A power distribution area electrical topology self-identification method based on intelligent fusion terminal

Abstract

The present application relates to the technical field of power grid industry, and more particularly to a power distribution area electrical topology self-identification method based on intelligent fusion terminal; the similarity of the coordinate sequence of the trajectory point on the complex plane is measured by introducing a thin plate spline function, the electrical affinity and repulsion relationship can still be effectively distinguished in the affine power supply area with close line impedance, and the graph Laplacian matrix is constructed and the relevant constraints are set to ensure that there is no false branch and negative conductance that violates Kirchhoff's law in the final output topology adjacency matrix, when the coordinate sequence of the trajectory point is preprocessed by median filtering, the local density clustering of the complex plane is further introduced, the local density of each trajectory point is calculated and compared with the preset local density threshold to identify the outlier in the coordinate sequence of the trajectory point, so that the influence of the synchronous sampling error and the transient disturbance is eliminated, and the calculation of the thin plate spline deformation energy has stronger robustness under non-ideal working conditions.

Description

Technical Field

[0001] This invention relates to the field of power grid industry technology, and in particular to a method for self-identification of electrical topology in distribution substations based on intelligent fusion terminals. Background Technology

[0002] Low-voltage distribution substations directly face end users, and the accuracy of their topology directly affects the effectiveness of applications such as three-phase imbalance management, refined line loss calculation, and rapid fault location. Utilizing node voltage phasors synchronously collected by intelligent fusion terminals for topology identification is one of the mainstream directions for automatic topology identification in low-voltage distribution substations. This method is based on Kirchhoff's laws, which state that nodes with closer electrical distances should have more similar voltage fluctuation patterns. Therefore, by calculating the correlation (such as the Pearson correlation coefficient), mutual information, or performing sparse regression between node voltage time-series signals, connection relationships can be inferred. However, in real-world distribution substations, especially in older urban communities or urban villages, there are numerous power supply areas with dense branches, similar cable lengths, and multiple households connected via T-junctions on end poles. In these areas, the line impedance parameters of several nodes are almost identical, and the random fluctuation patterns of the loads they supply are highly coupled. For example, the electricity consumption behaviors of adjacent households tend to be similar, leading to a strong overall coordinated deformation of the voltage trajectories of these nodes in the complex plane.

[0003] Therefore, in order to minimize the reconstruction error numerically, existing algorithms are prone to forcibly assigning a non-zero connection weight between nodes that should have infinite electrical distance but have no direct physical connection in reality, thereby generating false branches. When multiple such false branches form a closed loop, the branch conductance obtained by fitting voltage data will have an inexplicable negative value. As a result, in the weak identification area where the impedance is close, a physically infeasible topology map will be output, causing all subsequent applications such as line loss calculation and power flow analysis based on the topology to fail. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a method for self-identification of electrical topology in distribution substations based on intelligent fusion terminals. This method solves the technical problem that in areas such as old urban communities or urban villages, some nodes exhibit strong overall coordinated deformation of voltage trajectories on the complex plane, and the calculated branch conductance may have inexplicable negative values ​​when generating the topology map.

[0005] To address the aforementioned technical problems, this invention provides the following technical solution: a method for self-identification of electrical topology in distribution substations based on an intelligent fusion terminal, comprising the following steps:

[0006] S1. Synchronous acquisition of positive sequence phasors of three-phase voltage fundamental wave and generation of complex plane trajectory.

[0007] By deploying intelligent fusion terminals at each node of the distribution transformer area and achieving microsecond-level synchronous sampling based on satellite timing, the fundamental positive-sequence phasor of the three-phase voltage is extracted synchronously, and its expression is:

[0008]

[0009] In the above formula, Let i represent the fundamental positive-sequence phasor of the three-phase voltage at node i. Let be the positive sequence voltage magnitude of node i at time t. This represents the phase angle of node i at time t;

[0010] Based on the positive-sequence phasors of the three-phase fundamental voltage, the coordinate sequence of the trajectory points of each node voltage on the complex plane is constructed, and its expression is:

[0011]

[0012]

[0013]

[0014] In the above formula, This represents the sequence of coordinates of the points on the trajectory of the voltage at node i in the complex plane. and Let x and y represent the x and y coordinates of node i in the complex plane at time t, respectively;

[0015] S2. Electrical distance metric based on bending energy of thin plate spline function.

