Low-voltage power distribution network topology identification method and device under data insufficiency condition

Abstract

The present application relates to the technical field of low-voltage power distribution network topology identification, and particularly relates to a low-voltage power distribution network topology identification method and device under data insufficient conditions, which comprises the following steps: obtaining the voltage amplitude, active power time series of each user node, and the voltage amplitude time series of each phase of the root node; calculating the Pearson correlation coefficient of each user node and each phase voltage sequence of the root node to identify the access phase of each user node; for the user nodes in the same phase, determining the response relationship of the change of the square of the voltage amplitude to the change of the active power based on the voltage amplitude, active power and the voltage amplitude time series of the corresponding phase of the root node, and identifying the upstream and downstream connection relationship according to a preset rule; and connecting the user nodes according to the upstream and downstream connection relationship and combining the root node to generate the power distribution network topology. The present application only relies on two types of data, i.e. voltage amplitude and active power, and can accurately identify the topology without reactive power, thereby overcoming the dependence of traditional methods on complete measurement data.

Description

Technical Field

[0001] This invention relates to the field of low-voltage distribution network topology identification technology, and in particular to a method and apparatus for low-voltage distribution network topology identification under conditions of insufficient data. Background Technology

[0002] In recent years, with the State Grid's continuous promotion of digital and intelligent transformation, the reliability, convenience, and intelligence of power supply services have been continuously improved. However, as the last link in power supply services directly facing users, the low-voltage distribution network has received significantly less attention and resource investment, and its level of intelligence is far inferior to that of transmission and distribution lines with higher voltage levels. The low-voltage distribution network has a complex structure and has long lacked effective management methods. In addition, frequent user access, cancellation, and line relocation have resulted in missing or incorrect topology information for most low-voltage distribution areas in the distribution system. At the same time, most users in low-voltage distribution areas use single-phase power supply, and frequent expansion and renovation cause the phase sequence of user connections to change frequently, resulting in delayed updates of grid ledger information, chaotic user phase sequence, and missing line parameters, which seriously restricts the level of lean management of low-voltage distribution areas.

[0003] An accurate and complete transformer substation topology map is the foundation for lean operation and maintenance of low-voltage distribution networks. Based on reliable topological relationships, it is essential to accurately locate low-voltage users, address three-phase imbalances, optimize reactive power compensation schemes, and perform precise analysis of substation line losses. Therefore, obtaining an accurate low-voltage transformer substation topology is a primary prerequisite for improving the level of distribution network operation and maintenance management and the quality of power supply services.

[0004] Current topology identification technologies primarily rely on data-driven methods, utilizing measurement data collected by smart meters for topology identification. Existing methods include voltage-correlation-based topology identification, density-based clustering algorithms, and machine learning-based topology identification algorithms. However, all of these methods require relatively complete data support—when data is sufficient, smart meters can typically record various measurement data such as voltage amplitude, active power, and reactive power. But in practical engineering, due to limitations in communication bandwidth and smart meter hardware costs, the types of data uploaded by smart meters to terminals in remote rural areas are very limited, usually only including voltage amplitude and active power data, lacking reactive power records. When data is insufficient, the identification accuracy and reliability of existing methods decrease significantly, making it difficult to meet practical engineering needs.

[0005] Therefore, how to accurately identify the topology of low-voltage distribution networks under insufficient data conditions that rely only on voltage amplitude and active power is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of existing technologies, such as strong dependence on complete measurement data and significant decrease in topology identification accuracy when reactive power is lacking, and to provide a method and device for topology identification of low-voltage distribution networks under conditions of insufficient data.

[0007] In a first aspect, the present invention provides a method for topology identification of low-voltage distribution networks under conditions of insufficient data, comprising:

[0008] Obtain the voltage amplitude time series and active power time series of each user node, as well as the voltage amplitude time series of each phase of the root node; Based on the Pearson correlation coefficient between the voltage amplitude time series of each user node and the voltage amplitude time series of each phase of the root node, the phase of the root node to which each user node is connected is identified. Based on the root node phase, voltage amplitude time series, active power time series, and voltage amplitude time series of each root node phase connected to each user node, determine the response relationship of the square change of voltage amplitude of each user node to the change of active power within the same root node phase, and identify the upstream and downstream connection relationship between each user node under the same root node phase according to the response relationship and the preset discrimination rules. Based on the upstream and downstream connection relationship, each user node within the same root node is connected, and the topology of the distribution network is generated by combining the root node.

[0009] Preferably, identifying the root node to which each user node is connected includes: The root node corresponding to the maximum absolute value of the Pearson correlation coefficient is determined as the root node connected to the corresponding user node.

[0010] Preferably, determining the response relationship between the squared change in voltage amplitude of each user node within the same root node phase and the change in active power includes: Based on the voltage amplitude time series, active power time series of each user node within the same root node phase, and the voltage amplitude time series of the corresponding phase of the root node, a matrix equation for the linearized Distflow power flow model is established. The matrix equation uses the difference between the squared difference of the voltage amplitude of each user node and the squared difference of the voltage amplitude of the corresponding phase of the root node as the dependent variable, the active power difference of each user node as the independent variable, and the hybrid sensitivity matrix as the coefficient matrix to be solved. The matrix equation is solved using the least squares method to obtain the values ​​of each element in the mixed sensitivity matrix, and the mixed sensitivity matrix is ​​used to characterize the response relationship.

