Determining phase connection in a power grid

Abstract

The present disclosure relates to a method for determining phase connections of power grid components in a power grid, the method comprising evaluating a relative similarity of time series of measured voltage data of the power grid components by clustering the time series of measured voltage data of the power grid components; grouping the power grid components into a plurality of clusters based on the evaluated relative similarity; and evaluating phase connections of the power grid components in each cluster of the plurality of clusters. The present disclosure also relates to a corresponding device and computer program.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to a method, apparatus and computer program product for determining phase connections of power grid components in a power grid. BACKGROUND

[0002] Power grids have traditionally been designed to handle unidirectional energy flow and are often over-dimensioned to ensure that they do not get stressed under heavy load conditions. While this strategy worked well for decades due to its simple design and operating rules, this is no longer the case.

[0003] With the increasing popularity of variable renewable resources like wind and solar, and the electrification of the transportation and heating sectors, the complexity of power grids is rapidly increasing, requiring the optimization and coordination of many active components. As a result, power grids are becoming more and more unpredictable and require improved solutions for active grid control.

[0004] In this context, many utilities are rolling out metering infrastructure and various tools have been developed and implemented in order to monitor power system behavior with more detailed geographical and temporal information, such as supervisory control and data acquisition (SCADA), smart meters and line sensors. However, creating observability from non-coherent data streams remains a challenge, especially considering that the amount of data collected is limited compared to the overall grid size.

[0005] With the advent of such advanced monitoring tools, identifying and correcting errors in the power grid, such as errors in phase connections, topology or parameter errors, especially modeling such power grids, is becoming a very important topic, especially because distribution system operators (DSOs) often do not have a complete understanding of the underlying power grid. As a result, DSOs often cannot use model-based grid control solutions due to the lack of detailed knowledge of the underlying power grid. This lack of detailed measurement data is often the highest barrier for model-based grid control solutions.

[0006] In addition, there is a problem of poor data quality in many database records, such as in geographic information systems (GIS), because these records are often not updated when asset changes occur in the field. As a result, due to the lack of detailed measurement data and poor data quality from databases, DSOs can not have a complete understanding of the real state of the underlying power grid and the corresponding model, making it difficult to apply advanced grid control solutions, such as imbalance optimal power flow, voltage regulation.

[0007] Detailed knowledge of the phase at the point of common coupling of electrical components is an important aspect of the detailed knowledge of the power grid required to develop and improve power grid control solutions. In particular, in this case, detailed knowledge of the phase at the point of common coupling of electrical components between the phases of a three-phase system is of interest. Knowing the phase to which a component and the corresponding electricity meter is connected helps the distribution system operator to improve the overall efficiency and reliability of the system.

[0008] However, it is well known that details about the phase connection of electrical components are part of the knowledge of the power grid, which often contain errors, e.g. due to a wrong identification of the phase connection at the customer site. In the present disclosure, the term “phase connection” refers not only to single phase connections, e.g. connections with a firewire and with or without a zero wire, but also to multi-phase connections, e.g. connections with two or more firewires and with or without a zero wire. For example, if the phases are denoted with “a”, “b” and “c”, the term “phase connection” in the present disclosure refers to single phase connections (i.e. “a”, “b”, “c”) and multi-phase connections (i.e. “ab”, “ac”, “bc” and “abc”).

[0009] Figure 1 An exemplary power grid is shown. The power grid comprises an HV / MV (high voltage / medium voltage) substation 100, a 3-phase MV / LV (medium voltage / low voltage) transformer 101 and a 1 -phase MV / LV transformer 102. In this exemplary power grid, one of the power grid components 110 has a phase connection that does not correspond to an entry in the respective database. In addition, the power grid components in the branch depicted with 111 have a phase connection that does not correspond to an entry in the respective database. The same applies to power grid components 112 and 113. Thus, the knowledge (configuration) about the power grid is inaccurate, resulting in an inaccurate power grid model. Traditionally, the improvement of the database (e.g. GIS database) accuracy involves sending personnel to the field to manually verify the phase connections. However, depending on the system and the terrain surrounding, this can be a tedious and expensive task, as it can not be simple to accurately follow overhead and underground lines. SUMMARY

[0010] Therefore, there is a need to improve the determination of the phase connection of power grid components in a power grid.

[0011] In particular, the present disclosure relates to a method for determining a phase connection of a power grid component in a power grid. The method comprises evaluating a relative similarity of time series of measured voltage data of the power grid component by clustering the time series of measured voltage data of the power grid component; grouping the power grid component based on the evaluated relative similarity into a plurality of clusters; and evaluating a phase connection of the power grid component in each cluster of the plurality of clusters.

[0012] The various embodiments can preferably implement the following features:

[0013] The power grid preferably comprises or is a transmission grid and / or a distribution grid.

[0014] The power grid component preferably comprises or is a load, a meter connected to a load, a capacitor, a capacitor bank, a voltage regulator and / or a transformer.

[0015] Preferably, the method comprises receiving a time series of measured voltage data of a power grid component. Preferably, the time series of measured voltage data of a power grid component is received from a respective power grid component of a plurality of power grid components or from a meter connected to a respective power grid component of a plurality of power grid components.

[0016] Preferably, the time series of measured voltage data of a power grid component comprises one or more samples at different times. The samples can preferably have a certain time length.

[0017] Preferably, the assessing the phase connection is based on determining a majority of reference phase connections of the power grid components in at least one cluster of the plurality of clusters. Preferably, the method comprises assessing the majority of phase connections as the phase connection of the power grid components in the at least one cluster. Preferably, the reference phase connections of power grid components are from a database, e.g. a GIS database. In other words, the reference phase connections of power grid components can be information about phase connections that has been stored previously.

