Power quality abnormality tracing method and system based on multivariate statistics decoupling

Abstract

This invention discloses a power quality anomaly tracing method based on multivariate statistical decoupling, comprising: acquiring historical power quality data and relevant data at the time of analysis, and processing the data; identifying overall anomalies based on Hotelling T² control charts; if an overall anomaly is identified, performing anomaly statistical decoupling analysis based on Mason decomposition, and obtaining the order conditional statistics, unconditional statistics, and complete conditional statistics of each node, and determining whether each statistic reaches a significance level; when both the unconditional and complete conditional statistics of a node are significant, the node is the root cause; when the unconditional statistics of a node are not significant but the complete conditional statistics are significant, the node is a relational anomaly; when the unconditional statistics of a node are significant but the complete conditional statistics are not significant, the node is a cascading phenomenon; this invention improves the location efficiency, analysis accuracy, and decision-making pertinence of power quality operation and maintenance in distribution networks.

Description

Technical Field

[0001] This invention relates to the field of power distribution network technology, and more specifically, to a method and system for tracing the source of power quality anomalies based on multivariate statistical decoupling. Background Technology

[0002] In actual power distribution network operation, power quality anomalies typically exhibit characteristics such as multi-node coupling, multi-indicator linkage, and complex propagation relationships. The same anomaly is often accompanied by synchronous shifts in multiple monitoring quantities, making anomaly source identification and responsibility variable location difficult. Existing power quality analysis methods mostly focus on anomaly detection, limit violation identification, or simple ranking analysis, lacking a detailed characterization of the correlation between nodes and indicators during anomaly formation. They usually only provide an overall anomaly conclusion, failing to further distinguish between dominant, associated, and disturbed anomalies. This results in anomaly investigation still heavily relying on manual experience, leading to insufficient efficiency and accuracy in location. Meanwhile, traditional power quality contribution analysis and source tracing methods usually rely on large amounts of measured data, often requiring the acquisition of vector datasets of multiple variables such as power, voltage, and current, and the establishment of a relatively complete multi-source synchronous observation foundation. This is difficult to obtain in actual distribution networks, especially in low-voltage distribution substation scenarios, resulting in high implementation costs and low engineering feasibility, thus limiting the widespread application of these methods in practical operation scenarios.

[0003] Therefore, how to conduct further causal analysis based on existing anomaly identification results, focusing on the moment of anomaly occurrence, to isolate the coupling effects of multivariate correlations, quantitatively characterize the actual impact of each node or indicator on the overall anomaly, and achieve lightweight determination of anomaly source location and contribution without relying on large-scale, highly complete vector measurement data, has become a pressing technical problem in this field. Based on this, it is necessary to propose a power quality anomaly situation tracing method based on multivariate statistical control chart decoupling analysis. By decomposing and analyzing the correlation contribution of anomaly statistics in power quality monitoring data, this method identifies key influencing factors and their relationships in the anomaly formation process, providing a basis for rapid location, accurate handling, and operational decision-making for power quality anomalies. Summary of the Invention

[0004] The purpose of this invention is to propose a method and system for tracing the source of power quality anomalies based on decoupling of multivariate statistics. On the basis of existing anomaly identification results, the method performs causal analysis at the time of anomaly occurrence. By decomposing the anomaly statistics and removing the correlation coupling effects between multiple variables, the method quantitatively characterizes the actual degree of influence of each node or indicator on the overall anomaly, and realizes the differentiation and identification of dominant anomalies, related anomalies and disturbed anomalies, thereby improving the accuracy and pertinence of power quality anomaly source location.

[0005] Specifically, this invention provides a power quality anomaly tracing method based on multivariate statistical decoupling, comprising the following steps:

[0006] Acquire historical power quality data and relevant data for the time period to be analyzed, and process the data;

[0007] Overall anomalies were identified based on Hotelling T² control charts;

[0008] If an overall anomaly is identified, anomaly statistics decoupling analysis is performed based on Mason decomposition, and the order condition statistics, unconditional statistics, and fully conditional statistics of each node are obtained, and it is determined whether each statistic reaches a significant level.

[0009] Anomaly type identification: When both the unconditional statistic and the complete conditional statistic of a node are significant, the node is determined to be the root cause; when the unconditional statistic of a node is not significant but the complete conditional statistic is significant, the node is determined to be an anomaly in the relationship; when the unconditional statistic of a node is significant but the complete conditional statistic is not significant, the node is determined to be a symptom of a related phenomenon.