[0016] For any two nodes i and j, the sequence of coordinates of the trajectory points and Before dynamic time warping, this invention can further preprocess the trajectory point coordinate sequence of each node as needed, as follows:

[0017] First, using a length of Sliding window for trajectory point coordinate sequence Perform median filtering in the time domain to obtain the filtered sequence. Its expression is:

[0018]

[0019] in, and Let x and y represent the x and y coordinates at time t after filtering, respectively.

[0020] Similarly, a length of [length not specified] is also used. Sliding window for trajectory point coordinate sequence Perform median filtering in the time domain to obtain the filtered sequence. .

[0021] Then the filtered sequence Perform complex plane local density clustering to calculate the local density of each trajectory point. The calculation formula is as follows:

[0022]

[0023] In the above formula, Let represent the local density of the voltage at time t of the i-th node on the trajectory points in the complex plane. For Euclidean distance, The preset neighborhood radius, It is a unit step function, which takes the value 1 when the independent variable of the function is less than or equal to 0, and 0 otherwise.

[0024] Then remove local density Less than the preset local density threshold The outliers are identified, and the remaining trajectory points are used to form a sequence for subsequent dynamic time warping. Similarly, the filtered sequence can also be processed. The same process was performed to obtain .

[0025] Then, the preprocessed results and Replace them with the corresponding trajectory point coordinate sequences from before. and This serves as the final sequence of trajectory point coordinates, which is then dynamically time-warped to obtain the time-aligned sequence. For a matching point, its expression can be represented as: ,in, The aligned first position of the trajectory point coordinate sequence corresponding to node i One point, Indicates the sequence of coordinates of the trajectory points corresponding to node j. The corresponding points. Then, using thin-plate spline functions... right Interpolate the matching points so that Approaching And calculate the bending energy of the thin plate spline function. As a measure of electrical distance between nodes i and j The calculation formula is as follows:

[0026]

[0027] In the above formula, Two-dimensional coordinates on the complex plane. It represents a two-dimensional real number space.

[0028] In addition, in calculation Furthermore, an amplitude difference metric can be introduced. Specifically, firstly, an amplitude difference metric is calculated to characterize the difference in positive-sequence voltage amplitude between node i and node j at each time step. The calculation formula is as follows:

[0029]

[0030] In the above formula, This represents the total number of sampling times. and The positive-sequence voltage magnitudes of nodes i and j at time t are then measured, and the magnitude difference is measured. With electrical distance measurement Weighting is performed to obtain the final electrical distance metric. .

[0031] S3. Physical network modeling based on graph Laplace constraints.

[0032] The topology of the transformer area is abstracted as an undirected weighted graph with N nodes, and a symmetric adjacency matrix is ​​defined. The element in the i-th row and j-th column of a symmetric adjacency matrix Let represent the equivalent branch conductance between nodes i and j, and satisfy . Define the degree matrix ,in, Then construct the Laplace matrix. and constrain the Laplace matrix. And the sum of each row is 0; in addition, in constructing the Laplace matrix Furthermore, structural constraints on the transformer area topology can be added. Specifically, the symmetric adjacency matrix is ​​first restricted. The total number of non-zero elements in China does not exceed ,in, , which is the preset upper limit for the number of allowed redundant connections, when When, this constraint forces the optimized topology to satisfy a radial structure, when At this time, the constraint forces the optimized topology to satisfy the weak ring network structure to prevent multiple redundant branches caused by overfitting in node regions with similar impedances.

[0033] S4. Graph structure learning that integrates trajectory deformation priors and physical constraints.

[0034] A data matrix is ​​constructed based on the positive sequence voltage amplitude at any moment in the three-phase voltage fundamental positive sequence phasor of step S1. The element in the i-th row and t-th column of the matrix Let be the positive sequence voltage amplitude of node i at sampling time t. Let the total number of sampling times be denoted as , and then construct the following joint optimization function:

[0035]

[0036] And it satisfies the following constraints:

[0037]

[0038]

[0039]

[0040]

[0041]

[0042]

[0043] In the above formula, and They represent and The transpose of the matrix, Represents the trace of a matrix. It is the Frobenius norm. and For two regularization parameters, It is a matrix of all 1s.

