A method for identifying the topology of low-voltage distribution transformer substations based on the SC-DTW algorithm

Abstract

This invention discloses a method for identifying the topology of a low-voltage distribution network transformer based on the SC-DTW algorithm. The method includes obtaining the three phases of the secondary side of the low-voltage distribution transformer in the area to be identified, and the daily voltage time series cluster of the area, composed of the three phases of the secondary side and the user sides measured by the area's AMI system; calculating a spatial pole-logarithmic coordinate histogram to obtain the shape context representation at each point; calculating the shape context cost matrix between each daily voltage time series and replacing the Euclidean distance matrix used in the Dynamic Time Warping (DTW) algorithm; accumulating the Euclidean distance between each pair of points based on the generated warped paths to obtain the cumulative distance matrix between each daily voltage time series; using the cumulative distance matrix between each daily voltage time series as a measure of similarity between series, and using the k-means algorithm for clustering to obtain the label of each user's phase, thereby identifying the transformer topology of the low-voltage distribution network. This method saves installation and maintenance costs and is more feasible. It also provides better alignment and improves the accuracy of user clustering labels.

Description

Technical Field

[0001] This invention relates to the field of low-voltage distribution network technology, and in particular to a method for identifying the topology of low-voltage distribution transformer substations based on the SC-DTW algorithm. Background Technology

[0002] With the development of power grid state estimation technology, power system topology analysis methods have received widespread attention from experts and scholars. Traditional power system topology analysis methods generally represent the topology as a linked list relationship and use graph theory search techniques, such as depth-first search and breadth-first search, to analyze the connectivity of nodes. This method generally requires establishing a linked list reflecting the topology structure and performing topology analysis by processing the linked list. In modern distribution network systems, the structure and topology of medium- and high-voltage distribution networks are quite clear. However, in low-voltage distribution networks (LVDNs), due to unclear asset allocation in many areas, and even the lack of structural records in many rural or urban villages, the topology is unclear, making power grid state estimation difficult. Furthermore, topology is the foundation for line loss analysis and fault location; incorrect topology information restricts the accuracy of line loss analysis and the effectiveness of fault handling. With the continuous advancement of smart grid construction, Advanced Meter Infrastructure (AMI) is being deployed more and more in distribution networks, providing effective data information for the verification and correction of distribution network topology relationships.

[0003] Currently, LVDN topology identification methods are mainly divided into three categories: signal injection method, data tag method, and data analysis method. The signal injection method involves adding signal devices to the network structure and determining topology relationships through signal injection and reading, as exemplified by Chinese patents CN112468320A and CN110838758B. The data tag method involves adding coded communication devices to equipment at all levels of the distribution network to establish data tags, enabling self-identification of devices in the network, as exemplified by Chinese patents CN112086965A and CN111600748A. Both of these methods have high accuracy, but both require additional auxiliary equipment, resulting in high costs and difficult maintenance. The data analysis method, based on electrical quantity data such as voltage and current collected by advanced measurement systems, mines potential relationships between users to achieve topology identification. Compared to the first two methods, the data analysis method requires less modification and has a lower return on investment. For example, Chinese patent CN110768256B discloses a method, device, and system for identifying transformer substation topology based on voltage harmonic spectra. This method identifies the substation topology by comparing the voltage harmonic spectrum distances between the transformer and the meter. However, the voltage harmonic spectrum after time-frequency transformation only reflects the frequency domain characteristics of the voltage curve, resulting in the loss of time-series information. Another example is Chinese patent CN111835006A, which discloses a low-voltage transformer substation topology identification method based on voltage curves and least squares. This method identifies the substation topology by calculating voltage similarity and using a least squares model with respect to active power. However, the least squares model is based on Euclidean distance calculation, which is a point-to-point distance calculation method that couples the differences in voltage curve shape and voltage level, thus making it impossible to analyze these two differences independently. Summary of the Invention

[0004] The purpose of this section is to outline some aspects of embodiments of the present invention and to briefly describe some preferred embodiments. Simplifications or omissions may be made in this section, as well as in the abstract and title of this application, to avoid obscuring the purpose of these documents; however, such simplifications or omissions should not be construed as limiting the scope of the invention.

[0005] In view of the problems existing in the above and / or existing low-voltage distribution transformer area topology identification methods based on the SC-DTW algorithm, this invention is proposed.

[0006] Therefore, the problem to be solved by this invention is how to provide a method for identifying the topology of a low-voltage distribution transformer substation based on the SC-DTW algorithm.