[0010] Furthermore, the method also includes determining the source tracing result, and the method for determining the source tracing result is as follows:

[0011] The set of nodes identified as the root cause is denoted as C. m Then set C m The node in the equation is used as the power quality disturbance source node at that moment; when C m When there are multiple nodes, their priority investigation order is determined according to the sorting result of the order condition statistics, so as to obtain the anomaly source location result at that time.

[0012] The set of nodes identified as having abnormal relationships is denoted as R. m Then set R m The nodes in R are considered as key influencing nodes at that moment; when R m When there are multiple nodes, their order of influence is determined according to the sorting results of the order condition statistics, so as to obtain the key influencing node identification results at this abnormal moment;

[0013] The set of nodes identified as cascading phenomena is denoted as L. m Then set L m The nodes in the L are those affected by the abnormal propagation at that moment and require close monitoring; when L m When a node contains multiple nodes, its priority order is determined by the sorting results of the order condition statistics.

[0014] Furthermore, the method also includes generating disposal suggestions; the disposal suggestions include:

[0015] When a node is identified as the root cause, it indicates that the node still exhibits significant abnormalities after the influence of other nodes is removed. It is the dominant source of abnormality that causes the overall power quality abnormality at that moment or the priority to be investigated, and its handling priority is the highest.

[0016] When a node is determined to have an abnormal relationship, it indicates that the node mainly reflects abnormal propagation relationships, variable coupling relationships, or abnormal association structures, suggesting that the node may be located in an abnormal propagation path, and its handling priority is secondary.

[0017] When a node is identified as a cascading phenomenon, it indicates that the node's anomaly is mainly caused by the transmission or coupling of other anomaly sources. It is a symptom accompanying the abnormal result rather than the primary anomaly source, and its handling priority is the lowest.

[0018] Furthermore, the method for identifying overall anomalies based on the Hotelling T² control chart is as follows:

[0019] The Hotelling T² statistic corresponding to the time to be analyzed is calculated. Based on the historical sample size, variable dimensions, and significance level, the upper limit of the Hotelling T² control chart is calculated using the F distribution when the sample conditions are met. The Hotelling T² statistic corresponding to the time to be analyzed is compared with the upper limit of the control chart. If the Hotelling T² statistic is greater than the upper limit of the control chart, it is determined that there is an overall anomaly at that time, thus realizing the overall detection of abnormal power quality conditions.

[0020] Furthermore, the method for obtaining the order conditional statistics, unconditional statistics, and fully conditional statistics for each node, and determining whether each statistic reaches a significance level, is as follows:

[0021] Calculate the unconditional statistic T for all nodes at each anomalous time. 2 j Ordinal conditional statistic T 2 j·1,…,j−1 and the complete conditional statistic T 2 j·1,…,j−1,j+1,…,p Calculate the critical values ​​of unconditional statistics, ordinal conditional statistics, and complete conditional statistics:

[0022] ;

[0023] Where n is the number of historical samples; F 1−α (1, n−1) represents the quantile of the F distribution with 1 and n−1 degrees of freedom at the confidence level of 1−α.

[0024] The unconditional statistic, ordinal conditional statistic, or fully conditional statistic of a node is compared with the critical value UCL1. If the statistic is greater than the critical value, it is considered that the statistic has reached a significant level in the corresponding sense.

[0025] A power quality anomaly tracing system based on multivariate statistical decoupling includes:

[0026] The data acquisition and processing module acquires historical power quality data and relevant data for the time to be analyzed, and processes the data.

[0027] The overall anomaly identification module is used to identify overall anomalies based on the Hotelling T² control chart;

[0028] The outlier statistics decoupling analysis module is used to perform outlier statistics decoupling analysis based on Mason decomposition if an overall outlier is identified, and to obtain the order condition statistics, unconditional statistics and fully conditional statistics of each node, and to determine whether each statistic reaches a significance level.

[0029] The anomaly type identification module is used to determine that a node is the root cause when both its unconditional and complete conditional statistics are significant; to determine that a node is an anomaly in relation when its unconditional statistics are not significant but its complete conditional statistics are significant; and to determine that a node is a cascading phenomenon when its unconditional statistics are significant but its complete conditional statistics are not significant.

[0030] A non-transitory computer-readable storage medium storing a computer program that, when executed by a processor, implements the power quality anomaly tracing method based on multivariate statistical decoupling as described above.

[0031] An electronic device includes 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 power quality anomaly tracing method based on multivariate statistical decoupling as described above.