[0011] Furthermore, the matrix equations for establishing the linearized Distflow power flow model include: Establish a distflow power model between nodes; By taking the difference between adjacent time points for each variable in the Distflow power flow model, a difference form of the Distflow power flow model is obtained; By removing higher-order terms (above first order) from the difference form of the Distflow power flow model, a linearized expression is obtained. Based on the linearized expression, the relationship between the squared difference of the voltage amplitude of each user node and the difference of the active power of each user node is derived. The relationship is then written in matrix form to obtain the matrix equation.

[0012] Furthermore, the matrix equation of the linearized Distflow power flow model is as follows:

[0013] in The voltage magnitude squared difference matrix for each user node. This is the squared difference matrix of the voltage magnitudes of the phases corresponding to the root node. For a mixed sensitivity matrix, This is the active power difference matrix for each user node.

[0014] Furthermore, the rows of the hybrid sensitivity matrix correspond to user nodes as dependent variables, and the columns of the hybrid sensitivity matrix correspond to user nodes as independent variables; each element in the hybrid sensitivity matrix is ​​the hybrid sensitivity of the user node corresponding to the row with respect to the user node corresponding to the column, which is used to characterize the degree of response of the square change in the voltage amplitude of the user node corresponding to the row to the change in the active power of the user node corresponding to the column.

[0015] Furthermore, the preset discrimination rules include: Define a first discrimination index and a second discrimination index. The first discrimination index is equal to the mixed sensitivity of the first user node to its own active power minus the mixed sensitivity of the second user node to the active power of the first user node. The second discrimination index is equal to the mixed sensitivity of the second user node to its own active power minus the mixed sensitivity of the first user node to the active power of the second user node. If the first discrimination index is less than the first preset threshold and the second discrimination index is greater than the first discrimination index, then the first user node is determined to be the upstream node of the second user node; If the second discrimination index is less than the second preset threshold and the first discrimination index is greater than the second discrimination index, then the first user node is determined to be a downstream node of the second user node.

[0016] Furthermore, the method for determining the first preset threshold and the second preset threshold includes: Based on the differential form of the Distflow power flow model, the expression for the partial derivative of the squared difference of voltage magnitude of each user node within the same root node phase with the partial derivative of the active power difference of other user nodes is derived. Based on the physical characteristics of the low-voltage distribution network, determine the relationship between the partial derivatives of the squared difference of voltage amplitude of each user node within the same root node and the difference of active power of other user nodes. Based on the relationship between the magnitudes of the partial derivatives, the first preset threshold and the second preset threshold are determined.

[0017] Furthermore, the physical characteristics of the low-voltage distribution network include: the injected power of each user node is differentially independent, the line power is dominated by the injected power of the downstream user nodes, and the square of the voltage amplitude is greater than the power consumed by the user nodes.

[0018] In a second aspect, the present invention provides a low-voltage distribution network topology identification device under insufficient data conditions, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, wherein the processor executes the computer program to implement the low-voltage distribution network topology identification method under insufficient data conditions as described in the first aspect.

[0019] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention provides a method for identifying the topology of a low-voltage distribution network under conditions of insufficient data. By acquiring the voltage amplitude time series, active power time series, and voltage amplitude time series of each phase of the root node for each user node, the method uses the Pearson correlation coefficient to identify the phases connected to each user node. Based solely on the above measurement data, the method determines the response relationship of the square change in voltage amplitude of each user node within the same phase to the change in active power, thereby identifying the upstream and downstream connection relationships and generating the topology. This achieves accurate identification of the low-voltage distribution network topology without the need for reactive power data, effectively solving the problem of the failure of traditional methods due to the limited data types of smart meters. 2. This invention provides a low-voltage distribution network topology identification device under conditions of insufficient data. By embedding the aforementioned low-voltage distribution network topology identification method under conditions of insufficient data into a computer program in memory and executing it by a processor, the low-voltage distribution network topology identification algorithm can be deployed on conventional hardware platforms, reducing the dependence on complete measurement data, improving the engineering operability of topology identification in scenarios with insufficient data, and facilitating its application in remote rural areas with limited data collection conditions. Attached Figure Description

[0020] Figure 1 This is a flowchart of the low-voltage distribution network topology identification method under insufficient data conditions in the embodiments. Figure 2 This is a schematic diagram of the IEEE-33 node topology in the embodiment; Figure 3 This is a visualization of the C1 and C2 discrimination indices of node 7 and other nodes in the embodiment. Figure 4 This is a diagram showing the distribution network topology identification results in the embodiment. Detailed Implementation

[0021] The present invention will now be described in further detail with reference to specific embodiments. However, this should not be construed as limiting the scope of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention.