[0044] In this invention, in order to reliably identify topological connections that are indistinguishable or difficult to distinguish under a single operating condition, in step S4, voltage data of R different load periods are collected, where R ≥ 2. Then, steps S1 and S2 are executed for any given period r to obtain the voltage data matrix for that period r. and electrical distance metric set The joint optimization function can now be rewritten as:

[0045]

[0046] The constraints in the above equation remain unchanged. Then, the alternating direction multiplier method is used to solve the joint optimization function, with each time period sharing the same graph Laplacian matrix. and adjacency matrix The optimal conductance matrix is ​​obtained. This allows for the utilization of the diversity of load fluctuations at different times to achieve cross-validation and joint constraints, enabling reliable identification of topological connections that are indistinguishable or difficult to distinguish under a single operating condition.

[0047] In this invention, electrical distance measurement can be further used. conduct and The adaptive update, specifically, is first based on the electrical distance metric. Construct an initial Gaussian kernel similarity graph, whose adjacency matrix elements are: ,in, For all The standard deviation; then calculate the normalized Laplacian matrix of the Gaussian kernel similarity map. and to Sort the eigenvalues ​​in ascending order and take the first two eigenvalues. and Then calculate the characteristic gap ratio. The calculation formula is:

[0048]

[0049] Then, based on the characteristic gap ratio Calculate the smoothing coefficient Then calculate all electrical distance metrics in step S2. mean and standard deviation Then calculate the two regularization parameters according to the following formula. and The calculation formula is:

[0050]

[0051]

[0052] In the above formula, and To be respectively with and The corresponding preset base regularization coefficients are used to calculate the values ​​for each time period. and Then, calculate separately and The average value is used as the final value. and The data is then substituted into the joint optimization function. This adaptive mechanism strengthens the data fidelity term when the voltage signal graph has high smoothness and strengthens the topology prior constraint when the smoothness is low, so that the optimization objective automatically balances the two weights under different load fluctuation intensities in different transformer areas.

[0053] S5. Topology branch determination and result output.

[0054] Set conductivity threshold For the optimal conductance matrix Each element in ,like If a direct physical connection exists between nodes i and j, a distribution area topology adjacency matrix is ​​generated, and the corresponding branch conductance estimate is output.

[0055] In addition, this invention includes physical consistency verification and loop closure correction steps after outputting the topological adjacency matrix, as detailed below:

[0056] First, based on the optimal conductance matrix obtained in step S4 A node admittance network model for the transformer substation is constructed. A node with a known electrical location and good measurement conditions is selected as the voltage reference node. Using the node admittance network model and the estimated injected current values ​​of each node other than the reference node, the voltage estimate of each node is calculated. Then, calculate the voltage estimate of any node i and the positive sequence voltage amplitude measured in step S1. Root mean square residuals between The calculation formula is as follows:

[0057]

[0058] Then, based on a pre-set residual threshold Then The node is marked as a topologically suspicious node, and then all adjacent nodes j that have a direct physical connection with the topologically suspicious node i, as determined in step S5, are included in the suspicious node pair set. For the set of suspicious node pairs Each pair of nodes in Return to step S2 and recalculate. During the calculation, increase the constraint window width of the dynamic time warping or adjust the smoothing parameter of the thin-plate spline function. The smoothing parameter of the thin-plate spline function can be calculated based on the root mean square residual. Specifically, first calculate its voltage residual ratio. The calculation formula is as follows:

[0059]

[0060] Then, based on the voltage residual ratio The smoothing parameters of the thin-plate spline function are determined according to the following formula. :

[0061]

[0062] In the above formula, These are the initial smoothing parameters. , which is the preset adjustment factor.

[0063] Then recalculate its electrical distance metric. The corrected electrical distance metric is obtained, and then the results are recalculated and output in the order of steps S3, S4 and S5 according to the corrected electrical distance metric. If there are still suspicious nodes in the output results, the iteration continues until the maximum number of iterations is reached or there are no suspicious nodes in the topology, and the final distribution area topology adjacency matrix and branch conductance estimate are obtained.

[0064] By employing the above technical solution, the present invention provides a method for self-identification of electrical topology in distribution substations based on intelligent fusion terminals, which has at least the following beneficial effects:

[0065] 1. This invention introduces thin-plate spline functions to measure the similarity of trajectory point coordinate sequences on the complex plane. It can effectively distinguish electrical affinity within affine power supply regions where line impedances are similar. Furthermore, by constructing a graph Laplace matrix and setting relevant constraints, it ensures that there are no false branches or negative conductances that violate Kirchhoff's laws in the final output topological adjacency matrix, thereby improving the accuracy of the results.

