A progressive block-by-block verification power system simulation correctable domain identification method

Abstract

This invention proposes a progressive block-based verification method for identifying the correctable domain in power system simulation, belonging to the field of power system dynamic simulation technology. It addresses the technical problems of low accuracy and poor stability in existing correctable domain identification methods. The method includes: dynamic feature extraction and disturbance depth calculation; construction of a disturbance propagation skeleton; initial candidate region screening; block decoupling and hybrid dynamic simulation; error persistence assessment; recursive refinement and region compression; and correctable domain determination. This approach allows for real-time feedback between the block division results and simulation errors, and dynamically adjusts the partitioning method based on verification results, effectively improving the accuracy and stability of correctable domain identification.

Description

Technical Field

[0001] This invention relates to the field of power system dynamic simulation technology, and in particular to a progressive block verification method for identifying the correctable domain of power system simulation. Background Technology

[0002] Existing research on error identification and correctable domain delineation in dynamic simulation of power systems typically takes two approaches: one is to analyze the power grid topology, and the other is to quantify the characteristics of simulation errors. A common approach is to first construct a weighted adjacency matrix, using line impedance or electrical distance to characterize the coupling strength between nodes, and then, based on the differences between simulation results and measured data, delineate regions where errors may exist.

[0003] Building upon this, one approach focuses on calculating metrics such as perturbation depth and response amplitude to characterize the degree of perturbation at each node. This is then overlaid with simulation error metrics to filter out regions with large perturbations and errors as correctable domains. This method is straightforward and relatively easy to implement in engineering. In small to medium-sized systems, it can quickly narrow down the search range. However, as the system scales up and node coupling increases, relying solely on a single threshold screening makes it difficult to accurately distinguish between error sources and perturbed response regions, leading to potentially overestimating the severity of the problem.

[0004] Another approach further incorporates block decoupling and hybrid dynamic simulation. Specifically, it involves dividing the system into sub-regions according to topological or empirical rules, injecting measured PMU data at the boundaries, and then performing simulation verification on each subsystem separately. This method reduces the scale of a single computation and gradually approximates the error region. However, this type of method often relies on manual experience or fixed strategies in the block division stage, making the region division highly sensitive to initial conditions, thus affecting repeatability and stability. Furthermore, it lacks real-time feedback between the block division results and simulation errors, making it difficult to dynamically adjust the division method based on verification results.

[0005] Therefore, the accuracy and stability of the correctable domain identification in existing technologies are not high. Summary of the Invention

[0006] To address the technical problems of low accuracy and poor stability in existing correctable domain identification technologies, this invention provides a progressive block-based verification method for power system simulation correctable domain identification.

[0007] To address the aforementioned technical problems, in a first aspect, according to some embodiments, the present invention provides a progressive block-based verification method for identifying the correctable domain of power system simulation, comprising:

[0008] Dynamic feature extraction and disturbance depth calculation include: using the steady-state value before the disturbance occurs as a reference benchmark, calculating the relative changes of dynamic variables of each node, analyzing the dynamic response characteristics of key quantities, constructing a disturbance depth index, and obtaining the disturbance depth distribution vector of all nodes in the network.

[0009] Constructing a disturbance propagation skeleton includes: representing the system as an undirected graph based on the power grid topology, characterizing the disturbance propagation associations between nodes, retaining node pairs that satisfy the topological adjacency condition, and forming a network-wide propagation association matrix; constructing a disturbance propagation candidate edge set, and defining the union of high-association paths that meet the propagation strength requirements as the disturbance propagation skeleton set;

[0010] The initial candidate region screening includes: determining the node error index, constructing the comprehensive error index, determining the initial candidate node set, and merging adjacent candidate nodes into several candidate sub-regions;

[0011] Block decoupling and hybrid dynamic simulation specifically include: determining boundary conditions, performing hybrid dynamic simulation on the candidate region, and calculating error indices at the region level;

[0012] Error persistence assessment includes: determining an error persistence threshold based on a regional error persistence index; when the regional error is greater than the error persistence threshold, the regional error is determined to be persistent and retained as a candidate region;

[0013] Recursive refinement and region compression include: determining the candidate region set, performing recursive refinement, re-identifying the perturbation propagation skeleton of the local network, determining the dominant propagation path within the region, re-dividing the candidate sub-regions according to connectivity, and compressing the local structure again;

[0014] The determination of the correctable region includes: defining the correctable region as a set of minimal connected regions, thus forming the correctable region.

[0015] Optionally, in some embodiments, calculating the relative changes in the dynamic variables of each node specifically includes:

[0016] The node dynamic variables include at least voltage amplitude, active power, and frequency;

[0017] The voltage amplitude, the relative change of node i at time t, is expressed by Formula 1, as follows:

[0018] (1);

[0019] in, The average voltage amplitude of node i during steady-state operation before the disturbance;

[0020] The relative change in active power is expressed by Formula 2, as follows:

[0021] (2);

[0022] The relative change in frequency is expressed by Formula 3, as follows:

[0023] (3);

[0024] The key quantities include at least the maximum relative change, the average rate of change, the response start time, and the response duration;

[0025] The maximum relative change, used to characterize the maximum degree to which a node deviates from steady state during the entire disturbance process, is expressed by Formula 4, as follows:

[0026] (4);

[0027] in, This represents the relative change of a certain dynamic quantity at node i, where [ts, te] is the analysis time window;

[0028] The average rate of change, used to characterize the overall speed of change of the nodal response curve during the disturbance process, is expressed by Formula 5, as follows:

[0029] (5);

[0030] Where T is the number of sampling points;

[0031] The response start time is used to describe the time sequence in which nodes respond significantly to disturbances. Let the threshold η be the upper limit of the steady-state fluctuation range. When a node satisfies... minimum moment When this time comes, it is defined as the start time of the response of node i;

[0032] The response duration, used to describe the time it takes for a node to recover from a significant deviation from steady state to within the allowable deviation range, is expressed by Formula 6, as follows:

[0033] (6);

[0034] in, This is the moment when the node response re-enters the steady-state allowable band.

[0035] Optionally, in some embodiments, the construction of the perturbation depth index to obtain the perturbation depth distribution vector of all network nodes specifically includes:

[0036] The perturbation depth of node i is expressed using Formula 7, as follows:

[0037] (7);

[0038] Where α, β, and γ are weighting coefficients, satisfying , , , These are the maximum values ​​of the maximum relative change, the maximum average rate of change, and the maximum response duration for the corresponding indicators of all network nodes, respectively, used for normalization processing;

[0039] Furthermore, the various disturbance depths are combined into a comprehensive disturbance depth. The comprehensive disturbance depth for node i is defined as shown in Formula 8, as follows:

[0040] (8);

[0041] in, , , These represent the disturbance depths calculated based on voltage, active power, and frequency, respectively. , , For the corresponding weights, satisfying ;

[0042] The above calculations yield the disturbance depth distribution vector for all network nodes, as shown in Formula 9:

[0043] (9);

[0044] The perturbation depth distribution vector intuitively reflects the influence range of the perturbation in the system and the dynamic excitation process of each node.

[0045] Optionally, in some embodiments, the step of representing the system as an undirected graph based on the power grid topology, characterizing the disturbance propagation correlation between nodes, retaining node pairs that satisfy the topological adjacency condition, and forming a network-wide propagation correlation matrix specifically includes:

[0046] The system is represented as an undirected graph G=(V,E), where V represents the set of nodes and E represents the set of branches; for any two nodes i and j that have a direct connection, their adjacency relationship is defined as shown in Formula 10, as follows:

[0047] (10);

[0048] The response time difference between node i and node j is defined using Formula 11, as follows:

[0049] (11);

[0050] when When the value is greater than 0, it indicates that the significant response of node j is later than that of node i, and node i is located upstream in the propagation; when If the value is less than 0, it indicates that the propagation order of the two is inconsistent with the assumed direction;

[0051] For adjacent nodes i and j, the propagation correlation matrix is ​​shown in Formula XII, as follows:

[0052] (12);

[0053] in, , , These are weighting coefficients, reflecting the roles of perturbation depth propagation characteristics, temporal response consistency, and topological connectivity in propagation correlation, respectively, and satisfying the following conditions: ;

[0054] When constructing the propagation skeleton, only node pairs that satisfy the topological adjacency condition are retained, i.e., when A ij Calculate C when =1 ij Otherwise, set it to zero to form a network-wide propagation correlation matrix, as shown in Formula Thirteen, as follows:

[0055] (13).