[0007] To solve the above-mentioned technical problems, the present invention provides the following technical solution: a method for identifying the topology of a low-voltage distribution transformer substation based on the SC-DTW algorithm, which includes acquiring the three phases of the secondary side of the low-voltage distribution transformer in the substation to be identified and the daily voltage time series cluster of the substation composed of each user side measured by the substation AMI system.

[0008] For each point in the daily voltage time series cluster of the above-mentioned transformer area, a spatial pole-log coordinate histogram is calculated to obtain the shape context representation, i.e., SC, at each point.

[0009] Calculate the shape context cost matrix between the daily voltage time series.

[0010] The shape context cost matrix between the daily voltage time series is used instead of the dynamic time warping (i.e., the Euclidean distance matrix used in the DTW algorithm). The warped path that minimizes the cumulative shape context and satisfies the boundary conditions, monotonicity conditions, and step size conditions is calculated as the best alignment between the series.

[0011] Based on the generated regularized paths, the Euclidean distance between each pair of points is accumulated to obtain the cumulative distance matrix between the daily voltage time series.

[0012] The cumulative distance matrix between daily voltage time series is used as a measure of the similarity between series. The k-means algorithm is used to cluster the data to obtain the label of each user's phase, thereby identifying the transformer topology of the low-voltage distribution area.

[0013] As a preferred embodiment of the low-voltage distribution transformer substation topology identification method based on the SC-DTW algorithm described in this invention, the method for obtaining the daily voltage time series cluster of the substation to be identified includes a three-phase daily voltage time series of the secondary side of the low-voltage distribution transformer with a length of L (3-dimensional vector), and a daily voltage time series of each user side measured by the substation AMI system with a length of L (N-dimensional vector), where N is the number of users included in the substation AMI system measurement, and L is the number of data points included in each daily voltage time series.

[0014] As a preferred embodiment of the low-voltage distribution transformer area topology identification method based on the SC-DTW algorithm described in this invention, wherein the daily voltage time series cluster of the transformer area to be identified is an (N+3)×L matrix.

[0015] As a preferred embodiment of the low-voltage distribution transformer substation topology identification method based on the SC-DTW algorithm described in this invention, the step of obtaining the spatial polar logarithmic coordinates includes:

[0016] The entire space is divided into 12 directions with the data point as the center.

[0017] according to Divided into 5 layers along the radial direction, with the innermost layer having a radius of R. inner Take the minimum interval Δt of the daily voltage time series, and the outermost radius R outer Take R inner 25 =32 times;

[0018] The stretch / shrinkage factor SF=73, and the entire space is divided into 60 small grids.

[0019] As a preferred embodiment of the low-voltage distribution transformer area topology identification method based on the SC-DTW algorithm described in this invention, the shape context is obtained by calculating the number of points falling into each small grid to obtain the spatial polar logarithmic coordinate histogram of each point on the daily voltage time series.

[0020] As a preferred embodiment of the low-voltage distribution transformer substation topology identification method based on the SC-DTW algorithm described in this invention, wherein: the daily voltage time series and Shape Context Cost Matrix This can be expressed by the following formula.

[0021]

[0022] in, Indicates matching and The cost, and They represent the first and The first daily voltage time series and One point, and They represent and In the shape context, K=60, where K is the number of grid divisions.

[0023] As a preferred embodiment of the low-voltage distribution transformer area topology identification method based on the SC-DTW algorithm described in this invention, the Euclidean distance matrix used in the Dynamic Time Warping (DTW) algorithm is replaced by the shape context cost matrix between daily voltage time series, and the calculation minimizes the cumulative shape context, expressed by the following formula.

[0024]

[0025] in, and They represent the first and Daily voltage time series Indicates the first step on the normalized path. The value of each element.

[0026] As a preferred embodiment of the low-voltage distribution transformer area topology identification method based on the SC-DTW algorithm described in this invention, the cumulative distance matrix between the daily voltage time series is represented by the following formula.

[0027]

[0028] Where D represents the cumulative distance matrix.

[0029] As a preferred embodiment of the low-voltage distribution transformer area topology identification method based on the SC-DTW algorithm described in this invention, the steps of using the k-means algorithm to cluster and obtain the label of each user's phase include: (The text abruptly ends here, so the translation stops as well.)

