10 synchronous generators in a 10-unit, 39-node grid-connected new energy system under Mode 1, specifically the oscillating information transfer entropy butterfly diagram corresponding to Mode 1. In Mode 1, there is a bidirectional information transfer relationship between all 10 generators and the wind farm, but the transfer entropy values ​​on both sides are not symmetrical. For all generators, the transfer entropy from the wind farm to the generators is... Both are greater than the transfer entropy in the direction from the generator to the wind farm. This indicates that historical oscillation information from the wind farm contributes more strongly to the prediction of the dynamic response of each generator, and that the wind farm has a more significant causal driving effect on the generator units within the system. Therefore, it can be determined that the oscillation energy in Mode 1 mainly propagates from the wind farm to the synchronous generator side, and the wind farm exhibits strong oscillation source characteristics in this mode. This location result is consistent with the actual location of the oscillation source.

[0147] To further implement the above technical solution, S8 also includes: The system outputs the identification results of the dominant oscillation mode, directed causal graph, node in-degree sorting, oscillation source node, and main propagation path. The identification results can be output through a graphical interface, data file, monitoring platform interface, or online analysis platform on the dispatch side, and can be used for oscillation source tracing, operational risk assessment, and decision support in renewable energy grid-connected power systems.

[0148] This invention also discloses a subsynchronous oscillation tracing system for a new energy grid-connected system, including a data acquisition module, a data preprocessing module, an adaptive mode decomposition module, a dynamic causal analysis module, a directed causal graph construction module, an oscillation source localization module, a main propagation path extraction module, and a result output module.

[0149] The data acquisition module is used to acquire wide-area measurement data and topology connections of multiple monitoring nodes in the new energy grid-connected system.

[0150] The data preprocessing module is used to preprocess the acquired multi-timescale measurement data.

[0151] The adaptive mode decomposition module is used to perform adaptive variational mode decomposition on the preprocessed node response sequence and select the dominant subsynchronous oscillation mode.

[0152] The dynamic causal analysis module is used to calculate the optimal propagation delay, bidirectional propagation entropy, and causal correlation coefficient between nodes based on the constructed variable delay kernel density estimation propagation entropy model.

[0153] The directed causal graph construction module is used to construct subsynchronous oscillatory directed causal graphs based on significant directional causal relationships and causal correlation coefficients.

[0154] The oscillation source localization module is used to determine the oscillation source node based on the node's weighted in-degree and outward causality strength.

[0155] The main propagation path extraction module is used to select the dominant propagation path step by step based on the causal edge weight, starting from the oscillation source node.

[0156] The results output module is used to output the dominant oscillation mode, the directed causal graph, the in-degree sorting of nodes, the oscillation source node and the main propagation path, and to trigger an alarm mechanism.

[0157] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the aforementioned method for tracing the subsynchronous oscillation of a new energy grid-connected system.

[0158] A processing terminal includes a memory and a processor, wherein the memory stores a computer program that can run on the processor, characterized in that the processor executes the computer program to implement the aforementioned method for tracing the subsynchronous oscillation of a new energy grid-connected system.