[0066] 2. In the process of preprocessing the trajectory point coordinate sequence by median filtering, this invention further introduces complex plane local density clustering. By calculating the local density of each trajectory point and comparing it with a preset local density threshold, outliers in the trajectory point coordinate sequence are identified. This eliminates the influence of synchronous sampling errors and transient disturbances, making the calculation of the deformation energy of the thin plate strip more robust under non-ideal working conditions and avoiding the interference of abnormal jump points on subsequent electrical distance measurements.

[0067] 3. This invention further adds structural constraints to the transformer area topology when constructing the Laplace matrix. By forcing the optimization of the obtained topology to satisfy the radial structure or weak ring network structure through the total number of non-zero elements in the symmetric adjacency matrix, the topology obtained by identification conforms to the actual operation rules of the low-voltage distribution network in terms of structure, thereby improving the structural rationality of the topology.

[0068] 4. By further setting up physical consistency verification and closed-loop correction steps, this invention can effectively adaptively optimize the parameters in the electrical distance measurement calculation process and correct node pairs with abnormal voltage residuals, thus ensuring the dual consistency of the topology results in terms of electrical relationships and physical laws. Attached Figure Description

[0069] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0070] Figure 1 This is a flowchart of the self-identification method for electrical topology of distribution substations according to the present invention. Detailed Implementation

[0071] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. This will allow for a full understanding of how the present application uses technical means to solve technical problems and achieve technical effects, and to facilitate its implementation.

[0072] To address the technical issue of unexplained negative values ​​in branch conductance calculations during topology generation in areas such as old urban communities or urban villages where some nodes exhibit strong overall coordinated voltage trajectories on the complex plane, this embodiment provides a method for self-identification of electrical topology in distribution substations based on intelligent fusion terminals. The following example illustrates a low-voltage distribution substation in an old urban community. This substation contains one distribution transformer and 12 end-user nodes, with multiple T-junctions of similar cable lengths and dense branching, representing a typical power supply area where impedance is difficult to distinguish. Intelligent fusion terminals are deployed at each user node, possessing capabilities for synchronous three-phase voltage and current acquisition, satellite time synchronization, and edge computing. This embodiment, using 12 nodes as an example, details the complete implementation process, including the following steps:

[0073] S1. Synchronous acquisition of positive sequence phasors of three-phase voltage fundamental wave and generation of complex plane trajectory.

[0074] The intelligent fusion terminals deployed at each node of the distribution transformer area achieve microsecond-level synchronous sampling through the satellite timing function of the BeiDou satellite, synchronously acquiring the instantaneous values ​​of the three-phase voltage at a rate of 100 sampling points per second. The terminal edge computing unit performs a Fast Fourier Transform on the acquired data for each power frequency cycle (20ms) to extract the fundamental positive-sequence phasor of the three-phase voltage. Therefore, the expression for the fundamental positive-sequence phasor of the three-phase voltage at node i at time t is:

[0075]

[0076] In the above formula, Let i represent the fundamental positive-sequence phasor of the three-phase voltage at node i. Let be the positive sequence voltage magnitude of node i at time t. Let t represent the phase angle of node i at time t, where t = 1, 2, ..., T. In this embodiment, the acquisition time is 15 minutes, so T = 9000 sampling points.

[0077] Subsequently, based on the fundamental positive-sequence phasors of the three-phase voltages at each moment, a sequence of coordinates of the trajectory points of each node voltage on the complex plane is constructed, the expression of which is:

[0078]

[0079]

[0080]

[0081] In the above formula, This represents the sequence of coordinates of the points on the trajectory of the voltage at node i in the complex plane. and These represent the x and y coordinates of node i in the complex plane at time t, respectively. The calculated sequence of trajectory point coordinates is stored in the fusion terminal for subsequent analysis.

[0082] S2. Electrical distance metric based on bending energy of thin plate spline function.