[0022] Unless otherwise specified, the terms "upper," "lower," "left," "right," "center," "inner," and "outer," etc., used in the description of specific embodiments of the present invention to indicate orientation or positional relationships, are based on the orientation or positional relationships shown in the accompanying drawings, or the orientation or positional relationship in which the product / equipment / device is usually placed during use. These terms are merely for the purpose of facilitating the description of the present invention or simplifying the description in specific embodiments, and for enabling those skilled in the art to quickly understand the solution, and do not indicate or imply that a particular device / component / element must have a specific orientation, or be constructed and operated in a specific positional relationship. Therefore, they should not be construed as limitations on the present invention.

[0023] Furthermore, the use of terms such as "horizontal," "vertical," "suspended," "parallel," and "coaxial" does not imply that the corresponding device / component / element must be absolutely horizontal, vertical, suspended, parallel, or coaxial. Slight tilt or deviation is permissible, as long as it does not affect the normal function of the relevant component. For example, "horizontal" simply means that its direction is more horizontal relative to "vertical," not that the structure must be perfectly horizontal; a slight tilt is acceptable. "Coaxial" means that two components are arranged as coaxially as possible, allowing them to move coaxially or approximately coaxially when their relative positions change. Alternatively, it can be simplified to mean that the corresponding device / component / element, when arranged in "horizontal," "vertical," "suspended," "parallel," or "coaxial" directions, can have an error / deviation of ±10% relative to the corresponding direction, more preferably within ±8%, more preferably within ±6%, more preferably within ±5%, and more preferably within ±4%. For example, the deviation in the "coaxial" direction is controlled within 0.2-1mm, preferably within 0.2-0.5mm. As long as the corresponding device / component / element is within the error / deviation range, it can still achieve its function in the solution of the present invention.

[0024] Furthermore, the use of terms such as "first," "second," and "third" in terminology is merely for distinguishing descriptions of identical or similar components and should not be interpreted as emphasizing or implying the relative importance of a particular component.

[0025] Furthermore, in the description of the embodiments of the present invention, "several", "more than", and "a number of" represent at least two. The number can be any number, such as two, three, four, five, six, seven, eight, or nine, and can even exceed nine.

[0026] Furthermore, in the description of the technical solution of this invention, unless otherwise explicitly specified / limited / restricted, the terms "set up," "install," "connect," "link," "provided with," "laid out," and "arranged" should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to connection methods commonly used in the art, such as welding, riveting, bolting, and threaded connections. Such connections can be mechanical, electrical, or communication connections; they can be direct connections or indirect connections through an intermediate medium; and they can refer to the internal communication between two components.

[0027] Example 1 The technical solution of the present invention will now be described with reference to the accompanying drawings.

[0028] To facilitate a clear description of the technical solutions in the embodiments of the present invention, several technical terms used herein are first explained. A node refers to a basic unit in the distribution network topology, including root nodes and user nodes. A root node is the low-voltage side outlet of a public distribution transformer, and a user node is the access point for each single-phase user in a low-voltage distribution network. A phase refers to the specific assignment of phases A, B, and C in a three-phase AC power supply, used to identify the phase connected to a user node. Upstream and downstream connection relationships refer to the power supply sequence relationship between user nodes within the same phase. If the power supply path from the root node to a certain user node passes through another user node, then that other user node is the upstream node of the first user node, and the first user node is the downstream node of that other user node.

[0029] The technical solution provided in this invention can be applied to low-voltage distribution network topology identification scenarios, and is particularly suitable for remote rural areas where smart meters can only collect voltage amplitude and active power data, lacking reactive power data records. In these scenarios, distribution system ledger information is generally missing or incorrect, making traditional topology identification methods that rely on complete measurement data difficult to work effectively.

[0030] Figure 1 A flowchart illustrating a low-voltage distribution network topology identification method under insufficient data conditions, as provided in this embodiment of the invention. Figure 1 As shown, the method includes steps S1 to S4.

[0031] In step S1, the voltage amplitude time series and active power time series of each user node, as well as the voltage amplitude time series of each phase of the root node, are obtained.

[0032] For example, smart meters are installed at each user node to collect voltage amplitude and active power data at preset sampling intervals. The collected data is then uploaded to a data center or edge computing terminal via an electricity consumption information collection system. The voltage amplitude time series refers to a sequence of voltage amplitude measurements arranged in chronological order, and the active power time series refers to a sequence of active power measurements arranged in chronological order. The voltage amplitude time series of the root node is collected by a monitoring terminal installed on the low-voltage side of the public distribution transformer. After obtaining the aforementioned measurement data from the electricity consumption information collection system, the data center or edge computing terminal stores the voltage amplitude time series, active power time series of each user node, and voltage amplitude time series of each phase of the root node in local storage or a cloud database for subsequent steps.

[0033] In step S2, the root node phase to which each user node is connected is identified based on the Pearson correlation coefficient between the voltage amplitude time series of each user node and the voltage amplitude time series of each phase of the root node.

[0034] For example, for the target user node to be identified, the voltage amplitude time series of the target user node is extracted from the data obtained in step S1. And the voltage amplitude time series of phases A, B, and C at the root node. , , Calculate separately and between, and between, and The Pearson correlation coefficient between them.