[0032] The beneficial technical effects of this invention are as follows:

[0033] This invention provides a method for tracing the source of power quality anomalies based on decoupled analysis of multivariate statistical control charts. Building upon the overall anomaly identification using multivariate statistical control charts, it further introduces a statistical decomposition and decoupling analysis mechanism oriented towards the anomaly moment. This allows for detailed analysis of the overall anomaly, quantitatively identifying the actual role of each node or indicator in the anomaly formation process. It overcomes the shortcomings of existing methods, which typically only provide overall anomaly conclusions and struggle to further pinpoint the dominant anomaly source and distinguish accompanying anomalies. This method constructs a mean vector and covariance matrix based on historical monitoring data, combined with Hotelling... The T² control chart effectively detects overall power quality anomalies and utilizes Mason decomposition to obtain sequential condition T², unconditional T², and fully conditional T², thereby enabling the differentiation and identification of root causes, relational anomalies, and cascading phenomena. This provides a more accurate basis for anomaly source location, key influencing factor extraction, anomaly propagation relationship analysis, handling priority determination, and source tracing result derivation. Furthermore, this invention does not rely on a model for extrapolating power from source load power to power quality state quantities, nor on highly complete vector measured data such as power, voltage, and current. Instead, it can perform cause analysis and source tracing based on existing power quality monitoring data, reducing the method's dependence on data completeness and on-site synchronous measurement conditions. This improves its engineering applicability in actual distribution networks, especially in low-voltage distribution substations, and helps extend power quality analysis from anomaly detection to anomaly tracing and precise handling, thereby improving the location efficiency, analysis accuracy, and decision-making pertinence of power quality operation and maintenance in distribution networks. Attached Figure Description

[0034] Figure 1 This is a flowchart of the power quality anomaly tracing method based on multivariate statistical decoupling provided in the embodiments of the present invention;

[0035] Figure 2 This is the statistical decomposition result at 10:44 on the test day provided in Embodiment 2 of the present invention;

[0036] Figure 3 This is the statistical decomposition result at 12:00 on the test day provided in Embodiment 2 of the present invention;

[0037] Figure 4 This is the statistical decomposition result at 18:00 on the test day provided in Embodiment 2 of the present invention. Detailed Implementation

[0038] Example 1

[0039] This embodiment discloses a power quality anomaly tracing method based on multivariate statistical decoupling, the method including the following steps:

[0040] The process involves acquiring historical power quality data and relevant data for the time period to be analyzed, and then processing the data. Both the historical power quality data and the relevant data for the time period to be analyzed include time series data and power quality status quantities corresponding to multiple monitoring nodes or monitoring variables. The process includes format reading, column name consistency verification, and variable alignment of the historical data and the relevant data for the time period to be analyzed. Time series data and multivariate observation matrices are extracted to ensure that both types of data have consistent variable dimensions, node order, and statistical caliber, providing a unified data foundation for subsequent multivariate statistical analysis. Specifically...

[0041] Suppose a power distribution network contains p power quality monitoring nodes, denoted as nodes 1, 2, ..., p. Each node is equipped with power quality monitoring equipment (such as voltage, harmonic, and three-phase unbalance measurement equipment) to collect the power quality status of the node at the corresponding time. Of course, any monitoring point may be a state anomaly point when an anomaly occurs, or it may be identified as an anomaly source node in the subsequent source tracing analysis.

[0042] Suppose that a total of n multivariate observation data points are collected during the historical normal operation phase, and the observation vector at the i-th time point is denoted as:

[0043]

[0044] Among them, X ij This represents the power quality observation value of the j-th monitoring node at the i-th historical moment.

[0045] Calculate the sample mean vector based on historical samples. With the sample covariance matrix They are respectively denoted as:

[0046] ;

[0047] ;

[0048] in,

[0049] ;

[0050] ;

[0051] In the formula, X̄ j Let s represent the historical mean of the j-th monitoring node. jk Let s represent the sample covariance between the j-th node and the k-th node. When j=k, s jj The sample variance that degenerates into the historical sample sequence of the j-th monitoring node.

[0052] For any given moment in time to be analyzed, the power quality observation vector is denoted as:

[0053]

[0054] Among them, X j This represents the power quality observation value of the j-th monitoring node at the time to be analyzed.

[0055] Using the historical sample mean vector X̄ and covariance matrix S, calculate the Hotelling T² statistic at this moment:

[0056] ;

[0057] And calculate the upper limit of control:

[0058] ;

[0059] Where p is the number of monitoring nodes, n is the number of historical samples, α is the significance level, and F 1−α (p, n−p) represents the quantile of the F distribution with degrees of freedom p and n−p at confidence level 1−α; when T²>UCL, it is determined that there is an overall anomaly at this moment, and the subsequent statistical decoupling and source tracing analysis is performed; when T²≤UCL, it is determined that there is no overall anomaly at this moment.

