A power system out-of-step oscillation center dynamic positioning method based on wide-area synchronous measurement data

Abstract

The application discloses a power system out-of-step oscillation center dynamic positioning method based on wide-area synchronous measurement data and belongs to the technical field of power system safety control. The method comprises the following steps: collecting continuous wide-area synchronous measurement data and preprocessing; extracting multiple dynamic features to calculate line dynamic separation degree; constructing a node and line measurement reliability model; building a space-time expansion graph containing space edges and time edges; determining the space edge weight based on the dynamic separation degree and the reliability, and self-adaptively adjusting the time edge weight according to the migration evidence; establishing a trajectory-level joint optimization model to solve the machine group division sequence; and extracting the oscillation center cut edge and migration trajectory and optimizing the solution section. The application realizes trajectory-level joint optimization, suppresses positioning jump, enhances the robustness of non-ideal measurement, is suitable for high-proportion new energy power grids, and improves the system safety defense capability.

Description

Technical Field

[0001] This invention belongs to the field of power system safety control, and specifically relates to a dynamic positioning method for the out-of-step oscillation center of a power system based on wide-area synchronous measurement data. Background Technology

[0002] With the large-scale integration of wind power, photovoltaics, flexible DC transmission, energy storage, and power electronic interface devices into the power system, significant changes occur in the system's equivalent inertia, damping characteristics, and dynamic processes of power angle between regions. After a severe disturbance, a continuously increasing relative power angle difference may form between different regions, further developing into a state of out-of-synchronization oscillation where the regional power grid loses synchronization. If the out-of-synchronization oscillation state is not identified in time, the oscillation center is located, and appropriate disconnection or emergency control measures are not taken, it may lead to protection malfunctions, interconnected tripping of tie lines, unplanned system disconnection, or even large-scale power outages.

[0003] Existing methods for identifying out-of-synchronization oscillations and oscillation center location mainly include local protection methods based on impedance trajectories, location methods based on voltage amplitude minima or voltage phase angle relationships, wide-area criteria based on frequency difference or phase angle difference, cluster partitioning methods based on energy functions or coherence analysis, and active disconnection section search methods based on graph theory, spectral clustering, cut-set search, or mixed-integer programming. These methods have certain application value in traditional interconnected power grids, but they still have shortcomings in scenarios with high proportions of renewable energy integration, rapid changes in operating modes, non-ideal wide-area measurements, and significant oscillation center migration.

[0004] First, traditional local out-of-synchronization protection methods mainly rely on the impedance trajectory, voltage-current relationship, or phase angle change of a single line or local measuring point, which is difficult to reflect the dynamic separation process between multiple generator groups across the entire network. When the oscillation center shifts with changes in operating mode, disturbance location, new energy output, or control strategy, relying solely on local criteria can easily lead to misjudgments, missed judgments, or shifts in the disconnection section.

[0005] Second, while existing wide-area measurement methods can utilize information such as node voltage phase angle, frequency, and line power provided by synchronous phasor measurement units, many methods still employ a single-moment or single-window independent judgment approach. This involves calculating the oscillation center position at each moment separately and then connecting the positioning results of adjacent moments in chronological order to form a trajectory. These methods fail to incorporate the physical continuity and reasonable migration constraints between adjacent time windows into the same optimization model. In the presence of measurement noise, communication delays, packet loss, abnormal data, or rapid fluctuations in local renewable energy sources, the positioning results are prone to non-physical jumps.

[0006] Third, existing graph theory, graph cut, maximum flow, or spectral clustering methods are mostly used for power grid partitioning, active disconnection section search, or generator homogeneity grouping, typically focusing on network partitioning or candidate section optimization at a specific control moment. While these methods can describe network topology and edge cutting costs, they usually do not model the continuous migration process of the oscillation center as a trajectory-level joint optimization problem across time windows, and they also lack coupled characterization of measurement reliability, migration evidence, and time continuity constraints.

[0007] Fourth, existing split-line auxiliary decision-making typically searches for split-line sections based on indicators such as power balance, minimum power cut-off, minimum load loss, or line importance after the single-moment oscillation center or generator group allocation result has been determined. This sequential process allows oscillation center location errors to be directly transmitted to the split-line decision. If the oscillation center is in a continuous migration process, the single-moment location result may lead to delayed, offset, or unstable selection of split-line sections.

[0008] Therefore, there is a need for a dynamic tracking method for out-of-step oscillation centers that can fully utilize continuous wide-area synchronous measurement data and simultaneously consider spatial dynamic separation relationships and temporal continuous migration constraints. This method would make oscillation center localization no longer a simple stitching of results from multiple independent moments, but rather a trajectory-level optimization problem that spans a time window. This would improve the accuracy, continuity, and anti-interference capabilities of oscillation center localization, migration trajectory tracking, and candidate section determination. Summary of the Invention

[0009] Based on the above shortcomings, this invention proposes a dynamic positioning method for the out-of-step oscillation center of a power system based on wide-area synchronous measurement data. The purpose is to overcome the problems in the prior art, such as the oscillation center positioning results being easily affected by local measurement anomalies, the continuous positioning trajectory being prone to unreasonable jumps, the lack of unified optimization constraints for oscillation center migration, and the reliance on single-moment positioning results for auxiliary decision-making of the break section.

[0010] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for dynamic location of the out-of-step oscillation center of a power system based on wide-area synchronous measurement data, comprising the following steps:

[0011] S1: Collect continuous wide-area synchronous measurement data of the power system: The data includes node voltage phasors, amplitude, phase angle, frequency, frequency change rate, PMU data quality indicators, line active / reactive power and communication delay;

[0012] S2: Construct a continuous sliding time window and perform preprocessing: Construct a continuous sliding time window and perform time synchronization correction, bad data removal, missing value imputation, and filtering preprocessing on the data within the window;

[0013] S3: Calculate the dynamic separation degree of the line: For any transmission line, extract five types of dynamic features from the wide-area measurement of the two ends of the line from the continuous time window: phase angle difference, frequency difference, frequency change rate difference, active power oscillation component, and dominant oscillation mode difference. After normalization, the dynamic separation degree is obtained by weighted fusion to quantify the strength of dynamic separation on both sides of the line, which is used to determine whether the line is close to the boundary of the oscillation center.

[0014] S4: Calculate the reliability of node and line measurements: Based on PMU data quality, noise level, communication delay, and data integrity, quantify the reliability of each node measurement; then synthesize the line reliability from the node reliability at both ends, which is used to subsequently suppress the interference of abnormal data, delay, and packet loss on the positioning results;

[0015] S5: Constructing a spatiotemporal extension graph: The original power grid topology is replicated on a continuous time window to construct an extension graph composed of spatiotemporal nodes, spatial edges, and temporal edges; spatial edges depict the line connection relationships within a single window, and temporal edges constrain the cluster affiliation continuity of the same node in adjacent windows, so as to uniformly represent the dynamic migration process of the oscillation center.

[0016] S6: Determine spatial edge weights, migration evidence, and temporal edge weights: Determine spatial edge weights based on dynamic separation degree, measurement reliability, and line removability; construct migration evidence based on the dynamic separation degree changes of adjacent windows and adaptively adjust temporal edge weights.