[0056] Optionally, in some embodiments, the construction of the perturbation propagation candidate edge set, which defines the union of highly correlated paths that meet the propagation strength requirement as the perturbation propagation skeleton set, specifically includes:

[0057] The construction of the disturbance propagation candidate edge set includes: starting from the disturbance source node or the first response node, searching the entire network for propagation paths, and selecting the path with the largest cumulative weight from all possible paths as the main disturbance propagation path, specifically including:

[0058] Set the propagation association threshold Retain the associated edges that are above the threshold, and construct the perturbation propagation candidate edge set, as shown in Formula Fourteen, as follows:

[0059] (14);

[0060] Based on the candidate edge set, a propagation path search is performed across the entire network, starting from the disturbance source node or the first response node.

[0061] The path with the highest cumulative propagation correlation is selected as the main propagation path. Let a propagation path from the disturbance source node s to node m be denoted as... The cumulative propagation weight of this path is calculated using Formula 15, as follows:

[0062] (15);

[0063] The path with the largest cumulative weight is selected from all possible paths as the main propagation path of the perturbation, as expressed by Formula Sixteen:

[0064] (16);

[0065] The set of highly correlated paths that meet the propagation strength requirements is defined as the perturbation propagation skeleton set, specifically including:

[0066] The set of perturbation propagation skeletons is represented by Formula 17, as follows:

[0067] (17);

[0068] in, This represents the k-th dominant propagation path, where K is the number of main paths retained. In practical applications, K can be determined based on the cumulative propagation weight ratio or the proportion of nodes covered by the path.

[0069] The skeleton nodes are expanded by neighborhood expansion. For all nodes located on the propagation skeleton, the directly connected neighboring nodes with higher perturbation depths are included in the expanded skeleton set. The expanded skeleton is represented by Formula 18, as follows:

[0070] (18);

[0071] in, The perturbation depth threshold used when expanding the neighborhood.

[0072] Optionally, in some embodiments, the steps of determining the node error index, constructing a comprehensive error index, determining an initial candidate node set, and merging adjacent candidate nodes into several candidate sub-regions specifically include:

[0073] The simulation deviation of nodes is quantified by a time-domain overall error index. Let the simulated value and the measured value of node i at time t be respectively... and The node error index is expressed by Formula Nineteen, as follows:

[0074] (19);

[0075] Where T represents the number of sampling points within the analysis time window;

[0076] Let the voltage error, active power error, and frequency error at node i be respectively... , and The node synthesis error is calculated using Formula 20, as follows:

[0077] (20);

[0078] in, , , Let the error weighting coefficients satisfy: ;

[0079] If only a single dynamic quantity is used for analysis, then E is used directly. i If a multi-quantity joint evaluation is conducted, then use As a node error indicator;

[0080] For the sake of consistency, E i and All are denoted as nodal errors E i ;

[0081] Node i is retained as a candidate node only if it simultaneously satisfies the following conditions:

[0082] Condition 1: The node is located within the disturbance propagation skeleton or its extended neighborhood;

[0083] Condition 2: The node disturbance depth is greater than the preset threshold;

[0084] Condition 3: The node simulation error is greater than the preset threshold;

[0085] The initial set of candidate nodes is defined using Formula 21, as follows:

[0086] (twenty one);

[0087] in, This indicates the perturbation depth threshold. Indicates the simulation error threshold;

[0088] Let the mean and standard deviation of the disturbance depth of all nodes in the network be respectively and The mean and standard deviation of the error are respectively and The threshold can then be determined using formulas 22 and 23:

[0089] (twenty two);

[0090] (twenty three);

[0091] in, and This is an empirical coefficient;

[0092] Adjacent candidate nodes are merged into several candidate sub-regions, and the system adjacency matrix is ​​given by... If nodes i and j both belong to If Aij = 1, then the two are considered to belong to the same candidate region. This can be achieved through connected component search. Divide into R sub-regions, as shown in Formula 24:

[0093] (twenty four);

[0094] in, This represents the r-th candidate sub-region;

[0095] To avoid rendering subsequent block-based verification meaningless due to a single discrete node or extremely small region, we define a region. The number of nodes is Then only the sub-regions that meet the following conditions will be retained, as shown in Formula 25:

[0096] (25);

[0097] Where Nmin is the minimum size threshold of the candidate region;

[0098] The average perturbation depth and average error index at the regional level are calculated to evaluate the overall importance of each region. For the r-th candidate region, as shown in Formula 26, the following is an example:

[0099] (26);

[0100] (27);

[0101] To comprehensively assess the priority assessment value of a region, a regional priority index can be defined, as shown in Formula 28:

[0102] (28);

[0103] in, and Let the weighting coefficients satisfy: .

[0104] Optionally, in some embodiments, determining boundary conditions, performing hybrid dynamic simulation within the candidate region, and calculating region-level error indices specifically includes:

[0105] For each candidate sub-region The set of regional boundary nodes is determined based on its connection relationship with external systems. ;

[0106] Boundary nodes use actual measurements as input constraints, while nodes within the region are still updated by the simulation model. Boundary conditions are expressed using Equation 29:

[0107] (29);

[0108] in, Represents the measured dynamic quantity of boundary node i;

[0109] After boundary injection, a hybrid dynamic simulation is performed on the candidate region to obtain the simulation response curves of each internal node;

[0110] The data is compared with the corresponding measured data to calculate the regional error index, which is used to measure the simulation accuracy of the region under local decoupling conditions.

[0111] area The average error is expressed using Formula 30:

[0112] (30);

[0113] in, This is an error index for nodes within the region. This represents the number of nodes contained in the region.

[0114] Optionally, in some embodiments, determining an error persistence threshold based on a regional error persistence index; and determining that the regional error is persistent and retaining it as a candidate region when the regional error is greater than the error persistence threshold, specifically includes:

[0115] Set up a region The average error in the k-th round of recognition is The average error after completing local decoupling and hybrid dynamic simulation is The persistence of regional error is then expressed by formula 31:

[0116] (31);

[0117] in, The closer it is to 1, the smaller the change in regional error after localization, and the stronger the persistence of the error; The smaller the value, the more the regional error is significantly reduced after decoupling, and the greater the influence of external propagation on the deviation.

[0118] Error persistence threshold It is 0.7, when a certain region satisfies When the error is ≥0.7, the region is considered to have persistent error and should be retained as a key candidate region; when If the error is less than 0.7, it is considered that the error in this region mainly originates from external system transmission, and it should be removed from the candidate region or its subsequent analysis priority should be reduced.

[0119] Optionally, in some embodiments, the process of determining the candidate region set, recursively refining it, re-identifying the perturbation propagation skeleton of the local network, determining the dominant propagation path within the region, and re-dividing the candidate sub-regions according to connectivity to further compress the local structure includes:

[0120] Let the set of candidate regions retained after the k-th round of analysis be . Then, the object of the recursive analysis in the (k+1)th round consists of the regions in the kth round that satisfy the error persistence condition, which can be represented as:

[0121] (32);

[0122] in, This represents the r-th candidate region in the k-th round. It serves as an indicator of the persistence of its error;

[0123] The termination conditions are as shown in conditions four, five, and six:

[0124] Condition 4: When the number of nodes in a certain region is already below the preset scale threshold, it will no longer be further subdivided, but will be directly used as the final candidate region;

[0125] Condition 5: When the range of a region changes very little in two adjacent rounds of analysis, it indicates that its boundary has basically stabilized, and the recursion should be stopped.

[0126] Condition 6: When the error of the region after localization meets the engineering requirements, that is, further refinement can no longer significantly improve the recognition accuracy, the recursive process is terminated;

[0127] The defined correctable domain is a set of minimal connected regions, forming the correctable domain, specifically including:

[0128] The final correctable region is defined as the set of minimum connected regions that satisfy the above constraints, and the final identification result is denoted as... It is represented by formula thirty-three, as follows:

[0129] (33);

[0130] in, This represents the candidate regions that are retained after recursive filtering. This indicates the number of nodes or components contained in the region;

[0131] When there are multiple independent error-dominant regions in the system, multiple correctable regions can be output simultaneously.

[0132] In a second aspect, embodiments of the present invention also provide an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the method described in any of the first aspects above.