[0018] Preferably, the assessing the phase connection is based on determining a similarity value between at least one part of the time series of measured voltage data of at least one power grid component having a verified phase connection in at least one cluster of the plurality of clusters and at least one part of the time series of measured voltage data of at least one other power grid component in the at least one cluster. Preferably, the method comprises assessing the verified phase connection as the phase connection of the power grid components in the at least one cluster if the similarity value is above a predefined threshold. It is known to the person skilled in the art that a similarity value can be a value quantifying the similarity between variables, here the similarity between at least one part of the time series of measured voltage data of at least one power grid component having a verified phase connection in at least one cluster of the plurality of clusters and at least one part of the time series of measured voltage data of at least one other power grid component in the at least one cluster. The similarity value can be a correlation value known to the person skilled in the art for quantifying the strength of a relationship between variables. The verified phase connection can preferably be provided by a power grid provider. For example, the verified phase connection can be a phase connection of a transformer or capacitor belonging to a power grid provider. In other words, the verified phase connection can be a phase connection that is known to be true.

[0019] Preferably, the method comprises calculating a similarity value between at least one portion of a time series of measured voltage data of at least one electrical grid component in at least one cluster of the plurality of clusters and at least one portion of a time series of measured voltage data of at least one electrical grid component in another cluster of the plurality of clusters. Preferably, the method comprises classifying the at least one electrical grid component from the at least one cluster into the other cluster of the plurality of clusters if the similarity value is higher than a predefined threshold. Preferably, the method comprises re-evaluating the electrical grid components’ phase connections in the cluster and the other cluster.

[0020] Preferably, the method comprises determining the electrical grid components’ phase connections based on evaluating the electrical grid components’ phase connections. Preferably, the method comprises determining the electrical grid components’ phase connections based on evaluating the electrical grid components’ phase connections and / or re-evaluating the electrical grid components’ phase connections.

[0021] Preferably, the calculating and the classifying are repeated until the number of electrical grid components with a similarity value higher than the threshold exceeds a predefined number.

[0022] Preferably, evaluating the relative similarity is performed using a dimensionality reduction of the time series of measured voltage data of the electrical grid components, in particular a non-linear dimensionality reduction of the time series of measured voltage data of the electrical grid components.

[0023] The method preferably further comprises automatically determining at least one parameter of the clustering, in particular wherein the at least one parameter is a number of clusters and / or a parameter of a similarity measure of the clustering.

[0024] Preferably, automatically determining at least one parameter is performed using a clustering validity index, in particular maximizing and / or minimizing the clustering validity index, more particularly a Calinski-Harabasz index, a Silhouette index or a Davies-Bouldin index.

[0025] The time series of measured voltage data of all electrical grid components is preferably divided into a plurality of time segments. Preferably, each time segment comprises measured voltage data of all electrical grid components. Preferably, evaluating the relative similarity and grouping the electrical grid components into clusters is performed for each time segment, preferably individually for each time segment.

[0026] Preferably, the time segments are overlapping or non-overlapping.

[0027] The method preferably comprises evaluating the phase connectivity of the electrical grid components in at least one cluster of the plurality of clusters over at least a portion of the time period based on determining a majority of the evaluated phase connectivity of the electrical grid components for at least a portion of the time period. Preferably, the method comprises evaluating the majority of the phase connectivity as the phase connectivity of the electrical grid components in the at least one cluster.

[0028] Preferably, the method comprises balancing power between phases of at least a portion of the electrical grid components based on determining phase connectivity.

[0029] Preferably, the method comprises detecting a fault in at least one of the electrical grid components based on determining phase connectivity.

[0030] Preferably, the method comprises determining a previously determined phase connectivity of at least one of the electrical grid components based on determining phase connectivity.

[0031] Preferably, the method comprises determining a configuration of the electrical grid based on determining phase connectivity.

[0032] Preferably, the method comprises correcting at least one of missing data, measurement noise, synchronization error, or bias error of the time series of measured voltage data of the electrical grid components prior to evaluating the relative similarity.

[0033] Preferably, the method comprises normalizing the time series of measured voltage data of the electrical grid components prior to evaluating the relative similarity.

[0034] The present disclosure also relates to a device for determining phase connectivity of electrical grid components in an electrical grid. The device comprises a memory (in particular, a non-transitory memory) for storing computer instructions and a processor in communication with the memory, wherein, when the processor executes the computer instructions, the processor is configured to perform a method as described above.

[0035] The present disclosure also relates to a computer program product comprising instructions which, when the program is executed by a computer, cause the computer to carry out a method as described above.

[0036] Exemplary embodiments of the present disclosure are intended to provide features that will become readily apparent to those skilled in the art from the following description, when taken in conjunction with the accompanying drawings. In accordance with various embodiments, exemplary systems, methods, devices, and computer program products are disclosed herein. It should be understood, however, that these embodiments are presented by way of example and not limitation, and that modifications can be made by those skilled in the art who read this disclosure within the scope of the present disclosure.

[0037] Accordingly, the present disclosure is not limited to the exemplary embodiments and applications described and illustrated herein. Additionally, the particular order or hierarchy of steps in the methods disclosed herein are merely exemplary approaches. Based upon design preferences, the particular order or hierarchy of steps disclosed in the methods or processes can be re-arranged, while still falling within the scope of the present disclosure. Thus, those of ordinary skill in the art will understand that the methods and techniques disclosed herein are presented for exemplary purposes only, and that the present disclosure is not limited to the particular order or hierarchy presented. BRIEF DESCRIPTION OF DRAWINGS

[0038] The above and other aspects and embodiments are described in more detail in the drawings and specification.

[0039] Figure 1 An exemplary power grid with different error determinations is shown.

[0040] Figure 2 A flowchart of a method according to embodiments of the present disclosure is shown.

[0041] Figure 3 An exemplary measured voltage input matrix according to embodiments of the present disclosure is shown.

[0042] Figure 4 An exemplary measured voltage input matrix according to embodiments of the present disclosure is shown.

[0043] Figure 5a And Figure 5b An exemplary measured voltage input matrix according to embodiments of the present disclosure is shown.

[0044] Figure 6 An output matrix according to embodiments of the present disclosure is shown.

[0045] Figure 7 An example of majority voting according to embodiments of the present disclosure is shown.

[0046] Figure 8 An example of additional majority voting according to embodiments of the present disclosure is shown.

[0047] Figure 9 An example of initialization of clusters according to embodiments of the present disclosure is shown.