[0035] In one possible implementation, before calculating the Pearson correlation coefficient, the time series of each voltage amplitude are first differentially processed to extract the rapidly varying components of the voltage. Specifically, for a given voltage amplitude time series... Its difference sequence Defined as (t) = (t+1) - (t), where t represents time. The reason for using the differential sequence instead of the original voltage amplitude sequence to calculate the correlation coefficient is that differential processing can eliminate the trend effect caused by changes in the system operating point, highlight the synchronous characteristics of voltage fluctuations at each node, and thus improve the accuracy of phase identification.

[0036] The formula for calculating the Pearson correlation coefficient is:

[0037] Where x represents phase A, phase B, or phase C, and Voltage differential sequence for target user nodes voltage difference sequence with root node x The Pearson correlation coefficient between them for and covariance, for variance for The variance. Correlation coefficient. The closer the absolute value of is to 1, the higher the degree of linear correlation between the two sequences.

[0038] Calculated separately , , Then, the three correlation coefficients are compared, and the correlation coefficient with the largest absolute value is determined as the phase of the root node connected to the target user node. For example, if | |>| |and| |>| If |, then it is determined that the target user node is connected to the root node A.

[0039] By repeating the above process for each user node in the distribution network, the mapping relationship between all user nodes and the root node can be established, and the identification of the root node connected to each user node can be completed.

[0040] This step utilizes the physical characteristic that the voltage fluctuations of each user node on the same phase are highly synchronized, enabling accurate determination of the user's connected phase without the need for additional hardware equipment, thus avoiding the inefficient operation of manual door-to-door inspection in traditional methods.

[0041] In step S3, based on the root node phase to which each user node is connected, the voltage amplitude time series, the active power time series, and the voltage amplitude time series of each phase of the root node, the response relationship of the square change of voltage amplitude of each user node within the same root node phase to the change of active power is determined, and the upstream and downstream connection relationship between each user node under the same root node phase is identified according to the response relationship and the preset discrimination rules.

[0042] For example, step S3 first groups the user nodes according to the phase of the root node they are connected to, based on the phase identification results of step S2. User nodes belonging to the same phase are grouped into the same group, while user nodes of different phases are processed independently in different groups. Then, for each user node in each group, the response relationship between the square of the voltage amplitude change and the active power change is determined for each user node in that group.

[0043] In one possible implementation, the specific process for determining the response relationship is as follows: First, based on the voltage amplitude time series, active power time series of each user node within the same root node phase, and the voltage amplitude time series of the corresponding phase of the root node, a matrix equation for the linearized Distflow power flow model is established. This matrix equation uses the difference between the squared differences of the voltage amplitudes of each user node and the squared differences of the voltage amplitudes of the corresponding phase of the root node as the dependent variable, the active power difference of each user node as the independent variable, and the hybrid sensitivity matrix as the coefficient matrix to be solved.

[0044] The specific process of establishing the matrix equations of the linearized Distflow power flow model includes the following sub-steps: In sub-step S31, a Distflow power flow model is established between the nodes. The Distflow model is a classic model describing the voltage drop relationship between two nodes with upstream and downstream relationships in a radial distribution network. For any pair of nodes with potential upstream and downstream relationships, if there is a direct electrical connection, then the model is satisfied between them. In this embodiment of the invention, since the connection relationship between each user node is precisely the unknown quantity to be identified, during the modeling stage, for any two different user nodes in the user node set, it is assumed that they have a potential adjacency relationship, and the Distflow model equation is established accordingly. The expression of the Distflow power flow model is:

[0045] Here, i and j are two nodes with a potential adjacency relationship, and it is assumed that i is the upstream node of j. and Let be the squares of the voltage magnitudes at nodes i and j, respectively. and Let be the resistance and reactance of the line between node i and node j, respectively. and These represent the total active power and total reactive power injected by node j into the upstream node, respectively.

[0046] In sub-step S32, the differences between adjacent time points are taken for each variable in the above Distflow power flow model to obtain the differential form of the Distflow power flow model. Specifically, the squared voltage amplitude v is replaced with the differential squared voltage amplitude Δv, the active power P is replaced with the differential active power ΔP, and the reactive power Q is replaced with the differential reactive power ΔQ, resulting in:

[0047] in, , , , , This indicates taking the difference of the whole fraction, where t represents time.

[0048] In sub-step S33, the nonlinear terms in the difference form of the Distflow power flow model are linearized to obtain a linearized expression. The difference form of the Distflow power flow model contains higher-order terms. This nonlinear term poses a challenge to subsequent solutions. Since this higher-order term is numerically small compared to the main linear term, removing it yields a linearized expression.

[0049] For any pair of nodes with a potential adjacency relationship, the linearized expression is:

[0050] in, r Represents the root node. r 1 indicates the downstream node adjacent to the root node. and They are nodes r With nodes r The resistance and reactance of the line between 1 and 2. and They are nodes r 1. Total active power and total reactive power injected into upstream nodes.

[0051] In sub-step S34, based on the linearized expression, the relationship between the squared difference of the voltage amplitude of each user node and the difference of the active power of each user node is derived, and the relationship is written in matrix form to obtain the matrix equation.