[0060] For the identified abnormal moments, this invention uses Mason's statistical decomposition concept to decouple the overall abnormal statistics.

[0061] First, the overall T² statistic is decomposed into several independent components; according to a predetermined node order, the overall statistic can be expressed as:

[0062] ;

[0063] Among them, T 2 1 represents the unconditional statistic of the first node, T 2 2·1 T represents the conditional statistic of the second node given the first node. 2 3·1,2 This represents the conditional statistic of the third node given the conditions of the first and second nodes, and so on, T 2 p·1,…,p−1 This represents the conditional statistic of the p-th node given the previous p-1 nodes. The decoupling formula for this statistic reflects the sequential contribution of each node to the population T². In this embodiment, these components are collectively referred to as the sequential conditional components.

[0064] The unconditional statistic of the j-th node is denoted as:

[0065] ;

[0066] In the formula, X jLet X̄ be the power quality observation value of the j-th node at the anomalous moment. j Let s be the historical mean of the j-th node. jj Let be the historical sample variance of the j-th node; this unconditional statistic is used to characterize the degree of deviation of the node from its historical normal level.

[0067] The order condition statistic for the j-th node when the set of preceding nodes {1,…,j−1} is a condition is denoted as:

[0068] ;

[0069] Among them, X̄ j·1,…,j−1 This represents the conditional mean estimate of the j-th node given the first j-1 nodes; s 2 j·1,…,j−1 This represents the conditional variance estimate of the j-th node given the preceding j-1 nodes; this order conditional statistic reflects the incremental contribution of the j-th node to the overall outlier statistic after considering the influence of the preceding nodes.

[0070] To further determine the degree of essential anomaly of a node after removing the influence of all other nodes, the complete conditional statistic of the j-th node under the condition of all other nodes is also calculated, denoted as:

[0071] ;

[0072] Among them, X̄ j·1,…,j−1,j+1,…,p This represents the conditional mean estimate of the j-th node given the other p-1 nodes excluding the j-th node; s 2 j·1,…,j−1,j+1,…,p This represents the conditional variance estimate of the j-th node given the p-1 nodes excluding the j-th node. This statistic is used to characterize whether the j-th node remains significantly anomalous after excluding the combined effects of other nodes.

[0073] In this implementation, the unconditional statistic T is calculated for all nodes at each anomalous time. 2 j Ordinal conditional statistic T 2 j·1,…,j−1 and the complete conditional statistic T 2 j·1,…,j−1,j+1,…,p To determine whether a single-node statistic has reached a significance level, the critical values ​​for the unconditional statistic, the ordinal conditional statistic, and the fully conditional statistic are calculated:

[0074] ;

[0075] Among them, F 1−α(1, n−1) represents the quantile of the F distribution with 1 and n−1 degrees of freedom at the confidence level of 1−α.

[0076] The unconditional statistic, ordinal conditional statistic, or fully conditional statistic of a node is compared with the critical value UCL1. If the statistic is greater than the critical value, it is considered that the statistic has reached a significant level in the corresponding sense.

[0077] Based on the calculation results of the above three types of statistics, anomaly type identification is performed for each node at anomaly times. When the unconditional statistic T of a certain node... 2 j and complete conditional statistic T 2 j·1,…,j−1,j+1,…,p When all are significant, the node is determined to be the root cause, indicating that the node has both a significant self-bias and remains significantly abnormal after removing the influence of other nodes; when the unconditional statistic T of a node is significant... 2 j Insignificant but complete conditional statistic T 2 j·1,…,j−1,j+1,…,p When significant, the node is determined to be an anomaly in the relationship, indicating that the node mainly exhibits an abnormal relationship structure between nodes; when the unconditional statistic T of a node is significant... 2 j Significant and complete conditional statistic T 2 j·1,…,j−1,j+1,…,p If the phenomenon is not significant, the node is determined to be a cascading phenomenon, indicating that although the node shows an offset, it is more likely to be an accompanying anomaly caused by the transmission effect of other abnormal nodes.

[0078] Finally, regarding the abnormal time t m (m=1,2,…), the nodes are sorted according to the anomaly type priority and the corresponding order condition statistics of each monitoring node j (j=1,2,…,p). Among them, the root cause nodes have the highest priority, followed by the relational anomaly nodes, and the related phenomenon nodes have the lowest priority. Within the same anomaly type priority, they are sorted from largest to smallest according to the order condition statistics to represent the incremental contribution of the corresponding node to the overall anomaly statistics at that anomaly time.