[0017] S7: Constructing a trajectory-level joint optimization model: Based on the spatial cut cost and time continuity cost as the basic objectives, generator coherence, power balance, and line safety constraints are introduced to construct a trajectory-level joint optimization model. By jointly optimizing the continuous window group of generators' ownership variables, the overall optimal solution for the oscillation center trajectory is achieved.

[0018] S8: Solving the Temporally Coupled Dynamic Graph Cut Model: For the trajectory-level joint optimization model, an appropriate algorithm is selected based on the complexity of the objective function to solve the model, outputting the optimal cluster partitioning sequence for a continuous window. Specifically, for the basic model solution: when the objective only contains spatial cut cost and temporal continuity cost, the spatial and temporal edges of the spatiotemporal extended graph are treated as undirected edges, and the minimum cut / maximum flow algorithm, α-extended graph cut algorithm, or equivalent binary labeling optimization algorithm are used to solve the optimization model, obtaining the continuous time window cluster partitioning sequence. For the enhanced model solution: when generator coherence, power balance, and line safety engineering constraints are introduced, Lagrange relaxation, two-stage candidate trajectory correction, and mixed integer programming methods are used; coherence / full terms are incorporated into edge weights, power balance terms are relaxed, or candidate trajectories of the basic model are first calculated and then constraints are corrected.

[0019] S9: Extract the set of oscillation center cut edges and migration trajectory: Based on the optimal cluster partitioning results, determine the set of oscillation center cut edges and the main oscillation center line window by window, generate a continuous migration trajectory and calculate the trajectory stability;

[0020] S10: Determining candidate splitting sections: in combination with oscillation center trajectories, stability degrees, power balance and safety constraints, stable and resectable candidate sections are screened, comprehensively sorted, and an optimal recommended splitting section is output.

[0021] Further, in step S3, the line dynamic separation degree has the expression:

[0022]

[0023] wherein, , , , , are non-negative weight coefficients and satisfy ; , , , , are respectively the normalized phase angle difference, frequency difference, frequency change rate difference characteristic, active power oscillation component characteristic and dominant oscillation mode difference.

[0024] Further, in step S4, the node measurement credibility has the expression:

[0025] wherein, is the PMU data quality flag or effective data proportion of node within window , with a value range of [0,1]; is measurement noise level or abnormal fluctuation intensity; is communication delay or time synchronization deviation; and are respectively noise normalization constant and delay normalization constant; is a data integrity coefficient used to reflect packet loss rate or missing proportion, the closer it is to 1, the more reliable the measurement of the node in the corresponding window is; the closer it is to 0, the lower the measurement credibility of the node is; the measurement credibility of line is synthesized from the credibility of the two end nodes, adopting the geometric mean or minimum value form:

[0026] or .

[0027] wherein represents the measurement credibility of node , Represents a node The reliability of the measurement.

[0028] Furthermore, in step S5, the spatiotemporal extension graph The expression is:

[0029] In the formula, Represents a set of spatiotemporal nodes. Represents the set of spatial edges. Represents the set of time edges;

[0030] set of spatiotemporal nodes The expression is:

[0031]

[0032] In the formula, Represents the original power grid node In the Spatiotemporal nodes within a time window; Indicates the number of windows participating in trajectory-level joint optimization; A set of nodes;

[0033] spatial edge set The expression is:

[0034]

[0035] In the formula, For the set of routes;

[0036] Spatial edges represent the actual line connection relationships of the power grid within the same time window, and are used to characterize whether nodes on both sides of the line in the current window should be assigned to different oscillator groups;

[0037] Time edge set The expression is:

[0038]

[0039] In the formula, Represents the original power grid node In the Spatiotemporal nodes within a time window;

[0040] The time edge represents the continuous relationship of cluster affiliation of the same grid node between adjacent time windows. Through the coupling of the spatial edge and the time edge, the original static topology is extended into a spatiotemporal graph that can describe the continuous migration process of the oscillation center.

[0041] Furthermore, in step S6, the spatial edge weights The expression is:

[0042]

[0043] In the formula, To prevent positive numbers from being divided by zero; Penalty weights for measuring credibility; The weight for the cutaway penalty of the line; Static penalty for line cutaway; Indicates the line In the Dynamic separation degree of each time window; Indicates the line In the The reliability of measurements within a time window;

[0044] To allow for reasonable migration of the oscillation center during real-time dynamic processes, while suppressing spurious jumps caused by noise or local anomalies, evidence of migration near nodes is constructed based on changes in the dynamic separation of lines in adjacent windows. The expression is:

[0045]

[0046] In the formula, Represents a node The set of adjacent nodes; The line weight is determined by line capacity, voltage level, topological importance, or measurement reliability. Indicates the line In the Dynamic separation degree of each time window;

[0047] Time edge The cost of cutting The expression is:

[0048]

[0049]

[0050] In the formula, As the basic weight for time continuity; Increase weights for low credibility; This is the sensitivity coefficient for migration evidence; Minimizes edge weight in time; Adjacent window nodes The joint credibility; This indicates evidence of migration near the node; Represents a node In the The reliability of measurements within a time window; Represents a node In the The reliability of measurements within a time window.

[0051] Furthermore, in step S7, the expression for the trajectory-level joint optimization model is:

[0052]

[0053]

[0054] In the formula, The spatial cutting cost is used to select candidate boundaries for the oscillation center within each time window; As a cost of time continuity, it is used to constrain the cluster affiliation changes of the same node in adjacent windows; This allows us to obtain the cluster partitioning sequence within a continuous time window; where a binary cluster affiliation variable is defined: In the formula, Represents a node In the This time window belongs to the first oscillator group; Represents a node In the This time window belongs to the second oscillator group; Represents a node In the Binary cluster attribution variable values ​​for each time window; Represents a node In the Binary cluster attribution variable values ​​for each time window; For spatial boundary weights; The cost of cutting off time;

[0055] In the enhanced form, the joint optimization objective further incorporates generator coherence, power balance, and line safety constraints:

[0056]

[0057] Among them, generator coherence cost The expression is:

[0058]

[0059] In the formula, and For generator node index; Indicates generator node In the Binary cluster attribution variables for each time window; Indicates generator node In the Binary cluster attribution variables for each time window;

[0060] Power balancing costs The expression is:

[0061]

[0062] Line security costs The expression is:

[0063]

[0064] In the formula, For the set of generator nodes; Indicates generator With generator In the window Internal coherence; Indicates the net injected power at the node; Represents a node In the Active power generation within a time window; Represents a node In the The active power of the load in each window; This indicates the removal of the security check penalty; , and These are the corresponding weights; and This is the generator node index.