[0133] Thirdly, according to embodiments of the present invention, a computer-readable storage medium is also provided, on which a computer program is stored, wherein the computer program, when executed by a processor, implements the steps of the method described in any of the first aspects above.

[0134] The above-mentioned technical solution of the present invention has at least the following beneficial technical effects: Based on the dynamic trajectory of node voltage amplitude, active power, frequency and other factors, this application extracts features such as maximum change, average change rate, response start time and response duration, and calculates the disturbance depth of each node. This index is used to determine whether the dynamic characteristics of the node under a specific disturbance are fully excited, and avoids invalid verification of nodes that are not sufficiently disturbed and have low verification value. This application also provides a method for constructing a disturbance propagation skeleton that integrates disturbance depth, response time difference, and topological adjacency. Based on the power grid topology, this method calculates the propagation correlation between nodes by combining the order of dynamic responses and the degree of disturbance of each node, extracts the main propagation path and extended propagation skeleton after the fault, and limits the search range of the correctable region through this skeleton, which can avoid blind screening based solely on the error magnitude. Furthermore, this application proposes a triple criterion screening method under the constraint of the propagation skeleton. This method uses disturbance propagation correlation, disturbance depth threshold, and simulation error threshold as constraints simultaneously to screen candidate nodes that simultaneously meet the criteria of being "located within the main propagation range, sufficiently disturbed, and significantly faulty". Based on topological connectivity, a candidate correctable region is formed. This method can eliminate nodes with insufficient disturbance and error nodes on non-main propagation paths, improving the accuracy and compactness of the initial candidate region. This application also decouples candidate regions locally, injects PMU / WAMS measured trajectories into region boundary nodes, and uses measured data to represent the dynamic impact of external systems on the study region. The dynamic response within the region is still calculated by the simulation model. By comparing the changes in region error before and after decoupling, it determines whether significant errors still exist within the candidate region. Furthermore, it establishes an error persistence criterion based on the changes in error before and after decoupling. This criterion characterizes the degree of error persistence by the ratio of the error after decoupling to the error before decoupling. When the error persistence exceeds a threshold, it is determined that a dominant model or parameter error may exist within the region. When the error significantly decreases, it is determined that the region is mainly affected by external error propagation and is eliminated. This application also features a progressive block verification and region compression mechanism. This mechanism further subdivides candidate regions with high error persistence and repeatedly performs propagation skeleton analysis, block decoupling verification, and error persistence assessment, gradually compressing the search range from the entire network to the smallest connected region. Ultimately, the region that simultaneously satisfies the conditions of propagation correlation, sufficient perturbation, significant error, and error persistence is determined as the simulation correctable region. This application, through the above method, can dynamically adjust the partitioning method based on the real-time feedback between the block division results and simulation errors, thereby effectively improving the accuracy and stability of correctable domain identification. Attached Figure Description

[0135] To more clearly illustrate the technical solutions in the embodiments of the present invention or in the conventional art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0136] Figure 1 This invention provides a progressive block-based verification method for identifying the correctable domain in power system simulation.

[0137] Figure 2 This is a schematic diagram of a 10-machine, 39-node system provided in an embodiment of the present invention.

[0138] Figure 3 This is a schematic diagram of a disturbance depth result provided in an embodiment of the present invention.

[0139] Figure 4 This is a schematic diagram of calculating the simulation error index of each node provided by an embodiment of the present invention. Detailed Implementation

[0140] 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.

[0141] Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concept of the present invention.

[0142] It should be noted that the sequence number mentioned in this application does not necessarily mean that the execution must be strictly in the correct order in the actual implementation process. The sequence number is used to distinguish each step, facilitate explanation, and prevent confusion.

[0143] Furthermore, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0144] The core objective of this invention is to improve the accuracy and stability of correctable domain identification, enabling the identification results to more closely approximate actual error sources. To this end, the method first utilizes WAMS / PMU measured data to extract dynamic response characteristics of the system and constructs a disturbance propagation framework to clarify the main action paths of disturbances in the power grid. Based on this, and combining disturbance depth with simulation error indices, candidate regions are preliminarily screened to reduce interference from irrelevant regions at the source.

[0145] After initial screening, this invention further introduces a block decoupling and hybrid dynamic simulation process to verify candidate regions layer by layer. By injecting measured data into the boundaries of sub-regions, the local simulation response is recalculated, and the error changes before and after decoupling are compared to determine whether the region still retains significant errors. This process effectively distinguishes between error source regions and error propagation regions, thereby avoiding the inclusion of non-critical regions in the correctable domain.

[0146] In terms of the identification process, this invention constructs a progressive processing mechanism of "screening—decoupling—verification—compression". Each round of calculation adjusts the candidate region range based on the error changes, gradually converging the identification process and ultimately obtaining the least connected correctable domain. Compared to a one-time screening method, this progressive approach can more stably locate the error-dominant region.

[0147] Through the above design, this invention achieves unified modeling of disturbance propagation information, simulation error characteristics, and the block decoupling process, forming a closed-loop identification method with feedback capability. This method can automatically narrow the error search range under complex power grid conditions, improve the efficiency of dynamic simulation verification, and provide clearer regional boundaries for subsequent model parameter verification.

[0148] This method, based on measured data from a wide-area measurement system (WAMS / PMU), first extracts the dynamic spatiotemporal distribution characteristics of the power system during disturbances, then characterizes the main propagation paths of disturbances in the network, and finally constructs the main framework for disturbance propagation. Based on this, combining simulation error evaluation results with a multi-level block decoupling mechanism, candidate regions are progressively screened, compressed, and dynamically verified, ultimately identifying the correctable domain that has a dominant influence on the simulation results. This invention primarily addresses the problems of accurately shrinking error regions and clearly defining the boundaries of correctable domains in large-scale complex power grids. By unifying the disturbance propagation mechanism, simulation error distribution characteristics, and the block decoupling verification process into a single identification framework, this method can more effectively target key regions, reduce the blind spots in subsequent model parameter verification, and improve the efficiency and reliability of dynamic simulation verification.

[0149] The main technical concept of this application is as follows:

[0150] (1) Construction of the perturbation propagation skeleton.

[0151] First, based on measured data from WAMS / PMU, the dynamic response information of the system during the disturbance process is extracted, focusing on analyzing the time-series variation characteristics of key quantities such as voltage amplitude, active power, and frequency. By calculating the disturbance depth and response time difference of each node, the degree of disturbance and the order of response in different regions are quantified. On this basis, combined with the power grid topology, a propagation correlation model between nodes is constructed, and the main propagation paths of the disturbance in the network are extracted, forming the disturbance propagation framework. The purpose of this step is to clarify the dominant direction of the disturbance's impact, providing physical constraints for subsequent region selection.

[0152] (2) Preliminary screening of candidate correctable domains.

[0153] After obtaining the perturbation propagation skeleton, system nodes are screened using it as a constraint. Specifically, a set of nodes that simultaneously satisfy the perturbation depth threshold and the simulation error threshold is selected, and they are required to be located within or near the propagation skeleton. This process quickly eliminates nodes that are only affected by propagation but do not have error-dominant characteristics, thus forming a smaller and more targeted initial candidate region.

[0154] (3) Block decoupling and local simulation verification.

[0155] For the initial candidate region, it is divided into several relatively independent sub-regions based on network topology. PMU measured data is injected at the boundary nodes of each sub-region, and hybrid dynamic simulation is performed within the region. By comparing the simulation results with the measured data, the simulation error level of each sub-region is re-evaluated. This step can verify the model accuracy within a local range, providing a basis for subsequent region compression.

[0156] (4) Error persistence determination and region compression.

[0157] After completing the local simulation, the error changes of each sub-region before and after decoupling are further analyzed. If a region maintains a high error level after localization, it is considered to be error-dominant and should be retained; if the error decreases significantly, it indicates that the deviation mainly originates from external propagation and should be removed from the candidate set. By introducing an error persistence criterion, the error source region and the error propagation region can be effectively distinguished, and the candidate range can be gradually narrowed.

[0158] (5) Progressive closed-loop identification mechanism.

[0159] The above steps constitute a progressive recognition process. After each round of block decoupling and error determination, the candidate region is updated based on the result, and the block decoupling and verification operations are repeated for the remaining regions. As the number of iterations increases, the candidate region continuously shrinks, and the recognition results gradually converge. The final region obtained is the minimum connected correctable domain that has a continuous dominant effect on the simulation results. This process forms a closed-loop structure of "propagation constraint - region selection - block verification - result feedback," achieving layer-by-layer localization from global to local.