[0159] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0160] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for tracing the source of subsynchronous oscillations in a new energy grid-connected system, characterized in that, Includes the following steps: S1. Acquire wide-area measurement data of multiple monitoring nodes in the new energy grid-connected system and the topological connection relationship between each monitoring node; S2. Preprocess the wide-area measurement data to obtain the node response sequence of each monitoring node; S3. Perform adaptive variational mode decomposition on the node response sequence to extract the dominant oscillation feature sequence of each monitoring node in the subsynchronous frequency band. The adaptive variational mode decomposition described in S3 includes: S31. Perform adaptive variational mode decomposition on the node response sequence, calculate the energy loss coefficient based on the energy difference between the node response sequence and the reconstructed sequences of each intrinsic mode component, and sequentially increase the number of candidate mode decompositions. When the energy loss coefficient is less than the preset energy loss threshold, determine the current number of candidate mode decompositions as the final number of mode decompositions, and decompose the node response sequence into several intrinsic mode components. S32. Calculate the center frequency, modal energy, and correlation between each intrinsic mode component and the original node response sequence. Determine the intrinsic mode components whose center frequency is located in the subsynchronous frequency band and whose modal energy or correlation meets the preset threshold condition as the dominant oscillation mode. Extract each intrinsic mode component as the dominant oscillation feature sequence. S4. Based on the topological connection relationship, construct a variable time delay kernel density estimation transfer entropy model corresponding to the monitoring nodes with electrical association; S5. Based on the variable delay kernel density estimation propagation entropy model, search for the optimal propagation delay between each monitoring node, and calculate the bidirectional propagation entropy between each monitoring node according to the optimal propagation delay. S6. Determine the causal driving direction between each monitoring node based on the bidirectional transfer entropy, calculate the causal correlation coefficient as the edge weight, and construct a subsynchronous oscillation directed causal graph. S7. Determine the oscillation source node based on each monitoring node in the directed causal graph, and extract the dominant propagation path step by step based on the edge weight, starting from the oscillation source node. S8. Output the identification results corresponding to the dominant oscillation feature sequence, the directed causal graph, the weighted in-degree sorting of each monitoring node, the oscillation source node, and the dominant propagation path.

2. The method for tracing the source of subsynchronous oscillations in a new energy grid-connected system according to claim 1, characterized in that, The wide-area measurement data mentioned in S1 includes at least one of the following: voltage, current, active power, reactive power, and phase angle information of each monitoring node. The monitoring nodes include wind farm grid connection points, photovoltaic power station grid connection points, synchronous generator endpoints, flexible AC transmission device access points, flexible DC transmission device access points, converter grid connection equipment access points, and combinations thereof.

3. The method for tracing the source of subsynchronous oscillations in a new energy grid-connected system according to claim 1, characterized in that, The preprocessing described in S2 includes: S21. Perform time alignment and outlier removal processing on the wide-area measurement data of each monitoring node to obtain the oscillation response sequence of each monitoring node; S22. Normalize the oscillation response sequence. The normalization process includes at least one of the following: per-unit normalization, mean-variance normalization, maximum-minimum normalization, or conversion according to rated capacity and rated voltage. S23. The oscillation response sequence after normalization is used as the node response sequence to reduce the influence of different voltage levels of each monitoring node on the subsequent analysis results.

4. The method for tracing the source of subsynchronous oscillations in a new energy grid-connected system according to claim 1, characterized in that, The construction of the variable-delay kernel density estimation transfer entropy model described in S4 includes: S41. Construct a source variable history embedding vector for the source node corresponding to the monitoring node with electrical association, and construct a target variable history embedding vector for the target node corresponding to the monitoring node with electrical association. S42. Change the lag time of the target variable historical embedding vector or the lag time of the source variable historical embedding vector to construct a variable delay transfer entropy expression; S43. Using a multivariate kernel density estimation method, nonparametric estimation is performed on the joint probability density and conditional probability density in the variable time delay transfer entropy expression to obtain the variable time delay kernel density estimated transfer entropy model.

5. The method for tracing the source of subsynchronous oscillations in a new energy grid-connected system according to claim 1, characterized in that, S5 includes: S51. For monitoring nodes with electrical connections, calculate the propagation entropy value corresponding to each candidate delay in the candidate delay set, and determine the candidate delay when the propagation entropy reaches the maximum value as the optimal propagation delay. S52. Based on the optimal propagation delay, calculate the first transmission entropy in the direction from the first node to the second node and the second transmission entropy in the direction from the second node to the first node, respectively, to obtain the bidirectional transmission entropy.