[0079] For the abnormal time t m The set of nodes identified as the root cause is denoted as C. m Then set C m The node in the equation is used as the power quality disturbance source node at that moment; when C m When there are multiple nodes, their priority investigation order is determined according to the sorting results of the sequence condition statistics, so as to obtain the anomaly source location result at that time.

[0080] For the abnormal time t m The set of nodes identified as having abnormal relationships is denoted as R.m Then set R m The nodes in R are considered as key influencing nodes at that moment; when R m When there are multiple nodes, their influence strength is determined according to the sorting results of the order condition statistics, so as to obtain the key influencing node identification results at the time of the anomaly.

[0081] For the abnormal time t m The set of nodes identified as related phenomena is denoted as L. m Then set L m The nodes in the L are those affected by the abnormal propagation at that moment and require close monitoring; when L m When a node contains multiple nodes, its priority order is determined by the sorting results of the order condition statistics.

[0082] Therefore, at the abnormal time t m The causal tracing results are derived from the set of disturbance source nodes C. m The set of key influencing nodes R m And the set of nodes L that needs close attention m The three types of nodes and their ranking results collectively characterize the dominant source, associated influence path, and disturbance propagation behavior of the power quality anomaly at that moment, and generate corresponding handling suggestions accordingly. Specifically, when a node is identified as the root cause, it indicates that the node still exhibits significant anomalies after the influence of other nodes is removed, making it the dominant anomaly source causing the overall power quality anomaly at that moment or a priority target for investigation, and its handling priority is the highest. When a node is identified as having an abnormal relationship, it indicates that the node mainly reflects anomalies in anomaly propagation relationships, variable coupling relationships, or associated structures, suggesting that the node may be located within anomaly propagation paths, and its handling priority is the second highest. When a node is identified as a symptom, it indicates that the node's anomaly is mainly caused by the propagation or coupling influence of other anomaly sources, belonging to the accompanying manifestation of the anomaly rather than the primary anomaly source, and its handling priority is the lowest.

[0083] Example 2

[0084] As an example, this embodiment provides a specific analysis example based on the method of Embodiment 1:

[0085] An improved IEEE 33-node distribution network incorporating three photovoltaic (PV) users was selected as a case study. The PV users, numbered 7, 17, and 24, acted as disturbance sources connected to the distribution network. First, 24-hour voltage data from a period of low PV output without voltage exceedances were used as historical data to construct control limits. Second, 24-hour voltage data from a period of high PV output with significant voltage exceedances were used as test data to conduct power quality source tracing tests. This demonstrated whether the proposed method could identify PV sources causing power quality problems based on voltage curves. Finally, the accuracy of the source tracing was assessed by comparing the distance between the high-contribution nodes identified by multivariate statistical control and the actual PV connection nodes.

[0086] The voltage sampling data for this IEEE 33 node is collected once per minute, resulting in a total of 1440 sampling points over a 24-hour period. In this specific example, p is 33 and n is 1440.

[0087] The IEEE 33-node distribution network contains 33 power quality monitoring nodes, denoted as node 1, 2, ..., 33. Each node is equipped with power quality monitoring equipment to collect power quality status parameters at that node at a given time. Any monitoring point may exhibit an anomaly when an anomaly occurs, or it may be identified as the source node of the anomaly in subsequent source tracing analysis. Assume that a total of 1440 multivariate observation data points were collected during the historical normal operation phase, and the observation vector at the i-th time point is denoted as:

[0088]

[0089] Among them, X ij Let represent the power quality observation value of the j-th monitoring node at the i-th historical moment. Based on the historical samples, calculate the sample mean vector and sample covariance matrix, denoted as:

[0090] ;

[0091] ;

[0092] The formula for calculating each element in the vector is:

[0093] ;

[0094] ;

[0095] In the formula, X̄ j Let s represent the historical mean of the j-th monitoring node. jk This represents the sample covariance between the j-th node and the k-th node; when j=k, s jj The sample variance that degenerates into the historical sample sequence of the j-th monitoring node.

[0096] For any given moment in time to be analyzed, the power quality observation vector is denoted as:

[0097] ;

[0098] Among them, X j This represents the observation value of the j-th monitoring node at the time to be analyzed;

[0099] Using the historical sample mean vector X̄ and covariance matrix S, calculate the Hotelling T² statistic at this moment:

[0100] ;

[0101] And calculate the upper limit of control:

[0102] ;

[0103] Where p is the number of monitoring nodes, n is the number of historical samples, α is the significance level, and F 1−α (p, n−p) represents the quantiles of the F distribution with degrees of freedom p and n−p at a confidence level of 1−α. When T²>UCL, a global anomaly is determined to exist at that moment, and subsequent statistical decoupling and source tracing analysis is performed; when T²≤UCL, no global anomaly is determined to exist at that moment.