[0065] Furthermore, in step S9, the expression for the set of oscillation center cut edges is:

[0066] In the formula, Represents a node In the The optimal cluster affiliation variable value within a time window; Represents a node In the The optimal cluster affiliation variable value within a time window; Indicates the first The set of oscillation center cut edges within a time window, when The expression for selecting the main oscillation center line, which includes multiple lines and is considered as a whole as the boundary region of the oscillation center, or based on dynamic separation, spatial edge weights, line capacity, or measurement point reliability, is as follows:

[0067]

[0068] In the formula, Indicates the first The main oscillation center line within a time window;

[0069] Arranging the cut edge set in chronological order within a continuous time window, the expression for the oscillation center migration trajectory is obtained as follows:

[0070]

[0071] The expression for the migration speed or migration intensity of the oscillation center is:

[0072]

[0073] In the formula, This represents the graph distance, center point distance, shortest path distance, or overlap rate distance between adjacent window oscillation center cut edge sets; This represents the time interval between the end times of two adjacent windows;

[0074] To evaluate trajectory stability, we define the first... Candidate cut edges near the window trajectory stability The expression is:

[0075]

[0076] In the formula, The number of lookback windows used for statistical stability; For indicator functions, when the line Appeared in the The set of cut edges for each window In the middle, then If it does not appear, then .

[0077] Furthermore, in step S10, the candidate cross-section The expression for the comprehensive solution cost is:

[0078]

[0079] In the formula, , , and These are the normalized cut-off power, power imbalance, line safety penalty, and trajectory consistency cost, respectively. These are non-negative weighting coefficients;

[0080] The expression for selecting the section with the minimum comprehensive solution cost from the candidate section set as the preferred solution section is:

[0081]

[0082] In the formula, Represents the set of candidate solution sections; Indicates a candidate solution section; Indicates candidate solution cross section The overall cost of decoupling.

[0083] This invention also provides a dynamic positioning system for the out-of-synchronous oscillation center of a power system based on wide-area synchronous measurement data, used to implement the dynamic positioning method for the out-of-synchronous oscillation center of a power system based on wide-area synchronous measurement data as described above, comprising:

[0084] Data acquisition module: used to acquire continuous wide-area synchronous measurement data of the power system;

[0085] Data preprocessing module: used to construct a sliding time window and preprocess the data;

[0086] Feature calculation module: used to calculate the dynamic separation degree of the line and the reliability of node and line measurements;

[0087] Spatiotemporal graph construction module: used to construct a spatiotemporal extended graph containing spatial edges and temporal edges;

[0088] Edge weight determination module: used to calculate spatial edge weights and adaptive temporal edge weights;

[0089] Optimization and Solving Module: Used to construct and solve the trajectory-level joint optimization model, outputting the cluster partitioning sequence;

[0090] Trajectory extraction module: used to generate the migration trajectory of the oscillation center and calculate the trajectory stability;

[0091] The segmentation decision module is used to determine and sort the candidate segments for segmentation, and output the preferred recommended segments.

[0092] The present invention also provides an electronic device, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: when the processor executes the program, it implements a dynamic positioning method for the out-of-step oscillation center of a power system based on wide-area synchronous measurement data as described above.

[0093] The beneficial effects and advantages of this invention are as follows:

[0094] First, this invention transforms the oscillation center location from a single-moment independent judgment into a trajectory-level joint optimization problem spanning continuous time windows. By constructing a spatiotemporal extension graph containing spatial and temporal edges, trajectory jumps caused by simply splicing together time-by-moment location results can be avoided.

[0095] Second, this invention constructs spatial edge weights through dynamic separation degree, and uses phase angle difference, frequency difference, frequency change rate difference, line active power oscillation component and dominant mode difference together to characterize the dynamic separation degree on both sides of the line, which has a stronger information fusion capability compared with single physical quantity criteria.

[0096] Third, this invention incorporates PMU quality indicators, noise levels, communication delays, and data integrity into the measurement reliability model, and uses reliability to correct spatial and temporal weights, thereby reducing the impact of abnormal measurement points, delayed data, and missing data on the oscillation center localization results.

[0097] Fourth, this invention adaptively adjusts the temporal edge weights through migration evidence. When there is no obvious migration evidence in adjacent windows, the temporal continuity constraint is strong, which can suppress spurious jumps; when the dynamic separation near a node changes continuously, the temporal edge weights are reduced, allowing the oscillation center to migrate with the real dynamic process.

[0098] Fifth, this invention can integrate generator coherence, power balance and line safety constraints into a unified optimization or post-processing correction process, so that the oscillation center tracking results not only meet the dynamic measurement characteristics, but also have good physical consistency and engineering feasibility.

[0099] Sixth, the present invention outputs not only the oscillation center position at a certain moment, but also the oscillation center cutting sequence, migration trajectory, migration speed, trajectory stability and separation candidate section ranking results within a continuous time window, which can provide more complete information for wide-area protection, online stability control and out-of-step separation tuning.

[0100] In summary, this invention, through wide-area synchronous measurement and multi-feature fusion, can quickly and accurately locate the oscillation center in the early stages of disturbances, avoiding misjudgments and omissions in traditional local protection, thus gaining valuable time for emergency control; effectively reducing the risk of cascading trips and unplanned disconnections of tie lines; enhancing the anti-interference and stability control capabilities of the power system under non-ideal measurement and variable operating modes; ensuring timely, reliable, and controllable disconnection decisions, preventing large-scale regional and cross-regional power outages from the source, and significantly improving the overall security and defense level of the power grid. Attached Figure Description

[0101] Figure 1 This is a flowchart of the overall process of the dynamic tracking method for the out-of-step oscillation center of a power system based on time-coupled dynamic graph cutting in this invention.

[0102] Figure 2 This is a schematic diagram of the continuous sliding time window construction in this invention;

[0103] Figure 3 This is a schematic diagram of the spatiotemporal extension graph structure in this invention, which includes spatial edges within the same time window and temporal edges between adjacent time windows;

[0104] Figure 4 This is a schematic diagram illustrating the relationship between migration evidence and adaptive temporal edge weights in this invention;

[0105] Figure 5 This is a schematic diagram of the trajectory-level joint optimization model in this invention;

[0106] Figure 6 This diagram illustrates the comparison of average edge distances between tracking results from different methods in a mixed non-ideal measurement scenario with IEEE 39 nodes.

[0107] Figure 7 A schematic diagram comparing the average migration delay of different tracking methods in a mixed non-ideal measurement scenario with 39 nodes in IEEE;

[0108] Figure 8 This diagram illustrates the relative improvement of the patented method compared to baseline_simple across different scenarios and metrics. Detailed Implementation

[0109] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. It should be understood that the following embodiments are only used to explain the present invention and are not intended to limit the scope of protection of the present invention.