[0030] k sequences are randomly selected from the daily voltage time series cluster V of the transformer area as the initial centroids;

[0031] Computing sequence clusters Each sequence in With center of mass distance ;

[0032] Will The smallest one is Corresponding category ,renew Recalculate the centroid .

[0033] As a preferred embodiment of the low-voltage distribution transformer substation topology identification method based on the SC-DTW algorithm described in this invention, the step of obtaining the label of each user's phase by clustering using the k-means algorithm further includes,

[0034] Iterate until all centroids have not changed or the maximum number of iterations has been reached, then stop iterating and obtain the label of each user's phase;

[0035] Identify the transformer topology of the low-voltage distribution area.

[0036] The beneficial effects of this invention are as follows: Compared with signal injection technology and data tagging technology, this invention calculates based on the measurement data of the existing AMI system, without the need for additional hardware equipment, saving installation and maintenance costs and making it more feasible in engineering. Compared with the classic DTW algorithm, the SC-DTW algorithm proposed in this invention introduces morphological features into the measurement of voltage time series similarity, and replaces the Euclidean distance matrix used by the classic DTW algorithm with the shape context cost matrix of data points, so that the optimal alignment avoids the ill-conditioned alignment caused by the use of Euclidean distance, and the alignment effect is significantly better, thereby improving the accuracy of user clustering labels. Attached Figure Description

[0037] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:

[0038] Figure 1 This is a schematic diagram of the shape context outline region;

[0039] Figure 2 The optimal regular path and corresponding best alignment obtained using the classic DTW algorithm;

[0040] Figure 3 The optimal regularized path and corresponding optimal alignment obtained using the SC-DTW algorithm proposed in this invention;

[0041] Figure 4 The results show the topology of a low-voltage distribution network household transformer identified using the SC-DTW algorithm proposed in this invention. Detailed Implementation

[0042] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0043] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0044] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0045] Example 1

[0046] Reference Figures 1-4 This is the first embodiment of the present invention, which provides a method for identifying the topology of a low-voltage distribution transformer substation based on the SC-DTW algorithm, including:

[0047] S1: Obtain the three-phase secondary side of the low-voltage distribution transformer in the area to be identified and the daily voltage time series cluster of the area, which is composed of the three phases of the secondary side of the transformer and the user side of each user side measured by the area's AMI system;

[0048] Furthermore, the daily voltage time series cluster V of the distribution area to be identified is obtained, which consists of two parts: one is the daily voltage time series of the three phases on the secondary side of the low-voltage distribution transformer, expressed by the following formula:

[0049]

[0050] Second, the daily voltage time series of each user side measured by the AMI system in the distribution area is expressed by the following formula:

[0051]

[0052] It is an N×L matrix, so the daily voltage time series cluster of the distribution area to be identified is a (3+N)×L matrix, where N is the number of users included in the AMI system metering of the distribution area, and L is the number of data points included in each daily voltage time series.

[0053] S2: Calculate the spatial pole-log coordinate histogram for each point in the daily voltage time series cluster of the above-mentioned transformer area to obtain the shape context representation, i.e., SC, at each point;

[0054] Furthermore, a spatial pole-logarithmic coordinate histogram is calculated for each point in the daily voltage time series cluster of the transformer area obtained in step S1 to obtain the shape context representation at each point. Specifically, the entire space centered on the data point is divided into 12 equal directions, and then... Divided into 5 layers along the radial direction, the innermost layer radius Rinner is taken as the minimum interval Δt of the daily voltage time series, and the outermost layer radius R outer Pick Rinner 2 5 =32 times. For time series, the x-axis represents the time scale, and the y-axis represents the voltage. The x-coordinate and y-coordinate have different units and different orders of magnitude. Given that the shape context uses a circular (isotropic) neighborhood, the y-coordinate must be linearly stretched or shrunk to ensure that the y-coordinate is comparable to the x-coordinate, as shown in the following equation:

[0055]

[0056] in It is the original voltage value of a certain sequence in the daily voltage time series cluster of the transformer area, and the denominator is... Its function is to The value is mapped to the range [0,1]. SF is the stretch / shrink factor; in this invention, SF=73 is used to ensure that the points are evenly distributed within the shape context, neither too sparse nor too compact. The entire space is thus divided into 60 small grids, as shown below. Figure 2As shown. By calculating the number of points falling into each small grid, the spatial polar logarithmic coordinate histogram of each point on the daily voltage time series is obtained, i.e., the shape context.