[0052] The above linearization expression can be written in the form of voltage drop between adjacent nodes:

[0053] Summing yields:

[0054] in, From the root node To the node The intermediate node numbers that the power supply path passes through sequentially, among which root node r The downstream adjacent nodes, For the target node The upstream adjacent node; and Representing nodes respectively With nodes The resistance and reactance of the circuit (e and f are character symbols), the first subscript. Indicates the upstream node, second position Indicates downstream nodes, for example, Represents the root node With nodes The resistance of the lines between them Represents a node With nodes Reactance of the line between them; and Representing nodes respectively The total active and reactive power injected into upstream nodes (f is a character abbreviation), and the power injected into the node itself. different, Equal to node The sum of the active power injected by all its downstream nodes and the reactive power. Similarly; This represents the set of nodes from node j to the root node. This represents the upstream node adjacent to node b.

[0055] Change the order of summation:

[0056] Clearly, the sensitivity between node j and node i It can be represented as:

[0057] in, Let be the sensitivity of the squared change in the voltage magnitude at node j to the change in the active power at node i. Let be the sensitivity of the squared change in voltage magnitude at node j to the change in reactive power at node i. Let node j and node i share the sum of the resistances of all lines on the path. It is the sum of the reactance of all lines on the path shared by node j and node i.

[0058] but:

[0059] Written in difference form:

[0060] Written in matrix form:

[0061] in, It is the squared difference matrix of the voltage magnitude at each node. It is the difference matrix of the squared magnitudes of the root node voltages. and These refer to the active and reactive power sensitivities between each node. and These are the active and reactive power difference matrices for each node.

[0062] Since the reactive power value is unknown, regression can be performed using only the active power to obtain the mixed sensitivity. Therefore, by removing the reactive power, the relationship between the squared difference of the voltage amplitude at each user node and the difference of the active power at each user node is obtained, which is the matrix equation of the linearized Distflow power flow model mentioned above:

[0063] in The voltage magnitude squared difference matrix for each user node. This is the squared difference matrix of the voltage magnitudes of the phases corresponding to the root node. For a mixed sensitivity matrix, This is the active power difference matrix for each user node.

[0064] The matrix equation is the difference between the squared difference of the voltage amplitude of each user node and the squared difference of the voltage amplitude of the corresponding phase at the root node. The dependent variable is the difference in active power at each user node. As the independent variable, the mixed sensitivity matrix is ​​used. Let be the coefficient matrix to be solved.

[0065] In one possible implementation, the sensitivity matrix is ​​mixed. The rows correspond to user nodes that are the dependent variables, and the columns correspond to user nodes that are the independent variables. Each element in the table represents the mixed sensitivity of the user node corresponding to the row with respect to the user node corresponding to the column, which characterizes the degree of response of the squared change in the voltage amplitude of the user node corresponding to the row to the change in the active power of the user node corresponding to the column.

[0066] Then, the least squares method is used to solve the above matrix equation to obtain the values ​​of each element in the mixed sensitivity matrix.

[0067] Specifically, for any pair of user nodes i and j, the corresponding scalar equation is extracted from the above matrix equation:

[0068] in, The squared difference of the voltage magnitude at user node i. The squared difference of the voltage magnitude corresponding to the phase at the root node. Let the active power differential be that of user node j. is the element in the i-th row and j-th column of the mixed sensitivity matrix, which is the mixed sensitivity of user node i relative to user node j.

[0069] According to the least squares method, The estimated value is:

[0070] in, express transpose, Describing covariance, Represents variance. This represents finding the inverse of a matrix.

[0071] Repeat the above least squares estimation process for each pair of user nodes i and j to obtain all The values, when arranged in rows and columns, form the complete mixed sensitivity matrix. .

[0072] In one possible implementation, the sensitivity matrix is ​​mixed. The elements in each column are not independent of each other. For the first column... j The column, and its corresponding coefficient is:

[0073] Let be the regression coefficient between the reactive power difference and the active power difference at node j. According to the above formula, it is obvious that... It is a node j Power factor tangent The weighted average at each time point. Since user loads in low-voltage distribution networks are typically inductive, the power factor angle θ satisfies... ,therefore This property guarantees the mathematical validity of subsequent criteria.

[0074] Solved mixture sensitivity matrix It fully characterizes the response relationship between the square of the voltage amplitude change and the active power change of each user node within the same phase.

[0075] After obtaining the hybrid sensitivity matrix, the upstream and downstream connection relationships between user nodes under the same root node are identified based on the hybrid sensitivity matrix and the preset discrimination rules.

[0076] In one possible implementation, the preset discrimination rule includes: defining a first discrimination index and a second discrimination index, wherein the first discrimination index is equal to the mixed sensitivity of the first user node to its own active power minus the mixed sensitivity of the second user node to the active power of the first user node; and the second discrimination index is equal to the mixed sensitivity of the second user node to its own active power minus the mixed sensitivity of the first user node to the active power of the second user node.