[0160] The following is an explanation.

[0161] like Figure 1 As shown, Figure 1 This is a flowchart illustrating a progressive, block-based verification method for identifying the correctable domain in power system simulation.

[0162] A progressive block-based verification method for identifying the correctable domain in power system simulation includes:

[0163] S1. Dynamic feature extraction and disturbance depth calculation, including: using the steady-state value before the disturbance occurs as a reference benchmark, calculating the relative changes of dynamic variables of each node, analyzing the dynamic response characteristics of key quantities, constructing a disturbance depth index, and obtaining the disturbance depth distribution vector of all network nodes.

[0164] S2. Constructing the disturbance propagation skeleton, including: based on the power grid topology, representing the system as an undirected graph, characterizing the disturbance propagation association between nodes, retaining node pairs that satisfy the topological adjacency condition, and forming a network-wide propagation association matrix; constructing a set of disturbance propagation candidate edges, and defining the union of high-association paths that meet the propagation strength requirements as the disturbance propagation skeleton set;

[0165] S3. Initial candidate region screening, including: determining node error index, constructing comprehensive error index, determining initial candidate node set, and merging adjacent candidate nodes into several candidate sub-regions;

[0166] S4. Block decoupling and hybrid dynamic simulation, specifically including: determining boundary conditions, performing hybrid dynamic simulation on the candidate region, and calculating the error index at the region level;

[0167] S5. Error persistence assessment, including: determining an error persistence threshold based on a regional error persistence index; when the regional error is greater than the error persistence threshold, determining that the regional error has persistence and retaining it as a candidate region;

[0168] S6. Recursive Refinement and Region Compression, including: determining the candidate region set, recursively refining, re-identifying the perturbation propagation skeleton of the local network, determining the dominant propagation path within the region; re-dividing the candidate sub-regions according to connectivity, and compressing the local structure again;

[0169] S7. Determining the correctable region, including: defining the correctable region as a set of minimal connected regions to form the correctable region.

[0170] The following is a detailed explanation.

[0171] 1. Dynamic feature extraction and perturbation depth calculation.

[0172] First, assume that the power grid under study has N observation nodes equipped with PMUs. For each node, the measured dynamic sequence within a certain time window before and after the disturbance is collected, including voltage amplitude. Active power ,frequency Equal measurement. Considering the potential differences in recording length and sampling intervals for different disturbance events, this invention first performs uniform preprocessing on the measurement sequences of each node. The preprocessing process mainly includes: outlier removal, missing point interpolation, time axis alignment, and noise suppression. For data with inconsistent sampling intervals, linear interpolation or cubic spline interpolation is used to map them to a uniform time scale; for high-frequency noise, moving average or low-pass filtering methods are used for smoothing to ensure the stability of subsequent calculation results.

[0173] After data preprocessing, the relative changes in dynamic variables at each node are calculated using the steady-state values ​​before the disturbance as a reference. Taking voltage amplitude as an example, the relative change of node i at time t is defined as:

[0174] (1);

[0175] in, Let be the average voltage amplitude of node i during steady-state operation before the disturbance. Similarly, the relative changes in active power and frequency can be obtained separately:

[0176] (2);

[0177] (3);

[0178] To quantify the dynamic response characteristics of nodes in the time domain, this invention further extracts the following feature indicators:

[0179] (1) The maximum relative change is used to characterize the maximum degree to which a node deviates from the steady state during the entire disturbance process, and is defined as:

[0180] (4);

[0181] in, This represents the relative change of a certain dynamic quantity at node i, where [ts,te] is the analysis time window.

[0182] (2) Average rate of change, used to characterize the overall speed of change of the nodal response curve during the disturbance process, is defined as:

[0183] (5);

[0184] Where T is the number of sampling points.

[0185] (3) Response start time, used to describe the time sequence in which nodes respond significantly to disturbances. Let the threshold η be the upper limit of the steady-state fluctuation range, when the node satisfies... minimum moment The time is defined as the start time of node i's response. This metric reflects the propagation delay of disturbances in the network.

[0186] (4) Response duration, used to describe the time it takes for a node to recover from a significant deviation from steady state to within the allowable deviation range, is defined as:

[0187] (6);

[0188] in, This is the moment when the node response re-enters the steady-state allowable band.

[0189] Based on the aforementioned characteristic indicators, this invention constructs a perturbation depth index to comprehensively reflect the degree of excitation of node dynamic characteristics. Considering that different single indicators can only describe the degree of perturbation of a node from one aspect, this invention adopts a weighted synthesis method, incorporating the maximum relative change, average rate of change, and response duration into the perturbation depth calculation model. The perturbation depth of node i is defined as:

[0190] (7);

[0191] Where α, β, and γ are weighting coefficients, satisfying , , , These are the maximum values ​​of the corresponding indicators for all nodes in the network, used for normalization processing.

[0192] If multiple dynamic quantities (such as voltage, active power, and frequency) are considered simultaneously, the depths of various disturbances can be further combined into a comprehensive disturbance depth. For example, the comprehensive disturbance depth for node i can be defined as:

[0193] (8);

[0194] in, , , These represent the disturbance depths calculated based on voltage, active power, and frequency, respectively. , , For the corresponding weights, satisfying .

[0195] Through the above calculations, the disturbance depth distribution vector of all network nodes can be obtained:

[0196] (9);

[0197] This vector intuitively reflects the scope of the disturbance's influence on the system and the degree of dynamic excitation of each node. Nodes with greater disturbance depths indicate stronger responses and more fully exposed dynamic characteristics during the disturbance process, thus having higher value in subsequent identification of the correctable domain.

[0198] 2. Construction of the perturbation propagation framework.

[0199] After completing the extraction of node dynamic features and the calculation of disturbance depth, it is necessary to further identify the main propagation paths of disturbances in the power grid.

[0200] First, based on the power grid topology, the system is represented as an undirected graph G=(V,E), where V represents the set of nodes and E represents the set of branches. For any two nodes i and j that have a direct connection, their adjacency relationship is defined as:

[0201] (10).

[0202] Based on this, and combining the node perturbation depth Di and the node response start time obtained in the previous section... This describes the perturbation propagation correlation between nodes. Considering that perturbation propagation is not only related to the degree of perturbation of nodes, but also closely related to the order of responses and network connectivity, this invention defines the response time difference between node i and node j as:

[0203] (11).

[0204] when When the value is greater than 0, it indicates that the significant response of node j is later than that of node i, and node i is more likely to be located upstream in the propagation; when A value less than 0 indicates that the propagation order of the two nodes is inconsistent with the assumed direction. To quantitatively describe the propagation relationship between nodes, this invention further defines a propagation correlation index. For adjacent nodes i and j, their propagation correlation can be expressed as:

[0205] (12);

[0206] in, , , These are weighting coefficients, reflecting the roles of perturbation depth propagation characteristics, temporal response consistency, and topological connectivity in propagation correlation, respectively, and satisfying the following conditions: .

[0207] Considering that there may be no direct connection between different nodes, only node pairs that satisfy the topological adjacency condition are retained when constructing the propagation skeleton. That is, Cij is calculated when Aij=1, and otherwise set to zero. This results in a network-wide propagation correlation matrix:

[0208] (13);

[0209] To avoid interference from weakly correlated branches in propagation path identification, this invention introduces a propagation correlation threshold. Only retain the associated edges that are above this threshold to construct a set of candidate edges for perturbation propagation:

[0210] (14);

[0211] Based on the candidate edge set, a propagation path search is performed across the entire network, starting from either the disturbance source node or the first response node. To highlight the dominant propagation direction, this invention prioritizes the path with the highest cumulative propagation correlation as the main propagation path. Let a propagation path from the disturbance source node s to node m be denoted as... The cumulative propagation weight of this path is defined as:

[0212] (15);

[0213] Furthermore, the path with the largest cumulative weight is selected from all possible paths as the main propagation path of the perturbation:

[0214] (16);

[0215] For large-scale power grids, a single disturbance may propagate in parallel along multiple branches. To more comprehensively reflect the dominant propagation range of the disturbance, this invention defines the union of all highly correlated paths that meet the propagation strength requirements as the disturbance propagation skeleton set. :

[0216] (17);

[0217] in, This represents the k-th dominant propagation path, where K is the number of main paths retained. In practical applications, the value of K can be determined based on the cumulative propagation weight ratio or the proportion of nodes covered by the path.