[0083] Next, we will analyze the sequence of coordinates of the trajectory points corresponding to any two nodes i and j. and Dynamic time warping is performed, but in order to eliminate outliers caused by synchronization sampling errors and transient disturbances, this embodiment further preprocesses the trajectory point coordinate sequence of each node as follows before dynamic time warping:

[0084] First, using a length of Sliding window for trajectory point coordinate sequence The x and y coordinates are subjected to time-domain median filtering to obtain the filtered sequence. Its expression is:

[0085]

[0086] Taking the x-axis as an example, the expression for the filtered x-axis at time t is:

[0087]

[0088] Similarly, median filtering can also be applied to the ordinate.

[0089] Of course, a length of is also used. Sliding window for trajectory point coordinate sequence Perform time-domain median filtering to obtain the corresponding filtered sequence. In addition, to ensure symmetry between the two sides of the center point, The value of is best taken as an odd number.

[0090] Then the filtered sequence Perform complex plane local density clustering to calculate the local density of each trajectory point. The calculation formula is as follows:

[0091]

[0092] In the above formula, Let represent the local density of the voltage at time t of the i-th node on the trajectory points in the complex plane. For Euclidean distance, As a preset neighborhood radius, this embodiment takes 0.02 times the per-unit value of the voltage amplitude. For a unit step function, when Set the value to 1 if the condition is met, otherwise set it to 0. The calculated value is... It reflects the fact that the point is the center and the radius is The number of other trajectory points contained in the neighborhood of .

[0093] Then remove local density Less than the preset local density threshold Outliers in this embodiment The remaining trajectory points are used to form a sequence for subsequent dynamic time warping. Similarly, the same applies to the filtered sequence. The same process was performed to obtain Pre-processed and It effectively filters out abnormal jump points caused by communication delays or instantaneous impact loads.

[0094] Then, the preprocessed results and Replace them with the corresponding trajectory point coordinate sequences from before. and The final sequence of trajectory point coordinates is then used for dynamic time warping (DTW). Since voltage fluctuations at different nodes may have slight phase shifts on the time axis, DTW uses nonlinear time alignment to find the optimal matching path between the two sequences, ultimately yielding the time-aligned sequence. For a matching point, its coordinate expression can be represented as: ,in, The aligned first position of the trajectory point coordinate sequence corresponding to node i One point, Indicates the sequence of coordinates of the trajectory points corresponding to node j. The corresponding points. Then, using thin-plate spline functions... right Interpolate the matching points so that Approaching Thin plate spline function The expression can be:

[0095]

[0096] In the above formula, The independent variable is Thin-plate spline function The output value, Let be the affine transformation matrix. It is a translation vector. Radial basis function coefficients.

[0097] Next, the bending energy of the thin-plate spline function is calculated. As a measure of electrical distance between nodes i and j The calculation formula is as follows:

[0098]

[0099] In the above formula, Two-dimensional coordinates on the complex plane. Represents a two-dimensional real number space. Electrical distance measurement. The larger the value, the greater the nonlinear distortion required to map the voltage trajectory of node i to the voltage trajectory of node j, and the weaker the electrical affinity between the two.

[0100] This embodiment calculates... Furthermore, an amplitude difference metric was introduced. Specifically, an amplitude difference metric was first calculated to characterize the difference in positive-sequence voltage amplitude between node i and node j at each time step. The calculation formula is as follows:

[0101]

[0102] In the above formula, This represents the total number of sampling times. and The positive-sequence voltage magnitudes of nodes i and j at time t are then measured, and the magnitude difference is measured. With electrical distance measurement Weighting is performed to obtain the final electrical distance metric. This method allows for the calculation of the final electrical distance metric for each pair of nodes.

[0103] S3. Physical network modeling based on graph Laplace constraints.

[0104] The topology of the transformer area is abstracted as an undirected weighted graph with N=12 nodes, and a symmetric adjacency matrix is ​​defined. The element in the i-th row and j-th column of a symmetric adjacency matrix Let represent the equivalent branch conductance between nodes i and j, and satisfy . Define the degree matrix ,in, Then construct the Laplace matrix. and constrain the Laplace matrix. And the sum of each row is 0. Additionally, in constructing the Laplace matrix... Furthermore, structural constraints on the transformer area topology can be added. Specifically, the symmetric adjacency matrix is ​​first restricted. The total number of non-zero elements in China does not exceed ,in, , which is the preset upper limit for the number of allowed redundant connections, when When, this constraint forces the optimized topology to satisfy a radial structure, when At this time, the constraint forces the optimized topology to satisfy the weak loop network structure to prevent overfitting and multiple redundant branches in node areas with similar impedances. Considering that the old community distribution network in this embodiment is mainly a radial structure with only a few weak loops formed by tie switches, an upper limit is set for the number of allowed redundant connections. Thus constraining the symmetric adjacency matrix The total number of non-zero elements is no greater than 12-1+1=12. This constraint can prevent multiple redundant spurious branches from being generated at T-junctions with similar impedances.