[0110] Example 1

[0111] This embodiment provides a dynamic tracking method for the out-of-step oscillation center in power systems based on time-coupled dynamic graph cut. This method can be applied to power systems containing synchronous phasor measurement units, wide-area measurement systems, dispatch automation systems, or online safety and stability control systems. The power system can be a transmission network, a regional interconnection system, a high-proportion renewable energy access system, a power system with flexible DC or energy storage access, or a complex interconnected system containing multiple oscillator groups and multiple regional tie lines. In this embodiment, the following conventions are used uniformly: the original power grid topology is... ,in, A set of nodes; For a set of routes; routes are uniformly represented as ;No. Each sliding time window is ;line In the window The dynamic separation degree within is ;node The measurement reliability is ,line The measurement reliability is The cost of spatial edge cutting is Evidence of migration near the node is The time edge cut cost is The node cluster affiliation variable is: The cluster partitioning result obtained by trajectory-level joint optimization is as follows: ;No. The set of oscillation center cut edges for each window is The stability of the line trajectory is Candidate solution sections are The overall process of this embodiment is as follows: Figure 1 As shown, the specific steps include the following:

[0112] Step S1: Collect continuous wide-area synchronous measurement data:

[0113] Continuous synchronous measurement data of key nodes and key lines in the power system are acquired through wide-area synchronous measurement systems, synchronous phasor measurement units, or dispatch automation systems. The wide-area measurement data includes node voltage phasors and node voltage amplitudes directly measured or estimated by synchronous phasor measurement units. Node voltage phase angle Node frequency Rate of change of frequency PMU Data Quality Markers And timestamps; also includes the line active power calculated from the voltage and current phasors at both ends of the line or uploaded by the dispatch automation system or SCADA / RTU. and line reactive power The communication delay is estimated from the measurement timestamp, the data concentrator or master station reception time, and communication link status information. .

[0114] The key nodes include generator outlet busbars, busbars on both sides of regional tie lines, new energy centralized access busbars, important load busbars, important substation busbars, and backbone network nodes; the key lines include regional tie lines, important transmission channels, candidate disconnection lines, and lines where oscillation centers may migrate.

[0115] Step S2: Construct a continuous sliding time window and perform preprocessing:

[0116] Construct a continuous sliding time window based on the sampling time of the synchronous measurement data:

[0117]

[0118] In the formula, This represents the k-th time window; This indicates the end time of the k-th window; Indicates the window length; This represents the number of windows participating in trajectory-level joint optimization; the sliding step size between adjacent windows is... , It is equal to one or more PMU sampling periods. The construction process of the continuous sliding time window is as follows: Figure 2 As shown.

[0119] For each time window, the data undergoes time synchronization correction, bad data removal, missing value imputation, low-pass or band-pass filtering, trend term extraction, and measurement quality indicator alignment. For data with significant communication delays or abnormal timestamps, synchronization compensation is performed before calculating dynamic separation. For data that cannot be reliably compensated, its measurement reliability is reduced.

[0120] Step S3: Calculate the dynamic separation degree of the line:

[0121] For any transmission line in the power grid In the k-th time window The dynamic difference characteristics of the nodes at both ends of the line are extracted, including phase angle difference characteristics, frequency difference characteristics, frequency change rate difference characteristics, active power oscillation component characteristics, and dominant oscillation mode difference characteristics. The formula is as follows:

[0122]

[0123]

[0124]

[0125] In the formula, This indicates the phase angle difference characteristics between the two ends of the line within the window; Indicates frequency difference characteristics; Represents the difference in frequency change rate; rms represents the root mean square operation; Represents a node exist Phase angle at any given moment; Represents a node exist Phase angle at any given moment; Represents a node exist Frequency of time; Represents a node exist Frequency of time; Represents a node exist Rate of change of frequency at any given moment; Represents a node exist The rate of change of frequency at any given moment.

[0126] The active power oscillation component of the line is obtained by analyzing the active power of the line. Obtained by removing low-frequency trends or moving averages:

[0127]

[0128]

[0129] In the formula, For window The low-frequency trend term of the active power of the internal line is obtained by moving average, low-pass filtering, wavelet decomposition or empirical mode decomposition; This indicates the active power oscillation component of the line; This indicates the characteristics of the active power oscillation component.

[0130] Dominant oscillation mode differences Extracted from the node frequency matrix or phase angle matrix. Taking the node frequency matrix as an example, let... For window After the frequency sequences of each node are mean-reduced to form a matrix, the covariance matrix is ​​decomposed into eigenvalues, and the eigenvector corresponding to the largest eigenvalue is obtained. As the dominant oscillation mode vector, the mode difference between the two ends of the line is:

[0131]

[0132] In the formula, and They are nodes and nodes In the dominant oscillation mode vector, if the nodes at both ends of the line belong to the same oscillator group, their mode components are similar; if the line crosses two relative oscillator groups, their mode components differ significantly.

[0133] The above features are robustly normalized, and the line dynamic separation degree is... Defined as:

[0134]

[0135] In the formula, , , , , The weight coefficients are non-negative and satisfy the following conditions: ;; , , , , These are the characteristics of the normalized phase angle difference, frequency difference, frequency change rate difference, active power oscillation component characteristics, and dominant oscillation mode differences, respectively. The larger the value, the stronger the dynamic separation between the nodes at both ends of the line within the window, and the more likely the line is to be located at or near the boundary of the oscillation center.

[0136] Step S4: Calculate the reliability of node and line measurements:

[0137] To avoid abnormal PMU data, communication delays, noise, or packet loss directly dominating oscillation center localization, this method introduces node measurement reliability. In the window Internal measurement reliability The defining formula is:

[0138]

[0139] In the formula, For nodes In the window The PMU data quality flag or effective data ratio within the range of [0,1]; To measure noise levels or the intensity of abnormal fluctuations; This could be due to communication delay or time synchronization deviation. and These are the noise and delay normalization constants, respectively; This is the data integrity coefficient, used to reflect the packet loss rate or the proportion of missing data. The closer the value is to 1, the more reliable the measurement of that node within the corresponding window is; The closer it is to 0, the lower the reliability of the measurement at that node.

[0140] line The measurement confidence level can be synthesized from the confidence levels of the two endpoints, using the geometric mean or minimum value form:

[0141] or

[0142] In the formula, Represents a node The reliability of the measurement Represents a node The reliability of the measurement.

[0143] When there is obvious data anomaly, delay, or missing data at any end of the line measurement point The reduction suppresses the dynamic separation evidence corresponding to the line in the subsequent spatial boundary weight construction.

[0144] Step S5: Construct the spacetime extension graph:

[0145] Assume the original topology of the power system is as follows:

[0146]

[0147] Represents the set of power grid nodes. This method represents a set of transmission lines, and then continuously updates the original power grid topology. Copying over a time window to construct a spatiotemporal expansion graph:

[0148]

[0149] In the formula, Represents a set of spatiotemporal nodes. Represents the set of spatial edges. Represents the time edge set.

[0150] set of spatiotemporal nodes Defined as:

[0151]

[0152] In the formula, Represents the original power grid node In the Spatiotemporal nodes within a time window; Indicates the number of windows participating in trajectory-level joint optimization; It is a set of nodes.

[0153] spatial edge set Defined as:

[0154]

[0155] In the formula, This is a set of routes.

[0156] Spatial edges represent the actual line connection relationships of the power grid within the same time window, and are used to characterize whether the nodes on both sides of the line in the current window should be assigned to different oscillator groups.

[0157] Time edge set Defined as:

[0158]

[0159] The time edge represents the continuous cluster affiliation of the same grid node between adjacent time windows. Through the coupling of spatial and temporal edges, the original static topology is extended into a spatiotemporal graph capable of describing the continuous migration process of the oscillation center. The structure of the spatiotemporal extended graph is as follows: Figure 3 As shown.