6. The method for tracing the source of subsynchronous oscillations in a new energy grid-connected system according to claim 5, characterized in that, The construction of the directed causal graph described in S6 includes: S61. For monitoring nodes with electrical connections, compare the magnitude of the bidirectional transmission entropy. If the transmission entropy in the direction from the first node to the second node is greater than the transmission entropy in the direction from the second node to the first node, then determine that the first node is the driving node and the second node is the response node. The causal driving direction is from the first node to the second node. S62. Calculate the causal correlation coefficient based on the difference in bidirectional transfer entropy, the normalized difference in bidirectional transfer entropy, the maximum transfer entropy value, or the significance test result. S63. Using each monitoring node as a vertex, the causal driving direction as a directed edge, and the causal correlation coefficient as the edge weight, construct an initial directed causal graph, remove the directed edges between monitoring nodes that do not meet the preset significance threshold, and obtain the subsynchronous oscillation directed causal graph.

7. The method for tracing the source of subsynchronous oscillations in a new energy grid-connected system according to claim 1, characterized in that, The location of the oscillation source node and the extraction of the dominant propagation path mentioned in S7 include: S71. Calculate the weighted in-degree of each node in the directed causal graph, and determine the oscillation source node based on the minimum weighted in-degree; S72. Starting from the oscillation source node, select the directed edge with the largest causal correlation coefficient from the downstream candidate causal edges of the current starting point as the next propagation branch. S73. Repeat S72 until there are no candidate causal edges that satisfy the causal strength threshold, the path non-loop constraint, or the propagation hierarchy constraint, thus forming the dominant propagation path.

8. The method for tracing the source of subsynchronous oscillations in a new energy grid-connected system according to claim 1, characterized in that, S8 further includes: based on the dominant oscillation characteristic sequence, the directed causal graph, the weighted in-degree sorting of each monitoring node, the identification results corresponding to the oscillation source node and the dominant propagation path, outputting the identification results through at least one of the following forms: graphical interface, data file, monitoring platform interface or scheduling side online analysis platform.

9. A subsynchronous oscillation tracing system for a new energy grid-connected system, employing the subsynchronous oscillation tracing method for a new energy grid-connected system as described in any one of claims 1-8, characterized in that, include: The data acquisition module is used to acquire wide-area measurement data of multiple monitoring nodes in the new energy grid-connected system and the topological connection relationship between each monitoring node; The data preprocessing module is used to preprocess the wide-area measurement data to obtain the node response sequence of each monitoring node; An adaptive mode decomposition module is used to perform adaptive variational mode decomposition on the node response sequence and extract the dominant oscillation feature sequence of each monitoring node in the subsynchronous frequency band. The adaptive variational mode decomposition includes: Adaptive variational mode decomposition is performed on the node response sequence. The energy loss coefficient is calculated based on the energy difference between the node response sequence and the reconstructed sequences of each intrinsic mode component. The number of candidate mode decompositions is increased sequentially. When the energy loss coefficient is less than a preset energy loss threshold, the current number of candidate mode decompositions is determined as the final number of mode decompositions. The node response sequence is then decomposed into several intrinsic mode components. Calculate the center frequency, modal energy, and correlation between each intrinsic mode component and the original node response sequence. Identify the intrinsic mode components whose center frequency is located in the subsynchronous frequency band and whose modal energy or correlation meets the preset threshold conditions as the dominant oscillation mode. Extract each intrinsic mode component as the dominant oscillation feature sequence. The dynamic causal analysis module is used to construct a variable delay kernel density estimation transfer entropy model corresponding to the monitoring nodes with electrical connections based on the topological connection relationship, search for the optimal propagation delay between each monitoring node, and calculate the bidirectional transfer entropy between each monitoring node based on the optimal propagation delay. The directed causal graph construction module is used to determine the causal driving direction between each monitoring node based on the bidirectional transfer entropy, calculate the causal correlation coefficient as the edge weight, and construct a subsynchronous oscillation directed causal graph. An oscillation source localization module is used to determine the oscillation source node based on each monitoring node in the directed causal graph; The main propagation path extraction module is used to extract the dominant propagation path step by step based on the edge weight, starting from the oscillation source node. The result output module is used to output the identification results corresponding to the dominant oscillation feature sequence, the directed causal graph, the weighted in-degree sorting of each monitoring node, the oscillation source node, and the dominant propagation path.

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