[0048] Figure 10 A flowchart of a method according to embodiments of the present disclosure is shown, particularly additional clustering after a first clustering.

[0049] Figure 11 shows classifying power grid components into another cluster according to embodiments of the present disclosure.

[0050] Figure 12 A plot of the Karinsl-Halabasa score for automatic tuning is shown in accordance with embodiments of the present disclosure.

[0051] Figure 13 A plot of the distribution of the confidence score of connected phases determined after spectral clustering using a sliding window is shown in accordance with embodiments of the present disclosure.

[0052] Figure 14 An embedding space after input data processing and phase determination method is shown in accordance with embodiments of the present disclosure.

[0053] Figure 15 A portion of a bus system with corresponding reference connected phases is shown in accordance with embodiments of the present disclosure.

[0054] Figure 16 A portion of a bus system with determined connected phases is shown in accordance with embodiments of the present disclosure.

[0055] Figure 17a And Figure 17b A plot of the accuracy distribution of 520 random initializations of a bus system is shown in accordance with embodiments of the present disclosure. DETAILED DESCRIPTION

[0056] In the following, exemplary embodiments of the present disclosure will be described. Note that some aspects of any one described embodiment can also be found in some other embodiments unless otherwise stated or apparent. However, for improved intelligibility, each aspect will be described in detail only at the first mention and any repeated explanation of the same aspect will be omitted.

[0057] Figure 2 A flowchart of a method in accordance with embodiments of the present disclosure is shown.

[0058] In S201, a relative similarity of time series of measured voltage data of a power grid component is determined by clustering the time series of measured voltage data of the power grid component.

[0059] According to embodiments, the time series of measured voltage magnitudes can be used as the time series of measured voltage data. The input signal / input data of the method can be raw data or pre-processed data.

[0060] According to embodiments, the time series of measured voltage data is obtained from a plurality of power grid components, e.g. loads, in particular from electricity meters located at end consumer sites. Although this obtaining is not Figure 2part of the method shown in the embodiments, but the skilled person will appreciate that the obtaining / receiving of data can also be part of certain embodiments of the present disclosure. These voltage measurements can be time-stamped with a measurement resolution interval of a few minutes. One or more intervals can have at least one of the following durations: 15 minutes, 30 minutes, or 1 hour. However, the present disclosure is not limited to the mentioned resolution intervals.

[0061] According to embodiments, the measured voltage data of the complex numbers can be obtained in Cartesian or polar coordinate representation and the voltage data, e.g. voltage magnitudes, to be processed in the method according to the present disclosure can be calculated accordingly.

[0062] In Figure 2 the embodiments shown, the time series of measured voltage data of the grid components comprises a plurality of samples at different times. The samples can have a certain time length. However, the present disclosure is not limited thereto and each time series can have only one sample. Having several grid components, e.g. loads, and time series of measured voltage data comprising several samples can result in a measured voltage input matrix of dimension wherein is the number of grid components GC and is the number of samples in the time series. Figure 3 An exemplary measured voltage input matrix is shown in . The measured voltage input matrix comprises for each of the number of 302 grid components a voltage measurement at different times 304. In other words, for each of the number of 302 grid components, the time series of measured voltage data 301 comprises different samples at different times 304. The data structure is shown as a matrix. However, any other suitable data structure can be used.

[0063] In embodiments of the present disclosure, time series of voltage measurement data from other parts of the grid, e.g. other grid components, can be used to increase the accuracy and robustness of the method of the present disclosure. Such time series of voltage measurement data can correspond to the grid component voltage measurements in all dimensions, e.g. time resolution and amount of data.

[0064] According to embodiments, if the measurement intervals are small and thus the number of samples is high, the time series of voltage measurement data should be averaged to the same interval size. Embodiments of the present disclosure, Figure 4The extended measured voltage input matrix In Figure 4 the measured voltage input matrix is extended by m additional time series of additional components 401.

[0065] In embodiments of the present disclosure, pre-processing can be performed on the time series of voltage measurement data to remove gross errors. For example, the time series of voltage measurement data can contain a series of errors including missing data, measurement noise, synchronization errors, and meter bias errors. In pre-processing, missing data values can be interpolated, while other errors can not necessarily be corrected. According to embodiments, in order not to exclude data points for which measurement data is missing, the data points can be interpolated based on surrounding measurement points. Additionally or alternatively, additional information is used to further clean the time series of voltage measurement data, for example, meter accuracy class information can be used to perform noise removal and estimate the signal without measurement noise.

[0066] In embodiments of the present disclosure, further pre-processing is performed by mean normalization of the voltage measurement data, for example, rescaling the data to have zero mean and range [-1, 1]. This step can be performed to improve overall accuracy. For example, for each voltage time series, the mean, maximum, and minimum can be calculated according to the following equations, and the measurement data can be normalized:

[0067]

[0068] wherein, is a vector with initial voltage measurement data, and is a normalized vector.

[0069] In embodiments of the present disclosure, the time series of voltage measurement data 301 is divided into time periods, as shown in Figure 5a and Figure 5b However, it will be appreciated by the skilled person that the present disclosure is not limited to such division of time periods. According to embodiments, each time period comprises measured voltage data of all grid components under consideration. In other words, when considering the measured voltage input matrix the division of time periods is performed column-wise. Figure 5a shows a measured voltage input matrix with overlapping time periods 501, 502, and 503, also referred to as a sliding window, and Figure 5b shows a measured voltage input matrix with non-overlapping time periods 501, 502, and 503, also referred to as a tumbling window.

[0070] In embodiments of the present disclosure, the division into time segments can depend on the amount of available data and the measurement time resolution. The size of the time segments can range from only a few time instances per time segment to hundreds or thousands of instances. The choice of the time segment size can represent a trade-off between the amount of data that has to be saved in memory, the computation time and the confidence of the final assessment. According to embodiments, the time segment size can be in the range of hours or days and can depend on the time resolution.

[0071] As mentioned above, the relative similarity of the time series of measured voltage data of the power grid component is assessed by clustering the time series of measured voltage data of the power grid component.