[0160] Step S6: Determine spatial edge weights, migration evidence, and temporal edge weights:

[0161] For spatial edges This method defines the space cut cost. The cost should satisfy the following: the greater the dynamic separation between the two ends of the line, the smaller the cost of being divided into the boundary of the oscillation center; the lower the reliability of the line measurement, the greater the cost of being abnormally divided; the less suitable the line is as a break-off boundary, the greater its division cost.

[0162] Spatial boundary weight Defined as:

[0163]

[0164] In the formula, To prevent positive numbers from being divided by zero, To measure the credibility penalty weight, As the cutaway penalty weight, Static penalty for line cutaway. This refers to the dynamic separation degree of the line. For important transmission channels, lines supplying important loads, lines that cannot be disconnected, or lines that are not permitted to serve as oscillation center boundaries, Take the larger value; for lines that are allowed as candidate solution sections, Take the smaller value. For example, for lines that allow for separation and are suitable as candidate separation sections, take... For general transmission lines, take For important transmission channels, important load power supply lines, or lines that are not suitable for priority disconnection, take... For lines that cannot be disconnected, lines that are prohibited from being disconnected according to dispatching procedures, or critical supply lines, take... .

[0165] To allow for reasonable migration of the oscillation center during real-time dynamic processes, while suppressing spurious jumps caused by noise or local anomalies, this method constructs evidence of migration near nodes based on changes in the dynamic separation of lines in adjacent windows. The formula is as follows:

[0166]

[0167] In the formula, Represents a node The set of adjacent nodes, The line weight is determined by line capacity, voltage level, topological importance, or measurement reliability. The larger the value, the more likely it is to be a node. The more pronounced the change in dynamic separation between adjacent windows, the more likely the boundary of the oscillation center is to migrate in the vicinity of that region.

[0168] Time edge The cost of cutting Defined as:

[0169]

[0170]

[0171] In the formula, As the basic weight for time continuity; Increase weights for low credibility; This is the sensitivity coefficient for migration evidence; Minimizes edge weight in time; Adjacent window nodes The joint credibility of the equation. This equation has the following meaning: when there is migration evidence near a node... When the time edge weight is small and the measurement reliability is high, it is larger to suppress unreasonable cluster affiliation jumps; when When the time margin is large, the time margin decreases accordingly, allowing the boundary of the oscillation center to shift with the actual dynamic process; when the measurement reliability is low, i.e. At that time, through Enhanced temporal continuity constraints prevent spurious transitions caused by low-quality measurements. The relationship between transfer evidence and adaptive temporal edge weights is as follows: Figure 4 As shown.

[0172] Step S7: Construct a trajectory-level joint optimization model:

[0173] Define the binary cluster affiliation variable:

[0174]

[0175] In the formula, Represents a node In the This time window belongs to the first oscillator group; Represents a node In the This time window belongs to the second oscillator group.

[0176] The basic trajectory-level optimization objective is:

[0177]

[0178]

[0179]

[0180] In the formula, The spatial cutting cost is used to select candidate boundaries for the oscillation center within each time window; As a cost of time continuity, it is used to constrain the cluster affiliation changes of the same node in adjacent windows; For spatial boundary weights; The cost of cutting off time; Represents a node In the Binary cluster attribution variable values ​​for each time window; Represents a node In the Binary cluster attribution variable values ​​for each time window; Represents a node In the The binary cluster attribution variable values ​​for each time window. Unlike time-by-time independent localization, this method directly solves the problem on the entire spatiotemporal extension map. This allows us to obtain the cluster partitioning sequence within a continuous time window. The trajectory-level joint optimization model is as follows: Figure 5 As shown.

[0181] In the enhanced form, the joint optimization objective can be further incorporated with generator coherence, power balance, and line safety constraints:

[0182]

[0183] In the formula, the generator coherence cost is:

[0184]

[0185] The cost of power balancing is:

[0186]

[0187] The cost to line safety is:

[0188]

[0189] In the formula, For the set of generator nodes; Indicates generator With generator In the window Internal coherence; Indicates the net injected power at the node; Represents a node In the Active power generation within a time window; Represents a node In the The active power of the load in each window; This indicates the removal of the security check penalty; , and These are the corresponding weights. For line safety terms that can be incorporated into the edge weights, they can be directly used as part of the spatial edge weights; for power balance terms that are difficult to directly satisfy the graph cut submodule form, Lagrange relaxation, two-stage candidate trajectory correction, rolling optimization, or mixed integer programming can be used to solve them.

[0190] Step S8: Solve the temporally coupled dynamic graph cut model:

[0191] When the objective function takes the basic form In this case, both spatial and temporal edges can be treated as undirected edges in the spacetime graph, and the edge weights can be used to define the edges. and Construct the graph cut cost. Solve using the minimum cut / maximum flow algorithm, the α-extended graph cut algorithm, or the equivalent binary labeling optimization algorithm to obtain the globally optimal or near-optimal cluster partitioning sequence.

[0192] When the objective function further includes engineering constraints such as power balance, line safety, and generator coherence, it can be solved using any of the following methods: First, convert the generator coherence term into additional edge weights between generator nodes; second, incorporate the line safety term into the spatial edge weights; third, use Lagrange relaxation to form the node potential function or cut edge correction term for the power balance term; fourth, first solve the basic spatiotemporal graph cut model to obtain candidate trajectories, and then perform power balance and line safety corrections in the neighborhood of the candidate trajectories; fifth, use mixed integer programming to solve the complete model in offline verification or small-to-medium-scale systems.

[0193] In online applications, a scrolling time-domain optimization method can be used. Whenever a new window appears... Upon arrival, select the nearest [location / location]. Each window constructs a local spatiotemporal expansion map, and uses the results of the previous round of cluster division as initial values ​​or boundary conditions to update the oscillation center trajectory and the candidate cross-section for disengagement, thereby taking into account both real-time performance and trajectory stability.

[0194] Step S9: Extract the set of oscillation center cut edges and migration trajectory:

[0195] Find the optimal cluster partitioning sequence Then, for each time window The lines whose two-end nodes are assigned to different clusters are extracted as the set of cut edges for the oscillation center:

[0196]

[0197] In the formula, Represents a node In the The optimal cluster assignment result within a time window; Represents a node In the The optimal cluster assignment result within a time window; Indicates the first The set of oscillation center cut edges within a time window, if It includes multiple lines, which can be regarded as a whole as the boundary region of the oscillation center. Alternatively, the main oscillation center line can be selected based on dynamic separation, spatial boundary weights, line capacity, or measurement point reliability.

[0198]

[0199] In the formula, Indicates the first The main oscillation center line within a time window;

[0200] Arrange the cut edge set in continuous time window in chronological order to obtain the migration trajectory of the oscillation center:

[0201]

[0202] The migration velocity or migration intensity of the oscillation center can be expressed as:

[0203]

[0204] In the formula, This represents the graph distance, center point distance, shortest path distance, or overlap rate distance between adjacent window oscillation center cut edge sets; This represents the time interval between the end times of two adjacent windows.

[0205] To evaluate trajectory stability, we define the first... Candidate cut edges near the window trajectory stability The expression is:

[0206]

[0207] In the formula, The number of lookback windows used for statistical stability; For indicator functions, if the line Appeared in the The set of cut edges for each window In the middle, then If it does not appear, then . The larger the value, the higher the line value. The stronger the persistence of the boundary as the center of oscillation.