[0057] S3: Calculate the shape context cost matrix between the voltage time series of each day;

[0058] Calculate the daily voltage time series based on the shape context between the calculated daily voltage time series obtained in step S2. and Shape Context Cost Matrix Since the shape context is represented by a histogram distribution, meaning both rows and columns are binary unordered variables, it is natural to... The concept of a statistic can be applied to measuring the correlation between two sequences, as shown in the following formula:

[0059]

[0060] in Indicates matching and The cost, and They represent the first and The first daily voltage time series and One point, and They represent and In the shape context, K is the number of grid divisions in step S2, K=60.

[0061] S4: Replace Dynamic Time Warping (DTW) with the shape context cost matrix between the voltage time series of each day. The Euclidean distance matrix used in the DTW algorithm is used to calculate the warped path that minimizes the cumulative shape context and satisfies the boundary conditions, monotonic conditions and step size conditions. This path serves as the best alignment between the series.

[0062] S5: Based on the generated regularized path, accumulate the Euclidean distance between each pair of points to obtain the cumulative distance matrix between the daily voltage time series;

[0063] S6: Using the cumulative distance matrix between daily voltage time series as a measure of similarity between series, the k-means algorithm is used to cluster the data to obtain the label of each user's phase, thereby identifying the transformer topology of the low-voltage distribution area.

[0064] Example 2

[0065] Reference Figures 1-4This is the second embodiment of the present invention, which differs from the first embodiment in that it further includes:

[0066] S4: Replace Dynamic Time Warping (DTW) with the shape context cost matrix between the voltage time series of each day. The Euclidean distance matrix used in the DTW algorithm is used to calculate the warped path that minimizes the cumulative shape context and satisfies the boundary conditions, monotonic conditions and step size conditions. This path serves as the best alignment between the series.

[0067] Furthermore, the Euclidean distance matrix used in the DTW algorithm is replaced by the shape context cost matrix between the daily voltage time series obtained in step S3. A regularized path that minimizes the cumulative shape context and satisfies the boundary conditions, monotonicity conditions, and step size conditions is then calculated and used as the optimal alignment between the series. The essence of the DTW algorithm is an optimization problem—finding the path with the minimum total cost that satisfies certain constraints, as shown in the following equation:

[0068]

[0069] Constraints

[0070] 1) Boundary conditions: and

[0071] 2) Continuity: If and Then it must satisfy and

[0072] 3) Monotonicity: If ,and Then it must satisfy and

[0073] in and They represent the first and Daily voltage time series Indicates the first step on the normalized path. The value of each element, the classic DTW algorithm It is derived from the Euclidean distance matrix. This invention uses the shape context cost matrix between the daily voltage time series obtained in step S3. Instead of the Euclidean distance matrix used in the DTW algorithm, i.e. Then, the solution is obtained using a dynamic programming algorithm, as shown in the following equation:

[0074]

[0075] in It is the cumulative distance. yes and The distance, i.e. The optimal normalized paths and corresponding optimal alignments obtained using the classic DTW algorithm and the SC-DTW algorithm proposed in this invention are as follows: Figure 3 (a) and Figure 3 As shown in (b), it can be seen that the SC-DTW algorithm proposed in this invention avoids the ill-conditioned alignment caused by using Euclidean distance compared with the classic DTW, and the alignment effect is significantly better.

[0076] S5: Based on the generated regularized path, accumulate the Euclidean distance between each pair of points to obtain the cumulative distance matrix between the daily voltage time series;

[0077] Furthermore, by accumulating the shape context cost between each pair of points in the optimal alignment of the daily voltage sequences obtained in step S4, the cumulative distance matrix D between each daily voltage time series is obtained, as shown in the following equation:

[0078]

[0079] S6: The cumulative distance matrix between the daily voltage time series is used as a measure of the similarity between the series. The k-means algorithm is used to cluster the data to obtain the label of the phase to which each user belongs, thereby identifying the transformer topology of the low-voltage distribution area.

[0080] Furthermore, the cumulative distance matrix D between the daily voltage time series obtained in step S5 is used as a measure of the similarity between the series, and the k-means algorithm is used to cluster them to obtain the label of the phase to which each user belongs. First, k series are randomly selected from the daily voltage time series cluster V of the transformer area as the initial centroids. Since the phase sequence that a user may belong to is three phases A, B, and C, we take... The initial centroid is Then, the sequence clusters are calculated using the cumulative distance matrix D from step S5. Each sequence in With center of mass Distance: ,Will The smallest one is Corresponding category ,renew Recalculate the centroid The iteration continues until all centroids have not changed or the maximum number of iterations has been reached. Then, the iteration stops and the labels of each user's phase are obtained, thereby identifying the user transformer topology of the low-voltage distribution radio area.