[0072] In the following, embodiments of the present disclosure are described, wherein the time series of measured voltage data are divided into time segments and wherein spectral clustering is used to assess the relative similarity of the time series of measured voltage data of the power grid. However, the skilled person will understand that the present disclosure is not limited to the use of spectral clustering and division into time segments.

[0073] Spectral clustering is based on a non-linear dimensionality reduction (however, other clustering methods using non-linear dimensionality reduction are also known to the skilled person and can be used). The spectral clustering according to embodiments comprises:

[0074] - creating an affinity (similarity) matrix from the measured voltage input matrix wherein the affinity matrix represents a measure of similarity between all combinations of two voltage time series. Various methods can be used to construct the affinity matrix, including but not limited to the Pearson correlation factor, the Radial Basis Function (RBF) or the linear / polynomial / cosine pair-wise kernel. The following exemplary results are given for the affinity matrix construction using the RBF kernel, as follows:

[0075]

[0076] wherein represents the square of the Euclidean distance between the voltage measurement pairs, and is a similarity parameter.

[0077] - the normalized Laplacian transformation of the affinity matrix is performed as follows:

[0078]

[0079] wherein is the identity matrix, and is the degree matrix​ ).

[0080] - performing a partial eigen decomposition of the Laplacian matrix Eigen decomposition is performed and the first n eigenvectors corresponding to the largest eigenvalues are selected. These are further used as representative eigenvectors for additional clustering, e.g. k-means clustering or using a Gaussian Mixture Model etc. The eigenvalues and eigenvectors are computed such that:

[0081]

[0082] According to embodiments, to speed up this process, a partial eigen decomposition can be performed by only computing the first n eigenvectors corresponding to the largest eigenvalues.

[0083] - performing a subsequent clustering on the computed eigenvectors, e.g. k-means clustering or a Gaussian Mixture Model etc.

[0084] One concept of the present disclosure is that the tuning / determination of at least one parameter of the clustering, in particular a hyperparameter of the spectral clustering hyperparameters, is performed automatically. For example, according to embodiments of the present disclosure, the optimal number of clusters as well as the optimal parameters of the similarity measure, e.g. the of the RBF computation for the affinity matrix, are selected automatically. This allows the present disclosure to be easily applied to a range of power grids and available measurement data without the need for extensive manual expert tuning.

[0085] In embodiments of the present disclosure, the determination / tuning of at least one parameter of the clustering, e.g. the optimal hyperparameters, is performed using an internal clustering validity index. According to embodiments, the Calinski-Harabasz index is used which depends on the variation between clusters and within clusters. However, in general, other internal validity indices can also be used, e.g. the silhouette index, the Davies-Bouldin index etc.

[0086] According to embodiments, the automatic (hyper)parameter tuning / determination is performed as follows:

[0087] 1) Select a range of hyperparameter values that should be tuned. The similarity parameter should cover several orders of magnitude, e.g. The minimum number of clusters can be set to 3.

[0088] 2) For the selected voltage measurement time series, compute the affinity matrix and the corresponding Laplacian transform. The selected voltage time series can be the entire time series or a selected part(s) thereof.

[0089] 3) Perform a (partial) eigen decomposition of the Laplacian matrix.

[0090] 4) For each combination of hyperparameters, a corresponding number of feature vectors is selected and a subsequent clustering, e.g. k-means clustering or using Gaussian Mixture Models, etc., is performed. Based on the obtained clusters, an internal validity score is calculated.

[0091] 5) The best hyperparameters are selected based on the extremum of the internal validity score. Depending on the used index, the maximum or minimum is the best, e.g. the maximum for the Calinski-Harabasz index.

[0092] The final output of the (spectral) clustering is a matrix, as shown in Figure 6 with dimensions number of grid components 302 x number of time periods 600, and wherein the entries of the matrix correspond to the clusters of grid components 303 and the respective time period.

[0093] In other words, the grid components 303 are grouped into a plurality of clusters based on evaluating the relative similarity, S202.

[0094] Please note that Figure 6 the matrix in shows the values “1”, “2” or “3” for each entry belonging to one of the grid components 303 at the respective time period of the time periods 600, wherein the values correspond to the cluster of the grid components 303 at each time period. It is to be understood by the skilled person that the values “1”, “2” or “3” are merely for illustration, any suitable naming / numbering scheme can be applied.

[0095] In S203, the phase connectivity of the grid components in each of the plurality of clusters is evaluated. In other words, for each cluster, all grid components in the cluster are evaluated to have the same phase connectivity. In this context, it should be emphasized again that the term “phase connectivity” in the present disclosure generally refers to how the phases of the grid components are connected. In other words, the term “phase connectivity” refers not only to single phase connections, e.g. connections with a hot line and with or without a neutral line, but also to multi-phase connections, e.g. connections with two or more hot lines and with or without a neutral line. For example, if the phases are denoted with “a”, “b” and “c”, the term “phase connectivity” in the present disclosure refers to single phase connections (i.e. “a”, “b”, “c”) and multi-phase connections (i.e. “ab”, “ac”, “bc” and “abc”). It is to be understood by the skilled person that the term “phase connectivity” does not give any spatial indication, i.e. the term generally does not give an indication about the location of the connection.

[0096] According to embodiments, assessing the phase connection is based on determining a majority of reference phase connections of grid components in the cluster. In other words, for all or at least a part of the grid components in the cluster, there is knowledge about the reference phase connection. Such reference phase connections can be obtained in / from a database, e.g. a GIS database. However, as mentioned above, the reference connections, in particular from a database, can be incorrect, e.g. due to a poor quality of the database and can not reflect the true state of the phase connection of the respective grid component. An example of such a majority vote is shown in Figure 7 with two exemplary clusters 701 and 702. In cluster 701, the cluster reference phase connections "a" and "b" are shown, and in cluster 702, the reference phase connections "a", "b" and "c" are shown, but it is to be understood that this is merely for illustration. In cluster 701, there are 10 grid components with reference connections. 8 grid components have the reference phase connection "a", and 2 grid components have the reference phase connection "b". Thus, the majority of cluster 701 is the reference phase connection "a". The phase connection of the grid components in cluster 701 is then assessed to be the phase connection "a", 703. In cluster 702, the majority is the reference phase connection "b", 704, and this reference phase connection is assessed to be the phase connection of the grid components in cluster 702.