[0208] Step S10: Determine the candidate cross-section for disassembly:

[0209] Based on the oscillation center migration trajectory obtained in step S9 Set of oscillation centers and cut edges within each time window Cluster partitioning result Z*, trajectory stability Based on power balance constraints, line safety constraints, and control time limits, candidate sections for out-of-step disconnection are determined, and the candidate sections are comprehensively ranked. Cut edges or combinations of cut edges that appear stably within multiple consecutive windows and meet the cut-off constraints are determined as priority candidate sections.

[0210] First, according to recent The set of oscillation center cut edges within a time window is used to construct the current window. The initial candidate route set is as follows:

[0211]

[0212] For candidate routes Stable candidate edges are selected using trajectory stability, and the cut-off criterion for the line is defined as follows:

[0213]

[0214] Right now Indicates the line Allowed as a disconnect line, Indicates the line Not allowed as a solution route. Therefore, the set of stable candidate routes is:

[0215]

[0216] In the formula, This is the trajectory stability threshold.

[0217] Based on the cluster partitioning results of the current window, the node set is divided into:

[0218]

[0219]

[0220] In the formula, Indicates the first The first set of nodes of the oscillating cluster determined by the optimal cluster partitioning result within a time window; Indicates the first The set of nodes of the second oscillating cluster, determined by the optimal cluster partitioning results within a time window.

[0221] The connection lines between the two aircraft groups are as follows:

[0222]

[0223] Based on this, a set of candidate solution sections is constructed:

[0224]

[0225] In the formula, Indicates a candidate solution section. Indicates the candidate section to be removed Afterward, the power grid can form a connected subsystem that is basically consistent with the oscillating machine group, without generating unnecessary small islands.

[0226] For any candidate solution section Calculate its resection power:

[0227]

[0228] In the formula, Indicates the first Lines in a time window The active power.

[0229] Cut-off section Later, several isolated islands were formed. Its power imbalance is defined as:

[0230]

[0231] in: Represents a node In the window Net active power injection within, This indicates the total number of isolated islands.

[0232]

[0233] In the formula, Represents a node Power generation capacity, Represents a node The load power.

[0234] The line safety penalty for candidate sections is defined as follows:

[0235]

[0236] In the formula, Indicates the line Safety or non-removable penalty items.

[0237] The consistency cost between the candidate cross-section and the migration trajectory of the oscillation center is defined as:

[0238]

[0239] If the lines in the candidate cross-sections consistently appear in the recent oscillation center trajectory, then Smaller; conversely, larger.

[0240] After normalizing the above indicators, candidate cross-sections The comprehensive solution cost is defined as:

[0241]

[0242] In the formula, , , and These are the normalized cut-off power, power imbalance, line safety penalty, and trajectory consistency cost, respectively. These are non-negative weighting coefficients.

[0243] Finally, the section with the lowest overall solution cost is selected from the candidate section set as the preferred solution section:

[0244]

[0245] In the formula, Represents the set of candidate solution sections; Represents any candidate solution section; Indicates candidate solution cross section The overall cost of decoupling.

[0246] In summary, this embodiment constructs a spatiotemporal extension graph containing both spatial and temporal edges, transforming the grouping of generators and the extraction of oscillation centers within a continuous time window into a trajectory-level joint optimization problem. Spatial edge weights are jointly determined by line dynamic separation degree and measurement reliability. Temporal edge weights are adaptively adjusted using oscillation center migration evidence. Generator coherence, power balance, and line safety constraints are incorporated as optional constraints or post-processing correction terms into the disengagement auxiliary decision-making process, thereby outputting a continuous, stable, and engineering-executable oscillation center migration trajectory and candidate disengagement sections.

[0247] Example 2

[0248] Offline verification:

[0249] To verify the effectiveness of the method of this invention under non-ideal wide-area measurement conditions, chain network synthesis examples and IEEE 39-bus topology-level synthesis examples can be constructed for testing. Test scenarios include normal measurement scenarios, noise scenarios, packet loss scenarios, communication delay scenarios, bad data spike scenarios, and mixed comprehensive non-ideal measurement scenarios containing noise, packet loss, delay, and bad data spikes.

[0250] In the non-ideal measurement scenario of mixed synthesis in chain networks, the traditional time-by-time localization method is denoted as `baseline_simple`, the method that only introduces measurement reliability but does not perform temporal coupling optimization is denoted as `baseline_rho`, and the complete method of this invention is denoted as `patent`. Test results show that `baseline_simple` has a Top-1 accuracy of 0.5517 and a spurious jump rate of 0.6390; `baseline_rho` has a Top-1 accuracy of 0.6217 and a spurious jump rate of 0.5661; the method of this invention improves the Top-1 accuracy to 0.9517, achieves a tolerance-1 accuracy of 1.0000, reduces the average edge distance to 0, and lowers the spurious jump rate to 0.0458. These results demonstrate that under non-ideal measurement conditions with superimposed noise, packet loss, latency, and bad data spikes, this invention can significantly suppress spurious oscillation center jumps that are prone to occur in time-by-time localization methods through spatiotemporal expansion graphs and temporal continuity constraints.

[0251] In the bad data spike scenario of the chain network spike, the false jump rate of baseline_simple is 0.6085, and the Top-1 accuracy is 0.5750. baseline_rho, by suppressing the impact of some bad data through measurement credibility, improves the Top-1 accuracy to 0.9500 and reduces the false jump rate to 0.0898. The complete method of this invention further utilizes joint optimization of temporal edge constraints and trajectory level, achieving a Top-1 accuracy of 0.9750, a tolerance 1 accuracy of 1.0000, a mean edge distance of 0, and a false jump rate of 0.0441. These results demonstrate that combining measurement credibility with temporal continuity constraints can effectively improve the robustness of the oscillation center trajectory to bad data spikes.

[0252] In the IEEE 39-bus topology-level mixed synthesis non-ideal measurement scenario, due to the existence of a ring network structure and multiple adjacent candidate connection edges, the single-edge complete hit rate is not suitable as the sole evaluation metric. It is more appropriate to comprehensively observe tolerance 1 accuracy, average edge distance, spurious jump rate, and migration delay. The comparison results are as follows: Figure 6 and Figure 7 As shown, Figure 6This paper presents a comparison of the average edge distances of different methods in a mixed non-ideal measurement scenario with 39 nodes in the IEEE network. A smaller average edge distance indicates that the tracked oscillation center is closer to the reference center. It can be seen that the average edge distances of `baseline_simple` and `baseline_rho` are 2.205 and 2.227, respectively, indicating that relying solely on time-series localization or introducing measurement confidence alone cannot effectively improve localization errors in complex topologies. In contrast, `patent_no_rho`, `patent_fixed_tau`, and `patent_full` all reduce the average edge distance, with `patent_full` having the lowest value of 1.792. This result demonstrates that the method of this invention, by introducing temporal coupling, measurement confidence, and adaptive time edge weights, can obtain tracking results closer to the true oscillation center in complex ring network topologies. Figure 7 The average response delays of different methods during the migration of the oscillation center are presented. A smaller average migration delay indicates that the method can track changes in the true oscillation center more promptly. The average migration delays for `baseline_simple` and `baseline_rho` are both 7.700, indicating that simply solving time-by-time or adding only measurement confidence has limited improvement on the migration response speed. The migration delay for `patent_fixed_tau` reaches 8.300, indicating that while fixed-time edge weights may enhance trajectory smoothness, they can easily lead to over-smoothing, slowing down the method's response to the true migration. The full method, `patent_full`, has the lowest average migration delay at 6.600, indicating that adaptive time edge weights can suppress spurious jumps while avoiding excessive constraints on the true migration, thereby improving the timeliness of dynamic tracking.