[0104] For identified anomalous moments, this invention employs Mason's statistic decomposition approach to decouple the overall anomalous statistic. First, the overall T² statistic is decomposed into several independent components. Following a predetermined node order, the overall statistic can be expressed as:

[0105] ;

[0106] Among them, T 2 1 represents the unconditional statistic of the first node, T 2 2·1 T represents the conditional statistic of the second node given the first node. 2 3·1,2 This represents the conditional statistic of the third node given the conditions of the first and second nodes, and so on, T 2 p·1,…,p−1 This represents the conditional statistic of the p-th node given the previous p-1 nodes; the decoupling formula of this statistic reflects the sequential contribution of each node to the total T², so in this embodiment these components are collectively referred to as sequential conditional components.

[0107] The unconditional statistic of the j-th node is denoted as:

[0108] ;

[0109] In the formula, X j Let X̄ be the observation value of the j-th node at the anomalous moment. j Let s be the historical mean of the j-th node. jj Let be the historical sample variance of the j-th node; this unconditional statistic is used to characterize the degree of deviation of the node from its historical normal level.

[0110] The order condition statistic for the j-th node when the set of preceding nodes {1,…,j−1} is a condition is denoted as:

[0111] ;

[0112] Among them, X̄ j·1,…,j−1 This represents the conditional mean estimate of the j-th node given the first j-1 nodes; s 2 j·1,…,j−1 This represents the conditional variance estimate of the j-th node under the same conditions; this order conditional statistic reflects the incremental contribution of the j-th node to the overall outlier statistic after considering the influence of preceding nodes.

[0113] To further determine the degree of essential anomaly of a node after removing the influence of all other nodes, the complete conditional statistic of the j-th node under the condition of all other nodes is also calculated, denoted as:

[0114] ;

[0115] Among them, X̄ j·1,…,j−1,j+1,…,p This represents the conditional mean estimate of the j-th node given the other p-1 nodes excluding the j-th node; s 2 j·1,…,j−1,j+1,…,p This represents the conditional variance estimate of the j-th node under the same conditions; this statistic is used to characterize whether the j-th node remains significantly abnormal after excluding the combined effects of other nodes.

[0116] In this implementation, the unconditional statistic T is calculated for all nodes at each anomalous time. 2 j Ordinal conditional statistic T 2 j·1,…,j−1 and the complete conditional statistic T 2 j·1,…,j−1,j+1,…,p To determine whether a single-node statistic has reached a significance level, the univariate critical value is calculated:

[0117]

[0118] Among them, F 1−α(1, n−1) represents the quantiles of the F-distribution with 1 and n−1 degrees of freedom at confidence level 1−α. When the statistic corresponding to a node is greater than UCL1, the node is considered to be significant in the corresponding sense.

[0119] After applying the algorithm, three root causes of statistical control anomalies were identified within 1440 time points of the photovoltaic system, located at 10:44, 12:00, and 18:00 on the test day, with a calculated critical value of 3.85. The statistical distribution of the remaining 32 nodes, excluding the root node, is as follows: Figure 2 , 3 As shown in Tables 1, 2, and 3, the distribution of the top five statistical contributions is as follows.

[0120] Table 1. Source analysis results of voltage problems in the IEEE 33-node distribution network area at 10:44.

[0121] 1 24 6.7 4.045 4.781 root cause yes 2 17 4.21 0.108 8.079 abnormal relationship yes 3 23 3.018 2.839 7.737 abnormal relationship no 4 21 0.785 3.883 0.708 Collateral phenomena no 5 7 0.026 3.989 1.995 Collateral phenomena yes

[0122] Table 2. Source analysis results of voltage problems in the IEEE 33-node distribution network area at 12:00.