[0097] As an alternative or complementary approach to assessing a majority of reference phase connections, according to embodiments of the present disclosure, assessing the phase connection is based on a similarity value between at least one part of a time series of measured voltage data of at least one grid component in the cluster with a verified phase connection and at least one part of a time series of measured voltage data of at least one other grid component in the cluster. For example, if grid components are known to have a verified phase connection, e.g. because these grid components belong to a grid provider that has manually checked the phase connections, a similarity value, e.g. a correlation value, between the voltage measurements of these grid components and other grid components in the cluster can be calculated. If the similarity value is above a predefined threshold, the respective verified phase connection is assessed to be the phase connection of the grid components in the cluster. The assessment can also be performed based on the highest similarity value.

[0098] If a division of time periods has been performed, the above described assessment of the phase connection is performed over all time periods. Alternatively, the above described assessment of the phase connection is performed over at least a part of the time periods, and the remaining time periods can be discarded. A further majority is determined, i.e. a majority of the assessed phase connections of the grid components of each time period or at least a part of the time periods in the above alternative. The determined majority of the assessed phase connections is then assessed to be the phase connection of the respective grid components in the cluster. Figure 8This additional majority "vote" is illustrated exemplarily. For each grid component 303 and time period 600, a phase connection "a", "b", or "c" is evaluated, and the phase connection 800 of the corresponding grid component is obtained based on the majority vote. For example, in the case of 10 time periods, a phase connection is evaluated as "b" 9 times, "c" once, and is "finally" evaluated as the phase connection corresponding to the majority of phase connections, i.e., phase connection "b".

[0099] According to an embodiment, the phase connections of power grid components are determined based on the evaluation of phase connections of power grid components. These determined phase connections can then be compared with corresponding entries in a database, i.e., compared with information about phase connections in the database. Because the actual phase connections may be unknown, it may not be easy to assess whether detected errors are due to incorrect reference phase connections or incorrect phase determination. Therefore, in embodiments of this disclosure, to estimate the confidence level of the determination, a confidence score is calculated for each or at least part of the evaluated phase connections. In other words, according to an embodiment, a confidence score is calculated for the phase connections of power grid components in a cluster based on the occurrence rate of phase connections of power grid components over a time period.

[0100] In embodiments of this disclosure, the confidence score for the assessment of phase connections of power grid components is based on the occurrence rate of assessed phase connections on different time slices and can be defined as the number of assessments for a specific phase connection divided by the number of time slices. Formally, for a multiple set containing all time slices of assessed phase connections from a given power grid component... The assessed connection confidence level It is given by the following formula:

[0101]

[0102] in, It is an indicator function, that is, if If , then it equals 1.

[0103] This confidence score is an indicator of the assessed reliability of a connection, i.e., the degree of consistency with which a power grid component is assessed as having a specific connection across all time periods. Using a sliding window results in a larger number of time periods and generally a higher confidence score compared to a rolling window. Those skilled in the art will understand that other methods for calculating confidence scores are also known to them, such as using the average probability that a power grid component belongs to a particular cluster.

[0104] In the above example, where one phase connection is evaluated as "b" and one as "c", the confidence score for "b" is 90% and for "c" is 10%. A high confidence score can indicate that the method of the present disclosure consistently evaluates the same phase connection, but does not necessarily mean that the phase connection is correct. However, for grid components that are not strongly correlated and thus more likely to be misclassified, the confidence score is inherently lower. It is within the knowledge of the skilled person how to define an acceptable threshold for "confidence".

[0105] According to the present disclosure, the above described clustering provides a phase connection evaluation with sufficient accuracy and confidence. However, in some power grids, due to the above described majority vote rule, grid components with a low occurrence compared to other phase connection types can be misclassified.

[0106] For example, if there are only a few multi-phase connections in a large power grid with thousands of single-phase grid components, these multi-phase connections are likely to be misclassified as single-phase grid components. Therefore, according to embodiments, a further (subsequent) clustering, e.g. a multi-tree clustering, can be performed as a second step to improve the accuracy and robustness of the overall method.

[0107] This further clustering can be based on iteratively adding grid components whose profile is most related to the profiles of the grid components already contained in a cluster.

[0108] According to embodiments of the present disclosure, for the aforementioned further clustering, possible clusters are first initialized. Possible phase connection clusters can include single-phase connections (i.e. "a", "b", "c") and multi-phase connections (i.e. "ab", "ac", "bc" and "abc").

[0109] In embodiments of the present disclosure, possible clusters of the further clustering, e.g. a multi-tree clustering, can be initialized. The initialization can be performed in a variety of ways, one example is shown below:

[0110] 1 ) using the results of the first clustering, e.g. spectral clustering as exemplary described above, where clusters are initialized with voltage measurements of grid components whose evaluated phase connection is equal to the possible cluster phase connection whose confidence score is above a selected threshold and, optionally, whose evaluated phase connection is equal to the reference phase connection. In this case, it should be noted that the confidence score can be calculated as described above but is not limited thereto. For example, the confidence score can also be calculated using the average likelihood that a grid component belongs to a certain cluster.

[0111] 2) In addition to the initialization from item 1), voltage measurements from other grid components can be used, which are known to have a true phase connection, i.e. they are validated, e.g. voltage regulators or transformers.

[0112] In embodiments of the present disclosure, the first step of initializing possible phase connection clusters is to add the voltage measurements from item 1) to the corresponding cluster based on the evaluated phase connections. Note that after performing this step, some clusters can be empty, e.g. if only single-phase grid components are predicted with a confidence score above a set value. In this case, empty multi-phase clusters can be initialized according to single-phase measurements known to be measured at the same electrical node.

[0113] Figure 9 An example of initializing multi-tree clusters according to embodiments of the present disclosure is shown. Single-phase clusters 907, 908, and 909 are initialized with single-phase measurements, and multi-phase cluster 910 is initialized with the average of single-phase measurements. The respective single-phase measurements 906, the respective voltage measurements 905, and the respective measurement devices 904 are shown. Specifically, for each phase 901, 902, and 903 of the HV / MV substation, a single-phase measurement is performed.