[0253] Furthermore, ablation experiments can verify the function of each component of this invention. Introducing measurement confidence alone can improve localization results in some bad data scenarios, but because it still uses a time-by-time independent solution method, it cannot fundamentally solve the trajectory-level spurious transition problem. While fixed-time edge weights can reduce the spurious transition rate, they may lead to excessive trajectory smoothing, causing significant migration delays when the oscillation center actually migrates. This invention adaptively adjusts the time edge cut cost through migration evidence, achieving a balance between suppressing spurious transitions and tracking true migration, thereby improving the accuracy, continuity, and robustness of dynamic tracking of out-of-step oscillation centers under non-ideal wide-area measurement conditions. The relative improvement of the method of this invention compared to baseline_simple in different scenarios and metrics is as follows: Figure 8As shown, in the mixed scenario of chained networks, Top-1 accuracy is improved by 72.5%, and the false jump rate is reduced by 92.8%; in the spike scenario of chained networks, the false jump rate is also reduced by 92.8%, indicating that the method has significant robustness advantages under non-ideal measurement and bad data spike conditions. In the mixed scenario of complex topology of IEEE 39 nodes, the average edge distance is reduced by 18.7%, the false jump rate is reduced by 46.9%, and the migration delay is reduced by 14.3%. This shows that under complex topology, the advantages of the method of the present invention are mainly reflected in more stable trajectories, closer positioning to the reference center, and more timely migration response, rather than just an improvement in the perfect hit rate at a single moment. Overall, this figure illustrates the effectiveness of the method of the present invention in terms of accuracy, stability, and dynamic response capability from the perspective of comprehensive improvement.

[0254] As can be seen from the above embodiments, this invention does not perform post-processing of multiple single-moment oscillation center location results, but rather simultaneously optimizes spatial edge cutting and temporal continuity constraints within a unified spatiotemporal extension graph. Therefore, this invention can output cluster partitioning results within a continuous time window. Oscillation center cut edge sequence Migration trajectory trajectory stability The candidate section ranking results for resolving the oscillation are applicable to dynamic tracking and resolving auxiliary decision-making of out-of-step oscillation centers under conditions of high proportion of new energy access, rapid changes in operating mode, and non-ideal wide-area measurement.

Claims

1. A method for dynamic localization of the out-of-synchronous oscillation center in a power system based on wide-area synchronous measurement data, characterized in that, Includes the following steps: S1: Collect continuous wide-area synchronous measurement data of the power system, including node voltage phasors, amplitude, phase angle, frequency, frequency change rate, PMU data quality indicators, line active / reactive power and communication delay; S2: Construct a continuous sliding time window and perform preprocessing: Construct a continuous sliding time window and perform time synchronization correction, bad data removal, missing value imputation, and filtering preprocessing on the data within the window; S3: Calculate the dynamic separation degree of the line: For any transmission line, extract five types of dynamic features from the wide-area measurement of the two ends of the line from the continuous time window: phase angle difference, frequency difference, frequency change rate difference, active power oscillation component, and dominant oscillation mode difference. After normalization, the dynamic separation degree is obtained by weighted fusion to quantify the strength of dynamic separation on both sides of the line, which is used to determine whether the line is close to the boundary of the oscillation center. S4: Calculate the reliability of node and line measurements: Based on PMU data quality, noise level, communication delay, and data integrity, quantify the reliability of each node measurement; then synthesize the line reliability from the node reliability at both ends, which is used to subsequently suppress the interference of abnormal data, delay, and packet loss on the positioning results; S5: Constructing a spatiotemporal extension graph: The original power grid topology is replicated on a continuous time window to construct an extension graph composed of spatiotemporal nodes, spatial edges, and temporal edges; spatial edges depict the line connection relationships within a single window, and temporal edges constrain the cluster affiliation continuity of the same node in adjacent windows, so as to uniformly represent the dynamic migration process of the oscillation center. S6: Determine spatial edge weights, migration evidence, and temporal edge weights: Determine spatial edge weights based on dynamic separation degree, measurement reliability, and line removability; construct migration evidence based on the dynamic separation degree changes of adjacent windows and adaptively adjust temporal edge weights. S7: Constructing a trajectory-level joint optimization model: Based on the spatial cut cost and time continuity cost as the basic objectives, generator coherence, power balance, and line safety constraints are introduced to construct a trajectory-level joint optimization model. By jointly optimizing the continuous window group of generators' ownership variables, the overall optimal solution for the oscillation center trajectory is achieved. S8: Solving the Temporally Coupled Dynamic Graph Cut Model: For the trajectory-level joint optimization model, an appropriate algorithm is selected based on the complexity of the objective function to solve the model, outputting the optimal cluster partitioning sequence for a continuous window. Specifically, for the basic model solution: when the objective only contains spatial cut cost and temporal continuity cost, the spatial and temporal edges of the spatiotemporal extended graph are treated as undirected edges, and the minimum cut / maximum flow algorithm, α-extended graph cut algorithm, or equivalent binary labeling optimization algorithm are used to solve the optimization model, obtaining the continuous time window cluster partitioning sequence. For the enhanced model solution: when generator coherence, power balance, and line safety engineering constraints are introduced, Lagrange relaxation, two-stage candidate trajectory correction, and mixed integer programming methods are used; coherence / full terms are incorporated into edge weights, power balance terms are relaxed, or candidate trajectories of the basic model are first calculated and then constraints are corrected. S9: Extract the set of oscillation center cut edges and migration trajectory: Based on the optimal cluster partitioning results, determine the set of oscillation center cut edges and the main oscillation center line window by window, generate a continuous migration trajectory and calculate the trajectory stability; S10: Determine candidate sections for disengagement: Combining the oscillation center trajectory, stability, power balance and safety constraints, screen stable and removable candidate sections and sort them comprehensively, outputting the optimal recommended disengagement section.

2. The method for dynamic localization of the out-of-synchronization oscillation center of a power system based on wide-area synchronous measurement data according to claim 1, characterized in that, In step S3, the line dynamic separation degree The calculation formula is: In the formula, , , , , The weight coefficients are non-negative and satisfy the following conditions: ; , , , , These are the characteristics of the normalized phase angle difference, frequency difference, frequency change rate difference, active power oscillation component characteristics, and dominant oscillation mode differences, respectively.