[0218] To improve the engineering applicability of the propagation skeleton, this invention can also expand the neighborhood of the skeleton nodes. That is, for all nodes located on the propagation skeleton, the directly connected neighboring nodes with higher perturbation depths are included in the expanded skeleton set. The expanded skeleton can be represented as:

[0219] (18);

[0220] in, This is the perturbation depth threshold used during neighborhood expansion. This process avoids missing critical nodes highly relevant to the main propagation path due to limited PMU deployment or local response delays.

[0221] Finally, this step outputs a set of perturbation propagation skeletons and their extended results. These results reflect the dominant propagation channels of perturbations in the system and provide clear range constraints for the initial screening of correctable regions. Compared to relying solely on perturbation depth for region identification, the perturbation propagation skeleton can more accurately distinguish between the "main perturbation propagation region" and the "passively perturbed region," thereby improving the targeting and accuracy of subsequent correctable region identification.

[0222] 3. Initial candidate region screening.

[0223] To quickly eliminate a large number of nodes that are not closely related to error identification in the entire network, and retain only candidate regions with high core value, the computational scale is reduced for subsequent block decoupling and local simulation verification.

[0224] For each node i equipped with a PMU, the difference between the simulation results and the measured results is calculated. To avoid bias in the identification results caused by errors in a single time moment or a single variable, this invention uses a time-domain overall error index to quantify the simulation deviation of the node. Let the simulated value and the measured value of node i at time t be respectively... and The node error index is then defined as:

[0225] (19);

[0226] Where T represents the number of sampling points within the analysis time window. This indicator uses the normalized root mean square error form, which can eliminate the influence of differences in the dimensions and fluctuation amplitudes of different nodes, making the error levels between different nodes comparable.

[0227] If multiple dynamic quantities, such as voltage, active power, and frequency, are considered simultaneously, the error indices for each quantity can be calculated separately, and a comprehensive error index can be constructed. Let the voltage error, active power error, and frequency error at node i be respectively... , and The node synthesis error is defined as follows:

[0228] (20);

[0229] in, , , Let the error weighting coefficients satisfy: .

[0230] In subsequent screening, if only a single dynamic quantity is used for analysis, Ei can be used directly; if multiple quantities are evaluated jointly, then use... As a nodal error index, for the sake of consistency, it will be denoted as nodal error E below. i .

[0231] Based on the node perturbation depth Di and perturbation propagation skeleton set obtained in the previous section and the nodal error E calculated in this step. i This invention employs a triple constraint to filter initial candidate nodes. That is, node i is retained as a candidate node only if it simultaneously meets the following conditions:

[0232] • The node is located within the perturbation propagation skeleton or its extended neighborhood;

[0233] • The node disturbance depth is greater than a preset threshold;

[0234] • The node simulation error is greater than the preset threshold.

[0235] Therefore, the initial candidate node set is defined as follows:

[0236] (twenty one);

[0237] in, This indicates the perturbation depth threshold. This represents the simulation error threshold. The perturbation depth threshold ensures that the node's dynamic characteristics have been fully excited, the simulation error threshold ensures that the node does indeed have a significant simulation deviation, and the propagation skeleton constraint ensures that the node is within the dominant propagation range of the perturbation. Combining these three factors can effectively eliminate nodes that are "insufficiently perturbed but have large errors" or "have small errors but are located in the propagation channel."

[0238] To improve the robustness of the screening, the threshold can also be determined statistically. Let the mean and standard deviation of the disturbance depth of all nodes in the network be respectively... and The mean and standard deviation of the error are respectively and Then the threshold can be set as:

[0239] (twenty two);

[0240] (twenty three);

[0241] in, and This is an empirical coefficient that can be adjusted based on system size and disturbance type. This approach avoids the insufficient adaptability issues that arise from fixed threshold settings.

[0242] Preliminary screening results It is still a set of nodes, which may not directly correspond to the actual operable area. Therefore, this invention further utilizes the power grid topology to perform connectivity analysis on candidate nodes, merging adjacent candidate nodes into several candidate sub-regions. Let the system adjacency matrix be... If nodes i and j both belong to And satisfy A ij If the value is 1, then the two are considered to belong to the same candidate region. This can be achieved through connected component search. Divide into R sub-regions:

[0243] (twenty four);

[0244] in, Let represent the r-th candidate sub-region. To avoid the subsequent block verification becoming meaningless due to a single discrete node or a very small region, this invention can also constrain the size of the sub-region. Let the region represent the r-th candidate sub-region. The number of nodes is Then only the sub-regions that meet the following conditions will be retained:

[0245] (25);

[0246] Where Nmin is the minimum size threshold for candidate regions. If the number of nodes in a certain region is lower than this value, it can be merged into an adjacent region according to engineering needs, or directly marked as a low-priority candidate set.

[0247] After obtaining each candidate sub-region, this invention further calculates the average perturbation depth and average error index at the region level to evaluate the overall importance of each region. For the r-th candidate region, we have:

[0248] (26);

[0249] (27);

[0250] To comprehensively measure the priority assessment value of a region, the regional priority index can be defined as follows:

[0251] (28);

[0252] in, and Let the weighting coefficients satisfy: .

[0253] The higher the regional priority index, the higher the dynamic excitation level and the more significant the simulation error in that region. Therefore, it should be given priority in the subsequent block decoupling verification.

[0254] 4. Block decoupling and hybrid dynamic simulation.

[0255] For each candidate sub-region The set of regional boundary nodes is determined based on its connection relationship with external systems. Boundary nodes primarily correspond to the connection points between the candidate region and the external system. These nodes not only facilitate power exchange between regions but also characterize the transmission of external disturbances to the internal region. To ensure that the boundary conditions within the decoupled region remain consistent with the real system, this invention directly injects PMU / WAMS measured data at the boundary nodes to represent the equivalent dynamic impact of the external system on the study region.

[0256] In the hybrid dynamic simulation, boundary nodes use actual measurements as input constraints, while nodes within the region are still updated by the simulation model. The boundary conditions can be expressed as:

[0257] (29);

[0258] in, This represents the measured dynamic quantity of boundary node i. In practical applications, the injected voltage amplitude, phase angle, active power, reactive power, or a combination thereof can be selected based on the simulation platform and measurement conditions. In this way, the true boundary response of the candidate region during the disturbance process can be maintained without reconstructing the entire external system.

[0259] After boundary injection, a hybrid dynamic simulation is performed on the candidate region to obtain the simulation response curves of each internal node. These curves are then compared with corresponding measured data to calculate a region-level error index, which measures the simulation accuracy of the region under local decoupling conditions. The average error is defined as:

[0260] (30);

[0261] in, This is an error index for nodes within the region. This represents the number of nodes contained in the region.

[0262] If a region still exhibits significant errors after decoupling, it indicates that the model parameters or component models within that region are more likely to have problems, and the error is not simply caused by propagation from the external system. Conversely, if the regional error decreases significantly after decoupling, it suggests that the original deviation in that region was more influenced by external propagation, and it may not necessarily be an error-dominant region itself. In this way, hybrid dynamic simulation can not only reassess the simulation capabilities within a region but also provide direct evidence for subsequent determination of error persistence.

[0263] 5. Error persistence assessment.

[0264] If a region exhibits a large error in the original system, but its local simulation error decreases significantly after introducing boundary measured data and decoupling from the external system, it indicates that the original deviation in that region was largely caused by the propagation from the external system, and its internal model itself may not have significant problems. Conversely, if a region still maintains a large error level after decoupling, it indicates that the internal model parameters or component models in that region are more likely to be the direct source of the simulation deviation, and should be retained and proceeded to the next round of detailed analysis.

[0265] Therefore, this invention defines a regional error persistence index to quantify the degree to which the error level of the same region is maintained before and after decoupling. Let the region... The average error in the k-th round of recognition is The average error after completing local decoupling and hybrid dynamic simulation is The persistence of regional error is then defined as:

[0266] (31);

[0267] in, The closer it is to 1, the smaller the change in regional error after localization, and the stronger the persistence of the error; The smaller the value, the more significantly the regional error is reduced after decoupling, and the deviation is more likely to come from external propagation influences.