[0114] As an example, as shown in Figure 9 The single-phase voltage measurements at the medium voltage side of the HV / MV substation can be used to initialize a three-phase cluster by calculating the average voltage over the three phases and setting it as the initial voltage measurement.

[0115] Figure 10 A flowchart of a further clustering after the (spectral) clustering described above is shown.

[0116] After the initialization, if performed, a similarity value between at least one part of a time series of measured voltage data of at least one grid component in at least one cluster of the plurality of clusters and at least one part of a time series of measured voltage data of at least one grid component in another cluster of the plurality of clusters is calculated, S1001.

[0117] According to embodiments, for one or more (e.g. each, the) grid component with a confidence score below a set / predefined threshold , a minimum distance to each (initialized) cluster is calculated. Note that the confidence score can come from the previous clustering mentioned above or another method of calculating a confidence score, e.g. using the average likelihood that a grid component belongs to a certain cluster. The minimum distance can be calculated based on the highest similarity value, e.g. the correlation value / coefficient between the measurement data of the selected grid component and the measurement data from the other grid component(s), e.g. all grid components that have been classified / grouped into a cluster. The formal expression can be:

[0118]

[0119] wherein and are voltage measurements from grid components and ; is the total number of clusters, and is the cluster index; is the covariance between voltage measurements and ; and and are the standard deviations of voltage measurements and , respectively.

[0120] In S1002, at least one grid component from at least one cluster is classified into another cluster of the plurality of clusters if the similarity value is above a predefined threshold. In other words, if the similarity between the data of a selected grid component and the data of one or more grid components of another cluster is above a predefined threshold, for example when the selected grid component has a minimum computed distance to said another cluster, the selected grid component is added to said another cluster.

[0121] An example of such classification / re-grouping into another cluster is exemplarily shown in Figures 11a to 11c . As shown in Figure 11a and Figure 11b , measured data (e.g. measured voltage data) 1101 from a grid component is compared to measured data of grid components in a cluster 1100 and a corresponding correlation coefficient 1102 is computed. Then, as shown in Figure 11c , a minimum distance 1103 is computed based on the correlation coefficient and the grid component is classified into the cluster with the minimum distance 1104.

[0122] According to embodiments, the process of S1002 is repeated until a certain number of clusters with a similarity value above a certain threshold or all grid components are classified into another cluster.

[0123] In S1003, the phase connections of the grid components in said cluster and said another cluster are re-evaluated. In other words, at least the phase connections of the grid components in the cluster from which the classified cluster is obtained and the phase connections of the grid components in said another cluster into which the grid components are classified are re-evaluated. However, the present disclosure is not limited thereto and re-evaluation of other clusters (e.g. all clusters) can also be performed.

[0124] The re-evaluation can be performed as the previous evaluation described above. For example, according to embodiments, the re-evaluation of the phase connection is based on determining a majority of the reference phase connections of the electrical grid components in the cluster. As an alternative or in addition to the majority of the re-evaluation of the reference phase connection, according to embodiments of the present disclosure, the evaluation of the phase connection is based on a similarity value between at least a portion of a time series of measured voltage data of at least one electrical grid component in the cluster having a verified phase connection and at least a portion of a time series of measured voltage data of at least one other electrical grid component in the cluster.

[0125] In case of partitioning the time period, the re-evaluation can further comprise the evaluation described above over all time periods or at least a portion of the time periods and the subsequent majority determination. To avoid unnecessary repetitions, reference is made to the above evaluation, in particular the above majority determination.

[0126] According to embodiments, the phase connection of the electrical grid component is determined based on the evaluation of the phase connection of the electrical grid component and the re-evaluation of the phase connection of the electrical grid component. As described above, these determined phase connections can then be compared to the respective entries in the database, i.e. to the information about the phase connection in the database.

[0127] According to embodiments, in case the phase connection of the electrical grid component is determined based on both the evaluation of the phase connection of the electrical grid component and / or the re-evaluation of the phase connection of the electrical grid component, the result of the determination can be partitioned into the following sets

[0128] - the reference phase connection is equal to the evaluated phase connection of the electrical grid component from the first (spectral) cluster and the electrical grid component having an evaluated phase connection with a confidence score greater than a defined threshold. The determined phase connection of such a load is equal to the reference connection.

[0129] - the reference phase connection is different to the evaluated connection of the electrical grid component from the first (spectral cluster) or the evaluated phase connection has a confidence score less than a defined threshold. In general, the (final) determined phase connection can be determined by various means, including a manual check, a visual check based on street images from open source maps, or completely relying on the data driven result obtained. For example, if it is the latter case, the (final) determined phase connection of such an electrical grid component can be decided as follows:

[0130] - if the re-evaluated phase connection is equal to the (first) evaluated phase connection from the (spectral) cluster, the determined phase connection is equal to the evaluated and the re-evaluated phase connection.

[0131] - if the reassessed phase connections differ from the (first) assessed phase connections from the (spectral) clustering, the determined phase connections can be the phase connections with the higher confidence score. Such grid components can be additionally marked as potential candidates for further manual and / or visual inspection.

[0132] In the following, exemplary test results according to the present disclosure will be discussed. Exemplary results of the present disclosure on an IEEE-8500 bus system are discussed. To simulate real-world conditions, real power measurement time series are added to the grid components (here: loads) and a series of power flows is performed to extract corresponding voltage measurements. Then, various errors are added to the extracted voltage data, including measurement noise, meter bias, synchronization error, and missing data error.

[0133] Finally, the input data used to test the proposed method are:

[0134] • Raw voltage measurements from a load smart meter for 1 month.

[0135] • Reference labels of the erroneous load smart meter.

[0136] Before feeding the input signals to the method according to the present disclosure, the raw voltage measurements have been pre-processed, i.e. missing data have been interpolated and time series have been mean-normalized. After input data pre-processing, one automatic hyperparameter tuning is performed on the full time series using the Karinski-Halabas internal score.