3. The method for dynamic localization of the out-of-synchronous oscillation center of a power system based on wide-area synchronous measurement data according to claim 2, characterized in that, In step S4, the node measurement reliability is... The calculation formula is: In the formula, For nodes In the window The PMU data quality flag or effective data ratio within the range of [0,1]; To measure noise levels or the intensity of abnormal fluctuations; This could be due to communication delay or time synchronization deviation. and These are the noise and delay normalization constants, respectively; This is the data integrity coefficient, used to reflect the packet loss rate or the proportion of missing data. line The measurement confidence level is synthesized from the confidence levels of the two endpoints, using either the geometric mean or the minimum value: or . In the formula, Represents a node The reliability of the measurement Represents a node The reliability of the measurement.

4. The method for dynamic localization of the out-of-synchronous oscillation center of a power system based on wide-area synchronous measurement data according to claim 3, characterized in that, In step S5, the spatiotemporal extension graph The definition of is: In the formula, Represents a set of spatiotemporal nodes. Represents the set of spatial edges. Represents the set of time edges; set of spatiotemporal nodes Defined as: In the formula, Represents the original power grid node In the Spatiotemporal nodes within a time window; Indicates the number of windows participating in trajectory-level joint optimization; A set of nodes; spatial edge set Defined as: In the formula, For the set of routes; Time edge set Defined as: In the formula, Represents the original power grid node In the Spatiotemporal nodes within a time window.

5. The method for dynamic localization of the out-of-synchronous oscillation center of a power system based on wide-area synchronous measurement data according to claim 4, characterized in that, In step S6, spatial edge weights The calculation formula is: In the formula, To prevent positive numbers from being divided by zero; Penalty weights for measuring credibility; The weight for the cutaway penalty of the line; Static penalty for line cutaway; Indicates the line In the Dynamic separation degree of each time window; Indicates the line In the The reliability of measurements within a time window; To allow for reasonable migration of the oscillation center during real-time dynamic processes, while suppressing spurious jumps caused by noise or local anomalies, evidence of migration near nodes is constructed based on changes in the dynamic separation of the lines in adjacent windows. The formula is as follows: In the formula, Represents a node The set of adjacent nodes; The line weight is determined by line capacity, voltage level, topological importance, or measurement reliability. Indicates the line In the Dynamic separation degree of each time window; Time edge The cost of cutting Defined as: In the formula, As the basic weight for time continuity; Increase weights for low credibility; This is the sensitivity coefficient for migration evidence; Minimizes edge weight in time; Adjacent window nodes The joint credibility; This indicates evidence of migration near the node; Represents a node In the The reliability of measurements within a time window; Represents a node In the The reliability of measurements within a time window.

6. The method for dynamic positioning of the out-of-synchronous oscillation center of a power system based on wide-area synchronous measurement data according to claim 5, characterized in that, In step S7, the expression for the trajectory-level joint optimization model is: In the formula, The spatial cutting cost is used to select candidate boundaries for the oscillation center within each time window; As a cost of time continuity, it is used to constrain the cluster affiliation changes of the same node in adjacent windows; This allows us to obtain the cluster partitioning sequence within a continuous time window; where a binary cluster affiliation variable is defined: In the formula, Represents a node In the This time window belongs to the first oscillator group; Represents a node In the This time window belongs to the second oscillator group; Represents a node In the Binary cluster attribution variable values ​​for each time window; Represents a node In the Binary cluster attribution variable values ​​for each time window; For spatial boundary weights; The cost of cutting off time; In the enhanced form, the joint optimization objective further incorporates generator coherence, power balance, and line safety constraints: Among them, generator coherence cost The expression is: In the formula, and For generator node index; Indicates generator node In the Binary machine group attribution variables for each time window; Indicates generator node In the Binary machine group attribution variables for each time window; Power balancing costs The expression is: Line security costs The expression is: In the formula, For the set of generator nodes; Indicates generator With generator In the window Internal coherence; Indicates the net injected power at the node; Represents a node In the Active power generation within a time window; Represents a node In the The active power of the load in each window; This indicates the penalty for delisting from the security check. , and These are the corresponding weights.

7. The method for dynamic localization of the out-of-synchronous oscillation center of a power system based on wide-area synchronous measurement data according to claim 6, characterized in that, In step S9, the expression for the set of oscillation center cut edges is: In the formula, Represents a node In the The optimal cluster affiliation variable value within a time window; Represents a node In the The optimal cluster affiliation variable value within a time window; Indicates the first The set of oscillation center cut edges within a time window, when It includes multiple lines, which are considered as a whole as the boundary region of the oscillation center, or the main oscillation center line is selected based on dynamic separation, spatial edge weights, line capacity, or measurement point reliability. Its expression is: In the formula, Indicates the first The main oscillation center line within a time window; Arrange the cut edge set in continuous time window in chronological order to obtain the migration trajectory of the oscillation center. The expression is: Oscillation center migration speed or migration intensity The expression is: In the formula, This represents the graph distance, center point distance, shortest path distance, or overlap rate distance between sets of cut edges at adjacent window oscillation centers; This represents the time interval between the end times of two adjacent windows; To evaluate trajectory stability, we define the first... Candidate cut edges near the window trajectory stability The expression is: In the formula, The number of lookback windows used for statistical stability; For indicator functions, when the line Appeared in the The set of cut edges for each window In the middle, then If it does not appear, then .

8. The method for dynamic positioning of the out-of-synchronous oscillation center of a power system based on wide-area synchronous measurement data according to claim 7, characterized in that, In step S10, candidate cross-sections The expression for the comprehensive solution cost is: In the formula, , , and These are the normalized cut-off power, power imbalance, line safety penalty, and trajectory consistency cost, respectively. These are non-negative weighting coefficients; The cross section with the lowest overall resolution cost is selected from the candidate cross section set as the preferred resolution cross section. The expression is: In the formula, This represents the set of candidate solution sections. Represents any candidate solution section; Indicates candidate solution cross section The overall cost of decoupling.

9. A dynamic positioning system for the out-of-synchronous oscillation center of a power system based on wide-area synchronous measurement data, used to implement the dynamic positioning method for the out-of-synchronous oscillation center of a power system based on wide-area synchronous measurement data as described in any one of claims 1-8, characterized in that, include: Data acquisition module: used to acquire continuous wide-area synchronous measurement data of the power system; Data preprocessing module: used to construct a sliding time window and preprocess the data; Feature calculation module: used to calculate the dynamic separation degree of the line and the reliability of node and line measurements; Spatiotemporal graph construction module: used to construct a spatiotemporal extended graph containing spatial edges and temporal edges; Edge weight determination module: used to calculate spatial edge weights and adaptive temporal edge weights; Optimization and Solving Module: Used to construct and solve the trajectory-level joint optimization model, outputting the cluster partitioning sequence; Trajectory extraction module: used to generate the migration trajectory of the oscillation center and calculate the trajectory stability; The segmentation decision module is used to determine and sort the candidate segments for segmentation, and output the preferred recommended segments.

10. An electronic device, comprising: The memory, the processor, and the computer program stored in the memory and executable on the processor are characterized in that: when the processor executes the program, it implements a dynamic positioning method for the out-of-step oscillation center of a power system based on wide-area synchronous measurement data as described in any one of claims 1-8.

Images