[0077] Specifically, for any two user nodes i and j within the same phase, from the hybrid sensitivity matrix... Extract four elements: , , , Define the first discriminant criterion. Second discriminant index as follows:

[0078]

[0079] First discriminant indicator The second discrimination criterion measures the difference between the voltage response of user node i to a change in its own power and the voltage response of user node j to a change in the power of user node i. This measures the difference between the voltage response of user node j to changes in its own power and the voltage response of user node i to changes in the power of user node j.

[0080] If the first discrimination index Less than the first preset threshold and the second discrimination index Greater than the first discriminant index If the second discrimination index is true, then user node i is determined to be the upstream node of user node j. Less than the second preset threshold and the first discrimination index Greater than the second discriminant index If so, then user node i is determined to be a downstream node of user node j. Optionally, that is... When (at which point the first preset threshold is a positive number approaching 0), user node i is determined to be the upstream node of user node j; (At this time, the second preset threshold is a positive number that approaches 0), and user node i is determined to be the downstream node of user node j.

[0081] The mathematical basis of the above discrimination rule comes from the physical characteristics of low-voltage distribution networks. The physical characteristics of low-voltage distribution networks include: the injected power of each user node is differentially independent, the line power is dominated by the injected power of downstream user nodes, and the square of the voltage amplitude is greater than the power consumed by the user nodes.

[0082] In a low-voltage distribution network, the injected power differentials of each user node are independent of each other, that is: ; The line power is mainly dominated by the power injected by downstream nodes, and is less affected by the power injected by upstream nodes.

[0083] in, Represents a node j The set of all downstream nodes, N The symbol represents the set of all nodes, and "\" represents the difference operation. That is, the partial derivative of the line active power difference with respect to the active power difference of downstream nodes is approximately 1, and the partial derivative with respect to non-downstream nodes is approximately 0; the square of the voltage amplitude is numerically greater than the power consumed by the user nodes.

[0084] Based on the above physical characteristics, taking the value at time t as the ground state, the partial derivative relationship of the reactive power difference with respect to the active power difference can be derived:

[0085] in, Represents the tangent function. Represents the power factor angle, and in terms of express Since users in low-voltage distribution networks are primarily inductive loads, therefore Generally greater than 0.

[0086] Based on the above physical characteristics and the partial derivative relationship between the reactive power difference and the active power difference, the expression for the partial derivative of the squared voltage amplitude difference with respect to the active power difference can be expressed as follows: Does it belong to a node? The downstream node set is expanded in two cases. This partial derivative... This expression represents the change in the square of the voltage magnitude at node i when the active power at node k changes by a unit. Here, i in the numerator represents the target node whose voltage changes, and k in the denominator represents the independent node whose active power changes. In the expansion, expressions are given for two cases: when k is a downstream node of node j or node j itself (i.e.,...) ), and when k does not belong to the downstream node set of node j and is not node j itself (i.e. The expressions for the partial derivatives differ in the two cases.

[0087] when (Right now For nodes downstream nodes or nodes When the voltage amplitude squared difference is used (as is), the partial derivative expression of the voltage amplitude squared difference with respect to the active power difference is:

[0088] when (Right now Not a node The set of downstream nodes and not nodes When the voltage amplitude squared difference is used (as is), the partial derivative expression of the voltage amplitude squared difference with respect to the active power difference is:

[0089] Since the square of the voltage amplitude is much larger than the power consumed by users in a low-voltage distribution network, the following scaling relationship can be obtained:

[0090] Based on the scaling relationship described above, the partial derivative expression of the squared difference of voltage amplitude with respect to the active power difference is simplified. After ignoring terms of smaller magnitude, the partial derivative expression of the squared difference of voltage amplitude with respect to the active power difference can be further simplified to: when hour:

[0091] when hour:

[0092] Replace node k with and The partial derivative expression of the squared difference of voltage amplitude with respect to the active power difference is denoted as: Then the relationship between the partial derivatives of the squared difference of voltage amplitude with respect to the difference of active power is: if the node and Adjacent, and yes If the upstream node is:

[0093] Conversely, if the node and Adjacent, and yes If the downstream node is:

[0094] The relationship between the partial derivatives of the squared difference of voltage amplitude and the difference of active power constitutes the theoretical basis for the preset discrimination rule. After replacing the partial derivatives with the corresponding elements in the hybrid sensitivity matrix, the construction methods and judgment logic of the first and second discrimination indices can be obtained: when the first discrimination index... Approximately equal to zero and the second discriminant index If the value is greater than the first discrimination criterion, then the first user node is determined. For the second user node The upstream node; conversely, when the second discrimination index is approximately zero and the first discrimination index is greater than the second discrimination index, the first user node is determined. For the second user node The downstream node.

[0095] It should be noted that the above "approximately equal to" is derived from the approximate simplification of terms with smaller magnitudes during the derivation process. Therefore, the theoretical derivation result presents a magnitude difference relationship of "approximately equal to 0", rather than a strict mathematical equation.

[0096] By performing the above discrimination process on each pair of user nodes within the same phase, the upstream and downstream connection relationships between all user nodes within that phase can be determined.