[0137] Figure 12 A representation of the Karinski-Halabas score for automatic tuning of the IEEE 8500 bus system according to an embodiment of the present disclosure is shown. As Figure 12 indicated, the values and are chosen for further single time period clustering.

[0138] Figure 13 A distribution of the confidence scores of the determined phase connections after spectral clustering using a sliding window of the IEEE 8500 bus system according to an embodiment of the present disclosure is shown. As Figure 13 exemplarily depicted in, the overall prediction accuracy after spectral clustering equals 98.0%, with the majority of the assessed phase connections having a confidence score of 90% or more. More precisely, about 86% of the assessed phase connections have a confidence score of 90% or more.

[0139] Out of these approximately 86% of grid components, the evaluated phase connections equal to the reference phase connections of the grid components that have been marked as trusted grid components and are further used to initialize the multi-tree clustering. 76% of the total grid components are considered to be trusted. Thus, the determined phase connections of these grid components equal the evaluated phase connections from the spectral clustering and the reference phase connections.

[0140] The remaining 24% of the determined phase connections are determined based on the results of the multi-tree clustering. After the multi-tree clustering, the phase connection determination accuracy is 98.1%, with the majority of errors around the head of the observed feeder. If additional single-phase voltage measurements from the substation are used to initialize the multi-tree clustering, the final accuracy rises to 99.6%.

[0141] Figure 14 An embedding space of an IEEE 8500 bus system after input data processing and phase determination method according to embodiments of the disclosure is shown. As Figure 14 As depicted in the middle, six clusters can be identified. The phase connections are indicated by the “square”, “triangle” and “circle” marker.

[0142] Figure 15 A part of an IEEE 8500 bus system with corresponding reference phase connections according to embodiments of the disclosure is shown. The filled markers represent phase connection errors within both branches and branch wholes, which are unknown in practice. In the enlarged part on the left, the errors of the reference phase connections of the whole branch 1501 and a single grid component 1502 are shown. Furthermore, the correct phase label of a single grid component 1503 is shown.

[0143] Figure 16 A part of an IEEE 8500 bus system with determined phase connections for load smart meters according to embodiments of the disclosure is shown. The filled markers represent errors that are not identified in the determined phase connections, i.e. the difference between the determined phase connections and the true data. In the enlarged part on the right, the uncorrected phase connections 1601 are shown.

[0144] Figure 17a and Figure 17b An accuracy distribution of 520 random initializations of an IEEE 8500 bus system, including the random combination of measurement errors and random clustering initialization, is shown. Figure 17a The accuracy after spectral clustering with and without additional substation measurements is shown, and Figure 17b The final accuracy after subsequent multi-tree clustering with and without additional substation measurements is shown.

[0145] While various embodiments of the present disclosure have been described above, it should be understood that they have been presented by way of example only, and not limitation. Likewise, the various figures can depict example architectures or configurations for the disclosure, which can be employed in any suitable environment. As such, the disclosure should not be construed as limited to the example architectures or configurations depicted in the figures. Rather, the various embodiments of the present disclosure are applicable and can be implemented in a variety of different environments and with various modifications not expressly depicted.

[0146] It should also be understood that any reference to an element herein using a designation such as "first," "second," and so forth does not limit the quantity or order of those elements. Rather, these designations can be used herein as a convenient method of distinguishing between various elements or instances of elements. Thus, a reference to first and second elements does not mean that only two elements can be employed, or that the first element must precede the second element.

[0147] In addition, those skilled in the art will appreciate that any of a wide variety of different technologies and methodologies can be used to represent information and signals. For example, data, instructions, commands, information, signals, bits, and symbols (for example, as can be referred to in the above description) can be represented by voltages, currents, electromagnetic waves, magnetic fields or particles, optical fields or particles, or any combination thereof.

[0148] Those skilled in the art will further appreciate that any of the various illustrative logical blocks, units, processors, means, circuits, methods and functions described in connection with the aspects disclosed herein can be implemented by electronic hardware (e.g., a number of logic elements, units, processors, circuits, and / or circuitry composed of a combination of analog and / or digital components), firmware, various forms of program or design code incorporating instructions (which can be referred to herein, for convenience, as "software" or a "software unit"), or any combination thereof.

[0149] To clearly illustrate this interchangeability of hardware, firmware and software, various illustrative components, blocks, units, circuits, and steps have been described above generally in terms of their functionality. Whether such functionality is implemented as hardware, firmware or software, or combinations thereof, depends upon the particular application and design constraints imposed on the overall system. Skilled artisans can implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present disclosure. According to various embodiments, a processor, device, component, circuit, structure, machine, unit, etc. can be configured to perform one or more of the functions described herein. The term “configured to” or “arranged to” used in the description in relation to a specified operation or function refers to a processor, device, component, circuit, structure, machine, unit, etc. that is physically constructed, programmed and / or arranged to perform the specified operation or function.

[0150] Further, those skilled in the art will appreciate that the various illustrative logical blocks, units, devices, components, and circuits described herein can be implemented or performed using integrated circuits (ICs) that can include a general purpose processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic device, or a combination of these or any other components. The logical blocks, units, and circuits can further include antennas and / or transceivers to communicate with various components within a network or within a device. The general purpose processor can be a microprocessor, but in the alternative, the processor can be any conventional processor, controller, or state machine. The processor can also be implemented as a combination of a conventional processor and a DSP, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration. If implemented in software, the functions can be stored on or transmitted over as one or more instructions or code on a computer-readable medium. Therefore, the steps of a method or algorithm disclosed herein can be implemented as software stored on a computer-readable medium. The software that implements the techniques described herein can be stored on or transmitted over as one or more instructions or code on a computer-readable medium. Computer-readable media includes both computer storage media and communication media including any medium that facilitates transfer of a computer program from one place to another. A storage media can be any available media that can be accessed by a computer. By way of example, and not limitation, such computer-readable media can comprise RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to carry or store desired program code in the form of instructions or data structures and that can be accessed by a computer. Also, any connection is properly termed a computer-readable medium. For example, if the software is transmitted from a website, server, or other remote source using a coaxial cable, fiber optic cable, or twisted pair, then the coaxial cable, fiber optic cable, or twisted pair are included in the definition of medium. Disk and disc, as used herein, includes compact disc (CD), laser disc, optical disc, digital versatile disc (DVD), and Blu-Ray® disc where disks usually reproduce data magnetically, while discs reproduce data optically with lasers. Combinations of the above should also be included within the scope of computer-readable media.