[0123] 1 17 2.586 4.498 4.981 root cause yes 2 7 5.41 4.54 1.094 Collateral phenomena yes 3 24 3.03 4.819 2.992 Collateral phenomena yes 4 12 1.181 4.379 1.265 Collateral phenomena no 5 11 0.039 4.784 2.69 Collateral phenomena no

[0124] Table 3. Source analysis results of voltage problems in the IEEE 33-node distribution network area at 18:00

[0125] 1 7 2.294359 3.906557 6.125269 root cause yes 2 8 5.420604 3.17773 4.438899 abnormal relationship no 3 24 6.979558 3.931584 3.197845 Collateral phenomena yes 4 17 1.67158 4.966206 1.611187 Collateral phenomena yes 5 28 0.78854 5.157707 1.01199 Collateral phenomena no

[0126] The results from the actual calculations in Tables 1, 2, and 3 demonstrate that the proposed power quality anomaly tracing method exhibits good effectiveness and engineering applicability. This method does not rely on additional operational information such as photovoltaic output, power flow distribution, or power injection; it accurately locates the key distributed photovoltaic power source causing the problem solely based on the voltage time series curves of each node in the distribution network. For the three typical anomaly times of 10:44, 12:00, and 18:00 on the test day, the actual photovoltaic access nodes all appeared at the top of the statistical contribution ranking, and the key photovoltaic source could be reliably identified. A small number of high-ranking nodes not directly connected to photovoltaics were also distributed in adjacent electrical areas, reflecting the cascading effects of the anomaly propagation. This indicates that the method of this invention can effectively trace the cause of distribution network anomalies based solely on voltage limit curves. It is particularly suitable for distribution network anomaly analysis scenarios where only voltage monitoring data is available on-site and complete source-load information is difficult to obtain, providing a reliable basis for quickly identifying the key distributed power source causing power quality problems.

[0127] Example 3

[0128] This embodiment provides a power quality anomaly tracing system based on multivariate statistical decoupling, including:

[0129] The data acquisition and processing module acquires historical power quality data and relevant data for the time to be analyzed, and processes the data.

[0130] The overall anomaly identification module is used to identify overall anomalies based on the Hotelling T² control chart;

[0131] The outlier statistics decoupling analysis module is used to perform outlier statistics decoupling analysis based on Mason decomposition if an overall outlier is identified, and to obtain the order condition statistics, unconditional statistics and fully conditional statistics of each node, and to determine whether each statistic reaches a significance level.

[0132] The anomaly type identification module is used to determine that a node is the root cause when both its unconditional and complete conditional statistics are significant; to determine that a node is an anomaly in relation when its unconditional statistics are not significant but its complete conditional statistics are significant; and to determine that a node is a cascading phenomenon when its unconditional statistics are significant but its complete conditional statistics are not significant.

[0133] A non-transitory computer-readable storage medium storing a computer program that, when executed by a processor, implements the power quality anomaly tracing method based on multivariate statistical decoupling as described above.

[0134] Furthermore, the present invention adopts the following technical solution:

[0135] An electronic device includes 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 power quality anomaly tracing method based on multivariate statistical decoupling as described above.

[0136] From the above description of the embodiments, those skilled in the art will clearly understand that the facilities of the present invention can be implemented using software plus necessary general-purpose hardware platforms. Embodiments of the present invention can be implemented using existing processors, or by dedicated processors used for this or other purposes for suitable systems, or by hardwired systems. Embodiments of the present invention also include non-transitory computer-readable storage media, comprising machine-readable media for carrying or having machine-executable instructions or data structures stored thereon; such machine-readable media can be any available medium accessible by a general-purpose or special-purpose computer or other machine with a processor. For example, such machine-readable media can include RAM, ROM, EPROM, EEPROM, CD-ROM or other optical disc storage, disk storage or other magnetic storage devices, or any other medium that can be used to carry or store the required program code in the form of machine-executable instructions or data structures and is accessible by a general-purpose or special-purpose computer or other machine with a processor. When information is transmitted or provided to a machine via a network or other communication connection (hardwired, wireless, or a combination of hardwired and wireless), that connection is also considered a machine-readable medium.

[0137] The technical solution of the present invention has been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after such changes or substitutions will all fall within the scope of protection of the present invention.

Claims

1. A power quality anomaly tracing method based on multivariate statistical decoupling, characterized in that, Includes the following steps: Acquire historical power quality data and relevant data for the time period to be analyzed, and process the data; Overall anomalies were identified based on Hotelling T² control charts; If an overall anomaly is identified, anomaly statistics decoupling analysis is performed based on Mason decomposition, and the order condition statistics, unconditional statistics, and fully conditional statistics of each node are obtained, and it is determined whether each statistic reaches a significant level. Anomaly type identification: When both the unconditional statistic and the complete conditional statistic of a node are significant, the node is determined to be the root cause; when the unconditional statistic of a node is not significant but the complete conditional statistic is significant, the node is determined to be an anomaly in the relationship; when the unconditional statistic of a node is significant but the complete conditional statistic is not significant, the node is determined to be a symptom of a related phenomenon.