[0105] S4. Graph structure learning that integrates trajectory deformation priors and physical constraints.

[0106] A data matrix is ​​constructed based on the positive sequence voltage amplitude at any moment in the three-phase voltage fundamental positive sequence phasor of step S1. The element in the i-th row and t-th column of the matrix Let be the positive sequence voltage amplitude of node i at sampling time t. Let the total number of sampling times be denoted as , and then construct the following joint optimization function:

[0107]

[0108] And it satisfies the following constraints:

[0109]

[0110]

[0111]

[0112]

[0113]

[0114]

[0115] In the above formula, and They represent and The transpose of the matrix, Represents the trace of a matrix. It is the Frobenius norm. and For two regularization parameters, It is a matrix of all 1s, where, This term represents the total variation of the graph signal, used to characterize the smoothness of the voltage signal on the graph. This term controls the complexity of the graphical Laplacian matrix to prevent overfitting. This penalty applies to nodes with large electrical distances, reducing the likelihood of them being assigned a direct connection.

[0116] In this embodiment, to reliably identify topological connections that are indistinguishable or difficult to distinguish under a single operating condition, the present invention collects voltage data for R=3 different load periods during step S4. The first period is the midday off-peak load period (12:00-12:15), the second period is the evening peak load period (19:00-19:15), and the third period is the early morning stable load period (03:00-03:15). These periods can be sequentially labeled as period 1, 2, and 3. Then, for any given period... By performing steps S1 and S2 respectively, the voltage data matrix for that time period r is obtained. and electrical distance metric set The joint optimization function can now be rewritten as:

[0117]

[0118] The constraints in the above equation remain unchanged. Then, the alternating direction multiplier method is used to solve the joint optimization function, with each time period sharing the same graph Laplacian matrix. and adjacency matrix Auxiliary variables can be introduced. Construct the augmented Lagrangian function and update it alternately. , , And Lagrange multipliers, until convergence to obtain the optimal conductance matrix. This allows for cross-validation and joint constraints by leveraging the diversity of load fluctuations at different times, enabling reliable identification of topological connections that are indistinguishable or difficult to distinguish under a single operating condition.

[0119] In the embodiment, further based on electrical distance measurement Determine the regularization parameter in the joint optimization function and Specifically, firstly, based on electrical distance measurements Construct an initial Gaussian kernel similarity graph, whose adjacency matrix elements are: ,in, For all standard deviation The final electrical distance metric is calculated; then the normalized Laplacian matrix of the Gaussian kernel similarity map is calculated. The eigenvalues ​​are sorted in ascending order, and the first two eigenvalues ​​are taken. and Then calculate the characteristic gap ratio. The calculation formula is:

[0120]

[0121] Then, based on the characteristic gap ratio Calculate the smoothing coefficient Then calculate all electrical distance metrics in step S2. mean and standard deviation Then calculate the two regularization parameters according to the following formula. and The calculation formula is:

[0122]

[0123]

[0124] In the above formula, and To be respectively with and The corresponding preset basic regularization coefficients are set to 0.1 and 1.0 in this embodiment, respectively, and are used to calculate the regularization coefficients for each time period. and Then, calculate separately and The average value is used as the final value. and The data is then substituted into the joint optimization function. This adaptive mechanism strengthens the data fidelity term when the voltage signal graph has high smoothness and strengthens the topology prior constraint when the smoothness is low, so that the optimization objective automatically balances the two weights under different load fluctuation intensities in different transformer areas.

[0125] S5. Topology branch determination and result output.

[0126] After obtaining the initial topology results, set the conductivity threshold. For the optimal conductance matrix Each element in ,like If a direct physical connection exists between nodes i and j, a distribution area topology adjacency matrix is ​​generated, and the corresponding branch conductance estimate is output.