[0081] In summary, by following the steps above, the topology of the low-voltage distribution network can be identified based on the daily voltage curve collected by the user's electricity meter. Figure 4 As shown, this facilitates the power grid company to promptly and accurately grasp the topological connection relationship of the low-voltage distribution network when low-voltage users experience changes in distribution area or phase sequence, making the calculation of three-phase imbalance and distribution area line loss more accurate.

[0082] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for identifying the topology of a low-voltage distribution transformer substation based on the SC-DTW algorithm, characterized in that: include, Obtain the three-phase secondary side of the low-voltage distribution transformer in the area to be identified, and the daily voltage time series cluster of the area, which is composed of the three phases of the secondary side of the transformer and the voltage of each user side measured by the area's AMI system; For each point in the above daily voltage time series cluster of the transformer area, a spatial pole-log coordinate histogram is calculated to obtain the shape context, i.e., SC, at each point; Calculate the shape context cost matrix between the voltage time series of each day; The shape context cost matrix between the voltage time series of each day is used instead of the dynamic time warping, i.e. the Euclidean distance matrix used in the DTW algorithm. The warping path that minimizes the cumulative shape context and satisfies the boundary conditions, monotonic conditions and step size conditions is calculated as the best alignment between the series. Based on the generated regularized paths, the Euclidean distance between each pair of points is accumulated to obtain the cumulative distance matrix between the daily voltage time series; The cumulative distance matrix between daily voltage time series is used as a measure of the similarity between series. The k-means algorithm is used to cluster the data to obtain the label of each user's phase, thereby identifying the transformer topology of the low-voltage distribution area.

2. The method for identifying the topology of a low-voltage distribution transformer substation based on the SC-DTW algorithm according to claim 1, characterized in that: The acquisition of the daily voltage time series cluster of the distribution area to be identified includes a three-phase daily voltage time series of the secondary side of the low-voltage distribution transformer with a length of L (3-dimensional vector), and a daily voltage time series of each user side measured by the distribution area AMI system with a length of L (N-dimensional vector), where N is the number of users included in the distribution area AMI system measurement, and L is the number of data points included in each daily voltage time series.

3. The method for identifying the topology of a low-voltage distribution transformer area based on the SC-DTW algorithm according to claim 2, characterized in that: The daily voltage time series cluster of the transformer area to be identified is an (N+3)×L matrix.

4. The method for identifying the topology of a low-voltage distribution transformer substation based on the SC-DTW algorithm according to claim 3, characterized in that: The steps for obtaining the spatial polar logarithmic coordinates include: The entire space is divided into 12 directions with the data point as the center. according to Divided into 5 layers along the radial direction, with the innermost layer having a radius of R. inner Take the minimum interval Δt of the daily voltage time series, and the outermost radius R outer Take R inner 2 5 =32 times; With a stretching and shrinking factor SF=73, the entire space is divided into 60 small grids.

5. The method for identifying the topology of a low-voltage distribution transformer substation based on the SC-DTW algorithm according to claim 4, characterized in that: The shape context is obtained by calculating the number of points falling into each small grid to obtain the spatial polar logarithmic coordinate histogram of each point on the daily voltage time series.

6. The method for identifying the topology of a low-voltage distribution transformer substation based on the SC-DTW algorithm according to claim 5, characterized in that: Daily voltage time series and Shape Context Cost Matrix This can be expressed by the following formula. in, Indicates matching and The cost, and They represent the first and The first daily voltage time series and One point, and They represent and In the shape context, K=60, where K is the number of grid divisions.

7. The method for identifying the topology of a low-voltage distribution transformer substation based on the SC-DTW algorithm according to claim 6, characterized in that: The Euclidean distance matrix used in the Dynamic Time Warping (DTW) algorithm is replaced by the shape context cost matrix between the daily voltage time series. The calculation that minimizes the cumulative shape context is expressed by the following formula. in, and They represent the first and Daily voltage time series Indicates the first step on the normalized path. The value of each element.

8. The method for identifying the topology of a low-voltage distribution transformer substation based on the SC-DTW algorithm according to claim 7, characterized in that: The cumulative distance matrix between the daily voltage time series This can be expressed by the following formula. in This represents the cumulative distance matrix.

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