[0268] Based on the above indicators and empirical evidence, this invention sets an error persistence threshold. It is 0.7. When a certain region satisfies When the error is ≥0.7, the region is considered to have persistent error and should be retained as a key candidate region; when If the error is less than 0.7, it is considered that the error in this region mainly originates from external system transmission and can be removed from the candidate region or its subsequent analysis priority can be reduced.

[0269] In this way, the error persistence assessment adds another layer of local verification conditions to the original "perturbation depth constraint" and "simulation error constraint." It no longer just looks at whether the error is large in a certain region, but further examines whether the error still exists after localization. This effectively reduces misjudgments and focuses more attention on the error regions that truly play a dominant role.

[0270] 6. Recursive refinement and region compression.

[0271] To further improve the accuracy of correctable domain identification, this invention continues to perform recursive refinement and region compression, further dividing and verifying the retained regions at a smaller scale, gradually compressing the search range to the minimum connectivity range. For each candidate region that meets the error persistence requirement, its corresponding local subnetwork is re-extracted, and this subnetwork is used as a new object to be analyzed. Then, the entire process of "dynamic feature extraction—perturbation propagation skeleton construction—initial candidate region screening—block decoupling and hybrid dynamic simulation—error persistence evaluation" is repeated. Compared with the first full-network analysis, this round of processing is only carried out in local regions, so the search objects are more concentrated, and the analysis results are more likely to approximate the error-dominant region.

[0272] To maintain the consistency of the recursive process, let the set of candidate regions retained after the k-th round of analysis be . Then, the object of the recursive analysis in the (k+1)th round consists of the regions in the kth round that satisfy the error persistence condition, which can be represented as:

[0273] (32);

[0274] in, This represents the r-th candidate region in the k-th round. It serves as an indicator of the persistence of its error.

[0275] During the recursive refinement process, each round of analysis performs two key operations: first, re-identifying the perturbation propagation skeleton of the local network to further determine the dominant propagation path within the region; and second, re-dividing candidate sub-regions according to connectivity to further compress the local structure. As the analysis object shrinks continuously, the propagation relationships and error distribution within the region become clearer, thereby gradually converging the boundary of the correctable domain.

[0276] To prevent the recursive process from proceeding indefinitely, the present invention sets the following termination condition:

[0277] (1) When the number of nodes in a certain region is lower than the preset scale threshold, it will no longer be further subdivided, but will be directly used as the final candidate region;

[0278] (2) When the range of a region changes very little in two adjacent rounds of analysis, it indicates that its boundary has basically stabilized and the recursion can be stopped.

[0279] (3) When the error of the region after localization meets the engineering requirements, that is, further refinement can no longer significantly improve the recognition accuracy, the recursive process is also terminated.

[0280] Through the aforementioned recursive compression mechanism, this invention can reduce the number of candidate regions round by round and gradually narrow the spatial range of each region. Compared with single-round screening methods, this method no longer attempts... Figure 1 Instead of providing the final result step by step, the candidate region boundaries are continuously corrected through multiple rounds of local verification, making the identification process more robust and more in line with the actual characteristics of error convergence in large-scale power systems.

[0281] 7. Correctable region determination.

[0282] After initial screening, block decoupling, error persistence assessment, and recursive refinement, the candidate region has gradually converged. At this point, the retained region is no longer just a general region that is "more disturbed" or "has a larger error," but a key region that simultaneously satisfies propagation correlation, dynamic excitation sufficiency, and error persistence.

[0283] Specifically, the regions ultimately retained should meet the following basic conditions: First, the region is located within the perturbation propagation framework or its extension range, and is consistent with the main perturbation propagation path of the system; second, the nodes within the region have a high perturbation depth, indicating that the dynamic characteristics have been fully stimulated and have parameter verification value; third, the region still maintains significant error after local decoupling, indicating that its deviation mainly originates from within the region rather than being caused by propagation from the external system; fourth, after multiple rounds of recursive refinement, the region boundary is basically stable, and further subdivision is unlikely to significantly improve the recognition accuracy.

[0284] Based on this, the present invention defines the final correctable domain as the set of minimum connected regions that satisfy the above constraints. Let the final identification result be... Then we have:

[0285] (33);

[0286] in, This represents the candidate regions that are retained after recursive filtering. This indicates the number of nodes or components contained in the region. When multiple independent error-dominant regions exist in the system, this invention allows for the simultaneous output of multiple correctable regions. In this case, each correctable region corresponds to a relatively independent error concentration region in the system, and error components can be located and parameters checked separately for each. For a single error source scenario, the final identification result usually appears as a connected region; while for a multi-error source scenario, multiple non-overlapping local regions may be obtained.

[0287] To illustrate the effectiveness of the present invention, the following verification is performed.

[0288] 1. Example verification.

[0289] To verify the effectiveness of the proposed correctable domain identification method, a standard 10-machine 39-node system was used for a computational example. This system includes 34 transmission branches, 12 transformer branches, and 19 loads. Figure 2 As shown. A three-phase short-circuit fault is set at node 13. The fault starts at time 1s and lasts for 0.2s. The total simulation time is 5s and the simulation step size is 0.01s.

[0290] Obtain the measured data and simulation data required for the case study verification.

[0291] Based on the voltage amplitude, active power, and frequency response curves of each observation node within a 5-second time window before and after the fault, the dynamic characteristics of the nodes are extracted and the disturbance depth is calculated. The node disturbance depth results are as follows: Figure 3 As shown.

[0292] Take the perturbation depth threshold This allows us to obtain the set of highly perturbated nodes:

[0293] .

[0294] Calculate the simulation error index Ei for each node, such as Figure 4 As shown.

[0295] Take the simulation error threshold =0.045 (blue line in the graph), from which we can determine the high error node as:

[0296] .

[0297] Taking the intersection of the two sets yields the initial set of candidate nodes:

[0298] .

[0299] These nodes simultaneously meet the following criteria: high degree of disturbance; significant simulation error; located near fault node 13 or near the main propagation channel.

[0300] Based on the system diagram, these nodes can be roughly divided into two candidate regions:

[0301] .

[0302] in: The core candidate region includes faulty node 13 and its directly adjacent nodes. : Secondary candidate regions formed by the outward propagation of disturbances.

[0303] Therefore, the regional average disturbance depth of the two regions can be calculated. and regional average simulation error As shown in Table 1:

[0304] Table 1 Candidate Region Indicators

[0305] Candidate region Mean Disturbance Depth Regional average simulation error 0.893 0.080 0.664 0.052

[0306] Judging from the results, The average perturbation depth and average simulation error are both higher than Therefore, This should be a priority area for verification.

[0307] For candidate regions Based on their connection to the external network, nodes 10, 11, and 14 are selected as boundary nodes, i.e.: For candidate regions Nodes 6, 16, and 19 are selected as boundary nodes, i.e.: .

[0308] Next, a hybrid dynamic simulation is performed. The "measured trajectory" obtained from the standard parameter simulation is injected into the boundary nodes, while the nodes inside the region are still dynamically simulated using the error-containing model. This method isolates the influence of external systems on the candidate region, allowing for a more accurate determination of whether persistent simulation errors exist within the candidate region. After completing the boundary injection and local hybrid dynamic simulation, the average error of the two candidate regions is recalculated. The results are shown in Table 2.

[0309] Table 2 Candidate region indices before and after decoupling

[0310] Candidate region Average error before decoupling Average error after decoupling Error persistence determination 0.080 0.072 0.900 reserve 0.052 0.030 0.577 Eliminate

[0311] The results in the table show that the region After the boundary measured data was injected, the average error only decreased from 0.080 to 0.072, and the error persistence index was 0.900, which is higher than the threshold. A value of 0.75 indicates that significant errors persist in this region even after local decoupling, suggesting that the errors are more likely due to model or parameter deviations within the region. Therefore, It is identified as an error persistence region and retained for the next round of recursive refinement.

[0312] In contrast, the region The average error decreased from 0.052 to 0.030, and the error persistence index was 0.577, which is below the threshold of 0.75. This result indicates that... The original error was significantly reduced after the influence of the external system was replaced by the measured boundary conditions. The deviation mainly stemmed from the external propagation of disturbances and errors, rather than being primarily caused by the model parameters within the region. Therefore, They were eliminated in this round of identification.

[0313] Through this round of block decoupling and hybrid dynamic simulation verification, the candidate region was compressed from two to one, resulting in the retained candidate region:

[0314] .