[0127] In addition, after outputting the topological adjacency matrix, this embodiment performs physical consistency verification and loop closure correction steps, as follows:

[0128] First, based on the optimal conductance matrix obtained in step S4 A network model of the admittance network of the transformer substation nodes is constructed. The node at the secondary side outlet of the transformer substation (numbered as node 1) is selected as the voltage reference node. The voltage amplitude of this node is stable and the measurement accuracy is high. Using the known estimated values ​​of the node injection current and the admittance matrix, the voltage estimates of each node are calculated layer by layer along the topology path starting from the reference node. Then, calculate the voltage estimate of any node i and the positive sequence voltage amplitude measured in step S1. Root mean square residuals between The calculation formula is as follows:

[0129]

[0130] Then, based on a pre-set residual threshold Volt, then The node is marked as a topologically suspicious node, and then all adjacent nodes j that have a direct physical connection with the topologically suspicious node i, as determined in step S5, are included in the suspicious node pair set. For the set of suspicious node pairs Each pair of nodes in Return to step S2 to recalculate the electrical distance metric. During the calculation, increase the constraint window width of the dynamic time warping or adjust the smoothing parameter of the thin-plate spline function. The smoothing parameter of the thin-plate spline function can be calculated based on the root mean square residual. Specifically, first calculate its voltage residual ratio. The larger this value, the less reliable the connection between the node pairs. The smoothing parameter should be increased accordingly to relax the smoothness constraints of thin-plate spline interpolation and produce a more significant distance correction effect. Its calculation formula is as follows:

[0131]

[0132] Then, based on the voltage residual ratio The smoothing parameters of the thin-plate spline function are determined according to the following formula. :

[0133]

[0134] In the above formula, This is the initial smoothing parameter, which can be set to 0.5. , is a preset adjustment factor, which can be 2.

[0135] Then recalculate its electrical distance metric. The corrected electrical distance metric is obtained, and then the results are recalculated and output in the order of steps S3, S4 and S5 according to the corrected electrical distance metric. If there are still suspicious nodes in the output results, the iteration continues until the maximum number of iterations (such as 5 times) is reached or there are no suspicious nodes in the topology. The final topology adjacency matrix and branch conductance estimate of the 12 nodes in the low-voltage distribution area are obtained. This topology does not have negative conductance branches and has been verified for consistency with measured voltage data. It can be directly used for subsequent three-phase imbalance management, line loss refinement and fault location.

[0136] Those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0137] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. Since the above embodiments are substantially similar to the method embodiments, their descriptions are relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0138] The above embodiments provide a detailed description of the present invention. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for self-identification of electrical topology in distribution substations based on intelligent fusion terminals, characterized in that, Includes the following steps: S1. Synchronously acquire the fundamental positive sequence phasors of the three-phase voltage at each node of the distribution substation area, and construct the coordinate sequence of the trajectory points of each node voltage on the complex plane; S2. Perform dynamic time warping on the trajectory point coordinate sequence corresponding to any two nodes i and j to obtain the time-aligned sequence. For matching points, use thin-plate spline functions to... Interpolate the matching points and calculate the bending energy of the thin plate spline function as a measure of the electrical distance between nodes i and j; S3. Abstract the transformer area topology into an undirected weighted graph with N nodes, and define a symmetric adjacency matrix. Sum-degree matrix Then construct the Laplace matrix. and constrain the Laplace matrix. And the sum of each row is 0; S4. Construct a data matrix based on the fundamental positive sequence phasors of the three-phase voltage, construct a joint optimization function and corresponding constraints based on the data matrix, and solve for the optimal conductance matrix. S5. Filter the elements in the optimal conductance matrix whose parameter values ​​are greater than the preset conductance threshold, and determine that there is a direct physical connection between the two nodes corresponding to the element, so as to generate the distribution area topology adjacency matrix and the corresponding branch conductance estimate.

2. The method for self-identification of electrical topology in a distribution substation according to claim 1, characterized in that, In step S2, before the dynamic time warping, a preprocessing step of the trajectory point coordinate sequence is included, the specific steps of which are as follows: Use a length of A sliding window is used to perform time-domain median filtering on the trajectory point coordinate sequence to obtain the filtered sequence; Perform complex plane local density clustering on the filtered sequence and calculate the local density of each trajectory point; Outliers with local densities less than a preset local density threshold in the filtered sequence are removed, and the remaining trajectory points are used as the final trajectory point coordinate sequence.