[0097] This step determines the upstream and downstream connection relationships between user nodes by relying only on two types of measurement data: voltage amplitude and active power, without requiring reactive power data, thus achieving accurate identification of topology relationships even under conditions of insufficient data.

[0098] In step S4, based on the upstream and downstream connection relationship, each user node within the same root node phase is connected, and the topology of the distribution network is generated by combining the root node.

[0099] For example, based on the upstream and downstream connection relationships between user nodes identified in step S3, starting from the root node, each user node is connected level by level in a sequence from upstream to downstream. Specifically, for a given phase, firstly, the first-level user nodes directly connected to the root node of that phase are determined, then the second-level user nodes directly connected to the first-level user nodes are determined, and so on, until all user nodes within that phase are connected to the topology. The above connection operation is performed for each phase, and finally, the topology branches of each phase are merged at the root node to generate a complete distribution network topology.

[0100] In one possible implementation, if a user node is determined to be an upstream node of another user node, then an edge is drawn between the upstream and downstream nodes in the topology graph, with the edge pointing from the upstream node to the downstream node. By combining all the directed edges between user nodes, a complete tree-like topology graph is formed.

[0101] This step transforms the identified upstream and downstream connections into a visualized tree topology, providing an accurate topological foundation for subsequent distribution network operation and maintenance management operations such as line loss analysis, fault location, and three-phase imbalance mitigation.

[0102] To verify the effectiveness of the low-voltage distribution network topology identification method under insufficient data conditions provided in this embodiment of the invention, this embodiment uses the IEEE 33-bus standard test system for simulation calculations. The network topology is as follows: Figure 2 As shown. The IEEE 33-node system is a classic radial distribution network test system, containing 33 nodes, where node 1 is the root node and the remaining nodes are load nodes. The system topology and node numbering are shown below. Figure 2 As shown in the image.

[0103] In the simulation, only the voltage amplitude time series and active power time series of each node are used as input data, excluding reactive power data, to simulate real-world scenarios where data is insufficient. According to the method provided in this embodiment, firstly, the phase affiliation of each node is identified based on the Pearson correlation coefficient; then, the matrix equation of the linearized Distflow power flow model is established, and the mixed sensitivity matrix is ​​solved using the least squares method; finally, the upstream and downstream connection relationships between each node are identified according to preset discrimination rules.

[0104] Figure 3 A visualization of the C1 and C2 discriminant indices for node 7 in the topology graph compared to other nodes. From... Figure 2 The topology shown indicates that the downstream nodes of node 7 are nodes 8 to 18, a total of 11 nodes. Figure 3 In the dataset, the scattered points enclosed by the gray circle, excluding the origin, number exactly 11. The C1 discriminant index of these scattered points is approximately 0, while the C2 discriminant index is significantly larger than the C1 index. Further data verification reveals that the scattered points within the gray circle correspond precisely to nodes 8 to 18, perfectly matching the theoretical downstream node distribution. This result verifies the correctness of the construction methods and judgment logic of the first and second discriminant indices.

[0105] Figure 4 This is a diagram showing the results of topology identification using the criteria proposed in this embodiment of the invention. From... Figure 4 As can be seen from the above, the topological structure identified by the method provided in the embodiments of the present invention is consistent with... Figure 2 The original topology of the IEEE 33-node network is consistent with the above. This method accurately identifies the upstream and downstream connections between all adjacent nodes and completely reconstructs the topology of the entire distribution network, proving that this method can accurately identify the topology of low-voltage distribution networks even with insufficient data relying only on voltage amplitude and active power.

[0106] The simulation results above verify the effectiveness and accuracy of the method provided in this embodiment of the invention. This method does not require reactive power data; it can complete topology identification using only voltage amplitude and active power time series. The simulation results are consistent with theoretical expectations, demonstrating its feasibility for practical engineering applications.

[0107] Based on the same inventive concept, this embodiment also provides a low-voltage distribution network topology identification device under conditions of insufficient data, including a memory, a processor, and a program stored in the memory and executable on the processor. When the processor executes the program, it implements the method described in any one of the above method embodiments.

[0108] For example, a processor may include one or more processing units, such as a neural network processing unit (NPU), an application processor (AP), a modem processor, a graphics processing unit (GPU), an image signal processor (ISP), a controller, a digital signal processor (DSP), a baseband processor, etc. The different processing units may be independent devices or integrated into one or more processors. The controller can generate operation control signals based on the instruction opcode and timing signals to control instruction fetching and execution.

[0109] The memory can be used to store executable program code, including instructions. Internal memory may include a program storage area and a data storage area. The program storage area may store the operating system, applications required for at least one function, etc. The data storage area may store data created during device use, etc. Furthermore, internal memory may include high-speed random access memory, and may also include non-volatile memory, such as at least one disk storage device, flash memory device, universal flash storage (UFs), etc. The processor executes various functional applications and data processing of the device by running instructions stored in internal memory and / or instructions stored in memory disposed within the processor.