[0315] To further narrow the correctable region, the retained region is recursively refined into smaller sub-regions, and hybrid dynamic simulation and error persistence assessment are performed again. It can be further divided into two sub-regions: .in, Located on the adjacent propagation channel of fault node 13, it mainly reflects the dynamic response after the disturbance is transmitted to the left network; This includes faulty node 13 and its directly adjacent node 14, which belongs to the core response area of ​​this fault and is also the area most likely to have the dominant model error.

[0316] Boundary measured data injection and local hybrid dynamic simulation were performed on the two sub-regions mentioned above. After the simulation was completed, the average error and error persistence index of each sub-region were recalculated, and the results are shown in Table 3.

[0317] Table 3 Candidate region indices before and after decoupling

[0318] Candidate region Average error before decoupling Average error after decoupling Error persistence determination 0.076 0.044 0.579 Eliminate 0.084 0.079 0.940 reserve

[0319] The results in the table show that the sub-regions After injecting the measured boundary data, the average error decreased from 0.076 to 0.044, and the error persistence index was 0.579, below the threshold of 0.75. This result indicates that although region 10-11-12 exhibited high perturbation depth and certain error in the initial screening stage, its error significantly decreased after local decoupling. It was mainly affected by error propagation in the fault core region and was not the dominant source of the simulation deviation. Therefore, this region was removed during the recursive refinement process.

[0320] In contrast, sub-region The average error after decoupling remained at 0.079, and the error persistence index was 0.940, higher than the threshold of 0.75. This result indicates that significant simulation deviations still exist in regions 13-14 after decoupling from the external system, and the model or parameters within these regions are more likely the direct cause of the simulation mismatch. Therefore, It was retained as a candidate region for the final correctable domain.

[0321] After this round of recursive refinement, the candidate region is further compressed from 5 nodes in the first round to 2 nodes, resulting in:

[0322] .

[0323] To further verify the effectiveness of the identified correctable domain, this example only applies to... The relevant model parameters within the region were verified, and the system dynamic simulation was carried out again. The changes in the errors of key nodes before and after verification are shown in Table 4.

[0324] Table 4: Results of error changes at key nodes before and after.

[0325] node Error before verification Error after verification 10 0.068 0.030 11 0.074 0.032 12 0.086 0.034 13 0.092 0.026 14 0.079 0.028 15 0.056 0.031 16 0.049 0.029

[0326] As can be seen from the results in Table 4, only for the final correctable domain After internal parameter verification, the error at node 13 decreased from 0.092 to 0.026, and the error at node 14 decreased from 0.079 to 0.028. Simultaneously, the errors at nodes 10, 11, 12, 15, and 16, which have strong coupling relationships with this region, also showed a significant decrease, indicating... The region has a dominant influence on the simulation error of surrounding nodes. From the perspective of the overall regional error, the average error of the key region was 0.080 before verification, which decreased to 0.030 after verification, representing a reduction of 62.5%.

[0327] This indicates that the correctable domain identified by this invention not only covers the main sources of error but also significantly improves the overall simulation consistency of the system after parameter verification. This result verifies the effectiveness of the proposed method in identifying error-dominant regions under fault scenarios and also demonstrates that the correctable domain obtained through progressive block verification has clear engineering verification value.

[0328] According to an embodiment of the present invention, an electronic device is also provided, as shown, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps of the method described in any of the above embodiments.

[0329] According to embodiments of the present invention, a computer-readable storage medium is also provided, on which a computer program is stored, wherein the computer program, when executed by a processor, implements the steps of the method described in any of the above embodiments.

[0330] This invention also provides a computer program product, including a computer program stored in a computer-readable storage medium; when a processor of an electronic device reads the computer program from the computer-readable storage medium, the processor executes the computer program, causing the electronic device to perform the steps of any of the methods described in the above embodiments.

[0331] Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0332] It should be understood that the specific embodiments described above are merely illustrative or explanatory of the principles of the invention and do not constitute a limitation thereof. Therefore, any modifications, equivalent substitutions, improvements, etc., made without departing from the spirit and scope of the invention should be included within the protection scope of the invention. Furthermore, the appended claims are intended to cover all variations and modifications falling within the scope and boundaries of the appended claims, or equivalent forms of such scope and boundaries.

Claims

1. A progressive block-based verification method for identifying the correctable domain in power system simulation, characterized in that, include: Dynamic feature extraction and disturbance depth calculation include: using the steady-state value before the disturbance occurs as a reference benchmark, calculating the relative changes of dynamic variables of each node, analyzing the dynamic response characteristics of key quantities, constructing a disturbance depth index, and obtaining the disturbance depth distribution vector of all nodes in the network. Constructing a disturbance propagation skeleton includes: representing the system as an undirected graph based on the power grid topology, characterizing the disturbance propagation associations between nodes, retaining node pairs that satisfy the topological adjacency condition, and forming a network-wide propagation association matrix; constructing a disturbance propagation candidate edge set, and defining the union of high-association paths that meet the propagation strength requirements as the disturbance propagation skeleton set; The initial candidate region screening includes: determining the node error index, constructing the comprehensive error index, determining the initial candidate node set, and merging adjacent candidate nodes into several candidate sub-regions; Block decoupling and hybrid dynamic simulation specifically include: determining boundary conditions, performing hybrid dynamic simulation on the candidate region, and calculating error indices at the region level; Error persistence assessment includes: determining an error persistence threshold based on a regional error persistence index; when the regional error is greater than the error persistence threshold, the regional error is determined to be persistent and retained as a candidate region; Recursive refinement and region compression include: determining the candidate region set, performing recursive refinement, re-identifying the perturbation propagation skeleton of the local network, determining the dominant propagation path within the region, re-dividing the candidate sub-regions according to connectivity, and compressing the local structure again; The determination of the correctable region includes: defining the correctable region as a set of minimal connected regions, thus forming the correctable region.

2. The method according to claim 1, characterized in that, The calculation of the relative changes in the dynamic variables of each node specifically includes: The node dynamic variables include at least voltage amplitude, active power, and frequency; The voltage amplitude, the relative change of node i at time t, is expressed by Formula 1, as follows: (1)； in, The average voltage amplitude of node i during steady-state operation before the disturbance; The relative change in active power is expressed by Formula 2, as follows: (2)； The relative change in frequency is expressed by Formula 3, as follows: (3)； The key quantities include at least the maximum relative change, the average rate of change, the response start time, and the response duration; The maximum relative change, used to characterize the maximum degree to which a node deviates from steady state during the entire disturbance process, is expressed by Formula 4, as follows: (4)； in, This represents the relative change of a certain dynamic quantity at node i, where [ts, te] is the analysis time window; The average rate of change, used to characterize the overall speed of change of the nodal response curve during the disturbance process, is expressed by Formula 5, as follows: (5)； Where T is the number of sampling points; The response start time is used to describe the time sequence in which nodes respond significantly to disturbances. Let the threshold η be the upper limit of the steady-state fluctuation range. When a node satisfies... minimum moment When this time comes, it is defined as the start time of the response of node i; The response duration, used to describe the time it takes for a node to recover from a significant deviation from steady state to within the allowable deviation range, is expressed by Formula 6, as follows: (6)； in, This is the moment when the node response re-enters the steady-state allowable band.

3. The method according to claim 1, characterized in that, The construction of the perturbation depth index yields the perturbation depth distribution vector of all network nodes, specifically including: The perturbation depth of node i is expressed using Formula 7, as follows: (7)； Where α, β, and γ are weighting coefficients, satisfying , , , These are the maximum values ​​of the maximum relative change, the maximum average rate of change, and the maximum response duration for the corresponding indicators of all network nodes, respectively, used for normalization processing; Furthermore, the various disturbance depths are combined into a comprehensive disturbance depth. The comprehensive disturbance depth for node i is defined as shown in Formula 8, as follows: (8)； in, , , These represent the disturbance depths calculated based on voltage, active power, and frequency, respectively. , , For the corresponding weights, satisfying ; The above calculations yield the disturbance depth distribution vector for all network nodes, as shown in Formula 9: (9)； The perturbation depth distribution vector intuitively reflects the influence range of the perturbation in the system and the dynamic excitation process of each node.