[0151] In addition, the various illustrative logical blocks, units, devices, components, and circuits described herein can be implemented or performed with integrated circuits (ICs) that can include a general purpose processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic device, or a combination of these or any other components. The logical blocks, units, and circuits can further include antennas and / or transceivers to communicate with various components within a network or within a device. The general purpose processor can be a microprocessor, but in the alternative, the processor can be any conventional processor, controller, or state machine. The processor can also be implemented as a combination of a conventional processor and a DSP, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration. If implemented in software, the functions can be stored on or transmitted over as one or more instructions or code on a computer-readable medium. Therefore, the steps of a method or algorithm disclosed herein can be implemented as software stored on a computer-readable medium.

[0152] Additionally, memory or other storage, as well as communication components, can be employed in embodiments of the disclosure. It will be appreciated that, for clarity- purposes, the foregoing description has described embodiments of the disclosure with reference to different functional units and processors. However, it will be apparent that any suitable distribution of functionality between different functional units, processing logic elements or domains can be used without detracting from the disclosure. For example, functionality illustrated to be performed by separate processing logic elements or controllers can be performed by the same processing logic element or controller. Hence, references to specific functional units are only to be seen as references to suitable means for providing the described functionality, rather than indicative of a strict logical or physical structure or organization.

[0153] Various modifications to the implementations described in this disclosure will be readily apparent to those skilled in the art, and the generic principles defined herein can be applied to other implementations without departing from the spirit or scope of the disclosure. Thus, the disclosure is not intended to be limited to the implementations shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for determining phase connections of power grid components in a power grid, the method comprising: evaluating a relative similarity of time series of measured voltage data of the power grid components by clustering the time series of measured voltage data of the power grid components; grouping the power grid components into a plurality of clusters based on the evaluation of the relative similarity; and evaluating a phase connection of the power grid components in each cluster of the plurality of clusters, wherein the evaluation of the phase connection is based on determining a majority of reference phase connections of the power grid components in at least one cluster of the plurality of clusters and evaluating the majority of phase connections as the phase connection of the power grid components in the at least one cluster, wherein the time series of measured voltage data of all power grid components are divided into a plurality of time periods, each time period comprising measured voltage data of all power grid components, and wherein the evaluation of the relative similarity and grouping the power grid components into clusters is performed for each time period, wherein the method further comprises evaluating a phase connection of the power grid components in at least one cluster of the plurality of clusters over at least a portion of the time periods based on determining a majority of evaluated phase connections of the power grid components of the at least a portion of the time periods and evaluating the majority of phase connections as the phase connection of the power grid components in the at least one cluster.

2. The method of claim 1, wherein, The evaluation of the phase connection is based on determining a similarity value between at least one portion of the time series of measured voltage data of at least one power grid component having a verified phase connection in at least one cluster of the plurality of clusters and at least one portion of the time series of measured voltage data of at least one other power grid component in the at least one cluster and evaluating the verified phase connection as the phase connection of the power grid components in the at least one cluster if the similarity value is above a predefined threshold.

3. The method according to claim 1 or 2, the method further comprising: calculating a similarity value between at least one portion of the time series of measured voltage data of at least one power grid component in at least one cluster of the plurality of clusters and at least one portion of the time series of measured voltage data of at least one power grid component in another cluster of the plurality of clusters; classifying at least one power grid component from the at least one cluster into the other cluster of the plurality of clusters if the similarity value is above a predefined threshold; and re-evaluating the phase connections of the power grid components in the cluster and the other cluster.

4. The method of claim 3, wherein, The method comprises determining the phase connections of the power grid components based on the evaluation of the phase connections of the power grid components.

5. The method of claim 3, wherein, The method comprises determining the phase connections of the power grid components based on the evaluation of the phase connections of the power grid components and / or the re-evaluation of the phase connections of the power grid components.

6. The method of any one of claims 4 or 5, wherein, The calculation and the classification are repeated until the number of power grid components having a similarity value above the threshold exceeds a predefined number.

7. The method of any one of claims 1, 2, 4, or 5, wherein, The evaluation of the relative similarity is performed using a dimensionality reduction of the time series of measured voltage data of the power grid components.

8. The method of claim 7, wherein, The evaluation of the relative similarity is performed using a non-linear dimensionality reduction of the time series of measured voltage data of the power grid components.

9. The method of any one of claims 1, 2, 4, or 5, wherein, The method further comprises automatically determining at least one parameter of the clustering.

10. The method of claim 9, wherein, The at least one parameter is a number of clusters and / or a parameter of a similarity measure of the clustering.

11. The method of claim 9, wherein, Automatically determining at least one parameter is performed using a cluster validity index.

12. The method of claim 11, wherein, Automatically determining at least one parameter is performed using maximizing and / or minimizing the cluster validity index.

13. The method of claim 11, wherein, Automatically determining at least one parameter is performed using a Krinsky-Halabys index, a profile index or a Davies-Poulding index.

14. The method of claim 1, wherein, The time period is overlapping or non-overlapping.

15. The method of any one of claims 1, 4, 5, or 14, wherein, The method comprises: balancing power between phases of at least a portion of the power grid components based on determining phase connectivity; and / or detecting a fault of at least one of the power grid components based on determining phase connectivity; and / or determining a previously determined phase connectivity fault of at least one of the power grid components based on determining phase connectivity; and / or determining a configuration of the power grid based on determining phase connectivity.

16. An apparatus for determining phase connections of power grid components in a power grid, the apparatus comprising a non-transitory memory for storing computer instructions and a processor in communication with the memory, wherein, The processor, when executing the computer instructions, is configured to perform the method of any one of claims 1 to 15.

17. A computer program product comprising instructions which, when the program is executed by a computer, cause the computer to carry out the steps of the method of any one of claims 1 to 15.

Images