3. The method for self-identification of electrical topology in a distribution substation according to claim 1, characterized in that, In step S2, the electrical distance measurement is further calculated by incorporating an amplitude difference measurement, as detailed below: Calculate the bending energy of the thin plate spline function as a measure of the electrical distance between nodes i and j; Calculate the magnitude difference measure used to characterize the difference in positive sequence voltage magnitude between node i and node j at each time step; The amplitude difference metric and the electrical distance metric are weighted together to obtain the final electrical distance metric.

4. The method for self-identification of electrical topology in a distribution substation according to claim 1, characterized in that, In step S3, the Laplace matrix During construction, restrict the symmetric adjacency matrix. The total number of non-zero elements in China does not exceed ,in, , which is the preset upper limit for the number of redundant connections allowed.

5. The method for self-identification of electrical topology in a distribution substation according to claim 1, characterized in that, In step S4, the expression for the joint optimization function is: ； And it satisfies the following constraints: ； ； ； ； ； ； In the above formula, and They represent and The transpose of the matrix, Represents the trace of a matrix. It is the Frobenius norm. and For two regularization parameters, Let N represent an N-dimensional column vector where all elements are 1. This represents the electrical distance metric between nodes i and j. Represents a symmetric adjacency matrix The element in the i-th row and j-th column.

6. The method for self-identification of electrical topology in a distribution substation according to claim 5, characterized in that, In step S4, the joint optimization function is constructed by collecting low-voltage data from R different load periods, where R ≥ 2, and specifically includes the following steps: Collect low voltage data for R different load periods, and perform steps S1 and S2 for any period r to obtain the voltage data matrix and electrical distance measurement set for that period r. The final joint optimization function is constructed based on the voltage data matrix and the set of electrical distance metrics.

7. The method for self-identification of electrical topology in a distribution substation according to claim 5, characterized in that, The regularization parameter and The specific steps for adaptive updating based on electrical distance metrics are as follows: An initial Gaussian kernel similarity graph is constructed based on the electrical distance metric, and its adjacency matrix elements are: ,in, For all Standard deviation; Calculate the normalized Laplacian matrix of the Gaussian kernel similarity map, sort its eigenvalues ​​in ascending order, and take the first two eigenvalues. and To calculate the characteristic gap ratio ; Based on the characteristic gap ratio Calculate the smoothing factor, and all electrical distance metrics. mean and standard deviation Calculate two regularization parameters and ; Calculate the regularization parameters for each time period. and The average value is used to obtain the final regularization parameter. and .

8. The method for self-identification of electrical topology in a distribution substation according to claim 1, characterized in that, In step S5, after the topological adjacency matrix is ​​output, a physical consistency verification and loop closure correction step is also included, as follows: A network model of the admittance of the transformer area nodes is constructed based on the optimal conductance matrix, and nodes are selected as voltage reference nodes. Using the nodal admittance network model and the estimated injected current of each node except the reference node, the estimated voltage of each node is calculated. Calculate the root mean square residual between the voltage estimate and the measured positive sequence voltage amplitude at any node i; Nodes with root mean square residuals greater than a preset residual threshold are marked as topologically suspicious nodes, and all adjacent nodes that have a direct physical connection with the topologically suspicious node are included in the suspicious node pair set. For each pair of nodes in the set of suspicious nodes, increase the constraint window width of the dynamic time warping or adjust the smoothing parameter of the thin plate spline function to recalculate the electrical distance metric to obtain the corrected electrical distance metric; Based on the corrected electrical distance metric, the results are recalculated and output in the order of steps S3, S4 and S5. If there are still suspicious nodes in the output results, the iteration continues until the maximum number of iterations is reached or there are no suspicious nodes, and the final distribution area topology adjacency matrix and branch conductance estimate are obtained.

9. The method for self-identification of electrical topology in a distribution substation according to claim 8, characterized in that, The smoothing parameters of the thin-plate spline function are calculated based on the root mean square residuals, and the specific steps are as follows: The voltage residual ratio is calculated based on the root mean square residual of the two nodes in each pair of nodes. The smoothing parameters of the thin-plate spline function are determined based on the voltage residual ratio.

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