4. The method according to claim 1, characterized in that, Based on the power grid topology, the system is represented as an undirected graph, which describes the disturbance propagation correlation between nodes, retains the node pairs that satisfy the topological adjacency condition, and forms a network-wide propagation correlation matrix, specifically including: The system is represented as an undirected graph G=(V,E), where V represents the set of nodes and E represents the set of branches; for any two nodes i and j that have a direct connection, their adjacency relationship is defined as shown in Formula 10, as follows: (10)； The response time difference between node i and node j is defined using Formula 11, as follows: (11)； when When the value is greater than 0, it indicates that the significant response of node j is later than that of node i, and node i is located upstream in the propagation; when If the value is less than 0, it indicates that the propagation order of the two is inconsistent with the assumed direction; For adjacent nodes i and j, the propagation correlation matrix is ​​shown in Formula XII, as follows: (12)； in, , , These are weighting coefficients, reflecting the roles of perturbation depth propagation characteristics, temporal response consistency, and topological connectivity in propagation correlation, respectively, and satisfying the following conditions: ; When constructing the propagation skeleton, only node pairs that satisfy the topological adjacency condition are retained. That is, Cij is calculated when Aij=1, otherwise it is set to zero, forming the propagation correlation matrix of the entire network, as shown in Formula 13, as follows: (13)。 5. The method according to claim 1, characterized in that, The construction of the perturbation propagation candidate edge set, which defines the union of highly correlated paths that meet the propagation strength requirements as the perturbation propagation skeleton set, specifically includes: The construction of the disturbance propagation candidate edge set includes: starting from the disturbance source node or the first response node, searching the entire network for propagation paths, and selecting the path with the largest cumulative weight from all possible paths as the main disturbance propagation path, specifically including: Set the propagation association threshold Retain the associated edges that are above the threshold, and construct the perturbation propagation candidate edge set, as shown in Formula Fourteen, as follows: (14)； Based on the candidate edge set, a propagation path search is performed across the entire network, starting from the disturbance source node or the first response node. The path with the highest cumulative propagation correlation is selected as the main propagation path. Let a propagation path from the disturbance source node s to node m be denoted as... The cumulative propagation weight of this path is calculated using Formula 15, as follows: (15)； The path with the largest cumulative weight is selected from all possible paths as the main propagation path of the perturbation, as expressed by Formula Sixteen: (16)； The set of highly correlated paths that meet the propagation strength requirements is defined as the perturbation propagation skeleton set, specifically including: The set of perturbation propagation skeletons is represented by Formula 17, as follows: (17)； in, This represents the k-th dominant propagation path, where K is the number of main paths retained. In practical applications, K can be determined based on the cumulative propagation weight ratio or the proportion of nodes covered by the path. The skeleton nodes are expanded by neighborhood expansion. For all nodes located on the propagation skeleton, the directly connected neighboring nodes with higher perturbation depths are included in the expanded skeleton set. The expanded skeleton is represented by Formula 18, as follows: (18)； in, The perturbation depth threshold used when expanding the neighborhood.

6. The method according to claim 1, characterized in that, The process of determining the node error index, constructing a comprehensive error index, determining the initial candidate node set, and merging adjacent candidate nodes into several candidate sub-regions specifically includes: The simulation deviation of nodes is quantified by a time-domain overall error index. Let the simulated value and the measured value of node i at time t be respectively... and The node error index is expressed by Formula Nineteen, as follows: (19)； Where T represents the number of sampling points within the analysis time window; Let the voltage error, active power error, and frequency error at node i be respectively... , and The node synthesis error is calculated using Formula 20, as follows: (20)； in, , , Let the error weighting coefficients satisfy: ; If only a single dynamic quantity is used for analysis, then E is used directly. i If a multi-quantity joint evaluation is conducted, then use As a node error indicator; For the sake of consistency, E i and All are denoted as nodal errors E i ; Node i is retained as a candidate node only if it simultaneously satisfies the following conditions: Condition 1: The node is located within the disturbance propagation skeleton or its extended neighborhood; Condition 2: The node disturbance depth is greater than the preset threshold; Condition 3: The node simulation error is greater than the preset threshold; The initial set of candidate nodes is defined using Formula 21, as follows: (21)； in, This indicates the perturbation depth threshold. Indicates the simulation error threshold; Let the mean and standard deviation of the disturbance depth of all nodes in the network be respectively and The mean and standard deviation of the error are respectively and The threshold can then be determined using formulas 22 and 23: (22)； (23)； in, and This is an empirical coefficient; Adjacent candidate nodes are merged into several candidate sub-regions, and the system adjacency matrix is ​​given by... If nodes i and j both belong to If Aij = 1, then the two are considered to belong to the same candidate region. This can be achieved through connected component search. Divide into R sub-regions, as shown in Formula 24: (24)； in, This represents the r-th candidate sub-region; To avoid rendering subsequent block-based verification meaningless due to a single discrete node or extremely small region, we define a region. The number of nodes is Then only the sub-regions that meet the following conditions will be retained, as shown in Formula 25: (25)； Where Nmin is the minimum size threshold of the candidate region; The average perturbation depth and average error index at the regional level are calculated to evaluate the overall importance of each region. For the r-th candidate region, as shown in Formula 26, the following is an example: (26)； (27)； To comprehensively assess the priority assessment value of a region, a regional priority index can be defined, as shown in Formula 28: (28)； in, and Let the weighting coefficients satisfy: .

7. The method according to claim 1, characterized in that, The determination of boundary conditions, performing hybrid dynamic simulation within the candidate region, and calculating the region-level error index specifically includes: For each candidate sub-region The set of regional boundary nodes is determined based on its connection relationship with external systems. ; Boundary nodes use actual measurements as input constraints, while nodes within the region are still updated by the simulation model. Boundary conditions are expressed using Equation 29: (29)； in, Represents the measured dynamic quantity of boundary node i; After boundary injection, a hybrid dynamic simulation is performed on the candidate region to obtain the simulation response curves of each internal node; The data is compared with the corresponding measured data to calculate the regional error index, which is used to measure the simulation accuracy of the region under local decoupling conditions. area The average error is expressed using Formula 30: (30)； in, This is an error index for nodes within the region. This represents the number of nodes contained in the region.

8. The method according to claim 1, characterized in that, The step of determining an error persistence threshold based on a regional error persistence index, and determining that the regional error is persistent when it exceeds the error persistence threshold, and retaining it as a candidate region, specifically includes: Set up a region The average error in the k-th round of recognition is The average error after completing local decoupling and hybrid dynamic simulation is The persistence of regional error is then expressed by formula 31: (31)； in, The closer it is to 1, the smaller the change in regional error after localization, and the stronger the persistence of the error; The smaller the value, the more the regional error is significantly reduced after decoupling, and the greater the influence of external propagation on the deviation. Error persistence threshold It is 0.7, when a certain region satisfies When the error is ≥0.7, the region is considered to have persistent error and should be retained as a key candidate region; when If the error is less than 0.7, it is considered that the error in this region mainly originates from external system transmission, and it should be removed from the candidate region or its subsequent analysis priority should be reduced.

9. The method according to claim 1, characterized in that, The process involves determining a set of candidate regions, recursively refining it, re-identifying the perturbation propagation skeleton of the local network, and determining the dominant propagation path within each region; then, it re-divides the candidate sub-regions according to connectivity, and further compresses the local structure, including: Let the set of candidate regions retained after the k-th round of analysis be . Then, the object of the recursive analysis in the (k+1)th round consists of the regions in the kth round that satisfy the error persistence condition, which can be represented as: (32)； in, This represents the r-th candidate region in the k-th round. It serves as an indicator of the persistence of its error; The termination conditions are as shown in conditions four, five, and six: Condition 4: When the number of nodes in a certain region is already below the preset scale threshold, it will no longer be further subdivided, but will be directly used as the final candidate region; Condition 5: When the range of a region changes very little in two adjacent rounds of analysis, it indicates that its boundary has basically stabilized, and the recursion should be stopped. Condition 6: When the error of the region after localization meets the engineering requirements, that is, further refinement can no longer significantly improve the recognition accuracy, the recursive process is terminated; The defined correctable domain is a set of minimal connected regions, forming the correctable domain, specifically including: The final correctable region is defined as the set of minimum connected regions that satisfy the above constraints, and the final identification result is denoted as... It is represented by formula thirty-three, as follows: (33)； in, This represents the candidate regions that are retained after recursive filtering. This indicates the number of nodes or components contained in the region; When there are multiple independent error-dominant regions in the system, multiple correctable regions can be output simultaneously.

10. A computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the method according to any one of claims 1-9.

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