[0110] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for topology identification of low-voltage distribution networks under conditions of insufficient data, characterized in that, include: Obtain the voltage amplitude time series and active power time series of each user node, as well as the voltage amplitude time series of each phase of the root node; Based on the Pearson correlation coefficient between the voltage amplitude time series of each user node and the voltage amplitude time series of each phase of the root node, the phase of the root node to which each user node is connected is identified. Based on the root node phase, voltage amplitude time series, active power time series, and voltage amplitude time series of each root node phase connected to each user node, determine the response relationship of the square change of voltage amplitude of each user node to the change of active power within the same root node phase, and identify the upstream and downstream connection relationship between each user node under the same root node phase according to the response relationship and the preset discrimination rules. Based on the upstream and downstream connection relationship, connect each user node within the same root node phase, and combine the root node to generate the topology of the distribution network; The determination of the response relationship between the squared change in voltage amplitude of each user node within the same root node phase and the change in active power includes: Based on the voltage amplitude time series, active power time series of each user node within the same root node phase, and the voltage amplitude time series of the corresponding phase of the root node, a matrix equation for the linearized Distflow power flow model is established. The matrix equation uses the difference between the squared difference of the voltage amplitude of each user node and the squared difference of the voltage amplitude of the corresponding phase of the root node as the dependent variable, the active power difference of each user node as the independent variable, and the hybrid sensitivity matrix as the coefficient matrix to be solved. The matrix equation is solved using the least squares method to obtain the values ​​of each element in the mixed sensitivity matrix, and the mixed sensitivity matrix is ​​used to characterize the response relationship.

2. The low-voltage distribution network topology identification method under insufficient data conditions according to claim 1, characterized in that, The identification of the root node to which each user node is connected includes: The root node corresponding to the maximum absolute value of the Pearson correlation coefficient is determined as the root node connected to the corresponding user node.

3. The low-voltage distribution network topology identification method under insufficient data conditions according to claim 1, characterized in that, The matrix equations for establishing the linearized Distflow power flow model include: Establish a distflow power model between nodes; By taking the difference between adjacent time points for each variable in the Distflow power flow model, a difference form of the Distflow power flow model is obtained; By removing higher-order terms (above first order) from the difference form of the Distflow power flow model, a linearized expression is obtained. Based on the linearized expression, the relationship between the squared difference of the voltage amplitude of each user node and the difference of the active power of each user node is derived. The relationship is then written in matrix form to obtain the matrix equation.

4. The low-voltage distribution network topology identification method under insufficient data conditions according to claim 3, characterized in that, The matrix equation of the linearized Distflow power flow model is as follows: in The voltage magnitude squared difference matrix for each user node. This is the squared difference matrix of the voltage magnitudes of the phases corresponding to the root node. For a mixed sensitivity matrix, This is the active power difference matrix for each user node.

5. The low-voltage distribution network topology identification method under insufficient data conditions according to claim 3, characterized in that, The rows of the hybrid sensitivity matrix correspond to user nodes that serve as dependent variables, and the columns of the hybrid sensitivity matrix correspond to user nodes that serve as independent variables. Each element in the hybrid sensitivity matrix represents the hybrid sensitivity of the user node corresponding to the row with respect to the user node corresponding to the column, and is used to characterize the degree of response of the squared change in the voltage amplitude of the user node corresponding to the row to the change in the active power of the user node corresponding to the column.

6. The low-voltage distribution network topology identification method under insufficient data conditions according to claim 5, characterized in that, The preset discrimination rules include: Define a first discrimination index and a second discrimination index. The first discrimination index is equal to the mixed sensitivity of the first user node to its own active power minus the mixed sensitivity of the second user node to the active power of the first user node. The second discrimination index is equal to the mixed sensitivity of the second user node to its own active power minus the mixed sensitivity of the first user node to the active power of the second user node. If the first discrimination index is less than the first preset threshold and the second discrimination index is greater than the first discrimination index, then the first user node is determined to be the upstream node of the second user node; If the second discrimination index is less than the second preset threshold and the first discrimination index is greater than the second discrimination index, then the first user node is determined to be a downstream node of the second user node.

7. The low-voltage distribution network topology identification method under insufficient data conditions according to claim 6, characterized in that, The method for determining the first preset threshold and the second preset threshold includes: Based on the differential form of the Distflow power flow model, the expression for the partial derivative of the squared difference of voltage magnitude of each user node within the same root node phase with the partial derivative of the active power difference of other user nodes is derived. Based on the physical characteristics of the low-voltage distribution network, determine the relationship between the partial derivatives of the squared difference of voltage amplitude of each user node within the same root node and the difference of active power of other user nodes. Based on the relationship between the magnitudes of the partial derivatives, the first preset threshold and the second preset threshold are determined.

8. The low-voltage distribution network topology identification method under insufficient data conditions according to claim 7, characterized in that, The physical characteristics of the low-voltage distribution network include: the injected power of each user node is differentially independent, the line power is dominated by the injected power of the downstream user nodes, and the square of the voltage amplitude is greater than the power consumed by the user nodes.

9. A low-voltage distribution network topology identification device under conditions of insufficient data, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the low-voltage distribution network topology identification method under the condition of insufficient data as described in any one of claims 1 to 8.

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