2. The power quality anomaly tracing method based on multivariate statistical decoupling according to claim 1, characterized in that: The method also includes determining the source tracing result, and the method for determining the source tracing result is as follows: The set of nodes identified as the root cause is denoted as C. m Then set C m The node in the equation is used as the power quality disturbance source node at that moment; when C m When there are multiple nodes, their priority investigation order is determined according to the sorting result of the order condition statistics, so as to obtain the anomaly source location result at that time. The set of nodes identified as having abnormal relationships is denoted as R. m Then set R m The nodes in R are considered as key influencing nodes at that moment; when R m When there are multiple nodes, their order of influence is determined according to the sorting results of the order condition statistics, so as to obtain the key influencing node identification results at this abnormal moment; The set of nodes identified as cascading phenomena is denoted as L. m Then set L m The nodes in the L are those that are affected by the abnormal propagation at that moment and need to be closely monitored; when L m When a node contains multiple nodes, their priority order is determined by the sorting results of the order condition statistics.

3. The power quality anomaly tracing method based on multivariate statistical decoupling according to claim 1, characterized in that: The method further includes generating disposal suggestions; the disposal suggestions include: When a node is identified as the root cause, it indicates that the node still exhibits significant abnormalities after the influence of other nodes is removed. It is the dominant source of abnormality that causes the overall power quality abnormality at that moment or the priority to be investigated, and its handling priority is the highest. When a node is determined to have an abnormal relationship, it indicates that the node mainly reflects abnormal propagation relationships, variable coupling relationships, or abnormal association structures, suggesting that the node may be located in an abnormal propagation path, and its handling priority is secondary. When a node is identified as a cascading phenomenon, it indicates that the node's anomaly is mainly caused by the transmission or coupling of other anomaly sources. It is a symptom accompanying the abnormal result rather than the primary anomaly source, and its handling priority is the lowest.

4. The power quality anomaly tracing method based on multivariate statistical decoupling according to claim 1, characterized in that: The method for identifying overall anomalies based on Hotelling T² control charts is as follows: The Hotelling T² statistic corresponding to the time to be analyzed is calculated. Based on the historical sample size, variable dimensions, and significance level, the upper limit of the Hotelling T² control chart is calculated using the F distribution when the sample conditions are met. The Hotelling T² statistic corresponding to the time to be analyzed is compared with the upper limit of the control chart. If the Hotelling T² statistic is greater than the upper limit of the control chart, it is determined that there is an overall anomaly at that time, thus realizing the overall detection of abnormal power quality conditions.

5. The power quality anomaly tracing method based on multivariate statistical decoupling according to claim 1, characterized in that: The method for obtaining the ordinal conditional statistics, unconditional statistics, and fully conditional statistics for each node, and determining whether each statistic reaches a significance level, is as follows: Calculate the unconditional statistic T for all nodes at each anomalous time. 2 j Ordinal conditional statistic T 2 j·1,…,j−1 and the complete conditional statistic T 2 j·1,…,j−1,j+1,…,p Calculate the critical values ​​of unconditional statistics, ordinal conditional statistics, and complete conditional statistics: ； Where n is the number of historical samples; F 1−α (1, n−1) represents the quantile of the F distribution with 1 and n−1 degrees of freedom at confidence level 1−α. The unconditional statistic, ordinal conditional statistic, or fully conditional statistic of a node is compared with the critical value UCL1. If the statistic is greater than the critical value, it is considered that the statistic has reached a significant level in the corresponding sense.

6. A power quality anomaly tracing system based on multivariate statistical decoupling, characterized in that, include: The data acquisition and processing module acquires historical power quality data and relevant data for the time to be analyzed, and processes the data. The overall anomaly identification module is used to identify overall anomalies based on the Hotelling T² control chart; The outlier statistics decoupling analysis module is used to perform outlier statistics decoupling analysis based on Mason decomposition if an overall outlier is identified, and to obtain the order condition statistics, unconditional statistics and fully conditional statistics of each node, and to determine whether each statistic reaches a significance level. The anomaly type identification module is used to determine that a node is the root cause when both its unconditional and complete conditional statistics are significant; to determine that a node is an anomaly in relation when its unconditional statistics are not significant but its complete conditional statistics are significant; and to determine that a node is a cascading phenomenon when its unconditional statistics are significant but its complete conditional statistics are not significant.

7. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the power quality anomaly tracing method based on multivariate statistical decoupling as described in any one of claims 1 to 5.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the power quality anomaly tracing method based on multivariate statistical decoupling as described in any one of claims 1 to 5.

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